Successful Science and Engineering Teaching Theoretical and Learning Perspectives
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Calvin S. Kalman
Successful Science and Engineering Teaching Theoretical and Learning Perspectives
Calvin S. Kalman Concordia University McGill University Montreal, QC Canada
[email protected] ISBN: 978-1-4020-6909-3
e-ISBN: 978-1-4020-6910-9
Library of Congress Control Number: 2008920272 © 2008 Springer Science + Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
This first volume is dedicated to my first wife Judy (Feb 23, 1946–June 29, 2006), our children Ben and Sam and our grandson Josh. As I have indicated in the acknowledgment section, this work would never have come to fruition if it had not been not for my first wife’s inspiration and ideas in addition to her unflagging support and encouragement. She was a truly great teacher and was a model for my own teaching.
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Acknowledgements
Firstly, I credit my first wife, Judy Kalman (Feb 23, 1946–June 29, 2006), who has had many successes in teaching writing at Concordia University and Dawson College with inspiring much of my effort to bring writing into the science classroom. She also convinced me to set aside my initial skepticism of writing methods such as journaling to attend an intensive 2-day workshop at the University of Vermont that impressed me enough to try some new techniques myself (the course dossier). She and Marjorie McKinnon were instrumental in convincing me to use collaborative groups in my teaching. At the time, Marjorie was associate director of the Concordia University centre for faculty development. My first efforts in innovative teaching based upon computer assisted instruction would never have come to fruition without the help of Ron Smith and David Kaufman. Craig Nelson, whom I have never met, inspired my idea to follow conceptual conflict collaborative group exercises with a writing activity. Without the support and many discussions provided by Mark Aulls, I would never have come to my understanding of how reflective-writing works that is demonstrated in Chapter 3. I am particularly grateful to Wim Gijselaers, Editor of the book series “Innovation and Change in Professional Education”. He went far beyond the duties of an editor in helping me make major changes to the draft of this book to bring it to the present form. I would like to thank Igal Galili for permission to include a long excerpt of one of his papers that appears in Science and Education. I also would like to thank John Wiley & Sons, Inc. for permission to include passages from an article by Dykstra et al. that appeared in Science Education and Encyclopædia Britannica, Inc for permission to reproduce an excerpt from the first edition of the encyclopedia. The short papers in Chapter 8 were originally intended as a chapter on constellation courses that I had edited as my part of a book on Science and Society. Funding never materialized and thus the book never appeared. I would like to thank Joseph L. Spradley, Arlen R. Zander, Martin A. Ludington, Alan J. Friedman, Lawrence S. Lerner, and Judith Eger (widow of Martin Eger), who kindly agreed to have these articles published here. It may have been serendipity as to my mind, they are an essential part of this book. Some parts of this book have appeared in articles I wrote for American Journal of Physics, Science and Education and Academic Exchange Quarterly and the Journal of College Science Teaching.
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Contents
Part I How Students Learn Science 1
2
3
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.1 The Beginnings of Physics Educational Research . . . . . . . . . . . . . . . 1.2 The First Graduate Programs in Physics Educational Research . . . . 1.3 Educational Research in Other Science/Engineering Disciplines . . .
3 5 5
Intellectual Development and Psychological Types . . . . . . . . . . . . . . . .
7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Piaget and the Intellectual Development of Students. . . . . . . . . . . . . 2.2.1 Intellectual Development Levels of University Students . . . . 2.3 Jung’s Theory of Psychological Types and the Meyers Briggs Indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Relating Meyers-Briggs Typing to Piaget Developmental levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Vygotsky’s Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 The Zone of Proximal Development (ZPD) . . . . . . . . . . . . . . 2.4.2 Development of the Functions in the ZPD . . . . . . . . . . . . . . . 2.4.3 Scaffolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Learning in the Sciences and Engineering . . . . . . . . . . . . . . . . . . . . .
7 8 9
12 13 13 14 14 14
Students Alternative Scientific Conceptions . . . . . . . . . . . . . . . . . . . . . .
17
3.1 Difficulties Facing a Student in a Gateway Course . . . . . . . . . . . . . . 3.1.1 Early Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Student Conceptual Difficulties . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Relating the Force Concept Inventory (FCI) to Piaget’s Model of Cognitive Development . . . . . . . . . . . . . . . . . . . . . 3.2 A Theory of Conceptual Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Posner, Strike, Hewson and Gertzog . . . . . . . . . . . . . . . . . . . 3.2.2 Do Students Enter Gateway Courses with a Coherent Set of Ideas About Science?. . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Framework Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 18 19
11
21 25 26 26 27 ix
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3.2.4
4
Stages Undergone by a Student Experiencing Conceptual Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 A Model Based upon the Notion of Conceptual Conflict . . . Appendix 1: Additional Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 2: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27 31 39 40
Writing to Learn: Reflective Writing . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
4.1 Scaffolding for Students by Encouraging Self-dialogue . . . . . . . . . . 4.1.1 Writing as Encouraging Self-dialogue . . . . . . . . . . . . . . . . . . 4.1.2 Talking to Someone About a Problem . . . . . . . . . . . . . . . . . . 4.1.3 Reflective-Writing and the Zone of Proximal Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Knowledge Telling Model and the Knowledge Transforming Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Knowledge Telling Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Writing of a Research Paper . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Writing a Biography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Knowledge Transforming Model . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Knowledge Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Qualitative Research on Reflective Writing . . . . . . . . . . . . . .
43 43 44 44 45 45 46 47 47 50 50
Part II Changing Student’s Epistemologies 5
6
Getting Students to Examine Their Epistemology. . . . . . . . . . . . . . . . .
59
5.1
Developing Critical Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Comfort Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Cultural Constructs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Role of Writing-to-Learn . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 A New Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Feyerabend’s Principle of Counterinduction . . . . . . . . . . . . . 5.2.2 A Collage of Opinions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 The Critique Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Examining the Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6 Student Ranking of Reflective Writing, Group Activities and the Critique Writing-to-Learn Activity . . . . . . . . . . . . . . Appendix: Critiques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59 59 60 60 61 61 61 61 62 64
Critical Thinking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6.1 Critical Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Domain Specific Attribute or Does It Involve General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Surveys of the Opinions of Philosophers and Scientists . . . .
69
65 67
69 69
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6.1.3 6.1.4 6.1.5
Working Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . McPeck’s Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Studying Philosophers of Science to Promote Critical Thinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.6 Why Have Students Study Philosophy of Science . . . . . . . . 6.1.7 Collaborative Group Work . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.8 Assignments for Individual Groups . . . . . . . . . . . . . . . . . . . 6.1.9 What Constitutes a “Good” Scientific Theory . . . . . . . . . . . 6.1.10 Bacon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Theoretical Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The Crucial Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Sir John Herschel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Crucial Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.3 Advent of the Wave Theory of Light in the Nineteenth Century . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Pierre Duhem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 A Scientific Theory Should Provide Coherent, Consistent, and Wide-Ranging Theoretical Organizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Twentieth Century Philosophers of Science. . . . . . . . . . . . . . . . . . . . 6.4.1 Popper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Kuhn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Lakatos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Feyerabend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Mary Hesse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Relation to Conceptual Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: Peer Evaluation of Group Members . . . . . . . . . . . . . . . . . . . . . 7
Educational Models Based upon Philosophy of Science . . . . . . . . . . . . 7.1 Students Coming into a Gateway Course Do Not Have a Coherent Well Defined Knowledge of the World . . . . . . . . . . . . . . 7.1.1 Changing Students’ Epistemologies . . . . . . . . . . . . . . . . . . 7.1.2 Framework Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Weakly Organized Knowledge Systems . . . . . . . . . . . . . . . 7.1.4 Structuralist Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.5 Posner, Strike, Hewson and Gertzog (1982) . . . . . . . . . . . . 7.2 Conceptual Conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Hewson and Hewson (1984) . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Tseitlin and Galili (2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 A Model for Education. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Relationship Between All Discipline-Cultures Comprising Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Pictures of Nature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4 A Dialogic Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70 70 71 72 72 73 73 74 75 76 76 77 77 79
80 82 82 84 87 89 90 93 94 95 95 95 96 96 97 98 99 99 99 100 101 101 102
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7.3.5 7.3.6 7.3.7 7.3.8 8
Physics Not Only as Knowledge, But Also as a Space of Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Discipline-Culture . . . . . . . . . . . . . . . . . . . . . . . . . . . Conceptual Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physics Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
103 104 107 108
Changing Student’s Epistemologies . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 8.1 Constructing an Epistemology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Students Do Not Conceive of the Subject in Terms of a Coherent Theoretical Framework . . . . . . . . . . . . . . . 8.1.2 Course Design (Kalman and Aulls, 2003) . . . . . . . . . . . . 8.1.3 Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
111 111 115 126 128
Part III Final Thoughts 9
Courses for Non-science Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 9.1 Three Types of Learners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Course Dossier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Passing the Word to the Student; Transforming Each Lecture into a Mini-research Paper . . . . . . . . . . . . . . . . . 9.2.2 End of Semester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Constellation Courses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Studies in Physics and Literature . . . . . . . . . . . . . . . . . . . 9.3.2 Physics and Society in Historical Perspective . . . . . . . . . 9.3.3 Science and Humanities Via Science Fiction . . . . . . . . . . 9.3.4 Philosophy in Physics and Physics in Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.5 Contemporary Physics: A Freshman Seminar for Physics Majors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.6 A Science-Humanities Course Series. . . . . . . . . . . . . . . . 9.3.7 A Cluster of Science-Humanities Courses for Mixed Audiences of Science and Non-science Majors . . . . . . . .
10
131 132 133 133 134 135 137 140 143 146 148 150
Computer Assisted Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 10.1 Using Computer Assisted Instruction in Science/Engineering Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 A Computer Language for Computer Assisted Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Noah Sherman’s Templates . . . . . . . . . . . . . . . . . . . . . . . 10.3 Tutorial on Calculus for the Introductory Mechanics Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
155 156 156 157 157
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10.3.2 Pre-test for the Calculus Tutorial . . . . . . . . . . . . . . . . . . 10.3.3 Testing of Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.4 Post-test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Using the Calculus Dialogue as a Tool to Investigate the Effects of Correlational Feedback on Learning and to Examine the Interaction of Correctional Feedback with Selected Learner Characteristics . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.4 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.5 Pre-lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.6 Instructional Logic for Main Lesson . . . . . . . . . . . . . . . 10.4.7 Operational Definitions of Treatments . . . . . . . . . . . . . . 10.4.8 Instructional Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.9 Measurement Instruments . . . . . . . . . . . . . . . . . . . . . . . 10.4.10 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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157 158 160 161
163 163 164 164 164 165 165 166 166 168 169 174
11 Summing Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Name Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
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Preface
The intent of this book is to describe how a professor can provide a learning environment that assists students to come to grips with the nature of science and engineering, to understand science and engineering concepts, and to solve problems in science and engineering courses. As such, this book is intended to be useful for any science or engineering professor, who wants to change their course to include more effective teaching methods, to instructors at post-secondary institutions, who are beginning their careers, and as a handbook for TA’s. Since the book is based upon articles that I have had published in Science Educational Research and which are grounded in educational research that I have performed (both quantitative and qualitative) over many years, it will also be of interest to anyone engaged in research into teaching science and engineering at the post-secondary level. I have also tried to include enough background so that the book could be used as a textbook for a course in educational practice in science and engineering. The book has two main axes of development. Firstly, how do we get students to change their epistemology so that their outlook on the course material is not that it consists of a tool kit of assorted practices, classified according to problem type, but rather that the subject comprises a connected structure of concepts. Secondly, helping students to have a deeper understanding of science and engineering. In Part I “How students learn Science”, I develop some basic background on current understanding of how students try to deal with courses in science and engineering. Perhaps this part would have had a better title as “How do students fail to understand science subjects in spite of the best efforts of well-intentioned instructors”. The capstone of this section, Chapter 3 deals with the fact that students have perceptions of the subject of our courses that are very different than the conceptual framework found in our courses and that it is very hard to get students to rid themselves of these notions. Those faculty, who are already familiar with the literature on conceptual change theory can skip this part and proceed directly to Part II. Part II, “Changing Students’ Epistemologies” is the heart of the book. In develops the kind of scaffolding needed to assist the student to achieve a deeper understanding of the subject such as reflective writing and conceptual conflict activities based upon methodologies involving use of collaborative groups and various forms of writing activities. It also develops the modern notion that simple conceptual change programs are not efficient since they try and attack the symptoms that prevent students’ xv
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Preface
success in science courses rather than the root causes that underlie this problem. Thus this part of the book examines the whole problem of helping students to become critical thinkers and helping them to change their epistemologies. The final part of the book looks in two successive chapters firstly at the special problems of courses for non-science students and secondly at using the computer to tutor students.
Chapter 1
Introduction The Beginnings of the Study of Science Education at Colleges and Universities
Many students were failing science courses not because they lacked the ability to understand the courses, but because the courses were not meeting their needs.
1.1
The Beginnings of Physics Educational Research
Arnold B. Arons, caused a paradigm shift in the way science education is performed at the post-secondary level. He realized that his “lucid lectures and demonstrations were depositing virtually nothing in the minds of the students”. This important point will be met with skepticism by most science and engineering professors. Indeed, when Arnold Arons first pointed this out, it was almost uniformly disbelieved. That Arnold Arons is right is illustrated in the following anecdote: Many years ago I attended a workshop given by Graham Gibbs, a noted expert on study skills. He related the following experience. Gibbs had been asked by a noted historian to help his class with note taking. Consequently, he attended a class to observe and then during the last 5 minutes of class speak about note taking. The professor was speaking about voyages to North America. The professor was such an engaging speaker that Graham Gibbs forgot why he was at the class. He seemed to even smell the salt water carried by the wind. With a start, he remembered why he was there and looked around the class. Surprisingly, at even the most interesting parts, students were staring out the window! This revelation led him to tear up his notes. At the end of the class, he handed the professor a transparency. “Write down the three most important points that you wanted students to take away from this class”, he instructed the professor. Then he asked the students to write down the three most important points that they had derived from the class. After the professor displayed the transparency, Gibbs asked how many students had written down all of the points that the professor had written on the transparency. Not a single student raised a hand. Gibbs then asked how many students had written down two of the points that the professor considered to be the most important points that students should have derived from the class. Not a single student raised their hand. When students were asked if they had written down one of the three points that the
C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
3
4
1 Introduction
professor wanted them to take away from the class, a few students near the front timidly raised a hand. Another difficulty with our science courses is that many students have great difficulty solving the assigned problems. Until midway through high school, students can be successful at solving problems in courses by memorizing templates for every situation encountered on an examination. That is, apply different templates to different knowledge subsets. Many students lack the ability to apply principles garnered from a problem to an apparently different problem. Other students can dismiss the conceptual basis of the problems, because their epistemology is formula driven and they accept calculated answers as a goal in itself. Arons wanted to find out what student learning problems were at a time when talks on teaching sponsored by the American Association of Physics Teachers had concentrated on presentation of material (Arons, 1998). Arons became convinced that if the mode of teaching was changed, many more students could understand science. Many students were failing science courses not because they lacked the ability to understand the courses, but because the courses were not meeting their needs. At the time it was difficult to get anyone to examine the root causes as to why students were having problems with the courses. Arons notes that scientists felt that research on educational methods for college and university science/engineering students should consist of “refining the delivery systems, the exposition, the text presentation, lecture presentation, the films and so forth, to the point that where they were so clear and so perfect that any passive student mind would assimilate them simply by having it drop in. That was what research was going to be—delivery—and there was no conception of listening to what the students said when you gave them the opportunity to reflect or talk about something”. Arnold Arons was joined in his efforts to look at the reasons why students in the introductory college and university physics courses had difficulties understanding the material presented to them in the late 1960s by Robert Karplus of the University of California at Berkeley. This led ultimately to a workshop on intellectual development (based on Piaget’s theory) on Feb 1, 1975 that I along 134 other members of the American Association of Physics Teachers (AAPT) attended in Annaheim, California. The day before, I had given a talk as part of a joint symposium of the AAPT and the American Physical Society on courses in physics and society. After that meeting, Roger Dittman, the chair of the symposium, I, and some others, decided to publish the proceedings. In the end, this did not happen. My part was to be on constellation courses (such courses attempt to relate physics and its developments to history, philosophy, religion, literature, the social sciences and the other natural sciences). My first incursion into scientific educational research occurred in 1971. I decided to implement a computer assisted (CAI) instruction program to help students who were having conceptual difficulties with the introductory course. Careful testing of questions is necessary. We introduced our CAI calculus dialogues during a summer session. We tried the dialogues on a few students at a time and immediately interviewed the students with respect to the reasons why they chose to answer in each question. The answers provided us with additional keywords, alterations in the language of the questions and the need for logic changes in the programs. We would then change the dialogues before the next few students made their attempt. We also discovered that the original dialogue was too long and needed to be split into
1.3 Educational Research in Other Science/Engineering Disciplines
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two parts. By the end of the summer session we had confidence in our dialogues (Kalman et al., 1974). Dave Kaufman used the work as the main thrust for what must be one of the first Ph.Ds. in physics educational research (1973). His Ph.D. work was presented at a meeting of the American Educational Research Association. (Kaufman et al., 1975). See Chapter 9 for details on computer assisted instruction.
1.2
The First Graduate Programs in Physics Educational Research
Around the time that Arons began discussions with Karplus, in 1968, Arnold Arons, moved to the University of Washington. There he began a collaboration with Lillian C. McDermott. This collaboration led to the formation of the Physics Education Group at the University of Washington. This was the formal beginning of a new field of scholarly inquiry for physicists: Physics Education Research. In the 1970s, Arnold Arons supervised the dissertation of a student who received a Doctor of Arts in physics at the University of Washington. Only this one student graduated in this program, which did not have the same requirements as a Ph.D. before the program was cancelled. In 1979, the physics department at the University of Washington awarded the first Ph.D. in physics for research in physics education to a student supervised by Lillian C. McDermott, director of the physics education group. Appendix D of the proceedings of the 1998 physics educational research conference lists a dozen such Ph.D. programs and four multidisciplinary programs that include physics education research in the USA. The importance of the University of Washington group was that it was not in a faculty of education. Professors were not solely trying to apply education and educational psychology principles to the study of science, but were “investigating difficulties students encounter in the study of physics and developing curriculum to overcome these difficulties” (Prospectus for new graduate students issued by The Physics Education Group, 1987).
1.3
Educational Research in Other Science/Engineering Disciplines
Discipline-based educational research in Mathematics began around 1988. Dubinsky at Georgia State University, began his research by extending Piaget’s work. He works on exploring the subconcepts students need to grasp before they can understand key mathematics concepts. He has designed activities, to help students acquire these subconcepts. Schoenfeld at the University of California applies cognitive psychology in mathematics education. There are also many faculty members in astronomy, biology, chemistry, engineering and geology, who are trying to apply the principles developed in physics and mathematics education, but there are no discipline based educational groups. In Biology there is the BioQUEST Curriculum Consortium (Beloit College). This project, was founded in 1986 by John Jungck, editor of The BioQuest Library
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1 Introduction
BioQUEST is a group of educators and researchers committed to providing students with biology research and research-like experiences. The Consortium began with an initiative of the Commission on Undergraduate Education in the Biological Sciences, established by liberal arts college biologists in the 1960s. The Consortium currently numbers more than 4,500 educators representing a diverse range of subject areas and educational levels. BioQUEST emphasizes the acquisition of scientific literacy through the collaborative intellectual activities of problem posing, problem solving, and the persuasion of peers. A major project has been the development of computer simulations that help students understand fundamental biological concepts. For example, students studying genetics can breed fruit flies and observe the inheritance of characteristics such as eye color. They can then augment their laboratory experience with software that simulates the breeding of thousands of virtual fruit flies, leading the student to discover the laws of genetics. The Consortium also conducts faculty-development workshops and distributes a free newsletter, BioQUEST Science and Mathematics Teaching Notes, three times a year to interested members of the education community. In Chemistry, the ChemLinks project was initiated by Brock Spencer of Beloit College and developed with members of the Midstates Science and Mathematics Consortium. Over 100 faculties from more than 42-year colleges, 4-year colleges, and universities have developed and tested modules dealing with chemistry, the environment, technology, and life processes. ChemLinks modules cover topics relevant to contemporary issues and take 3–5 weeks to complete. Students are guided to develop the chemistry knowledge needed to deal with these complicated issues. Modules incorporate collaborative activities and inquiry-based laboratory projects that replace traditional lectures, exams, and laboratories. As for engineering education, I want to mention Felder; for example Felder, R., Felder, G. and Dietz (2002). They discuss some work going on in engineering. In 1980, a consortium consisting of eight universities and the Center for Applications of Psychological Type was formed to study the role of personality type in engineering education. Felder has been particularly active in educational research in engineering. His work is found in the many references in Felder et al. (2002). Other active research includes an emphasis on setting up and solving a wide variety of problems of increasing complexity, with memory and rote substitution in formulas playing a relatively small role (Godleski, 1984). A longitudinal study carried out at the University of Western Ontario by Rosati (1993, 1997, 1999) examined factors related to success in the first year of the engineering curriculum.
Chapter 2
Intellectual Development and Psychological Types
According to Piaget, students cannot make the transition to a higher level of intellectual development until the student has reached the right level of maturity. McKinnon and Renner 1971 state the hypothesis: “The majority of entering college freshmen do not come to college with adequate skills to argue logically about the importance of a given principle when the context in which it is used is slightly altered”. Students develop faster if they are in an inquiry-based course rather than a teacher-centered course. It is really up to us as teachers to move these students to a higher level of intellectual development. Zone of Proximal Development (ZPD): Judging how well students can solve problems and at what level of difficulty is in Vygotsky’s opinion only one measure of the student’s developmental level. In his opinion, what the student can do with the assistance of others might be in some sense even more indicative of their mental development than what they can do alone.
2.1
Introduction
In Chapter 1, two points were introduced: 1. Lucid lectures and demonstrations often deposit virtually nothing in the minds of the students. 2. Many students lack the ability to apply principles garnered from a problem to an apparently different problem. Other students can dismiss the conceptual basis of the problems, because their epistemology is formula driven and they accept calculated answers as a goal in itself. The first point means that instructors in science courses cannot rely solely on lectures to reach students. I should make clear at the outset that I am not opposed to lecturing – in all but one of my courses, I do it all the time. Rather, it is necessary to supplement lectures with other activities. In the last chapter of Part I, I introduce one such activity; collaborative groups and in the first chapter of Part II, I introduce another such activity reflective writing, which is part of a class of activities
C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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called writing-to-learn. Other writing-to-learn activities are found in the rest of Part II and Chapter 9. This chapter attempts to explore the reasons why students are unable to apply principles garnered from a problem to an apparently different problem. In the next chapter, we will examine student’s epistemologies and see that students enter science and engineering courses with misconceptions and that students undergoing instruction in traditional ways do not rid themselves of most misconceptions. We will begin to examine activities that can help students deal with their misconceptions. For a student to truly succeed in this endeavor, a student must change their epistemology, which is the subject of Part II of this book.
2.2
Piaget and the Intellectual Development of Students
Why do students lack the ability to apply principles garnered from a problem to an apparently different problem? The answer to this question became clear in the 1970s. In this section, we shall see that students develop intellectually at different rates. Students, who might be thought to be of lower intellectual caliber because they “lack the ability to apply principles garnered from a problem to an apparently different problem”, have usually simply not yet developed that ability. Before the 1970s, the usual attitude of Science instructors towards their students was essentially that “cream rises to the top”. That is their courses would separate out the students, who could succeed at Science, from the other students. The criterion for success in Science at the university was the ability to solve problems on the end of course final examination. The notion that students did not do well on these examinations, not because of intellectual ability per se, but rather because of the lack of certain reasoning skills was shown in a study by McKinnon and Renner (1971). In this study, McKinnon and Renner looked into the reasoning powers of entering students at Oklahoma City University. Their results are shown in Fig. 2.1. McKinnon and Renner had been influenced by Robert Karplus to undertake this study. Karplus had been using the work of Piaget to examine the intellectual development of students in physics. According to Piaget, students cannot make the transition to a higher level of intellectual development until the student has reached the right level of maturity. A child’s intellectual development proceeds through a series of stages shown in Table 2.1. A student in what Piaget refers to as the concrete operational stage can “assimilate data from concrete experiments and arrange and rearrange them in his head” (Renner and Lawson, 1973) (with Tony Lawson, who is a biology professor, science education research moved out of being solely physics education research). Looking at the big picture using inductive and deductive reasoning is beyond a student at the concrete operational stage. Students who have not progressed beyond this stage are “object bound” cannot relate to verbally stated hypotheses. They “lack the ability to apply principles garnered from a problem to an apparently different problem”. Students who have reached what Piaget refers to as the formal stage are capable of reasoning with propositions only and do not need to refer to
2.2 Piaget and the Intellectual Development of Students
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25%
could answer questions correctly in transition
50%
entirely wrong
25%
Fig. 2.1 Results for students answering McKinnon and Renner reasoning test
Table 2.1 Stages of cognitive development according to Inhelder and Piaget (1958) Age Stage 1–1½ Sensory-motor 1½–6 Preoperational I (7, 8)–(11, 12) Early concrete operational IIA Late concrete operational IIB (14, 15)–Adult Early formal operational IIIA Late formal IIIB
objects. We might think that students, entering post-secondary institutions would have developed beyond the concrete operational stage and made the transition to the formal operational stage. As seen in Table 2.1, Piaget had thought that the transition to the formal stage occurred around the age of 14 or 15.
2.2.1
Intellectual Development Levels of University Students
Renner and Paske (1977) (Fig. 2.2) found that “approximately 50% of entering college freshmen are concrete operational. In view of this fact, concrete instruction seems to recommend itself to colleges for the first two years”. Prigo (1978) points out five studies that similarly find that “approximately 50% of incoming college students have not reached the intellectual stage of development where they can think abstractly (i.e. scientifically)”. McKinnon and Renner (1971) find that many of the 50% of students, who have not reached the formal level are not even close to that stage. Seventeen percent of all college freshmen do not conserve quantity and another 10% failed to recognize the equivalence of volume. Thus, 27% of students, who were tested, were at the lowest concrete operational state or less. Arons and Karplus (1976) put it this way: “Although the various investigations are beginning to reveal significant and interesting differences between social and economic groups, the grand averages have been emerging, with very little variation throughout the age and school level spectrum: about one-third have made the
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2 Intellectual Development and Psychological Types 17%
10% 50%
Formal Level Higher concrete Fail to recognize equivalence of volume Fail to conserve quantity
23%
Fig. 2.2 Piaget levels for entering university students
transition to formal operations, about one-third can be regarded as in the process of transition, and about one-third use primarily concrete patterns of reasoning”.
2.2.1.1
Concrete Learners
Concrete learners – as defined in Piaget’s work often do not understand abstract ideas without a period of physical manipulation. A good example is an experience described by Arons (1998): “I remember the episode quite vividly when I tumbled to something through what happened with a student. I drew a position-time diagram the conventional way and then the history, a horizontal line parallel to the t-axis and asked the student to interpret it and there was hemming and hawing and nothing happened and finally it occurred to me to say, ‘Look, the edge of the table here is a straight line, we’re talking about straight line motion. Put your hand on the edge of the table and do with your hand what that diagram says’. I watched the student, I saw the muscles twitch, and that’s what gave me the cue. I saw the muscles twitch and then the grin. ‘It’s standing still’. These findings are probably the reason why Paul Hewitt, author of the best selling Conceptual Physics found (1995): “The professor and the students view solving of problems in a very different way. The professor classifies the problems in terms of concepts, while the students classify them by situations”. The 50% of the students, who are at a concrete level of development are unable to think of the material in terms of general concepts that apply to many different situations. Since such students cannot understand the conceptual basis of the problems, they accept calculated answers as a goal in itself. Students, who are concrete thinkers, may claim that the professor is not doing their job if they teach concepts. They insist that professors spend as much time as possible working problems in class.
2.3 Jung’s Theory of Psychological Types
2.2.1.2
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Students Difficulties in Abstracting a Principle from Examples
McKinnon and Renner (1971) state the hypothesis: “The majority of entering college freshmen does not come to college with adequate skills to argue logically about the importance of a given principle when the context in which it is used is slightly altered”. Later studies have confirmed this hypothesis showing that students often have difficulty abstracting a principle from examples, encoding information into flexible memory representations, and accessing the appropriate principle in new problem contexts. (VanderStoep and Seifert, 1994). (One of my colleagues once stated that if he gave a problem to students involving the collision of a Volkswagen beetle and a cement mixer and then gave the identical problem to students on an examination involving the collision of a Mercedes and a Mack truck, many students would be unable to do the identical problem.) These students want professors to provide templates of problems that they can use to solve problems on exams. They cannot look at problems in the textbook and abstract principles of problem solving.
2.2.1.3
Intellectual Independence
Exploration, invention and discovery represent inquiry and lead the student to what Piaget (1973) has called “intellectual independence”. He further states: “The goal of intellectual education is not to know how to repeat or retain ready-made truths … It is in learning to master the truth by oneself at the risk of losing a lot of time and going through all the roundabout ways that are inherent in real activity”. Students develop faster if they are in an inquiry-based course rather than a teachercentred course. It is really up to us as teachers to move these students to a higher level of intellectual development. In teacher-centred instruction the student is not given opportunities to construct their own understandings of science. Information is poured into them without participation on their part. Various kinds of student-centred instruction force students to examine their views and can help them develop intellectually.
2.3
Jung’s Theory of Psychological Types and the Meyers Briggs Indicator
Why do so many entering students appear to be at what Piaget refers to as the concrete operational stage? These particular students have achieved the kind of marks required for college entrance. The answer may be found in Jung’s Theory of Psychological Types (Jung, 1971). This model arose from a long period of observation of people both in everyday life and in clinical settings. The Meyers Briggs indicator (MBTI) is based on an elaboration of this model. In Engineering Educational Research, this indicator is the major research tool as Felder et al. (2002) state in their
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study of the Myers-Briggs Type Indicator on a group of 116 students taking the introductory chemical engineering course at North Carolina State University; Probably the best-known instrument used to assess learning styles is the Myers-Briggs Type Indicator (MBTI). Studies of type effects in engineering education have been carried out by a consortium of eight universities and the Center for Applications of Psychological Type. (McCaulley et al., 1983, 1985; Rosati, 1993, 1997, 1999)
Jung had described four mental powers: two kinds of attitudes towards what is observed or thought; sensing (S) and intuition (N), and two kinds of judgment; thinking (T) and feeling (F). Jung had also described two kinds of attitudes toward the world; extroversion (E)and introversion (I). Isobel Myers added two additional attitudes; judgment (J) and perception (P). Isabel Briggs Meyers and her mother Katherine Briggs Meyers developed the MBTI based upon the analysis of data on 5,000 High school and an additional 5,000 medical students. Questions on the MBTI are meant to discriminate between E and I, S and N, T and F and J and P. Combining these possibilities in a four by four matrix gives rise to the 16 MBTI types. A study of the role of personality type in engineering education was undertaken in 1980 by a eight universities together with the Center for Applications of Psychological Type. They discovered that introverts, intuitors, and judgers generally outperformed their extraverted, sensing, and perceiving counterparts (McCaulley et al., 1983; McCaulley et al., 1985). Godleski (1984) also found that intuitives among engineering students consistently outperformed sensors except in courses emphasizing applications to “real” situations such as process design and cost estimation, where sensors did better. In a typical class in chemical engineering, there were roughly equal numbers of extraverts and introverts, the sensors outnumbered intuitors and judgers outnumbered perceivers by ratios of roughly 3:2, and thinkers substantially outnumbered feelers among both males and females with the overall ratio being roughly 7:3. ST was by far the predominant function, accounting for over 40% of both the male and female populations. (Felder et al., 2002)
Based on Meyers (1980) note that the ST student solves problems using an objective analysis in a flow-chart manner moving from one step directly to the next. In contrast the NF type would consider a subjective analysis of possibilities at each step and the NT type would attempt to be detached in examining all possibilities at all times.
2.3.1
Relating Meyers-Briggs Typing to Piaget Developmental levels
It is certainly possible that the majority of entering students cited by McKinnon and Renner (1971) to have difficulties in arguing logically about the importance of a given principle when the context in which it is used is slightly altered are not students who are stuck at the Piaget concrete level of development. Rather they are students, whose primary type is sensing. McKinnon and Renner had tested 131 students in the entering class at Oklahoma University on tasks that had been developed by Inhelder and Piaget (1958) for determining the developmental stages in the
2.4 Vygotsky’s Approach
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way children think about tasks and the ages in which their thought processes change stages. Students, whose dominant or auxiliary mental power is sensing will naturally prefer memorization and inductive reasoning. They prefer concrete facts to concepts. Piaget has labeled the physical manipulation of objects as a hallmark of the concrete stage of thought. Such students are capable of other forms of reasoning, but prefer not to reason in that way. McKinnon and Renner note that inquiry experiences “allowed students to function at a much higher level of thought than those courses in which students did not have the inquiry experience. The inquiry course is likely to focus on inductive reasoning an approach that appeals to the sensing power and thus is probably the reason why these courses are successful.
2.4 2.4.1
Vygotsky’s Approach The Zone of Proximal Development (ZPD)
Vygotsky (1978) has introduced another approach in examining how learning occurs. It is based on “a new and exceptionally important concept …: the zone of proximal development” (ZPD) (p. 85). He critiques the assumption that a students developmental level is entirely given by a battery of tests of varying difficulties. Judging how well they solve them and at what level of difficulty is in Vygotsky’s opinion only one measure of the student’s developmental level. In his opinion, what the student can do “with the assistance of others might be in some sense even more indicative of their mental development than what they can do alone. As an example, suppose that two students in the introductory course are tested to be at the concrete operational stage. This would mean that these students on their own can deal with tasks that have been standardized for the early concrete operational stage, but not beyond this. Suppose that you then initiate a solution of a problem requiring a higher level of development and ask the students to complete it or suppose that you offer leading questions. That is in some way the students are given some assistance in solving a higher-level problem. If in such a scenario, the first student can deal with problems up to the early formal level and the second student up to the late concrete level. Can we still say that the two students are at the same intellectual developmental level? Vygotsky argues that the two students are not actually at the same developmental level and that “the subsequent course of their learning would obviously be different”. The difference is called “the zone of proximal development. It is the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under … guidance or in collaboration with more capable peers” (p. 88). In Vygotsky’s view, whereas the tests show functions that have already matured, and characterize the level of mental development retrospectively, the ZPD corresponds to functions “that have not yet matured but are in the process of maturation, that is the ZPD characterizes mental development prospectively.
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2.4.2
2 Intellectual Development and Psychological Types
Development of the Functions in the ZPD
A fundamental principle of Vygotsky is that humans grow into higher levels of intellectual functioning through development of the functions in their ZPD. This process is likely to occur through social interaction with a teacher and with peers. Indeed, in his view, learning is ineffective, when the teaching is oriented towards developmental levels that have already been reached. “The only ‘good learning” is that which is in advance of development” (p. 89). In the light of the Meyers-Briggs data, we can also note that students can function using their auxiliary, tertiary or even least preferred powers. They prefer not to use these powers and have to be trained to use them. If they are only given examples that fit their preferences, they will never use these powers. “An essential feature of learning is that it creates the zone of proximal developmental processes that are able to operate only when the student is interacting with people in the student’s environment and in cooperation with the student’s peers. Once the processes have been internalized, they become part of the student’s independent developmental achievement” (p. 90). It would seem then from the Vygotskian perspective, it is a mistake to teach on the concrete level to students, who measure on a concrete level on a Piaget type test. “The only ‘good learning’ is that which is in advance of development” (p. 89).
2.4.3
Scaffolding
The role of the instructor in assisting students to develop student’s functions found in their ZPD has been characterized by Wood et al. (1976) as scaffolding. Activities need to be designed to nurture the growth of the student’s functions. The notion of scaffolding does not necessarily mean challenging students in the sense of getting them to realize that there are viewpoints that are diametrically opposed to their own views. In later chapters, I will bring up such a notion of cognitive conflict. Rather, it is the sense of assisting them to examine concepts and problems that are at a higher level than their actual developmental level, but which are nonetheless consistent with their ZPD. Such problems and concepts may be too difficult for them to cope with on their own. The Vygotskian notion is that such students can be scaffolded to successfully grapple with the concepts and problems in a social setting involving the instructor and/or their peers.
2.5
Learning in the Sciences and Engineering
We shall see that a great deal of research has been done into the mindset of students in the introductory gateway courses. There are many obstacles to be overcome in helping students learn science and engineering methodology and practice. We need to have a full understanding of these obstacles and then we have to devise a holistic
2.5 Learning in the Sciences and Engineering
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approach to in the Vygotskian sense scaffold the students to attain a scientific mindset. Such an approach must involve a variety of interventions in the classroom. Each student is an individual and an intervention that works well with one student may be largely ineffective with another student. No intervention could possibly work quickly with any student. Achieving a scientific mindset is likely to be a long process spanning the entire course.
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Chapter 3
Students Alternative Scientific Conceptions
Because a student’s understanding is different from the perspective found in the textbook and delivered by their instructor in the classroom, they misread the textbook and mishear the words of their instructor. “There is considerable evidence that they [students’ personal scientific conceptions] are not readily abandoned, but are retained together with the accepted scientific view” (McDermott, 1984). “Basic knowledge gain under conventional instruction is essentially independent of the professor” (Halloun and Hestenes, 1985a). The work of Halloun and Hestenes (1985a) appeared shortly after the paper of McDermott (1984). Taken together these two publications underlined the necessity for a theory of conceptual change that would provide the underpinnings of new instructional methodologies that could provide enhancements on the knowledge gains on the mechanics diagnostic test devised by Halloun and Hestenes beyond those made by conventional instruction. Learning is concerned with ideas, their structure and the evidence for them. It is not simply the acquisition of correct responses, a verbal repertoire or a set of behaviors.
3.1
Difficulties Facing a Student in a Gateway Course
Students entering the classroom in an introductory (“gateway”) science course face many obstacles. The difficulty of reading and understanding the material as presented in their textbooks is one such difficulty. On the surface, the textbooks typically have a deceptively easy language. Before publication, the books have been sent to many professors to carefully review the material for accessibility and suggest changes. If the student examines a section of the textbook using the reflective writing techniques found in Chapter 4, the student typically finds that many of the concepts are hard to understand. Even then, there are many concepts that the student may feel that they understand, but their understanding is very different (student alternate scientific conception) than the way scientists understand the conception. Historically, there has been a widespread recognition that students enter introductory (“gateway”) science courses with concepts (“personal scientific concepts”) that are different from C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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those found in the course. For example, most students entering an introductory Mechanics course believe that when you throw a ball up in the air, it must “rest” at the top of its motion for a short time. They cannot seem to separate the notion of zero velocity from stopped motion. They do not understand the role played by acceleration; the ball is subject at all times to the influence of a constant downwards acceleration produced by the attraction of the ball by the Earth. Since this acceleration is constant throughout the motion, the ball is never stopped. Because such a student’s understanding of the motion of the ball is different from the Newtonian perspective found in the textbook and delivered by their instructor in the classroom, they misread the textbook and mishear the words of their instructor. Mishearing is a common occurrence even in ordinary human relationships. Two friends have a fight. They do not speak to each other for some time because of remarks that one of the parties thought the other party said. One friend anticipating some remarks has misheard what the other friend has said. Commonly held notions that result in student’s learning difficulties are found in all Science and Engineering disciplines. Students entering introductory Astronomy courses often think that the weather is cold in the winter because the Earth is farther away from the Sun during the winter. In introductory Biology courses, students think that the biological material making up a plant has accumulated in the plant from materials already present in the soil. Students in Chemistry courses memorize balancing procedures, but do not connect them with concept of the law of multiple proportions – that the relative number of atoms of each type must be the same before and after a chemical reaction.
3.1.1
Early Investigations
This discovery about students has roots in Piaget’s early studies of the way children explain natural phenomena (Piaget, 1929). Major work began at the University of Washington-Seattle resulting in the formation of the physics education group in the physics department at the University of Washington headed by Lillian C. McDermott. McDermott’s early investigations arose out of an attempt to help new teachers by identifying concepts that interfered with learning. McDermott (1991) notes that “up until the late 1950s and 1960s, science in elementary and high school consisted mostly of reading and memorization. In high school as in college, the curriculum in physics was generally considered to consist of a course syllabus, a text, a collection of standardized problems, and a set of prescribed laboratory experiments”. McDermott (1991) notes that in the post-Sputnik era, “a series of national conferences encouraged individual faculty to produce new instructional materials for teaching introductory college physics (Fig. 3.1). However, the constraints were such that most instruction continued in the traditional manner”. Beginning in 1973, with the work of Driver, many people began to explore the concepts held by pre-university students. In particular in addition to Driver and McDermott, mention should be made of Viennot (1979). McDermott (1984) summarized the research on conceptual understanding in mechanics in the 10 years since Driver. She noted that many of the difficulties that students have are not new to experienced teachers.
3.1 Difficulties Facing a Student in a Gateway Course
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Fig. 3.1 McDermott’s (1991) perspective on research in physics education
“However, this information has generally been in anecdotal form, useful primarily to the instructor whose experience it reflects. … It is only recently that student difficulties in physics have begun to be documented in a sufficiently systematic manner for drawing generalizations that can be shared”. “There is considerable evidence that they [students’ personal scientific conceptions] are not readily abandoned, but are retained together with the accepted scientific view”. This kind of acceptance of new concepts, while maintaining old beliefs is what Piaget (1978) calls assimilation. We will in subsequent chapters discuss the kind of instruction that is needed to get students to completely abandon their misconceptions and totally accept the concepts taught in their courses – a process that Piaget (1978) calls accommodation.
3.1.2
Student Conceptual Difficulties
In the 1970s and early 1980s investigations into the thinking of university science and engineering students were conducted. These papers produced a
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3 Students Alternative Scientific Conceptions
catalogue of student conceptual difficulties. Not only did the nature of students’ alternative conceptions become clear but it also began to be seen that these conceptions were strongly held by students and they typically outlive the efforts by faculty to teach them scientific concepts that contradict them (Viennot, 1979). The strength of these convictions was confirmed by Halloun and Hestenes (1985a). Halloun and Hestenes (1985a) carried out a study on the teaching of Physics in High School and University. Figure 3.2 is based upon their Table 1. The first two results are based on high school classes in General Physics of about 25 students taught by the same teacher. The first bar represents a general class and the second bar represents an honours class (selected on the basis of high academic performance or high achievement test scores). Halloun and Hestenes expressed surprise at the level of the low pre-test scores, since they are very close to the chance level score of 20%. The next three bars represent scores by students in a College Physics course. Post-test results are not available for the first two classes. The third College Physics course was composed of 82 students. The level of the pre-test scores in the College Physics course is less than the post-test scores in the high school physics classes, which can be explained by the fact that 55% of the students in these courses had not taken physics in high school. The remaining four bars represent classes in University Physics composed of respectively 119, 70, 192 and 97 students taught by four different professors. All the courses in College Physics and University Physics were given at Arizona State University. The remarkable thing about the results is shown in Fig. 3.2 is the contrast between the consistency of the results in the four University Physics classes and the styles of the four lecturers in these courses. One of the professors was a theoretical physicist whose lectures emphasize the conceptual structure of physics with careful definitions and orderly logical arguments. The other professors are experimental physicists, but with different specialties. One professor incorporates many demonstrations in his lectures, and he expends great time and energy preparing them; he strives especially to help students develop physical intuition. Another professor emphasizes problem solving and he teaches by example, solving one problem after another in his lectures. The other experimental physicist teaching introductory physics for the first time followed the book closely in his lectures. All four professors are known as good teachers according to informal peer opinion and formal evaluations by students. Indeed the professor, who incorporates many demonstrations in his lectures, has twice received awards for his teaching (Halloun and Hestenes, 1985a). Since the gains found in Fig. 3.2 are identical for all four university classes, Halloun and Hestenes conclude that the “basic knowledge gain under conventional instruction is essentially independent of the professor”. (italics in original). This result of Halloun and Hestenes coupled with the work of McDermott and of Driver discussed in Section 3.1.1 led many of us interested in science and engineering education to the conclusion that we had to have a deeper insight into the problems faced by students in introductory courses. Being “good” as a teacher will not help students with conceptual difficulties.
3.1 Difficulties Facing a Student in a Gateway Course
21
70 60
Percent
50 40
Gain after Post-test Pre-test
30 20 10 0 Professor
Fig. 3.2 Average physics diagnostic test results by course and professor
3.1.3
Relating the Force Concept Inventory (FCI) to Piaget’s Model of Cognitive Development
The Force Concept Inventory (abbreviated as FCI) devised by Hestenes et al. (1992) is based on the original Halloun and Hestenes (1985a) Mechanics Diagnostic Test. It is designed not as a test of intelligence, but as a probe of belief systems and has been administered at a large number of universities from Arizona State University to Harvard. Coletta and Phillips (2005) analyzed individual normalized gains on the FCI and also probed the background of the student population using the Lawson Classroom Test of Scientific Reasoning at Loyola Marymount University, Southwestern Louisiana University, University of Minnesota and Harvard University. 3.1.3.1
Comparing the Lawson Test and the FCI
The FCI measures a student’s understanding of fundamental concepts. It does not relate to a student’s level of intellectual development. It is possible that student’s ability to do well on the FCI has something to do with their intellectual development. If so, this would help guide instructors in how to shape their teaching to assist students in introductory courses. The Lawson test (Lawson, 1978; see also Section 2.1) is a multiple-choice test that includes questions on conservation, proportional thinking, identification of variables, probabilistic thinking and hypotheticodeductive reasoning. This test can identify the intellectual development level of students (in the Piaget sense as described in Chapter 2).
22
3.1.3.2
3 Students Alternative Scientific Conceptions
Mode of Instruction
Coletta and Phillips attempt to see if special kinds of instruction could make a difference in FCI scores and if correlation between Lawson test scores and normalized FCI gains. A student-centered approach based upon interactive engagement with a significant lecture component was used at all four institutions. The class size differed widely. There were 285 students in 11 classes at Loyola Marymount University, 86 students in 2 classes at Southwestern Louisiana University, 1,648 students in 14 classes at University of Minnesota and 670 students in 4 classes at Harvard University. At Harvard University and at Southwestern Louisiana University, classes consist of lectures that are divided into short segments each of which is followed by conceptual, multiple choice questions. When a significant portion of the class obtains the wrong answer, students are instructed to discuss their answer with their partners and if the answers differ, to try and convince their partners of their answer. At the University of Minnesota, the majority of class time is spent by the lecturer giving demonstrations and modeling problem solving. Students are divided into small groups to examine concepts. At Loyola Marymount University, 134 of the students first covered each chapter in a “concepts” class. The material was then covered again in a “problems” class. Another 70 students were taught in lectures, interspersed with small group activities. The rest of the 81 students were taught using lectures with a strong conceptual component and frequent class dialogue. 3.1.3.3
Normalized FCI Gain
The value of each students normalized gain G; G = (post-score%–pre-score%)/(100–prescore%) was plotted versus the student’s pre-instruction score as seen in Figs. 3.3, 3.4, 3.5, and 3.6. Although the results at Loyola Marymount University (LMU), Southwestern Louisiana University (SMU), and University of Minnesota (UM) showed a significant positive correlation between pre-instruction FCI scores and normalized gains, the results at Harvard University (HU) showed no correlation at all. 3.1.3.4
FCI and Scientific Reasoning Ability
Coletta and Phillips felt that Piaget’s model of cognitive development might provide insight into the differences among students in introductory physics. For this reason, in 2003, they began to administer Lawson’s Classroom Test of Scientific Reasoning as well as the FCI to Loyola Marymount University students. Sixty five of the 285 Loyola Marymount University students tested with the FCI also took the Lawson test. There was a highly significant, positive correlation between students’ normalized FCI gains and their Lawson scores. To compare the correlation between Lawson test scores and the normalized gain with the correlation between FCI pre-scores and the normalized gain, they
Fig. 3.3 Plot of normalized FCI gains versus pre-instruction FCI scores for LMU pre-scores between 15% and 80% with individual student data averaged within 17 bins; s = 0.0062, r = 0.90, and p < 0.0001. The standard errors for G range from 0.03 to 0.06
Fig. 3.4 Plot of normalized FCI gains versus pre-instruction FCI scores for SLU pre-scores between 15% and 80% with individual student data averaged within 11 bins; s = 0.0063, r = 0.63, and p = 0.04. The standard errors for G range from 0.05 to 0.15
Fig. 3.5 Plot of normalized FCI gains versus pre-instruction FCI scores for UM pre-scores between 15% and 80% with individual student data averaged within 38 bins; s = 0.0037, r = 0.94, and p < 0.0001. The standard errors for G range from 0.03 to 0.05
24
3 Students Alternative Scientific Conceptions
Fig. 3.6 Plot of normalized FCI gains versus pre-instruction FCI scores for HU pre-scores between 15% and 80% with individual student data averaged within 22 bins; s = 0.0002, r = 0.04, and p = 0.87. The standard errors for G range from 0.03 to 0.09
divided the 65 student sample into two groups, those with FCI pre-scores ≤ 33% (33 students and those with FCI pre-scores ≤ 33% (32 students). Each of these groups was further divided according to the Lawson test scores yielding four groups in all: 1. Sixteen students with low FCI pre-test scores (23% average) and Lawson test scores < 60% (48% average) 2. Seventeen students with low FCI pre-test scores (21% average) and Lawson test scores ≥ 60% (76% average) 3. Fifteen students with high FCI pre-test scores (45% average) and Lawson test scores < 80% (69% average) 4. Seventeen students with high FCI pre-test scores (58% average) and Lawson test scores ≥ 80% (91% average) The results in Table 3.1 show a stronger relation between G and Lawson scores than between G and FCI pre-scores. For example, note that even though group 3 has a much greater average FCI pre-score than group 2, group 3 has a lower average G (0.30 versus 0.44) consistent with the lower average Lawson test score (69% versus 76%). In order to understand the result given in Section 3.1.3.3 that the Harvard data showed no correlation between G and FCI pre-scores, Coletta and Phillips examined the data from the 16 students, who scored highest on the Lawson test, the top quartile. They found no correlation (r = 0.005) between the FCI pre-scores and Lawson test scores for these students. For these same students, there was also no significant correlation between G and FCI pre-scores (r = 0.1).
3.2 A Theory of Conceptual Change
25
Table 3.1 Comparison of FCI pre-scores, Lawson test scores, and values of the FCI normalized gain G for the four groups described in Section 3.1.3.4 (s.e. is standard error) Average FCI Average Lawson Group pre-score (%) score (%) Average G ± s.e. 1 2 3 4
3.1.3.5
23 21 45 58
48 76 69 91
0.25 ± 0.04 0.44 ± 0.05 0.30 ± 0.04 0.59 ± 0.06
Conclusions
1. There is a strong, positive correlation between individual students’ normalized FCI gains and their pre-instruction FCI scores in three out of four of the populations tested. 2. There is a strong, positive correlation between class average normalized FCI gain and class average FCI pre-instruction scores for the 38 lecture style interactive engagement classes examined by Coletta and Phillips. 3. A sample of 65 students showed a very strong positive correlation between individual students’ normalized FCI gain and their scores on Lawson’s classroom test of scientific reasoning. The correlation between G and FCI pre-scores among these students is far less significant than the correlation between G and Lawson test scores. This correlation may indicate that variations in average reasoning ability in different student populations are a cause of some of the variations in the class average normalized gains that Coletta and Phillips observe. Conclusion (3) could provide an answer to why the Harvard University data shows no correlation between G and FCI pre-scores, while the other three schools show significant correlations. A possible answer is that the result is due to variations in the composition of the populations with regard to scientific reasoning ability. It is expected that a much higher fraction of Harvard students are formal operational thinkers and would thus have high scores on Lawson’s test. If so it is clear that instruction must be geared to the actual level of students’ intellectual development.
3.2
A Theory of Conceptual Change
The work of Halloun and Hestenes (1985a,b) appeared shortly after the paper of McDermott (1984). Taken together these two publications underlined the necessity for a theory of conceptual change that would provide the underpinnings of new instructional methodologies that could provide enhancements on the knowledge gains on the mechanics diagnostic test devised by Halloun and Hestenes beyond those made by conventional instruction.
26
3.2.1
3 Students Alternative Scientific Conceptions
Posner, Strike, Hewson and Gertzog
The first major attempt to produce such a theory had already been published in an article by Posner et al. (1982). They lamented the lack of a “well-articulated theory explaining or describing the substantive dimensions of the process by which people’s central organizing concept change from one set of concepts to another set incompatible with the first”. Posner et al. proposed to derive such a theory from current philosophy of science since “a central question of recent philosophy of science is how concepts change under the impact of new ideas or new information”. Their basis for this usage of philosophy of science is that in their opinion, learning is “a kind of inquiry”. “The student must make judgments on the basis of available evidence. … Learning is concerned with ideas, their structure and the evidence for them. It is not simply the acquisition of correct responses, a verbal repertoire or a set of behaviors. We believe that learning, like inquiry, is best viewed as a process of conceptual change”. Pintrich et al. (1993) stated the modern theory of conceptual change assumes that bringing about changes in an individual student is analogous to the nature of change in scientific paradigms proposed by philosophers of science, particularly Kuhn and Lakatos. A good discussion of this idea is also found in Duschl and Gitomer (1991). With these theoretical underpinnings, conceptual change models become the norm for research on learning in physical and social science and mathematics.
3.2.2
Do Students Enter Gateway Courses with a Coherent Set of Ideas About Science?
Halloun and Hestenes (1985b) proposed that students entered university with a conceptual outlook that corresponds to medieval impetus theory. Medieval impetus theory is indeed closely related to most students’ remarks on projectile motion especially to those remarks equating a change in momentum with the force of the hand. The details of the theory of Posner et al. will be postponed for a later chapter. It is however important to discuss one problem with their proposal immediately. It is intrinsic to the theory of Posner et al. that students enter gateway courses with a coherent set of ideas about science. Thus Posner et al. state that one of the two questions that their theory proposes to answer is “Under what conditions does one central concept come to be replaced by another?” It was certainly a given among everyone involved in science educational research in the late 1980s and early 1990s that students did have a coherent set of ideas about science. Thus for example in the in-depth analyses of student attitudes in Physics undertaken by Halloun and Hestenes (1985a), McDermott (1984), McDermott et al. (1987), Rosenquist and McDermott (1987), Gunstone (1987), Gunstone et al. (1992) and Bowden et al. (1992) it is shown that students enter introductory courses with viewpoints differing significantly from paradigms that will be taught them.
3.2 A Theory of Conceptual Change
3.2.3
27
Framework Theories
It is also intrinsic to some other types of theories that emerged in the 1990s that students have a coherent set of ideas about science. Vosniadou (1994) for example argues that concepts are entrenched and constrained within a larger theoretical structure. She postulates that students’ viewpoints about nature are contained in framework theories in addition to various specific theories. The learner’s framework theory is a function of ontological and epistemological presuppositions and is not available to her conscious awareness. However, this framework theory constrains the process of observing the physical world that is the basis of the students’ specific theories. These specific theories are consciously accessible, and consist of a set of interrelated propositions that describe the observed behavior of physical objects. Vosniadou identifies two kinds of conceptual change, enrichment and revision which are basically identical to Piaget’s notion of assimilation and accommodation. Enrichment is described as the simple addition of new information to existing knowledge, and achieved through the process of accretion. Revision is viewed as a substantial change that occurs when new information is inconsistent with specific theories or framework theories. Vosniadou suggests that students’ difficulties in making a conceptual change are not only because framework theories are coherent systems of explanations that are based on everyday experiences and grounded in years of confirmation, but additionally, because these are ontologically and epistemologically based. Thus a shift in any of a students’ beliefs will create a shift in the entire system of the framework theory and all the other knowledge built upon it.
3.2.4
Stages Undergone by a Student Experiencing Conceptual Change
Dykstra et al. (1992) note that Posner et al. (1982) describe a series of steps one goes through during conceptual change with which many would agree. They believe Posner et al. have identified important aspects of conceptual change: (1) becoming dissatisfied with a conception, (2) exploring plausible alternatives, and (3) choosing a fruitful one. Dykstra et al. attempt to distinguish the examples of conceptual change on the basis of (a) the type of change in student thinking which their techniques appear to engender and (b) the apparent differences in strategies between groups. Their goal is to answer the following set of questions: 1. Do these strategies induce conceptual change in the sense we have described? What measures does each group use to determine conceptual change and how do those measures compare with those we would use? 2. What seem to be the essential features of these strategies which induce conceptual change in our view and in the view of the groups which developed the strategies?
28
3 Students Alternative Scientific Conceptions
3. In what ways are the strategies we observe fundamentally different? In what ways are they fundamentally the same? 4. Are there any circumstances (conceptual, contextual, or otherwise) which seem to indicate the use of particular strategies? 5. What light can these observations and conclusions shed on our understanding of the nature of conceptions and conceptual change?
3.2.4.1
A Model of Conceptual Application
Dykstra et al. (1992) propose the following model of conceptual application: In contrast to modeling problem-solving skills, studying conceptions is more difficult because there is a “level of indirection” between what we observe students doing and the conceptions that give rise to their behaviors. Conceptions must be applied to problem situations and thus can only be identified indirectly by analyzing student responses, in contrast to skills which are specified in terms of observable features of the problem situation (Anderson et al. 1990) independently of what students may think. In order to identify students’ conceptions we must be able to make sense of their behaviors. We do this by applying a model of conceptual application, depicted in Fig. 3.7, which is based on the hypothesis that when conceptions are applied in specific problem contexts, they are manifest as characteristic behaviors. For example, when two interacting objects have different sizes, students associate a larger force with the larger object. We would expect to see behaviors resulting from such a belief in different problem situations sharing this feature. More convincing evidence that we have correctly identified an underlying conception, though, comes from considering multiple problem situations with additional features in which the conception is applicable. Only by keeping careful track of how students respond in a rich variety of situations will we be able to better infer which conceptions are responsible for their behavior. The specific behavior of associating a larger force with the larger of two interacting objects, for example, might also be the result of applying a conception like “force is a property of an object” rather than just a belief about different sized objects. By having students discuss a number of different kinds of problems, we should, according to the model, be able to work backwards to determine if there is a more general conception underlying the situated belief or if it is the result of several conceptions interacting. For instance, students apply “motion implies force” to a wagon pulled by a donkey. But, they also apply it to a body moving without apparent forces, which is a very different kind of situation. This leads students to remark that the body is moving because of a force that has been transferred to it from the body that originally set it in motion (similar to impetus).
3.2.4.2
Identifying Conceptions
Thus, the conceptual application model serves as a methodological framework for identifying conceptions. It is also explanatory of what we observe, enabling us to make sense of students’ behavior. However it is not a detailed psychological model in that it makes no claim as to the real mental or physical nature of conceptions nor does it specify the mechanisms by which they are applied. Rather, it is a model which when implemented can be used to catalogue, in a principled and organized
3.2 A Theory of Conceptual Change
29
Observed Problem-Solving Behavior normal force Since cart is moving “upward” then h pus there must be a force “upward” on it larger than any “downward” forces on it, so draw a force “upward” on it in the freebody diagram.
n give
art to c
gravity force
Problem Situation Cart coasting up an incline and back down: Draw a free-body diagram for the cart on the way up after leaving the hand. Conceptual Cues Features of the problem which trigger the application of a particular conception Conception (e.g., moving cart) “motion implies force”
Application Mechanism (e.g., analogy) “works like” pushing piano up ramp: the harder you push the faster it goes
Fig. 3.7 Model for conceptual application Note: A conception applied to a problem situation results in an observable problem-solving behavior. Note that in this example there is also evidence of force being “given” to an object as if it were a property of the object.
way, the kinds of descriptions that students give in answers to questions and which can be inferred from their problem-solving actions. Furthermore, whether or not conceptions exist is not important to our work. Like other mental constructs, they are useful for explaining student behavior, but they are not necessarily the mental constructs of the students themselves. The viability of these conceptions, therefore, rests on their capacity to satisfactorily explain student behaviors, to help us interpret teaching and learning experiences, and to aid in the design of effective new teaching and learning strategies. 3.2.4.3
Assimilation, Accommodation and Disequilibration
As previously noted, Piaget introduced assimilation, and accommodation the context of learning. Dykstra et al. (1992) incorporate these terms, along with disequilibration, into their discussion of conceptual change in order to better characterize, from the standpoint of learning and pedagogy, the necessary conditions for conceptual change: Assimilation is the recognition that an event (physical or mental) fits an existing conception (von Glasersfeld, 1987). This recognition process also involves a selective ignoring of discrepancies deemed not salient. Accommodation is a change in fundamental belief about how the world works, that is, a change in a conception, which enables an event to be assimilated that could not have been assimilated under previously held conceptions. Each
30
3 Students Alternative Scientific Conceptions of the three transitions in Fig. 3.8 involves accommodation. Where the initial conception becomes refined and where the first version Newtonian conception becomes refined, we would say that “within-conception” accommodation has occurred. In the former, for example, motion is differentiated into velocity and acceleration, but the conception that “motion implies force” remains essentially intact. “Conception-change” accommodation occurs at the vertical, bold, dashed line, i.e., where the conception changes from the initial, everyday conception to a more Newtonian conception. The difference between “within-conception” and “conception-change” accommodation is a difference in how fundamental the change in the students’ knowledge is (this will become clearer in the next section). It is not the same as the difference between what we believe Carey means by weak and strong knowledge restructuring, because “within-conception” accommodation is not the same as Carey’s weak knowledge restructuring. “Within-conception” accommodation does not occur without some change in the concepts involved whereas Carey’s weak restructuring involves no change in the component concepts.
Dykstra et al. (1992) believe that: for accommodation to occur, a student must become motivated to change by entering a state of cognitive disequilibration; sometimes profound, sometimes not, but always a disequilibration. Disequilibration usually occurs as the result of an event which does not fit with the student’s existing beliefs, that is, when the student’s expectations are not met. The fact that certain conceptions are not changed in the course of standard instruction may, therefore, be due to the failure of that instruction to disequilibrate students with respect to the conceptions they hold. If students can assimilate the words, ideas and experiences presented, then there is no disequilibration and no conceptual change. Thus, the point of instruction should be to induce conceptual change. It cannot accomplish this without causing disequilibration. It should be noted that disequilibration is not contradiction. The latter refers to a logical inconsistency whereas disequilibration is a conceptual incongruity. Disequilibration is not a consequence of formal, truth-valued statements, but, rather, of the surprise produced when an expected event does not occur. Conceptual change does not depend on contradiction, but on disequilibration.
force if motion
acceleration (force⇑ if v ⇑)
acceleration (net force⇒ if a ⇒)
velocity (force⇒ if v ⇒)
velocity (net force=0 if v ⇒)
rest (no force if not motion)
rest (net force=0 if v=0)
refined initial conception
first version Newtonian conception
net force if acceleration
no net force if no acceleration no force if not motion
initial conception
refined Newtonian conception
Fig. 3.8 A series of conceptual changes Note: The bold, vertical, dashed line at the center of the figure indicates a substantial conceptual change. The regular, vertical, dashed lines at either side indicate less substantial conceptual refinements (⇑– increases; “ = = > ” – remains constant).
3.2 A Theory of Conceptual Change
3.2.5
A Model Based upon the Notion of Conceptual Conflict
3.2.5.1
Get the Student to Critically Analyze the Two Concepts and Come to the Realization That the Personal Scientific Concept Needs to Be Replaced
31
Kalman et al. (1999) proposed a model based upon the notion of conceptual conflict (Nussbaum and Novick, 1982; Hewson and Hewson, 1984; Dreyfus et al., 1990; Limon, 2001). Hewson and Hewson (1984) suggest that if a student holds a personal scientific concept, he or she does so because the student finds it to be plausible. Thus instruction must not only be aimed at showing that the replacement concept is intelligible, but must also first seek to reduce the plausibility of the personal scientific concept. Although this may be a reasonable strategy with younger students who cannot become fully developed critical thinkers within the confines of the course, it is a rather cumbersome procedure. Kalman et al. argue that it is far better to get the student to critically analyze the two concepts and come to the realization that the personal scientific concept needs to be replaced. Part of the goal here is for students to clearly identify their interpretation of nature. Students must be reassured that they hold views, which are reasonable, but there is another viewpoint that is now held to be experimentally correct. Once the differing views of nature are clearly established, the role of experiment in deciding the issue can be emphasized. It is made clear that physics is an experimental science and the ultimate determination of how things actually work must be an appeal to experiment. 3.2.5.2
Collaborative Group Exercises
In accordance with the usual procedure in collaborative group exercises (Abrami et al. 1995) students are asked to take on a particular role within each group. Three to four students were assigned to a collaborative group. The students remain in the same group for all exercises, but may if they wish change roles of reporter, scribe, timekeeper or critic in each activity. For each exercise, students are presented with a demonstration or qualitative problem and are asked to discuss it for a fixed time limit. The time limits are set so that none of the groups will be waiting for other groups to complete the task. Typically all group members become actively involved often trying mini-experiments with erasers and other objects nearby. The energy of the group activity is then carried over to the reporting stage and usually fires the instructor with renewed energy (see Appendix 2 at the end of the chapter for the task sheets on the warm-up and regular sessions). The only training students received was a warm-up exercise in which students had to come to a joint decision on who were the three greatest scientists of all time. Unlike the regular treatment sessions all groups were asked to report on their findings. Aside from getting students used to the collaborative group framework, the purpose of this warm-up exercise was for the students to learn to come to a joint decision within a fixed time limit.
32
3 Students Alternative Scientific Conceptions
The principle used was to try to make it clear that there are at least two ways of looking at the problem. This must be done in a non-judgmental fashion. (For example until the Coriolis force was understood, one could logically take the position that the earth is at rest or the sun is at rest.) Compartmentalization could occur because students are not clear that there are two distinct conceptual ways of viewing a phenomenon. Having two groups with different concepts report to the class sets up a conceptual conflict. The spokespersons of each group then debate the issue between themselves and then the rest of the students are invited to address questions to this panel of “experts”. There don’t seem to be any negative connotations to the presentations of the personal scientific conceptions by an “expert”. (This issue was addressed by having students answer qualitative essay questions on the final exam.) To underline that there are two concepts in conflict, the two opposing issues presented by the two groups are clearly stated and the class then votes on which concept resolves the demonstration or qualitative problem. This voting is essential because students who have compartmentalized concepts often misinterpret statements in view of their eclectic viewpoint. Then the professor resolves the conflict by explaining with the aid of experiments how the replacement concept describes the demonstration or qualitative problem in accord with experimental findings, while the personal (alternative) scientific conception fails to do so.
3.2.5.3
Test Instrument
The test instrument was the Force Concept Inventory (FCI) (Hestenes et al., 1992) based on the original Halloun and Hestenes (1985a) instrument. It was used as a pre- and post-test. It is designed not as a test of intelligence, but as a probe of belief systems and has been administered at a number of universities from Arizona State University to Harvard. This instrument is reliable. (Nearly 1,000 students took the test with seven different professors teaching different sections at Arizona state and nearly identical test scores occurred in all the sections!) This test was used for norming purposes only. Three additional questions of the same type and style were specifically geared to this study.
3.2.5.4
Concepts Examined
The experiment was an attempt to produce conceptual change in terms of four common personal scientific concepts chosen, because in the opinion of Kalman et al. (1999), these seem to be pivotal in students’ transition from their personal scientific concepts to the Newtonian synthesis. These are: 1. The idea that bodies of different masses falling from rest through a non-viscous media for a short time (so that the resistance of the medium can be neglected) are found at later times to move at different speeds.
3.2 A Theory of Conceptual Change
33
2. The idea that a fast moving arrow stays in the air because of its great speed. 3. The idea that if a sandbag is dropped from an ascending balloon, immediately upon release the initial velocity of the sandbag is zero. 4. The idea that a ball, thrown in the air, is in equilibrium at the highest point in its motion. During the final intervention, for example, during the conceptual conflict discussion phase, students enunciated a variety of misconceptions including “force dependent on velocity” and the “force of the hand balancing the force of gravity at the top of the motion” Some also introduce an “ma” or a “momentum force”. As we are trying to get students to adhere to the Newtonian framework, the concept of equilibrium and the role of inertia in keeping the ball moving at the start of its motion have to be carefully dealt with. It is reemphasized to the students that if there would be no gravity, the first law would require the ball to keep going with its initial velocity forever. The hand exerts a force only while in contact with the ball changing its velocity from 0 to the “initial velocity” (students bring most of this out themselves).
3.2.5.5
First Experiments
Kalman et al. (1999) attempt to measure whether or not conceptual change occurs due to their model, but do not at this point evaluate directly changes in the critical thinking abilities of the students. In fall of 1995 they tested the collaborative learning approach on the four concepts by comparing two sections taught by the same instructor. In one section collaborative learning was used to teach the concepts; in the other a standard professor-centered approach was taken. To compare the two sections, they designed three questions of the same type and style as the force concept inventory (FCI). The pre- and post-tests administered to the students consisted of the FCI (except for question #12, which was not covered in this course) with these three additional questions appended as questions 30, 31, 32 (these additional three questions are found in Appendix 1). The results shown in Table 3.2 are only for students who wrote both the pre- and post-tests and who signed permission slips to be included in the experiment (only one student did not sign a permission slip). On the post-test, the mean scores on the additional three questions indicate that the treatment group was more successful in making a conceptual change than the control group.
3.2.5.6
A Modified Experiment with Stricter Controls
The same professor taught both sections in the same semester in the fall of 1995. There were doubts that there might be differences in the two groups that could have affected the outcome. This was due to the pre-test FCI result shown in Table 3.1 and the perception of the instructor that the treatment group was livelier than the control group. To remove these uncertainties, in the fall of 1996 a modified
34
3 Students Alternative Scientific Conceptions Table 3.2 Comparison of the experimental and control groups Fall 1995 Test Pre-test FCI + 3 additional questions Pre-test FCI Pre-test 3 additional questions Post-test 3 additional questions
Mean A = 10.94 B = 7.86 A = 10.61 B = 7.64 A = 0.33 B = 0.23 A = 1.25 B = 0.68
Equal variance t-test 0.061 0.058 0.465 0.033
SD A = 5.29 B = 6.32 A = 5.15 B = 5.99 A = 0.43 B = 0.59 A = 1.05 B = 0.78
A – Treatment group (22 students) Received treatment of four conflict lab sessions B – Control group (36 students) Concepts were taught via typical teacher-centered approach
experiment was made. This time in section A, concepts (2) and (3) were treated by the collaborative group method and concepts (1) and (4) were treated conventionally. In section B, the procedure was reversed – concepts (1) and (4) were treated by the collaborative group method and concepts (2) and (3) were treated conventionally. For analysis, a baseline of all FCI questions except 1, 5, 12, 16 and 22 was established. Question #12 was not covered by this course and the other questions do not relate to the concepts under study. There are also two natural groupings; Question set I consisting of question #16 of the FCI and the additional questions 30 and 31 relating to the two concepts treated by the collaborative group method in section A and Question set II consisting of questions 5 and 22 of the FCI and additional question # 32 relating to concept (4) concepts treated by the collaborative group method in section B. Analysis was done on only those students who wrote both the pre- and post- test and were present at the second conflict lab session. (Permission slips were handed out at that session and only students, who signed permission slips, are included in the results. The handing out of permission slips turned out to be a method of checking attendance as no students refused to sign slips and only one student did not hand in the slip.) Taken as a whole, looking at the pre- to post-test gains for question sets I and II in Table 3.3 it is seen that it is statistically significant that the treatment group was more successful in making a conceptual change than the control group. 3.2.5.7
Analysis of Individual Significant Questions
Question #1 of the FCI addresses the issue of concept 1. Part II of the first task sheet found in Appendix 2 refers to the treatment given for this concept. Dr. Kalman took a sheet of paper off the desk and a set of keys from his pocket and dropped them simultaneously from the same height. He then crumpled the paper and again dropped the paper and the keys simultaneously from the same height. It turned out that in this case the pre-test responses were already very high and the
3.2 A Theory of Conceptual Change
35
post-test responses were near perfect for both groups so no inference could be drawn for this concept. Question #30 is the only question that especially addressed concept 3; the idea that if a sandbag is dropped from an ascending balloon, immediately upon release the initial velocity of the sandbag is zero. Students were presented with the task sheet found in Appendix 2 on this subject and worked on this problem without any further explanation. (Note that these are the actual task sheets given to the students in the 1996 experiment and therefore this task sheet and the task sheet for concept 1 both contain the identical warm-up exercise.) It turned out that there was no statistical difference between the two groups in their improvements on post-test scores. See Table 3.2. For concept 2, (bullet compared to a dropped penny) section A was exposed to treatment and section A significantly improved compared to section B, whereas for concept 4, (forces acting on a thrown baseball) section B was exposed to treatment and significantly improved compared to section A. For these concepts, the groups were now experienced at working together having performed warm-up tasks and treatment on another concept. Students were presented with the task sheets found in Appendix 2 on these subjects and worked on these problems without any further explanation. Concept 2 (bullet compared to a dropped penny). Group A was treated. Both groups were tested on questions 16 of the FCI and additional question 31. For question 16 as seen in Table 3.2, the result is statistically significant. For question 31 the question is statistically indicative but not conclusive. Concept 4 (forces acting on a thrown baseball). Group B was treated. Both groups were tested on questions 5 and 32 of the FCI and additional question 32. As seen in Table 3.2, for question 5 the result is clearly statistical significance. For question 22 and question 32 the result is statistically significant. Re question #30, the only question that especially addressed concept 3; the idea that if a sandbag is dropped from an ascending balloon, immediately upon release the initial velocity of the sandbag is zero. The fact that that there was no statistical difference between the two groups in their improvements on post-test scores may have occurred because the groups were still not used to working together, but it is impossible to verify this. A more interesting explanation is that this also had something to do with the way the question was framed. The key point is as pointed out earlier that students lack the ability to apply principles garnered from a problem to an apparently different problem. (Gick and Holyoak, 1980, 1983) Students may not recognize that the problem of a brick falling off the edge of a descending construction elevator (question #30 in Appendix 1) is identical to the problem of a sandbag released from an ascending balloon. The premise of this paper is that the students’ development of critical thinking is essential. This is the only way that students will not simply accommodate the replacement concept by compartmentalization of their knowledge. After the first exercise, the students had not developed their critical thinking skills and the different appearance of question #30 caused them to utilize their personal scientific concept instead of the replacement concept. This would account for the result that no significant improvement of the treated group over
pretest posttest
31
16
Set 11 (5, 22, 32)
pretest posttest
pretest posttest
pretest posttest
pretest posttest
pretest posttest
pretest posttest
pretest posttest
1.31 1.88
pretest
Set 11 (6, 22, 32)
Set 1 (16, 30, 31)
0.54
pretest
Set 1 (15, 30, 31)
0.82 0.92
0.52 0.87
0.54 1.00
1.31
7.30
pretest
Baseline (FC1-1, 5, 12, 16, 22)
A (26 students)
Test
Question(s)
0.71 0.74
0.59 0.74
0.53 1.47
1.13 1.39
0.53
1.13
8.31
B (38 students)
Mean score group
Table 3.3 Comparison of the experimental and control groups Fall 1996
Wilcoxon 0.7671 McNomar 1.000
Wilcoxon 0.1088 McNomar 0.2500
Wilcoxon 0.3105 Mcnomar 0.4531
Wilcoxon 0.0249 McNomar 0.0215
Wilcoxon 0.0001 t test0.000
Wilcoxon 0.0455 t test 0.037
Wilcoxon 0.1075 t test 0.115
Wilcoxon 0.0033 t test 0.001
Mann Whitney U test 0.92 t test 0.95
Mann Whitney U test 0.39 t test 0.41
Mann Whitney U test 0.79 t test 0.38
Statistical significance
Control
Treatment
Control
Treatment
Treatment
Control
Control
Treatment
Status of group
2 (Bullet Compared to dropped penny)
2 (Bullet compared to dropped penny)
4 (Forces on a ball thrown in the air)
2 (Bullet compured to dropped penny) 3 (sandbag dropped from balloon)
Concept
36 3 Students Alternative Scientific Conceptions
32
22
5
pretest posttest
pretest posttest
pretest posttest
pretest posttest
pretest posttest
pretest posttest
0.40 0.43
0.10 0.36
0.21 0.36
0.27 0.55
0.12 0.53
0.26 0.55
Wilcoxon .249 McNemar .215
Wilcoxon .5286 McNemar .7261
Wilcoxon .018 McNemar .0063
Wilcoxon .0277 McNemar .0313
Wilcoxon .0033 McNemar .0010
Wilcoxon .2076 McNemar .2891
Treatment
Control
Treatment
Control
Treatment
Control
4 (Forces on a ball thrown in the air)
4 (Forces on a ball thrown in the air)
4 (Forces on a ball thrown in the air)
3.2 A Theory of Conceptual Change 37
38
3 Students Alternative Scientific Conceptions
the control group occurs for concept 3 whereas significant improvements were observed for concepts 2 and 4. To test this idea in September 1997 in a two semester course on physics for non-science students, Dr. Kalman tried the following experiment: After the students had read about inertia in the textbook, but only as applied to horizontal motion, Dr. Kalman presented the sandbag problem. By vote the entire class without exception concurred that the sandbag would fall immediately without rising. The correct result that the sandbag would initially continue with the same speed as the balloon was then fully explained in terms of inertia. The students expressed themselves as delighted with the correct answer. Dr. Kalman then presented an experiment from the “The Video Encyclopedia of Physics Demonstrations” (Berg, 1992) in which a ball was fired vertically from a “car” moving horizontally at constant velocity. The video asks where the ball will land; in front of, behind or on top of the “car” and then pauses. Fully one half of the class considered that the ball would hit the ground ahead of or behind the “car”.
3.2.5.8
Conclusions
Kalman et al. (1999) developed and tested a collaborative group model that is setup to promote conceptual conflict and to emphasize to students that there are two ideas in conflict. Studies were made in fall 1995 and fall 1996. In fall of 1995 they tested the collaborative learning approach on four concepts by comparing two sections taught by the same instructor. In one section, collaborative learning was used to teach the concepts; in the other a standard professorcentered approach was taken. Standard statistical tests show a gain for the group experiencing collaborative learning over the control group. Nonetheless, the professor teaching the sections, which were used to lecturing, supplemented by demonstrations and audiovisual aids, was dubious of the results. He suggested a further modified experiment, which was undertaken in the fall of 1996. This time in section A, concept 2 of a bullet compared to a dropped penny and concept 3 of a sandbag dropped from an ascending balloon were treated by the collaborative group method and concepts 1 comparing the fall of a sheet of paper with a set of keys and concept 4 examining the forces acting on a thrown baseball were treated conventionally. In section B, the procedure was reversed – concepts 1 and 4 were treated by the collaborative group method and concepts 2 and 3 were treated conventionally. Standard statistical tests show a gain for the group experiencing collaborative learning over the control group. The immediate goal of showing that the model can produce conceptual change for concepts that correspond to alternative concepts among many students was accomplished. The long-term goal is to bring as many students as possible to the highest level of critical thinking. A great deal more research is required to accomplish this goal. The collaborative group sessions must be fleshed out with other student – centered activities such as writing to learn. The discussion of writingto-learn activities commences in the next chapter.
Appendix 1: Additional Questions
39
Appendix 1: Additional Questions 30. An open elevator at a construction site is descending at constant speed and a brick is knocked off the edge. Which of the following graphs describes the motion of the brick?
31. Two astronauts are standing beside each other on the surface of the moon. One uses a rifle to fire a bullet horizontally and the other pitches a baseball horizontally at the same initial height as the bullet. If the bullet weighs one tenth as much as the baseball, the time it takes for the bullet and baseball to reach the ground will be: (A) About one tenth as long for the bullet (B) About one tenth as long for the baseball (C) About the same time for the bullet and baseball (D) Considerably less for the baseball, but not necessarily one tenth as long (E) Considerably less for the bullet but not necessarily one tenth as long
40
3 Students Alternative Scientific Conceptions
32. An astronaut is playing golf on the moon. The path of the ball is shown below:
Which of the following responses are correct: (A) At point C the golf ball is in equilibrium. No net force is acting on it. (B) At point C the only force acting on the golf ball is the gravitational force of the moon (C) At point A the net force on the golf ball is a combination of the force of the golf club and the force of gravity. (D) At point A the net force on the golf ball is mostly the force of the golf club. (E) At point B the force of the golf club on the golf ball is less than it was at point A.
Appendix 2 Task Sheets for warm-up and the four concept exercises.
Task Sheet Part I 1. Form a group with two others who have the same symbol at the bottom of their task sheet. 2. Assign roles to group members: timekeeper recorder and presenter. 3. Take 5 minutes to find out the background of the other group members. 4. Your group has 5 minutes to produce a list of the three most influential scientists that the world has ever seen. 5. Groups will be asked to report on their findings. Part II 6. Consider the paper and the keys in both experiments. Your group has 10 minutes to produce a transparency describing the following:
Appendix 2
41
(a) What is involved in the motion in each case? (b) Why do the keys and paper react differently in the first experiment? (c) What conclusions do you draw from the second experiment? 7. Two groups will report on their findings.
Task Sheet Part I 1. Form in the same groups as in last Friday’s class. If you were not present last Friday please come to the front. 2. Groups will discuss each topic for 10 minutes. 3. Each group member is either (a) Presenter (b) Recorder (c) Timekeeper. 4. Two groups will report to the class. The two presenters from the two groups will remain at the front to discuss viewpoints, first with each other then with the class. Dr. Kalman will moderate the discussion. 5. Afterwards Dr. Morris will clarify the “correct” situation from an experimental point of view. Part II (Put solutions on the supplied transparency. Hand in transparencies and markers at the end of class.) 6. A bullet is fired horizontally from one end of a 10 m long auditorium at 140 m/s. 1. Describe the motion of the bullet. 2. Compare its vertical motion with the motion of a penny dropped from the same height at the same time.
Task Sheet Part I 1. Form a group with two others who have the same symbol at the bottom of their task sheet. 2. Assign roles to group members: timekeeper recorder and presenter. 3. Take 5 minutes to find out the background of the other group members. 4. Your group has 5 minutes to produce a list of the three most influential scientists that the world has ever seen. 5. Groups will be asked to report on their findings. Part II 6. Consider a balloon traveling upwards at 8 m/s. A passenger drops a sandbag over the side of the balloon. Your group has 10 minutes to produce a transparency describing the motion of the sandbag. (Use diagrams and words.) 7. Two groups will report on their findings.
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3 Students Alternative Scientific Conceptions
Task Sheet Part I 1. Form in the same groups. If you were never in a group please come to the front. 2. Groups will discuss each topic for 10 minutes. 3. Each group member is either (a) Presenter (b) Recorder (c) Timekeeper. 4. Two groups will report to the class. The two presenters from the two groups will remain at the front to discuss viewpoints, first with each other then with the class. Dr. Kalman will moderate the discussion. 5. Afterwards Dr. Morris will clarify the “correct” situation from an experimental point of view. Part II (Put solutions on the supplied transparency. Hand in transparencies and markers at the end of class.) 6. Your group has 10 minutes to produce a transparency detailing the forces that act on a thrown baseball. 2
1
1. Just after it leaves your hand. 2. At the top of its motion. “Part of this chapter was published with kind permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc.”
Chapter 4
Writing to Learn: Reflective Writing The Bereiter-Scardamalia Model
One such student relates that last semester I was getting B’s in my courses. This semester because I am using reflective-writing in all of my courses to look at the material before I come to class, I am an A student. The increase in the student’s marks indicates that the self-dialogue helped the student develop functions within the zone of proximal development. Sometimes when you start reflective writing, you realize that you do not understand the content. While doing reflective writing you can often pin point particular important ideas you don’t understand. It causes you to have questions too. Sometimes that is painful because you expect yourself to have answers and don’t. I try to look up answers from books I have at home after doing reflective writing. But it has happened that I stumbled upon an answer myself during my reflective writing. Actually I do explore the answers to my questions while doing reflective writing. (Student view on the purpose of reflective writing.)
4.1 Scaffolding for Students by Encouraging Self-dialogue 4.1.1 Writing as Encouraging Self-dialogue “The specific human capacity for language enables children to provide for auxiliary tools in the solution of difficult tasks, to overcome impulsive action, to plan a solution to a problem prior to a solution and to master their own behavior” (Vygotsky, 1978). Discourse with others provides a scaffolding to enable the student to grasp complex concepts and solve complicated problems. In this chapter, I wish to make a case that certain kinds of writing can also provide scaffolding for students by encouraging self-dialogue. The basis for this case is found in the work of Bereiter and Scardamalia (1987). Indeed at the beginning of this work (pp. 4, 5) Bereiter and Scardamalia cite Vygotsky concerning writing. They note that Although children are often already proficient users of oral language at the time they begin schooling, it is usually some years before they can produce language in writing with anything like the proficiency they have in speech. … The most immediate obstacle is the written code itself … less obvious problems have to do with generating the content of discourse C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
43
44
4 Writing to Learn: Reflective Writing rather than with generating written language. Generating content is seldom a problem in oral discourse because of the numerous kinds of support provided by conversational partners. Without this conversational support, children encounter problems in thinking what to say, staying on topic, in producing an intelligible whole, and in making choices appropriate to an audience not immediately present.
4.1.2
Talking to Someone About a Problem
Consider what happens in talking to someone about a problem. Sometimes the person does not really contribute to the solution – we hear affirmative sounds, umhmm, yup, okay, etc. – as we outline the problem we start to solve the problem and indeed solve it without any help. In Vygotskian terms, the ability to solve the problem is in your zone of proximal development. Discussing the problem with someone else scaffolds you into developing the solution. You not only solved the problem, but you enhanced your problem solving skills. In the scenario, just described, the partner supplied nothing but verbal affirmative sounds. In principle, it should be possible for a student to have a self-dialogue that is used to explore problems and new concepts without having another person present. In this chapter, we will describe a mode of writing called reflective-writing that enables a student to initiate such a self-dialogue about the nature of such complicated problems and complex concepts.
4.1.3
Reflective-Writing and the Zone of Proximal Development
Once students realize the power of reflective writing, many students decide to use it in their other courses even though it isn’t required in those courses. One such student relates that last semester I was getting B’s in my courses. This semester because I am using reflective-writing in all of my courses to look at the material before I come to class, I am an A student. The increase in the student’s marks indicates that the self-dialogue helped the student develop functions within the zone of proximal development. Here is another example written by a former student to help future students: I would like to tell you how I feel about the reflective writing. At first, I found it pointless to do because I thought that you only wanted to force us to read the book. But now, I apply the reflective writing in all my courses because it forces me to de-stress. Indeed, I write what I did not understand and try to find the concept behind it. Furthermore, it enables me to write down clearly what I did not understand, and analyze and describe the problems so I do not need to stress about the unknown. Since I write down the problems, I get to know them and be ready to contend them instead of living in the mysterious world of the unresolved. At first I thought it was a poor methodology, but as now I do it for biology and chemistry as well as physics. I am less stressed. I need a GPA of 3.0. The reflective writing helps me to get ahead and to alleviate the fear of the barrier of 2.99.
4.2 The Knowledge Telling Model and the Knowledge Transforming Model
4.2
45
The Knowledge Telling Model and the Knowledge Transforming Model
4.2.1
Knowledge Telling Model
Bereiter and Scardamalia (1987) suggest that writing is composed in one of two manners, which they refer to as the Knowledge Telling Model and the Knowledge Transforming Model. We shall see that the use of writing to promote a self-dialogue in the sense of reflective writing falls within the framework of the Knowledge Transforming Model. According to Bereiter and Scardamalia, young students begin to engage in writing in a straightforward manner that they refer to as the Knowledge Telling Model illustrated in Fig. 4.1. This model allows them to generate text in a straight forward manner. “The writer can get started in a manner of seconds and
Representation of Assignment
C o n t e n t K n o w l e d g e
Construct Memory Probes for Topic
Retrieve Content Information
Appropriate?
No
Yes Append Information to Draft
Update Mental Representation of Text
Fig. 4.1 Knowledge telling model
D i s c o u r s e K n o w l e d g e
46
4 Writing to Learn: Reflective Writing
speedily produce an essay that is on topic and that will conform to the type of text called for” (Bereiter and Scardamalia, 1987). The student engaging in the Knowledge Telling process draws upon discourse knowledge solely to construct memory probes in order to retrieve content information relevant to the assignment. The information is retrieved and then examined to ensure that it fits in with the assignment. This procedure allows the student to begin writing almost immediately and to produce text on any reasonable specification of topic. It preserves the straight- ahead form of oral language production and requires no significant amount of planning or goal setting than ordinary conversation does. Hence, it should be little wonder if such an approach to writing were to be common among elementary school students and to be retained by many students on into university and career. The difference in the product produced by a university student using this model and an elementary school student using this same model can be attributed to abilities such as greater sophistication in language.
4.2.2
Writing of a Research Paper
There is a marked difference between the writing of a typical assignment for a post-secondary course and reflective writing. To make this clear this section includes a description of the writing of a typical research paper and the next section includes the description of the kind of writing produced in a reflective writing assignment. Abraham Pais1 has pointed out that the writing of a research paper corresponds to a simple formula (he wrote roughly 150 research papers): For a typical theoretical paper: Start a section 1, called Introduction, in the following way: It has been observed [or pointed out that. …] Early analyses of these phenomena [slew of references] had led to the conclusion that. … In the light of the more recent data it appears, however, that these previous results need to be extended [or modified or revised]. It is the purpose of the present paper to do so. In section 2 we summarize previous answers. In section 3 we introduce the following new feature […] and leave a number of more technical points for an appendix. In section 4 we summarize our conclusions and present a further outlook.
1 ABRAHAM PAIS was the last Jew to receive a doctorate degree in wartime Holland, having finished a Ph.D. at the University of Utrecht just days before Jews were barred altogether from the universities. His dissertation attracted the attention of the famous nobel laureate Nils Bohr, who sent a message inviting him to work with him in Denmark. Pais went underground for the duration of the war, unable to leave Holland to accept Nils Bohr’s invitation until 1946. Pais made several important contributions to the foundations of the modern theory of particle physics while working at the Institute of Advanced Study at Princeton and Rockefeller University. In addition to Bohr, Pais worked with Einstein, and many other famous physicists. These relationships, which he forged during his research career, gave him a unique perspective enabling him to write many highly acclaimed works on interweaving descriptions of the science of the twentieth century with descriptions of the scientists who produced the science.
4.2 The Knowledge Telling Model and the Knowledge Transforming Model
4.2.3
47
Writing a Biography
In contrast to this procedure, consider the description by Abraham Pais about how he wrote each chapter of his biographies of Albert Einstein and Niels Bohr and other such works: First I make a scribble, writing down things as they come to mind, correcting and changing things around, …the pages go into a drawer for a month…then I go back to the scribble … thinking over every sentence, every word as I go along. Again the pages go into a drawer, now maybe only for a week. Having done that, I have a draft, which in my experience is final at the 90% level.
4.2.3.1
Freewrite (Scribble)
This procedure that Pais used to write the biographies does not correspond to the Knowledge Telling process of Fig. 4.1. He begins with a freewrite (scribble) putting down an eclectic collection of everything that he knows that relates to the topic of the chapter. The Knowledge Telling process produces a draft that is close to the final version, but here only gradually by dint of a great deal of thinking and restating do fully formed thoughts emerge. This resembles the process that Bereiter and Scardamalia call “knowledge transforming”.
4.2.4
Knowledge Transforming Model
4.2.4.1
Student Writing Sample
Here is a sample of writing produced by a student in one of my classes: I suppose I should make the meaning of a projectile motion clear in my head …. I guess a projectile is an object moving freely under the influence of gravity alone. I don’t really understand but I think something about the air resistance being negligible was mentioned … OK. I’m going to back up my statement with an example. Let’s assume we want to look at the projectile motion of a ball … And to find details about the motion at certain instants, we have to take the horizontal & the vertical components into count. I also have to know a whole bunch of formulas for finding components of velocity of a certain particle. But all of those formulas could be derived from the basic formulas for constant velocity and acceleration that we studied before.
The form of the sample is a self-dialogue. The student has first read a section of the textbook. Then the student has examined the concepts in the section. This would include strategies such as summarizing, highlighting and/or highlighting relevant material. Then the student closes the book and freewrites on the section. Freewriting or nonstop writing was popularized by Elbow (1973). Countryman (1992) defines freewriting as writing rapidly for a short and fixed period. In freewriting, you start writing and keep writing without editing. You write down every word that you think. Write about what it means. Talk to yourself in your writing. If at any time
48
4 Writing to Learn: Reflective Writing
you feel that you can’t go on – your mind is a blank – write a “nonsense” word over and over, e.g. the last word that you wrote, wrote, wrote, wrote, … until you start writing again. Students are asked to use the freewrite to clarify their understanding of the assigned section. They asked to clarify exactly what they don’t know, and try to understand through their writing the material they don’t know. The entire exercise including the initial reading of the section, summarizing, underlining, and/or highlighting is referred to as reflective writing. 4.2.4.2
Instructions on Doing Reflective Writing
The instructions to students as to how to do reflective writing are as follows: ● ●
●
●
●
●
Read each section (or two sections if one of the sections is short). Carefully try to focus on what you don’t understand, and all points that you would like to be clarified. During your reading, use whatever techniques you usually use to understand required reading including underlining, highlighting, summarizing, and rereading. Having completed this task, freewrite about what you have read (about 2/3 of a page per section). Write about the section(s) that you have read. Write about what it means. Try to find out what you don’t know, and try to understand through your writing the material you don’t know. When you are finished, you will be prepared to ask questions in class about all the points that you don’t understand. Reflective-writing is not essay writing. You will usually not use capitals, and will often write fragments of sentences. If at any time you feel that you can’t go on – your mind is a blank – write a “nonsense” word over and over, e.g. the last word that you wrote, wrote, wrote, wrote, … until you start writing again.
Figure 4.2 exhibits reflective writing in the context of the Bereiter and Scardamalia Knowledge transforming model. The following is part of an interview with a student, who engaged in reflective writing in my courses: Interviewer: Alexei2:
What is the purpose of reflective writing? Reflective writing helps you recover the main points of sections of the chapter and put them together to get to the point of the whole chapter. I keep track of the main points section by section, you know. What’s the point? Where does it take me? Why is it important? You are also forced to think about the content. It’s not like memorizing. You have to understand what you are reading enough to know something to write about. Sometimes when you start reflective writing you realize you do not understand the content. While doing reflective writing you can often pin point particular important ideas you don’t understand. It causes you to have questions too. Sometimes that is painful because you expect yourself to have answers and don’t. I try to look up answers from books I have at home after doing reflective writing. But it has happened that I stumbled upon an answer
2 Student names have been changed to ensure anonymity. All students, whose work is cited, have given permission to have their work used.
4.2 The Knowledge Telling Model and the Knowledge Transforming Model
49
Mental Representation of Assignment
Problem Analysis and Goal Setting
Content Knowledge Discourse Knowledge
Prior content knowledge
Scientific genre knowledge
Content Problem Space Read a new section Identify concepts(may include highlighting summarizing or underlining)
Rhetorical Problem Space Freewrite on the section
Problem Translation
Construct canons of argument Develop knowledge of scientific genre
Problem Translation
Relate to previous sections (establish a roadmap)
Identify which concepts are clear and which are not Examine meaning of concepts
Knowledge Telling Process Identify questions that need to be answered in class
Fig. 4.2 Knowledge transforming model
myself during my reflective writing. Actually I do explore the answers to my questions while doing reflective writing. One more thing, if I really understand a topic, I really don’t need to reflective writing about it. But topics I don’t understand very well, it helps me a lot to understand them.
4.2.4.3
Interaction Between Content Processing and Discourse Processing
Reflective writing causes students to increase their conceptual acquisition through the interaction between content processing and discourse processing interactions shown in Fig. 4.2. According to Bereiter and Scardamalia, this interaction provides the stimulus for reflection in writing. “Thus it is that writing can play a role in the
50
4 Writing to Learn: Reflective Writing
development of their knowledge” (Bereiter and Scardamalia, 1987). A strategy such as summarizing science/engineering textual material without the reflective writing component falls into the Bereiter and Scardamalia knowledge-telling model rather than the knowledge-transforming model. The knowledge-telling model unlike the knowledge-transforming model does not foster the generation of new knowledge, because it relies on established connections between content elements and readily available discourse knowledge. “Thus from the perspective of the knowledge-telling model, knowledge is something one already has and remains intact; writing is a matter of conveying a section of this knowledge to someone else” (Bereiter and Scardamalia, 1987).
4.2.5
Knowledge Building
Paavola and Haakkarainen (2005) consider “learning as a process of knowledge creation, which concentrates on mediated processes where common objects of activity are developed collaboratively”. They review three approaches to knowledge creation, i.e. Bereiter’s (2002) knowledge-building, Engström’s (1987, 1999) expansive learning, and Nonaka and Takeuchi’s (1995) organizational knowledge-creation. Bereiter’s concept of knowledge-building processes could be related to Vygotsky’s idea of the zone of proximal development in that Bereiter describes such processes as involving working at the edge of one’s competence, progressively setting up higher standards of performance. Recall that in Chapter 2 we had remarked that Vygotsky stated learning is ineffective, when the teaching is oriented towards developmental levels that have already been reached. “The only ‘good learning’ is that which is in advance of development”. Paavola and Haakkarainen argue that the three models of Bereiter, Engström, and Nonaka and Takeuchi have some basic differences, but there are many similarities that can be seen to be a basis for a more general view, which they call the knowledge-creation metaphor. The basic point is a striving of the individual to build their knowledge beyond their present knowledge. Although Paavola and Haakkarainen are describing the metaphor in terms of the collaborative processes of a group of students, the metaphor can, be applied to the self-dialogic activity of reflective writing as we shall see in the next section.
4.2.6
Qualitative Research on Reflective Writing
In this section, the views of students on using reflective-writing in a course are presented. This is partially based upon Kalman (2003) and concerns qualitative research done by Kalman and Aulls on reflective writing on an introductory Physics course on Mechanics. A course in differential calculus was a co-requisite and techniques from calculus were utilized in the course. The majority of the students had had Physics in High School. The student population in the course in this study is multicultural and multilingual and ranges from freshman in university to graduate
4.2 The Knowledge Telling Model and the Knowledge Transforming Model
51
students. At this university, there are typically many foreign students including at least 20% from Middle Eastern countries. The University is one of the largest urban universities in Canada. It is a comprehensive university with roughly 15,000 fulltime and 10,000 part-time students in the faculties of Arts and Science, Commerce, Engineering and Fine Arts. A significant fraction of the students are returning to school, often after having completed a degree in another discipline. Students in this course include science majors, humanities majors and engineering majors. The course covers many concepts that are studied not only for their own sake but which are topics needed as a prerequisite for further Physics courses and many courses in other Science departments. These include how and why bodies move the way they do and such topics as the energy and momentum of bodies. The reflective writing activity was worth 15% and the midterm and final are each worth 30% of the student’s mark. The remaining marks are for weekly submission of quantitative problems (20%) and three assignments arising out of in-class collaborative group activities (5%). Over half the class (around 50 students) volunteered to take part in the study. Five students were selected from the volunteers. This is only 5% of the total class. Nevertheless, students were purposively selected who represented the disciplines from which the most students are drawn. Both men and women were selected for equity purposes. The students selected all passed the course and fell between the top 25% of the class and 75% on the final examination. Nabilla is from the United Arab Emirates. She is a Biology major and this is her first year of schooling in Canada. Alexei is a Mathematics and Statistics major who plans to switch soon into Computer Sciences. Solomon is a master’s student in Philosophy who is also doing a concurrent Biology degree. Ahmad is a Psychology major. He says that he acquired a solid Physics background in a small high school, and he was the top student. Lelana is an Engineering major. Her father is a Physics professor, who helped her during the course since there was no tutorial provided. The actual number of students from each discipline in the course, in the order given, was: 30% Science (mostly Biology), 20% Engineering, 20% Mathematics and Computer Sciences and 30% other (Humanities and Commerce). Half the students were males and the other half female.
4.2.6.1
Survey of Students
A 20-item survey was given to the students during the second week of the course. This was used to determine learning styles, student attitude towards experiences of doing reflective-writing, and student perspectives of whether or not reflective-writing participation resulted in a better understanding of textual material. The questions relevant to reflective writing are found in Table 4.1. Students responded to the survey using a five-point Likert scale. Two versions of the survey were used with half the class responding to each version. Each version used the same questions, but with a different order of the questions in each version, so that comparisons could be made for random answers.
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4 Writing to Learn: Reflective Writing Table 4.1 Responses to questions related to reflective-writing on survey in January Question
Alexei
I like the experience of Strongly reflective-writing agree Using reflective-writing Agree I seem to have a better understanding of the material
4.2.6.2
Solomon
Nabilla
Lelana
Ahmad
Strongly agree Strongly agree
Strongly agree Strongly agree
Agree
Agree
Agree
Disagree
Methodology
Students were interviewed by a trained graduate student. All student interviews devoted to reflective writing were organized by student and then collapsed over students for each temporal period of the course beginning and ending with an interview. These divisions reflected the accumulation of teaching-learning opportunities for building strategies to improve the quality of thinking about physics phenomena. Repeated reading of the three interviews for each student led to identifying re-occurring general and specific concepts that were common to all students and unique to particular students. We compared the three divisions of the course to see if students obtained reoccurring categories that might reveal underlying themes regarding their views towards reflective writing and its value to their deep rather than shallow physics course content. The results of the analysis of reflective writing products for each student were compared to the student interview analysis to assess whether they corresponded or conflicted with each other. We reasoned that the majority of students would have to show consistency in their views and actions within and between the three divisions of the course to be fully valid (Johnson, 2000).
4.2.6.3
“How Useful is Reflective Writing”
In the first group interview, done in the third week of the course in January, we asked them as a group ‘How useful is reflective writing?’ Responses to this question and the probe ‘So, is the reflective writing helpful’? are found in Table 4.2. A comparison of each student response in the two tables offers a consistent pattern for all of the students except for Nabilla. All the students acknowledge the activity caused them to read the textbook before class. Students differ in the extent to which reflective-writing leads to understanding textual content. Solomon and Alexei seem confident that reflective-writing enhances understanding. Nabilla, Lelana and Ahmad are more ambivalent regarding the nature of their understanding. After 6 weeks of instruction a midterm exam was given. Immediately after the exam, the first individual interviews took place. Nabilla has been making progress in using the reflective-writing tool. Now, 7 weeks into the course, she is using it for a critical examination of the textual material.
4.2 The Knowledge Telling Model and the Knowledge Transforming Model
53
Table 4.2 Response to the question and the probe on reflective writing and the concept assignment in the group interviews Student/ Question
How useful is reflective writing?
So is the reflective writing helpful?
Nabilla
If the assignments weren’t there I don’t think I’d open the book.
Ahmad
I think it’s good. I do not think it should be marked, it should be required. It solidifies my ideas.
You’re just writing what you think of, your opinions, and uh, if you agree with it, … and things that people don’t, they just disagree, so if I disagree I just say it ‘I disagree’, if not, then I say why do I disagree. It makes you read the book before coming to class…that is helpful.
Solomon
I find it very useful. I see in my writing a lot where I don’t understand a formula and then eventually it will make sense [as he does his reflective-writing]. I find it very useful because It’s a little bit like thinking out loud and then I am generally a fairly putting it on paper, …, it’s just that it’s quite lazy person and then surprising to see how much more it’s helpful it feels that I’m sort of once it’s put down on paper, … it’s also helpful forced to do it but then because even if I don’t find the answers at least while doing it I feel it I will find the questions, … Sometimes I find really helps. that that is the first step… in order to find the answers you need to find the right questions. Its good because it makes Its good because it’s making me read it. you read the chapters.
Alexei
Lelana
4.2.6.4
Samples of Reflective Writing
In her reflective writing, Nabilla writes; “The kinematic equations that we used in Chapter 2 are also applicable to projectile motions”. She uses this to make sense of the concept found in her reading of Chapter 4: A particle can be considered superposition of the term (Vot) which is the displacement if no acceleration is present. So if there were no gravitational acceleration, then the object would move horizontally and not in a vertical direction, since there’s no pull from the earth. So in this case the vertical distance which the particle falls is the same distance, as a freefalling object would fall. So we can say that a projectile motion is superposition of a motion with constant velocity (where there’s no gravitational acceleration) and a motion a freefalling object in the vertical direction when a = constant.
By the end of the course, Nabilla has a different perception of reflective writing; Interviewer: Nabilla:
What was the purpose of reflective writing? I’m just trying to make myself understand… if you understand it and write, you can understand it more… but obviously if I read and, if I write it down I’ll be concentrating more on it…so, I’d be double understanding it.
While Lelana perceives herself to rely most heavily on summary notes, she shows evidence of being able to get a deeper understanding of textual material
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4 Writing to Learn: Reflective Writing
when using reflective writing. In her reflective writing in January, she exhibits these strategies;
Connecting Current and Prior Textual Material: I suppose I should make the meaning of a projectile motion clear in my head …. I guess a projectile is an object moving freely under the influence of gravity alone. I don’t really understand but I think something about the air resistance being negligible was mentioned … OK. I’m going to back up my statement with an example. Let’s assume we want to look at the projectile motion of a ball … And to find details about the motion at certain instants, we have to take the horizontal & the vertical components into count. I also have to know a whole bunch of formulas for finding components of velocity of a certain particle. But all of those formulas could be derived from the basic formulas for constant velocity and acceleration that we studied before.
Self Checking of Conceptual Material: Well I guess I was surprised to read that even though an object would maintain constant velocity it would accelerate, well it kinda doesn’t make sense because if the object is not speeding and is traveling at a constant velocity, how would it accelerate? But then I suppose it was explained to me that acceleration depends on the change in the velocity and since velocity is a vector quantity, its magnitude and direction-I forgot to say change in magnitude & direction of velocity would cause the object to accelerate.
Conceptual Clarification in the Next Paragraph of Her Reflective Writing: O.K, let’s see if I can get this straight. Acceleration is created when either the magnitude or the direction of the velocity vector is changed.
4.2.6.5
Details on the Use of Reflective Writing as Knowledge-Transformation
The following shows details on the use of reflective writing as knowledge-transformation to get learners to “actively engage prior knowledge, construct links to data and observations.” (Prain and Hand, 2002) and additionally, to show that by using reflective writing the students themselves believe they achieved a better understanding of the material.
Constructing Links and Actively Engaging Prior Knowledge: Interviewer: Solomon:
Do you ask any questions during reflective writing? Typically it would be I don’t understand this concept, and then well, I guess maybe it works this way or that way and I’ll actually ask myself questions about the material…for more clarification, typically it’s because I don’t understand a link…how two things fit in the puzzle.
4.2 The Knowledge Telling Model and the Knowledge Transforming Model Interviewer: Alexei:
55
What is the purpose of reflective writing? Reflective writing helps you recover the main points of sections of the chapter and put them together to get to the point of the whole chapter. I keep track of the main points section by section, you know. What’s the point? Where does it take me? Why is it important?
Students’ Conceptual Understanding: Interviewer: Solomon: Interviewer: Solomon: Interviewer: Solomon:
Interviewer: Solomon: Interviewer: Alexei:
4.2.6.6
What do you think the purpose of reflective writing is? Getting a better understanding of what’s going on. How well would you say you understand the material in the section of the text before you start reflective writing? seven… That’s out of ten? Generally I know exactly what’s going on but there’s always a detail, sometimes the text is a little bit unclear, … they’ll go step by step by step, and between steps two and four, I don’t know where the book goes, there’s some kind of quantum leap of sorts…so then what I do with the reflective writing, I typically write about that and try to understand it. After reflective writing, how well do you understand the material in the text? We go from seven to eight or nine… What was the purpose of reflective writing? You are also forced to think about the content. It’s not like memorizing. You have to understand what you are reading enough to know something to write about. Sometimes when you start reflective writing you realize you do not understand the content. While doing reflective writing you can often pin point particular important ideas you don’t understand. It causes you to have questions too. Sometimes that is painful because you expect yourself to have answers and don’t. I try to look up answers from books I have at home after doing reflective writing. But it has happened that I stumbled upon an answer myself during my reflective writing. Actually I do explore the answers to my questions while doing reflective writing. One more thing. If I really understand a topic, I really don’t need to reflective write about it. But topics I don’t understand very well, it helps me a lot to understand them.
Conclusions
Altogether, the results of this study do point to the value of reflective writing as a tool to helping students take more responsibility for their learning. First, we confirmed that reflective writing each week places a demand on even good students that they would not have done on their own. That is being prepared each week to sum up what they are learning and to recognize what they are not learning or what needs to be clarified or further elaborated. Second, we tentatively confirmed that more students than not who pass the course are likely to find it to be a new and beneficial aid to learning how to relate the material to prior knowledge and new concepts to each other. Especially important was finding out that the students who benefit most from the
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4 Writing to Learn: Reflective Writing
academic activity slowly come to increasingly greater understanding of its benefits because they slowly become more strategic and able to self regulate the accomplishment of reflective writing so that it not only aids encoding of important information, but also often aids linking concepts and ideas to each other and thereby building a more tightly organized hierarchy of information in long term memory. To promote metacognitive activity during reflective writing, students should be asked to read each portion of the material very carefully before commencing their reflective writing. Moreover, students should attempt as far as possible to comprehend it during their reading using whatever techniques they find necessary including; underlining, highlighting summarizing and rereading. They are trying to focus on what they don’t understand, and all points that they would like to be clarified during the class. Having completed this task, they should immediately use non-stop reflective writing to examine the material that they have just read. During this reflective writing, they should write about what it means. They should attempt to find out exactly what they don’t know, and try to understand through their writing the material they don’t know.
Chapter 5
Getting Students to Examine Their Epistemology
Learning is concerned with ideas, their structure and the evidence for them. It is not simply the acquisition of correct responses, a verbal repertoire or a set of behaviors. As “Joe” Redish (2003) writes “if we want to adopt the view that we want to teach as many as possible of our students then we must adopt a mix of approaches and be prepared that some of them will not work for some students”.
5.1
Developing Critical Thinking
It is the goal of any introductory course in the university to guide students to an understanding of the basic principles of the subject and to guide them as well to higher orders of thinking (critical thinking). As will be discussed in Chapters 7 and 8, the way to get students to examine their alternative scientific conceptions (Chapter 3) is to get them to change their epistemologies. The first step in this direction is to get them to develop their critical thinking skills. Two elements in achieving this goal are discussed in this chapter; Feyerabend’s principle of counterinduction (Section 5.2.1.1) and writing-to-learn methods (Section 5.1.2) especially the critique exercise (Section 5.2.1.3). Kalman and Kalman (1998) discuss developing critical thinking using writing to learn technique. Another related method based upon philosophy of science is found in the next chapter.
5.1.1
Comfort Factor
Kalman and Kalman (1998) note that part of the reason why students do not develop their critical thinking skills may be found in the comfort factor. Students have picked up strategies which have worked in their previous schooling; memorization and delivery of memorized material, summary and personal response statements have brought them success and they resist the higher order strategies of critical thinking and interpretation which are expected of them, seeking the comfort C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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5 Getting Students to Examine Their Epistemology
level of what has worked for them before. We expect from our students synthesis, analysis, and interpretative writing and thinking; our students do not understand what we require of them and flounder. Students see examinations that are based only on problems and they think that they only need to be taught how to solve these problems.
5.1.2
Cultural Constructs
Aside from the question of cognitive strategies, students are, as James Britton et al. (1978) and others remind us, based in their culture and society (Barnes et al., 1989). Three concepts which most students have internalized and which seem to direct their scholarly endeavors are the requirement of closure, faith in objectivity, and resistance to writing about and/or analyzing perceived contradictions (Flower et al., 1990). These cultural constructs inform many of their academic enterprises. Students’ reading and cultural assumptions inform the texts they read and the lectures they hear. Our role as teachers is to present them not only with permission to argue with perceived authority, that is, to consider whether material is valid just because it is on the printed page or is part of a lecture, but also with the tools to effectively articulate the concepts and the problematic that their responses must address.
5.1.3
Role of Writing-to-Learn
Writing to learn is a technique that helps our students move from their previous experience to the higher orders of thinking that we are now demanding and that negotiates the distance between the student and the material and between the student’s expectations and our own. By teaching writing to learn techniques, reflective-writing in particular, we help our students to write their way into an understanding of the text itself and of their analysis and beliefs about that particular material. Peter Elbow (1973) points out that writing is a recursive act, and can be viewed as a holistic process, involving successive drafts that move unevenly from an imprecise understanding of a text or problem through increasingly more complex, lucid and coherent interpretations. Through this process, which can take on many forms (the course journal, the course dossier, peer review, and reflective-writing exercises), students come to mediate their own “knowledge” with the new knowledge that is presented to them in the course of their disciplinary studies. Writing to learn helps students to learn how to learn and to apply what they learn, rather than memorizing what an expert has established. Through writing to learn, students not only can acquire new knowledge, but can come to change those preconceived concepts with which they enter university, and which stand in the way of analytic and interpretive learning. Writing their way into problems helps students to become comfortable with unfamiliar material and to reach toward the highest order of thinking, the formulation of interpretive ideas, with enthusiasm and without fear.
5.2 A New Model
5.2 5.2.1
61
A New Model Feyerabend’s Principle of Counterinduction
In Winter 1999, Kalman et al. (2004) made modifications to the interventions previously explored by Kalman et al. (1999) (Section 3.2.5) in which the conceptual conflict model (using collaborative group exercises) was enhanced by the introduction of a writing-to-learn exercise called a critique. The form of the critique, which we shall discuss later in this section is based on Feyerabend’s (1993) principle of counterinduction; the process by which one theory or idea is used to effect change in its rival.
5.2.2
A Collage of Opinions
Let us begin with the hypothesis that many students are still playing the “what does the teacher want” game. As Sternberg (1990) notes “In most discourse communities, which are imbued with social traditions, great emphasis is given to such factors as deference to authority, unreflective intuition, social dexterity and timely action”. Moreover, Nelson (1964) points out that “for collaborative learning to be most effective, it is not sufficient simply to have students work together. … Left alone, they often simply create a collage of opinions”. In view of Nelson’s remarks quoted above, it is certainly possible that many students were simply confused by the collaborative group exercises. It is clear then that we must enhance the development of students’ critical thinking skills so that they will carefully examine the alternatives presented to them in the conceptual conflict exercises. This should greatly increase the likelihood that they examine their personal (alternative) scientific conceptions.
5.2.3 The Critique Exercise The critique is introduced into a course to critically examine alternative possibilities. It is based upon Feyerabend’s principle of counterinduction, which concerns the process by which one theory or idea is used to effect change in its rival. As Feyerabend has pointed out evaluation of a theoretical framework doesn’t occur until there is an alternative. More details are found in Chapter 7. The critiques are designed to cause the students to engage in the kind of critical discussion that Feyerabend says is required to decide which natural interpretations can be kept and which must be replaced. In the course considered by Kalman et al. (2004), the three critique exercises were worth 5% of their course marks. All but one of the questions on the two exams in the course were of the usual numerical type found in standard textbooks. The remaining question on the midterm and on the final was an essay type examination of one of the concepts covered by the critiques. All questions on the midterm and the final are of equal value. The midterm and final were each worth 30% of the student’s mark.
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5.2.4
5 Getting Students to Examine Their Epistemology
Examining the Course
The course was then examined in several ways. Firstly the efficacy of the enhanced model compared to the original model was examined by having the students take the same enhanced version of the force concept inventory (FCI) (Hestenes et al. 1992) as administered to the students in the previous study. Secondly a group of students in the course were interviewed on audio- and video- tape three times during the course to find out more about how the students used the various elements of the model both to get a better understanding of student learning and also to discover how to improve the model. Thirdly copies of all the written materials produced by students in the course were retained for later analysis. In this chapter, we restrict ourselves to the quantitative data on the enhanced model. The other information will be examined later on in this book.
5.2.4.1
Concepts Examined
For analysis, we establish a baseline of all FCI (Hestenes et al. (1992) questions except 1, 5, 12, 16 and 22. The questions in the baseline do not relate to the concepts under study. Question #12 was not covered by this course. Question 1 relates to the idea that bodies of different masses falling from rest through a nonviscous media for a short time (so that the resistance of the medium can be neglected) are found at later times to move at different speeds. In the 1996 experiment this was treated as a collaborative group exercise. It had turned out that the pre-test responses were already very high so that no inferences could be drawn from this experiment. This time, this experiment was done as a reflective-write pair share exercise (such exercises are described later in this book). No critique follow up was performed for this experiment and it is excluded from this analysis. The idea that if a sandbag is dropped from an ascending balloon, immediately upon release the initial velocity of the sandbag is zero, was treated by a collaborative group exercise and a critique. Only additional question 30 especially addressed this question. There had been some difficulties with this question in the previous analysis (Kalman et al., 1999; see Section 3.2.5). This time there was an additional technical difficulty with the readability of the associated graphs so that question was dropped from the analysis.
5.2.4.2
Analysis
The analysis was then done on the remaining two concepts considered in the previous analysis (Kalman et al., 1999): 1. (Bullet compared to dropped penny.) Personal (alternative) scientific conception; a fast moving bullet stays in the air because of its great speed.
5.2 A New Model
63
This concept was treated in winter 1998 and in winter 1999 as in the 1996 test by a conceptual conflict collaborative group exercise. Additionally there was a follow up by the critique found in the Appendix to this chapter. The relevant questions for this concept are question 16 of the FCI and additional questions 31 labeled as concept 2. 2. (Forces on a ball, thrown in the air.) Various personal (alternative) scientific conceptions; “force dependent on velocity”, “force of the hand balancing the force of gravity at the top of the motion”, an “ma” or a “momentum force” is in equilibrium with gravity at the highest point in its motion. This concept was treated in winter 1998 and in winter 1999 as in the 1996 test by a conceptual conflict collaborative group exercise. Additionally there was a follow up by the critique found in the Appendix to this chapter. The relevant questions for this concept are questions 5 and 22 of the FCI and additional questions 32 labeled as concept 4. The relevant questions for these two concepts as a whole are questions 5, 16 and 22 of the FCI and additional questions 31 and 32, labeled as set I. Analysis was done on only those students who wrote both the pre- and post-test and were present at all three conceptual conflict exercises for the winter 1998 and winter 1999 experiments and additionally only those students who wrote all three critiques for the winter 1999 experiment. These stringent requirements severely restricted the size of the sample.
5.2.4.3
Tests for Normality and Homogeneity of Variance
In comparing the 1998 and 1999 experiments, Kalman et al. first tested the populations for normality using both the Anderson-Darling and Kolmogorov-Smirnov tests. The results show no evidence of normality being violated. The Bartlett and Levene tests of homogeneity of variance were also applied where appropriate. The results showed no evidence of homogeneity of variance being violated.
5.2.4.4
Overall Gains
The overall gains for the 2 years were then compared using t tests. Some of the details are shown in Table 5.1. It was found that p < 0.0005 in all cases. Thus the addition of the critique produced a statistically significant improvement in winter 1999 compared with the use of collaborative groups alone in winter 1998. Table 5.2, contains a detailed comparison of the results for winter 1988 and winter 1999. Note that in every case the winter 1999 group scored considerably higher than the winter 1998 group. These results appear to be statistically significant. It should be noted that in addition to the statistically significant gains in the two tested concepts for the winter 1999 group over the winter 1998 group, there appears
64
5 Getting Students to Examine Their Epistemology Table 5.1 Comparison of the overall gains pre- to post-test 1998 with 1999 Test group Mean difference Standard deviation Pre-test 1998 vs. post-test 1998 Pre-test 1999 vs. post-test 1999
3.24 6.95
4.95 3.81
Table 5.2 Comparsion of the experiments winter 1998 and winter 1999 Mean Score (Standard Deviation) Group Statistical signifiA (33 Students) B (19 Students) cance (t test) Concept
Question(s)
Test
Baseline (FC1-1, 5, 12, 16, 22) Set I (1, 5, 16, 22, 31, 32) Set II (5, 16, 22, 31, 32) Concept 1 (16, 31)
pre-test 8.76 (3.95) post-test 11.36 (4.59)
9.79 (4.16) 14.05 (4.81)
p = 0.38 p = 0.051
pre-test 2.64 (1.39) post-test 3.64 (1.67) post-test 2.85 (1.50
2.05 (1.03) 4.79 (1.27) 3.95 (1.19)
p = 0.12 p = 0.012 p = 0.032
post-test 1.364 (0.742)
1.842 (0.375)
p = 0.012
Concept 2 (5, 22, 32)
post-test 1.485 (1.09)
2.105 (0.937)
p = 0.043
Bullet compared to dropped penny Forces on a ball thrown in the air
to be a strong indication that Winter 1999 students also scored better in the baseline consisting of questions that do not relate to the concepts under study. Recall that the purpose of the critiques is to enhance the development of students’ critical thinking skills so that they will carefully examine the alternatives presented to them in the conceptual conflict exercises. Such a spillover might indicate that in doing the critiques, students do actually increase their critical thinking skills and that with such an improvement students were led to reevaluate their entire conceptual framework.
5.2.5
Conclusions
Kalman et al. (2004) developed a technique based upon developing conceptual conflict through in-class collaborative group exercises with a follow-up of a writing exercise (critique) in which students examined the alternatives produced in the collaborative group exercise. The winter 1998 students only participated in collaborative group exercises. The winter 1999 students additionally did follow-up writing
5.2 A New Model
65
exercises (critiques). In every case the winter 1999 group scored considerably higher than the winter 1998 group. These results are statistically significant. In addition to the statistically significant gains in the two tested concepts for the winter 1999 group over the winter 1998 group, the Winter 1999 students also scored better in the baseline consisting of questions that do not relate to the concepts under study. Such a spillover might indicate that in doing the critiques, students are not only more likely to undergo conceptual change, but also actually increase their critical thinking skills and that with such an improvement students were led to reevaluate their entire conceptual framework.
5.2.6
Student Ranking of Reflective Writing, Group Activities and the Critique Writing-to-Learn Activity
At the end of the course, we asked students explicitly “I’d like you to rank these three activities provided by the instructor in terms of your own learning during the course. I’d then like you to explain the reasons why you have assigned a rating of one, two or three to each activity. Why has xxxx been the most important activity for your learning?” Other probes were then asked to be sure each student had said all they had to say and to determine if the student held any understanding of how the professor saw the activities working together to support their learning. The results of the rankings among the three activities are shown in Table 5.3.
Table 5.3 Student ranking of activities Student
Reflective writing (RW)
Nabilla
Ranked highest of all activities Ranked second. No change At first “freaking out” “Write Final Interview: “you start thinking which what you think about … and how does it make sense one makes more sense and which to you, what you understand, one’s logical” discussing it with yourself” Ranked last of all activities. Ranked highest. No change Originally liked it – RW is “to Final Interview: “the solidify your ideas about group work gives what you read.” you new ideas and helps you solidify your opinion about it.” Later dislikes: “I don’t put in a real effort.”
Ahmad
Groups (SGW)
Critique (Ctq) Ranked last. 1st interview: “Sometimes even questions that you asked to yourself you can find in the critique.” Ranked second. “SGW bombards you with many ideas…Ctq you’re going in the opposite direction, trying to get rid of all the ideas; come to one right idea.”
(continued)
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5 Getting Students to Examine Their Epistemology
Table 5.3 (continued) Student
Reflective writing (RW)
Groups (SGW)
Solomon Ranked highest of all activities. Ranked last. No change No change Final Interview: “When you’re Final Interview: reflective writing you’re “I don’t think thinking about the concepts it was helpful.” and it makes you work through them.” Alexis
Lelana
Critique (Ctq) Ranked second. No change Final Interview: “I don’t find it particularly helpful because I don’t feel at the end there’s a conclusion that is necessarily drawn out.” Ranked highest. No change
Ranked highest of all Ranked last. No activities. change “Because I have to write I will The problems were too Final Interview “Always have to think about it… trivial in SGW. interesting problems. what you understand about it You had to examine why or what you don’t it was so, examine why understand” Final Interview: others saw it in a “the way I thought about different way.” it, originally and the way I think about it now, is way different.” Ranked last of all activities. Ranked second. Ranked first. No Change 1st Interview: “I hate writing “It was a good experi- Final Interview: “Ctq most English essays. … And the helpful. … because ence, Ctq helped fact that I have to do it in the stuff we discussed and SGW as well … Physics – its just a pain. … … I never knew much different from the To actually sit down and physics classes I had about them. … It (the learn I have to read every before …in the other answers) did not directly single line and take notes as I ones the teacher just come from the book. I am reading it. writes a bunch of had to discuss with this formulas and it’s like and that person. It came memorize these.” from what I thought.”
No Change: student opinion of the activity remained the same throughout the course.
Students feel differently about the different activities. As “Joe” Redish (2003) writes “if we want to adopt the view that we want to teach as many as possible of our students then we must adopt a mix of approaches and be prepared that some of them will not work for some students”.
Appendix: Critiques
67
Appendix: Critiques
Penny
Bullet
Bullet
At the left we see a picture of a penny that is dropped. At the same time that it is dropped, a bullet is fired. At the centre and the right we see possible pictures of the motion of the bullet. Why would some people believe that the motion is as depicted in the centre and others believe that the motion is as depicted at the right. (Give as many reasons as possible for each viewpoint.)
Initial speed 0 m/s
Initial speed 10 m/s up
At the left we see a sandbag being dropped from a ballom. (Give as many reasons as possible for each viewpoint.) 2
1
What forces act on a thrown baseball: 1) Just after it leaves your hand. 2) At the top of its motion.
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Chapter 6
Critical Thinking
The invention of inertia requires an examination of what would be needed to have the Earth to rotate around its axis and a ball fall straight down beside the high tower. Such a notion requires a high order of critical thinking. Hardly the abilities found in most students entering an introductory course. Duhem’s viewpoint is that a single hypothesis by itself whether induced by observation or postulated by a guess is not really science. The essential difference between science and pseudoscience and non-science is that a scientific theory should provide coherent, consistent, and wide-ranging theoretical organizations. Kalman (2002) discusses how very important it is that students become aware of how science works so that they can undergo conceptual change; confront their personal (alternative) scientific conceptions.
6.1 6.1.1
Critical Thinking Domain Specific Attribute or Does It Involve General Principles
Kalman (2002) examines the general question of critical thinking: “Enabling students to think critically is one of the central objectives of liberal and professional education” (Nelson, 1994). What then is critical thinking and is this a domain specific attribute or does it involve general principles that once learnt can be applied across the disciplines.
6.1.2
Surveys of the Opinions of Philosophers and Scientists
Surveys of the opinions of philosophers and scientists on the nature of the cognitive and affective strategies required for critical thinking have been done by committees headed by Benjamin Bloom (Bloom et al. 1956a,b) and Peter Facione (1990). Bloom’s taxonomy is a useful reference point to position the learner with reference C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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to critical thinking. Subsequent to the publication of this taxonomy, many philosophers and educational psychologists explored critical thinking in detail. Marzano (1993) states: “Twenty years ago the call for the teaching of thinking was a small one by a few individuals and organizations. Now it permeates the discussions of educational reform. For example, the National Educational Science Board Commission on Precollege Education in Mathematics, Science and Technology (1983). The National Educational Association (1987) and the American Federation of Teachers (1985) have all strongly advocated the teaching of thinking as a necessary component of school reform”. As (Facione, 1990) puts it: researchers “have argued that effective and meaningful education requires that curricular, pedagogical and assessment strategies at all levels of education are coordinated so as to foster in students those cognitive skills and habits of inquiry associated with critical thinking. They have made the case that educating students to be critical thinkers is vital for the students themselves and for society in general”.
6.1.3
Working Definition
A working definition of critical thinking has been given as “the use of those skills or strategies that increase the probability of a desirable outcome. It is used to describe thinking that is purposeful, reasoned, and goal directed” (Halpern, 1997). Halpern elaborates that “The ‘critical’ part of critical thinking denotes an evaluation component… When we think critically, we are evaluating the outcomes of our thought processes–how good a decision is or how well a problem has to be solved. Critical thinking also involves evaluating the thinking process–the reasoning that went into the conclusion we’ve arrived at or the kinds of factors considered in making a decision. Critical thinking is also called directed thinking because it focuses on a desired outcome” (bolding in original). The evaluation component is exactly what the students require to examine their own conceptual framework and make a conceptual change to the framework underlying the course. McPeck (1981) has given a definition that resembles that of Halpern in some aspects, but argues that critical thinking is domain specific: The “most notable characteristic ‘a certain skepticism’ …towards a given statement, established norm or mode of doing things. This skepticism might ultimately give way to acceptance … it consists of alternative hypotheses and possibilities. The criterion for regarding skepticism as judicious an approach to incorrect or frivolous must be determined by the norm and standard of the subject area in question. Learning to think critically is in large measure learning to know when to question something and what sorts of questions to ask. Not just any question will do”.
6.1.4
McPeck’s Views
There has been an attempt in the critical thinking community to dismiss McPeck’s views. Thus Zieger (1998) in an annotated bibliography of critical thinking
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resources omits any reference to this work. Richard Paul’s review (Paul, 1985) is entitled “McPeck’s Mistakes” but Weinstein (1993) notes that despite this, “the book was not to be dismissed, … the book was to become a focus in the literature”. Indeed Weinstein states that “this issue has become the Great Debate in the field” and in a footnote notes that “The recent debate on general vs. domain specific critical thinking skills is exemplified by” a book edited by Stephen P. Norris (1992). According to Weinstein “An emphasis on the particularity of thinking practices results in a deep challenge to the notion of an available foundation upon which critical thinking can rest. Such views regard thinking, and the procedures and norms through which it is carried out, as imbedded in discourse frames, each with a particular character and of limited extent. … Accepting as the central goal of critical thinking ‘to enable students to become the maximally rational human beings that they are capable of being’, McPeck considers traditional discipline-based education to be ‘the most direct route, if not the only efficacious route, to teaching critical thinking’ ”. Weinstein contrasts McPeck’s views with those of Paul (1990). “Paul says that all knowledge requires critical thinking: ‘All the disciplines — mathematics, physics, chemistry, biology, geology, sociology, anthropology, history, philosophy, and so on— are modes of thought. … He sees critical thinking to require both cognitive and affective strategies”. Fogarty and McTighe (1993) have pointed out “research and experience show that cooperative learning enhances thinking processes. Through cooperative learning, students articulate their thoughts to each other and thus engage in an interactive approach to processing information”.
6.1.5
Studying Philosophers of Science to Promote Critical Thinking
Strike and Posner (1992) after noting “We have been substantially influenced by authors such as Kuhn (1970), Toulmin (1972) and Lakatos (1970). … They (Strike and Posner, 1992) also exhibit basic opposition to the empiricist tradition in epistemology as well as its manifestations in psychology”. Mathews (1994) notes that the debate of empiricism versus realism “has so dominated the history of philosophical reflection on the nature of science that it ought to feature in school discussions about the nature of science”. Keeping in mind Mathews (1994) suggestion and the requirements of conceptual change models, consider the following course objectives: (a) To understand how science functions. To this end, we will examine how some twentieth century philosophers of science understand the scientific process – how theories evolve. (b) To develop the critical thinking skills needed to critically analyze ideas and compare them with observations of how nature functions. Students need to distinguish between concepts, hypotheses and observations of nature.
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The above are the actual course objectives found in a course outline handed out to all students. A course based upon using philosophers of science to promote critical thinking.
6.1.6
Why Have Students Study Philosophy of Science
Students need to test their views to see if they are consistent. This is a part of their development of their critical thinking skills. Studying how scientists came to examine their views can help students come to examine their own views. In the same way, if students study different philosophers of science they can see that there are different ways of seeing the same material. This chapter is a source for basic information that faculty can use to present to students in their courses. Secondly, many models of conceptual change found in the next chapter are based upon models proposed by philosophers of science. This chapter provides the background needed to understand these models.
6.1.7
Collaborative Group Work
The course discussed in Kalman (2002) is based upon collaborative group work. Groups of 3–5 students are organized with the task of viewing course material through the eyes of a modern philosopher of science: Karl R. Popper, Thomas Kuhn, Imre Lakatos or Paul Feyerabend. The group work is seen as part of the overall attempt to get students to have a better understanding of science. For students to come to grips with the material, they must develop their critical thinking skills. They must come to understand and critically analyze their own views. Only then can they examine the evolution of science and develop ideas about how science works. The students present these ideas to the class and additionally hand in a written version. Only the written version is marked. The development of the written version is crucial in the development of the student’s critical thinking skills. Marzano (1993) notes that: “By definition composing is a highly complex task that includes such phases as planning, translating and reviewing, all of which require a great deal of conscious control. … The longer the process continues and the longer the transcript becomes, the greater the interdependency among decisions, In short, the process becomes one of making decisions based on increasingly more numerous and complex conditions”. Students are challenged to produce increasingly more complex expositions based upon input during the oral presentations and written comments on the written versions. To prevent piggy–backing, students hand in evaluation sheets with each assignment in which they rate the performance of each of the group members (see Appendix). In order that the rating not be seen as punitive, it is made clear that students will be given bonus marks for exceptional contributions. Normally students receive the mark actually given for the assignment.
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If any student is rated with a low participation for two consecutive assignments, the instructor takes this as a sign of a problem within the group and convenes a meeting with all group members to resolve any difficulties.
6.1.8
Assignments for Individual Groups
Each group of students studies the work of one philosopher of science such as Kuhn (1970), Lakatos (1970), or Popper (1965) throughout the course. Depending on the course, either 60 minutes a week or 60 minutes every second week or five 75-minute sessions are devoted to group presentations. For the first presentation, the instructions to the students are: “Introduce your group’s philosopher and explain the epistemology and methodology of your group’s philosopher”. For the remaining group presentations, students are asked to explain how certain scientific developments would be viewed by their philosopher. For each session, only one group studying each philosopher makes a 10 minute presentation. Other groups are called on to comment on the presentation and then the subject is thrown open to general discussion. The professor throughout these presentations acts to suggest further topics for exploration in the next presentations. For example; what is Popper’s attitude to verisimilitude? To further enhance the learning of the different philosopher’s approach a copy of one (excellent) group report is made available for copying by all students. The presentations follow the development over a period of time of certain ideas. Thus in an introductory calculus-based course on optics and modern physics for science students, the changing attitudes towards light are explored. The exact topics are: 1. Discuss the wave and particle theories of light from the point of view of your philosopher. (You might not find these views in a book – it is a problem for you to solve!) In particular, comment on the role of Young’s experiment as a crucial experiment. 2. Discuss the Ether theory (pre-1880) from the point of view of your philosopher. 3. Discuss the Michelson-Morley experiment from the point of view of your philosopher. 4. Discuss the existence of photons from the point of view of your philosopher.
6.1.9
What Constitutes a “Good” Scientific Theory
A major issue that is discussed by means of student presentation of these assignments is what constitutes a “good” scientific theory. This is an issue that Mathews ascribes of as in the liberal tradition:
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The liberal tradition maintains that science education should not just be on education or training in science … They should have a feeling for methodological issues, such as how scientific theories are evaluated and how competing theories are appraised…(Mathews, 1994, pp. 2, 3). First and foremost, they see that there are different views according to the different philosophers as to the answer to this question. Students become aware that the same textual material can be viewed in a variety of ways. On the first and last days of the course, students are asked to write about the following question: “In your view how does science work: How do theories come about and how do new theories take the place of older theories?” An analysis of these writings shows that most students enter the course with what might be termed a Baconian outlook on the function of science. This is in the sense of an emphasis on observation and induction. In Bacon’s own words: “But my course and method … is not to extract works from works or experiments from experiments, as an empiric, but from works and experiments to extract causes and axioms, and again from those causes and axioms new works and experiments, as a legitimate interpreter of nature” (Holton and Brush, 1973, p. 183). A reading of students’ writings made on the last day of the course indicates that student’s views are inevitably changed. Almost all students come to realize that older “replaced” theories were not necessarily “bad” and that presently accepted theories may very well change. Some students have maintained their original approach to the question posed at the beginning and end of the course, but have now produced a carefully thought out response. Most but not all students with a Baconian outlook switch to an outlook close to one of the other philosophers examined in the course. This provides evidence that students have met one of the goals of the course (a major step in producing conceptual change) – a critical analysis of their belief structure. On the final examination, students are required to examine a scientific theory that they have never seen before from the point of view of all the philosophers studied in the course. Almost all of the students are able to answer the question at a satisfactory level. This provides evidence that students have met another of the major goals of the course – The ability to analyze textual material from different points of view.
6.1.10
Bacon
The kind of science that occurs through discovery learning is basically Baconian. The philosophy of Francis Bacon dominated physics from the beginning of the seventeenth century to the end of the nineteenth century. The emphasis was on observation and induction: “But my course and method … is not to extract works from works or experiments from experiments, as an empiric, but from works and experiments to extract causes and axioms, and again from those causes and axioms new works and experiments, as a legitimate interpreter of nature”. Thus for Bacon the starting point of all Science is experiment. Regularities in the experiment would reveal laws and the laws (causes and axioms). These laws would be of interest in the sense that they would lead to further experimentation. The natural regular underpinnings of the world
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(laws) are thus revealed in experimentation. It is implicit that theory in science can be justified only if it has been deduced from performance of experiments. Such discovery learning is ideal to search for regularities in nature. For example, Keplar’s discovery of Bode’s law, Mendele’evs discovery of the table of the elements, Gell-Mann’s and Ne’eman’s discovery of the Eightfold way. In each case the law revealed missing “elements” that were found by later experiments. Basically, the Baconian idea is to search for order in the universe. A search could result in a law such as Bode’s law, which would not give any hint towards theory. The idea that a regularity in nature yields a law is Baconian. Towards the end of the nineteenth century, Balmer discovered a formula that fit four lines in the visible Hydrogen spectrum. After publication, many other lines predicted by the use of the formula were found in the visible spectrum and the ultraviolet. Balmer speculated that there were many other series of lines, which were later found. This encapsulates Bacon’s scientific method. Perform many experiments. Examine them for regularities. The regularities can be formulated into laws, which lead to further experimental predictions that can be verified. That this rapidly became the norm is clear from Newton’s famous statement in his work setting forth the laws of Mechanics (Philosophiae Naturalis Principia Mathematica) “Hypotheses non fingo” (I do not make hypotheses). Newton despite his prestige was concerned about accusations of making theoretical pronouncements that did not fit in with Bacon’s accepted views on the Scientific method. In actual fact Newton made hypotheses throughout the Principia.
6.2
Theoretical Science
If Science were as simple as Baconian induction, our students would have no problem coping with the material presented to them. Straight lecturing backed up by laboratory demonstrations would transmit the laws of science. This is indeed the kind of Science that students are led to believe that they will encounter in our courses. It is the impression that they generally receive in high school. It is not surprising that this attitude has prevailed since long after Newton, scientists in the nineteenth century were reluctant to admit that the scientific theories they proposed were complex. Darwin claimed that “he worked on true Baconian principles and without any theory collected facts on a wholesale basis”, but then in the identical work later on admits that he could not resist forming a hypothesis on every subject. He made this clear in a letter to Henry Fawcett written on September 18, 1861: “About thirty years ago there was much talk that geologists ought only to observe and not theorize; and I well remember someone saying that at this rate a man might as well go into a gravel pit and count the pebbles and describe the colors. How add it is that anyone should not see that all observation must be for or against some view if it is to be of any service”. A complex theoretical structure is in place – when experiments are undertaken. In studying modern philosophy of science, students can undergo a conceptual change of their views of science.
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Newton made no pretense of proving, in advance of empirical evidence, that any additional assumptions were uniquely self-evident and valid. Instead, he treated them as working assumptions to be accepted hypothetically for just so long as their consequences threw light, in exact detail, on hitherto-unexplained phenomena. Indeed, he made a practice of critiquing theory qua theory. In this, he is clearly not following the Baconian “scientific method”. There is the notion that the theory must be complete and based on an economy of concepts. Students, whose goal is solving problems, will have great difficulty with his approach. What is the student to make of Newton’s discovery that inertial mass and gravitational mass are the same? Newton recognized that mass as it appears in his universal law of Gravity is the source of gravity; in modern parlance, the gravitational charge. It was not at all obvious to Newton that this mass was identical with the mass that is responsible for the inertia of bodies. In order to test this principle, he noted that if the gravitational mass is the same as the inertial mass, the period of a pendulum should only depend on the length of the pendulum and the local value of the acceleration due to gravity, “g”. Newton then experimented with pairs of pendula of length approximately 3.4 m and whose bobs were identical boxes of wood containing different materials. At different times, the boxes were filled with wood, gold, silver, lead, water, salt, wheat and glass. Based on these measurements, Newton concluded that gravitational mass and inertial mass are equal to a precision of one part in a thousand. Much more accurate experiments were performed by Roland von Eötvös and his colleagues between 1889 and 1908. Experiments around 1970 gave the equality of inertial mass and gravitational mass to a precision of one part in a trillion. This principle became enshrined by Einstein as one of the starting points of his general theory of relativity. In this way, Newton devised in practice, what philosophers of science have since labeled the hypothetico-deductive method, in which the proper form of a theory is seen as a mathematical system in which particular empirical phenomena are explained by relating them back deductively to a small number of general principles and definitions. It was not, however until the nineteenth century that philosophers of science picked up on Newton’s methods.
6.3 6.3.1
The Crucial Experiment Sir John Herschel
Sir John Herschel was a distinguished scientist working in the first half of the eighteenth century. His “discourse on the study of natural philosophy” (1830) was widely read in the nineteenth century. Darwin read it and after completing this work, it is said that Darwin gained a burning zeal for science. Although Herschel respected the Baconian tradition, he was certain that advancement in science did not always proceed along the lines that Bacon had advocated. He maintained that theoretical statements derived inductively from experiments and wild guesses are equally acceptable provided that their deductive consequences
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are confirmed by observation. Thus it is the context of justification; the agreement with observations that is the most important criterion for scientific laws and theories to be acceptable. Indeed, Herschel emphasized the role of the “crucial experiment” in confirming theories. In his view an experiment is crucial in confirming a theory only if every other possible theory is incapable of explaining this particular experiment.
6.3.2
Crucial Experiments
Francis Bacon used the phrase instantia crucis, “crucial instance,” to refer to something in an experiment that proves one of two hypotheses and disproves the other. Bacon’s phrase was based on a sense of the Latin word crux, “cross,” which had come to mean “a guidepost that gives directions at a place where one road becomes two,” and hence was suitable for Bacon’s metaphor. Both Robert Boyle, often called the father of modern chemistry, and Isaac Newton used the similar Latin phrase experimentum crucis, “crucial experiment”. When these phrases were translated into English, they became crucial instance and crucial experiment (The American Heritage Dictionary of the English Language: Fourth Edition, 2000). The difference between Herschel and Bacon is, as previously noted, in the origin of theory. For Bacon theory had to be inductively derived from experiment. For Herschel, even a wild guess could result in a successful theory. One observation that Herschel and other nineteenth-century physicists considered to be an exemplar of a crucial experiment concerned the nature of light.
6.3.3
Advent of the Wave Theory of Light in the Nineteenth Century
Until the nineteenth century, physicists had favoured Newton’s particle theory of light over the wave theory of Huyghens. At the beginning of that century, Thomas Young performed an experiment which introductory textbooks claim to be the deciding (crucial experiment) to show that light was indeed made of waves. However, the physics community as a whole at the time did not accept that point of view. Thus we find the following statement by Henry Bougham (Edinburgh Review 1, 451 (Jan, 1803): The wave theory of Thomas Young (1801) “can have no other effect than to check the progress of science and renew all those wild phantoms of the imagination which… Newton put to flight from her temple”. Why then should students wholeheartedly accept the ex cathedra statement of their textbook that Young’s experiment is a crucial experiment? It took further experiments to convince the community (Fig. 6.1). In 1818 Augustin Fresnel presented to the Prize Essay Committee of the French Academy an improved version of the Hook–Huyghens wave theory that would
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Fig. 6.1 Excerpt from the 1st edition of the Encyclopedia Britannica published 1771
account for diffraction; the bending of light around obstacles. Simeon Poisson, a member of the committee, dismissed Fresnel’s theory as implausible. He reasoned that according to Fresnel’s theory if light would shine on a circular obstacle, there would be a illumination at the center of the obstacle nearly as intense as if on obstacle were present. A short time later, Domique Arago performed the experiment and found that such a bright spot actually occurred. (Actually, Maraldi had done the experiment 50 years earlier, but his result had been lost. [See J. Strong, 1958, pp. 181, 186].) Ironically, this effect is now known as the Poisson bright spot. The experimental verification of this unexpected result gave confidence in Fresnel’s wave theory of diffraction. According to Herschel the actual crucial experiment was made by the French scientists Armand H. L. Fizeau and Jean B. L. Foucault. during the mid1800s, As first noted by Descartes, if light is composed of particles, the speed of light in a transparent medium (such as glass or water) is greater than the speed of light in empty space. According to the wave theory, it must be less than the speed of light in a vacuum. On the basis of this difference, François Arago proposed a “crucial experiment” which would compare the two speeds, thus deciding once and for all whether light is a particle or a wave. Around 1850, Fizeau and Foucault
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separately measured the speed of light in water and established conclusively that the speed of light in water is less than the speed of light in a vacuum.
6.3.4
Pierre Duhem
Herschel’s views on the crucial experiment was disputed by the French theoretical physicist Pierre Duhem in the early 1900s. Duhem’s viewpoint (1906/1954) is that a single hypothesis by itself whether induced by observation or postulated by a guess is not really science. The essential difference between science and pseudoscience and non-science is that a scientific theory should provide coherent, consistent, and wide-ranging theoretical organizations. Observations are only scientifically relevant to the extent that they give guidance to how theories should be formulated and how they should be refined. Thus, no single observation can ever serve as a crucial experiment to confirm or refute any one specific hypothesis conclusively, taken apart from the whole complex of theory and interpretation. Scientists are always free to add new auxiliary hypotheses to the existing theory rather than to accept any single counter-example as a challenge to the general validity.
6.3.4.1
Reexamining the Experiments of Fizeau and Foucault
To illustrate his point, Duhem reexamined the “crucial experiment” of Fizeau and Foucault’s on the speed of light in water. In his view, the experiments of Fizeau and Foucault’s did not decide between two isolated hypotheses, but between two complete theoretical systems. True, the particle theory of light as formulated by pre nineteenth-century Newtonians is falsified, but in Duhem’s opinion, it is not inconceivable that a future theory might be built upon the hypothesis that light is made up of particles, with the aid of some new auxiliary hypotheses which would be different from those comprising the Newtonian system. In such a theory, the refraction of light might be explained in a different manner, so that it would be possible to account for the results of experiments of Fizeau and Foucault while still maintaining that light is a particle. Second, it is not at all certain that the current concepts “wave” and “particle” are the only possible ones; perhaps a new concept might be formulated, which would go beyond this dichotomy, possibly by combining some aspects of both concepts. This seems to have analogies with some models for teaching of students. Adding of auxiliary hypotheses in this manner is akin to Piaget’s notion of assimilation. It should be kept in mind that in introductory courses, many students are unlikely to enter the course with a clearly formed theory of the subject. The problem is to get them to change their epistemology (see Chapters 7 and 8) not their belief system. Nonetheless exposure to views such as those of Duhem could help them rethink their epistemologies.
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The Photo-Electric Effect
Shortly after Duhem formulated these two possibilities, Einstein, in explaining the phenomenon of the photo-electric effect, re-introduced into physics the idea of a particle nature of light, in his 1905 paper on light quanta. Ironically, the initial reaction to Einstein’s paper mirrored Henry Bougham (Edinburgh Review 1, 451 (Jan, 1803) view on the wave theory Thomas Young (1801) that it “can have no other effect than to check the progress of science and renew all those wild phantoms of the imagination which… Newton put to flight from her temple”. Planck in 1910 despairingly stated that by the acceptance of Einstein’s photons “the theory of light would be thrown back centuries”. In reality, Einstein’s paper paved the road to the development of quantum mechanics around 1925. In that year, 75 years after Foucault’s “crucial” experiment, the question of the nature of light was again open. Today, we do not even expect any more a simple answer such as “only wave” or “only particle” in the classical sense, a situation which provides a striking example of the acuteness of Duhem’s vision. Furthermore, it should be noted that nowhere in the present debate on the quantum mechanical nature of light is Foucault’s result even mentioned as evidence. The convincing experimental result that light travels more slowly in water has lost all relevance to the question of the nature of light.
6.3.5
A Scientific Theory Should Provide Coherent, Consistent, and Wide-Ranging Theoretical Organizations
Students’ epistemologies are problem driven. So they do not have a picture of a science as having an overall coherent structure. Examination of changes in science not due to experimentation but rather because of a realization that a fundamental inconsistency existed in scientific theories should help students in their journey to a new epistemology. 6.3.5.1
Maxwell’s Theory
According to Duhem a scientific theory should provide coherent, consistent, and wide-ranging theoretical organizations. Exemplars of such scientific theories are readily found in modern science. Think of Darwin’s theory of evolution. The need for coherence and consistency seems to have been a hallmark for major advances in science. Maxwell examined the state of Electricity and Magnetism in his day and noted that there was an inconsistency between the treatment of the electric and magnetic fields. The Electric field was related to a time changing Magnetic field through Faraday’s law, but in Ampere’s law the Magnetic field did relate to a time changing Electric field. Maxwell’s development of his theory invokes the need for the kind of wide-ranging organization required by Duhem and also use of the hypothetico-deductive method, which we saw that Newton incorporated in his
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development of his theories. In a paper in 1884, Hertz reformulated Maxwell’s fundamental equations essentially in the form that is used today. In 1888, Hertz was able to detect radiation in what we would now refer to as the radio and microwave regions and show that it traveled not at the infinite speed required by the rival theories of Neumann and Weber, but at the speed of light and that the microwaves travel in straight lines and could be reflected, refracted and polarized in the same way as light. In his book “Modern Views of Electricity (1889), Oliver Lodge claimed that Hertz’s experiments had “utterly and completely verified” Maxwell’s theory of Electricity and Magnetism.
6.3.5.2
Problems with Maxwell’s Theory
In 1905, the year that Einstein developed his theory of relativity, it had been more than 200 years since Newton had set forth his theory of mechanics. Maxwell’s theory of electricity and magnetism had barely been accepted by the majority of the physics community. Resistance by major theorists such as Lord Kelvin (Thomson, 1987) to Maxwell’s theory on the principle that all of physics should be based on Newton’s theory had just been overcome. Physicists were examining a basic discrepancy between the two theories. Ever since Galileo, it had been a basic principle that the laws of science should be the same to all observers situated in moving reference frames whose relative speed is uniform (referred to as inertial frames of reference) (Galilean principle of relativity). Newton’s mechanics was consonant with this principle. Maxwell’s equations, however appeared to change as you move from observer to observer.
6.3.5.3
On the Electrodynamics of Moving Bodies
In Einstein’s letter to his future wife Maria Mileva in August 1899, Einstein mentioned that he was carefully rereading a 1892 paper of Hertz in which a 1890 paper of Hertz was reprinted. Einstein as an undergraduate student was excited by Maxwell’s theory. He neglected his studies to study contemporary physics including Maxwell’s theory. As a consequence, he had to enter graduate school without the benefit of holding a research assistantship. Fortunately, the patent office was desperate to find individuals with knowledge of Maxwell’s theory, because of an escalating number of patent applications in this area. Einstein was able to complete his doctoral studies by supporting himself with the position of technical expert at the patent office. In the same year that he published his doctoral work, Einstein wrote his first paper on the special theory of relativity entitled “On the Electrodynamics Of Moving Bodies”. In this paper, Einstein turned the problem of a discrepancy between Maxwell’s theory and the Galilean principle of relativity on its head. One of the two principles that Einstein set out in his paper was that the application of the relativity principle was incorrect. It must be altered so that Maxwell’s equation would remain invariant in all inertial frames of reference. The other principle is that the speed of light is constant in a vacuum in inertial frames
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of reference. The consequent alterations to Newton’s theory of mechanics produce what we refer to as Einstein’s special theory of relativity. Theories such as Maxwell’s do not seem to arise by induction from experiment. Starting with Newton, elements of a theory are often based on the hypothetico-deductive method, in which the proper form of a theory is seen as a mathematical system in which particular empirical phenomena are explained by relating them back deductively to a small number of general principles. Again, in grounding a theory in experiment as Galileo did with consideration of the high tower experiment and motion on inclined planes, theories may make use of idealizations such as Galileo’s perfectly smooth infinite plane. Generally speaking, a scientific theory should provide coherent, consistent, and wide-ranging theoretical organizations. Although, experiments often serve to convince the scientific community that one theory is better than another, no theory can strictly speaking be falsified. Any theory containing a hypothesis which is in contradiction with experiment could as Duhem’s suggested, be resurrected with the aid of some new auxiliary hypotheses.
6.4
Twentieth Century Philosophers of Science
In the twentieth century there arose many attempts to produce philosophies of science that correspond to the above grander concepts of what makes up a scientific theory as opposed to Bacon’s simplistic ideas. I here examine the approaches of Karl Popper, Imre Lakatos, Thomas Kuhn and Paul Feyerabend.
6.4.1
Popper
Sir Karl Raimund Popper British philosopher, born in Austria believed that knowledge evolves from experience of the mind. He was the first philosopher of science to out rightly reject the traditional Baconian inductive method in the empirical sciences. This was in part based upon David Hume’s point that only an infinite number of such confirming results could prove a theory correct.
6.4.1.1
The Falsifiability Criterion
Instead Popper argued (Popper, 1965) that hypotheses can be deductively validated by what he calls the “falsifiability criterion”. Under this method, a scientist seeks to discover an observed exception to a postulated rule. The absence of contradictory evidence thereby becomes corroboration of his theory. According to Popper, astrology, Marxist history, and Freudian psychoanalysis are pseudosciences rather than empirical sciences, because of their failure to adhere to the principle of falsifiability.
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Scientific progress can indeed arise from falsification of hypotheses. A good example is Prout’s Hypothesis that all elements are condensations of different amounts of Hydrogen atoms. Much of the quantitative analysis that refuted it was done with the intent of testing this hypothesis.
6.4.1.2
What Makes a Theory Scientific
According to Popper, a theory is scientific only if it can be made to conflict with a basic statement; it must be predictive of novel facts, that is facts that were not understood in the light of previous knowledge. Again the progress of science consists of tentative theories – “All growth of knowledge consists of the improvement of existing knowledge which is changed in hope of approaching nearer to the truth”. In Popper’s mind, science consists of the search for the great, bold, falsifiable theories and for the crucial negative experiments. Experiments are successful even if, in spite of being well conducted, they disagree with theory, because they reveal an error in the primary assumptions. The quest for absolute truth is ideal. It is a goal unattainable by human hands and thus, science should not be approached from the sense of the quest for the absolute truth. Since a single contrary case is sufficient to show that a statement is not true, we can never be sure about the truth of any scientific statement. Popper’s criterion for a successful scientific theory is that it must not simply pass such experimental tests as may be applied but that it must be formulated in such a way that falsification is in principle possible. Karl Popper’s epistemology is grounded in the idea that scientific knowledge originates in an opinion, or a guess not founded on enough evidence. Popper believes that there will be progress in human knowledge as long as we make precisely formulated brave and bold conjectures, and guesses and we exploit our errors and learn from them even though we can’t verify any hypothesis. If any hypothesis is contradicted by empirical evidence, we learn something, and in that case, we propose new and better conjectures.
6.4.1.3
Principles
Popper believes that the growth of human knowledge should be based on our experiences and problems and our attempts to solve them. He believes that imagination should be an integral part in the formulation of theories. In devising a theory, a scientist should begin with a problem rather than with an observation or a fact. Popper proposes that a scientific theory should be based upon the following principles: 1. An examination of the theory for internal consistency. 2. An analysis of the theory to distinguish between its empirical and logical components and to clarify its logical dimension.
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3. In the case of a new theory, the theory must be examined to see if the new theory has more application to experiment than existing theories and if it has better explanations and solutions to problems. Popper believes that a better theory is the one that contains greater empirical content and greater predictive power. 4. An examination of the theory for testability of its conclusions. If the conclusions are true, the theory is supported but never verified. If it is false then the theory is falsified and scientists should begin searching for a new theory without abandoning the present theory until finding a better one.
6.4.2
Kuhn
Thomas Samuel Kuhn was born in Cincinnati, Ohio, and died 1996 in Cambridge Massachusetts. 6.4.2.1
Paradigms
In his landmark second book, The Structure of Scientific Revolutions (Kuhn, 1970), he questioned the traditional conception of scientific progress as a gradual, cumulative acquisition of knowledge based on rationally chosen experimental frameworks. He claimed that scientific research and thought are defined by “paradigms”. A mature science relies on only one paradigm. A paradigm is an accepted model or scheme. It encompasses a whole scientific culture, including a theory, experimental techniques, experimental methods and selected revealing experimental facts. He argued that the paradigm determines the kinds of experiments scientists perform, the types of questions they ask, and the problems they consider important. Scientists typically accept a prevailing paradigm and try to extend its scope by refining theories, explaining puzzling data, and establishing more precise measures of standards and phenomena. This effort is what Kuhn calls normal science and is a period of scientific investigations which most closely resemble Bacon’s notion of how knowledge is “discovered”. During this time, scientists are guided by a paradigm that determines the nature of problems and solutions considered scientific and solvable. The existence of a paradigm, whose purpose is to guide research, is the best criteria to establish that a research field has become a science. A new successful paradigm provides interesting new problems, theoretical & experimental to be solved. Eventually, however, efforts of scientists may generate insoluble theoretical problems or experimental anomalies that expose a paradigm’s inadequacies or contradict it altogether. Experimental results that can’t be explained by a functioning paradigm are dealt with in one of three ways according to Kuhn’s structure. It may be put aside, hoping that further research will resolve the difficulty. Alternatively, the paradigm can be “refined”. The altered paradigm still contains the basic thrust of the original paradigm.
6.4 Twentieth Century Philosophers of Science
6.4.2.2
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Scientific Revolution
Lastly, an accumulation of anomalies triggers a crisis. Crisis science is the beginning of Kuhn’s category of “extraordinary science”. This science is a period which is characterized by a breakdown in the dominant paradigm, and which eventually ends with a scientific “revolution”, and the adoption of a new, and incompatible paradigm to guide the field. Such a shift in the paradigm alters the fundamental concepts underlying research and inspires new standards of evidence, new research techniques, and new pathways of theory and experiment that are radically incommensurate with the old ones. Scientists change allegiance to a new paradigm because the new paradigm is more successful in solving problems or anomalies than the old one. Figures 6.2 and 6.3 are views of Kuhn’s philosophy of science produced by my students. As the wave theory developed after 1800, it contained the concept of the Ether as the medium in which light waves were propagated. In looking back on knowledge and experiments done before the adoption of a paradigm, Kuhn states that scientists will re-interpret their history. This was most evident in the reconceptualization of an experiment performed by Bradley in 1727–1728. The experiment was originally interpreted in terms of Newton’s particle theory of light and seems to indicate beyond a shadow of a doubt that the Earth is in motion with respect o a fixed reference frame. These results were reframed to be evidence of the existence of the ether, since the fixed reference frame in the wave theory of light would be the frame where the Ether is at rest. Kuhn would argue that scientists at the time didn’t perceive their reconceptualization as a reframing. Scientists would not have said “I used to see a stream of particles, but now I see a wave”. Scientists would have said “I used to ‘think’ that light was particles, but I was wrong. I am actually
Fig. 6.2 Progress of science according to Kuhn
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Fig. 6.3 Kuhn’s view
looking at a wave”. Bradley’s evidence was added to the body of knowledge supporting the current paradigm in that way. The response of scientists to anomalies can be viewed to take place within the context of the wave theory of light and the Ether hypothesis as the prevailing paradigm. In 1810 for example, Arago wrote to Fresnel posing a difficult problem from his experiments on refraction in a prism. He had hypothesized that the prism in his telescope would refract light differently depending on the speed of light through the Ether with respect to the earth. However, Arago discovered that the direction in which his telescope was pointed did not affect the refraction of light as he had expected. Fresnel responded by “refining” the ether theory. He wrote back to Arago with a modification that introduced the concept of “Ether drag”.
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The additions to the equations used provided a satisfactory “mopping up” for the ether theory, and allowed normal science investigations to continue. Indeed, in 1851 Fizeau tested Fresnel’s prediction and got perfect agreement verifying the modified Ether theory. The process of normal science inevitably leads to crisis. In the time from 1850–1880, there were already the beginnings of a crisis, stemming from the electromagnetic theory of Maxwell, himself a strong proponent of Ether theory, and working within the dominant paradigm. The electromagnetic equations posed by Maxwell in 1873 became highly problematic for the ether theory. Additionally an experiment performed in Berlin in 1881 by the American physicist A. A. Michelson, and refined in 1887 by Michelson and E. W. Morley in the United States became a serious anomaly for the wave theory-Ether paradigm. Michelson performed his experiments primarily to distinguish between rival ether theories of Stokes and Fresnel. To do this he set out to measure the speed of the Earth with respect to the Ether. He was unable to do this. It was reasoned that, if the speed of light were constant with respect to the proposed Ether through which the Earth was moving, that motion could be detected by comparing the speed of light in the direction of the Earth’s motion and the speed of light at right angles to the Earth’s motion. No difference was found. This null result posed a serious difficulty for the ether theories. The crisis was only resolved with the new paradigm introduced by Albert Einstein in 1905 in his special theory of relativity incorporating the proposal that the Ether did not exist and that the speed of light is a universal constant.
6.4.3
Lakatos
Imre Lakatos was born in Hungary and died in England. He also rejects Popper’s quest for a logarithmic, logical set of steps that can or should be taken in order to evaluate the validity of a theory. Like Kuhn, he believes that the sociological organization of science is part of its “logic”. However, he believes Kuhn’s description of scientific revolutions make the process look like a completely mob reaction, impossible to differentiate from a religious activity.
6.4.3.1
Scientific Research Programs
Both Popper and Kuhn treat changes in scientific theories as sequential; one scientific theory replacing another. Popper does allow for the possibility that if a scientific theory is falsified, there could be a period where more than one proto-theory exists and Kuhn considers the possibility that before a “science” is established, there may be more than one competing “school” of thought. The norm for both Kuhn and Popper is, nonetheless a sequential succession. We have seen, however that major progress in science most often occurred when there was more than one theory in competition. Thus Galileo’s discovery of inertia occurred because of the confrontation between the Copernican and Ptolemaic theories. The development of
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Maxwell’s theories owes much to the confrontation between the wave and particle theories of light. Michelson’s experiment was done to confront the rival ether theories of Stokes and Fresnel and Einstein devised the special theory of relativity by pitting Maxwell’s theory against Newton’s mechanics. Basically, Lakatos (1970) views the history of science in terms of competing research programs, which unlike Kuhn’s paradigms, can coexist. Furthermore building on Duhem’s notion that hypotheses cannot be refuted, for Lakatos, there is no such thing as a sudden paradigm shift, and there is no such thing as an absolute refutation.
6.4.3.2
Progressive and Degenerative Research Programs
For Lakatos, a research program that does not need to add ad hoc hypotheses in the face of empirical evidence is progressing. A research program is said to be progressing as long as its theoretical growth is in advance of its empirical growth. Thus, Fesnel’s prediction in 1810 of an ether wind in advance of Fizeau’s experiment in 1851 would be an indication that at that time the wave/ether theory of light was a progressive research program. Lakatos refers to developments such as Fresnel’s prediction as progressive program shifts. As with Kuhn’s paradigms, Lakatos’s research programs contain a whole scientific culture, including a theory, experimental techniques, experimental methods. Lakatos, does differentiate elements in research programs. There is the hard core (“negative heuristic”), which contains the absolutely essential elements. For the wave/ether theory, these would minimally include the notion that light is a wave and that the medium of this wave is the Ether. The hard core cannot be altered. Additionally the Program contains other elements (“positive heuristic”) such as experimental techniques and resources, additional hypotheses such as Fresnel’s notion of an Ether wind, and accepted practices of how data can be interpreted. Figure 6.4 is a rendering by my students of a research program according to Lakatos. A research program is said to be degenerating if new experimental data cannot be interpreted within the existing program, but only through the addition of hypotheses that cannot of themselves be used to predict new empirical results and only serve to account for the new data (ceterus paribus hypotheses). Lakatos would view attempts by theoreticians to shore up the wave/Ether program after the Michelson-Morley experiment as a degenerative problem shift and evidence that the wave/Ether theory had, after 1881 become a degenerating research program.
6.4.3.3
The Demarcation Problem
For Popper the demarcation between a scientific and a pseudo scientific theory is the existence of hypotheses that can be falsified. For Lakatos, hypotheses can never be falsified and the demarcation between a science and a pseudo science is that in a science, there always exists a progressive research program. Lakatos views a progressive research program as a sequence of scientific theories based upon a
6.4 Twentieth Century Philosophers of Science
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Fig. 6.4 Research programme according to Lakatos
common hard core. Thus, the wave/Ether program corresponded to a different theory before and after Fresnel’s proposal of an Ether wind.
6.4.4
Feyerabend
Paul Feyerabend was born in Germany and spent much of his career in the United States, where he died. As noted earlier in our discussion of Galileo, Paul Feyerabend felt that one of the major vehicles for the progress of science is the confrontation between scientific theories. Thus as opposed to Kuhn’s view that a mature science contains only one paradigm, Feyerabend (1981, 1993) would posit that it is most desirable to have as many competing theories as possible. Thus for him, Lakatos’s distinction between progressive and degenerating theories is undesirable. A socalled degenerating theory often takes a progressive turn later on and in any case it stimulates other theories to move forward. In this context, Feyerabend’s anarchistic methodology has one simple rule: there is no rule. The successful and creative scientist breaks rules, reverses rules, defends ad hoc hypotheses, works inductively then deductively, and works sometimes for unity and sometimes for plurality, i.e.
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anything goes. Moreover such efforts are liable to produce the kind of plurality of theories that Feyerabend considers to be essential for maximum progress in the sciences.
6.4.4.1
Incommensurability
Feyerabend also made a contribution to the notion of incommensurability in the context of the succession of one theory by another. From Feyerabend’s perspective in a clash between theories, the strongest alternative results in the replacement of older theories. This leads to a succession of theories T’, T’’, T’’’… As shown in Fig. 6.5, three rules relate successive theories: Incommensurability corresponds to questions that have meaning only in a particular theory. Thus if there is an overlap between successive theories, there are meaningful questions that can be asked within the context of both theories. For example within both the wave and particle theories, we can ask the question does light bend around an obstacle (diffraction of light). Where there is no overlap, there exist questions that are only meaningful within the context of one theory, but have no meaning whatsoever in the context of another theory. Thus for example, a question on the nature of the Ether is meaningful in the context of the wave/ether theory, but is meaningless in the context of Einstein’s special theory of relativity.
6.5
Mary Hesse
Richard Manson from the Biographical Dictionary of twentieth-century philosophers, gives a brief introduction to her philosophical work: Hesse has been one of the most important figures in the philosophy of science from the 1960s, particularly because of her emphasis on the place of analogy, models and metaphors in the development of the sciences. … She shares with Kuhn and Feyerabend a use of examples from the history of science to undermine empiricist and deductivist theories of scientific development and method. The starting-point for her own critique of empiricism
Fig. 6.5 Incommensurability according to Feyerabend
6.5 Mary Hesse
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has been the thesis of the underdetermination of (scientific) theories by (observational) data. This had been stated by Duhem and understood by Quine, but Hesse appreciated its critical significance for truth-as-correspondence as a possible objective for scientific theories (or even as a end-point for their convergence). She has recognized that relativism is a consequence of the thesis, but has said that her aim has been to “steer a course between the extremes of metaphysical realism and relativism”.
For us the interest is her work on hermeneutics. She builds on the modern theory of hermeneutics developed by Hans-Georg Gadamer based upon notions put forth by his teacher Heidegger. Gadamer argued that it is through language that the world is opened up for us. Our prejudices, whatever aspects of our cultural horizon that we take for granted, are brought into the open in the encounter with the past. As a part of the tradition in which we stand, historical texts have an authority that precedes our own. We get an idea that in science this could be analogous to students’ encounters with scientific texts while bringing with them their own conceptions of the world as discussed in Chapter 4. Gadamer refers to this movement of understanding as the fusion of horizons. As we come, through the work of interpretation, to understand what at first appears alien, we participate in the production of a richer, more encompassing context of meaning. The resulting interaction of text and reader is Gadamer’s version of the hermeneutic circle. The interplay between the parts and the whole of a text is the way in which our reading adds to the complexity and depth of its meaning. Jürgen Habermas emphasized that the hermeneutic circle view, must involve critical judgment and reflection. Mary Hesse accepts Jürgen Habermas proposition that science cannot be considered as neutral imquiry. But unlike Habermas, she feels that hermeneutics has a role to play in all the sciences: It is convenient to take as starting point a perceptive discussion by Jurgen Habermas of similarities and differences between empirical and hermeneutic method in his book published in English as Knowledge and Human Interests. I shall consider first a group of distinctions concerning traditional problems of the language and epistemology of science taken from his exposition of Wilhelm Dilthey. These are distinctions that I believe are made largely untenable by recent more accurate analyses of natural science. (Hesse, 1980, p. 169)
There follows a detailed description of five points. Mary Hesse’s feeling is that the distinctions that Habermas was making are based on the instrumentalist perspective promoted by the Vienna circle prior to World War I: What is immediately striking to readers versed in recent literature in philosophy of science is that almost every point made about the human sciences has recently been made about the natural sciences, and that the five points made about the natural sciences presupposes a traditional empiricist view of natural science that is almost universally discredited. In this traditional view it is assumed that the sole basis of scientific knowledge is the given in experience, that descriptions of this given are available in a theory- independent and stable language, whether of sense data or of common sense observations, that theories make no ontological claims about the real world except in so far as they
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Martin Eger (2006) points out that this point is provocative, because hermeneutics had been taken by many philosophers to be the demarcation criterion between the human and natural sciences. In reaching her conclusions, Mary Hesse makes a distinction between the low-level deductions arrived at by Baconian induction and high-level theories of the type propounded by Maxwell and Einstein. A highlevel theory can never be derived from experiment by induction in part because it is underdetermined by empirical evidence. Eger points out that high-level theories should be regarded “as metaphors of the environment, not as pictures, not even as partial, always to be improved, correspondences with some underlying but pre-existing domain of natural kinds”. A low-level description of the fall of an object by a formula relating time and distance is a direct testable statement. A high-level description of the fall using Einstein’s General theory of Relativity by means of a metric tensor is according to Eger as much of a metaphorical manner of speaking “as those who use the popular phrase ‘space-warp’”. Since metaphors are intrinsically a part of high-level theories, then hermeneutics are needed for the study of these theories. “Scientific theory is a reading of the ‘book of nature,’ requiring circular reinterpretations between theory and observation and also theory and theory, and also requiring ‘dialogue’ about the meaning of theoretical language within the scientific community” (Hesse, 1986, p. 181). The hermeneutical circle described by Hesse is exactly that employed by a student using reflective writing to understand text (Fig. 4.2. Knowledge transforming model. The interplay back and forth between the rhetorical space and the content problem space shown in this diagram is precisely the hermeneutical circle described by Hesse). The examination by Maxwell of the state of Electricity and Magnetism in his day as described in Section 6.3.5.1 and his discovery of an inconsistency between the treatment of the electric and magnetic fields is likewise a hermeneutical circle between theory and theory. Another example is turning the problem of a discrepancy between Maxwell’s theory and the Galilean principle of relativity on its head found in Section 6.3.5.3.
6.6 Relation to Conceptual Change
6.6
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Relation to Conceptual Change
Kalman (2002) discusses how very important it is that students become aware of how science works so that they can undergo conceptual change; confront their personal (alternative) scientific conceptions. This is inhibited where students are presented with “the Whig view of history that science is a steady and cumulative progression toward the pinnacle of modern achievements” (Brush, 1974). Monk and Osbourne (1997) elaborate: “This phrase (Whig view) is used to describe a historical approach which interprets the past in terms of present ideas and values, elevating in significance all incidents and work that have contributed to current society, rather than attempting to understand the then social context and the contingent factors in its production”. The “heart of education lies exactly where traditional advocates of a liberal education always said it was—in the processes of inquiry, learning and thinking, rather than in the accumulation of disjointed skills and senescent information” (Facione, 1990). The Whig view of the history of science encourages students to look at science as the accumulation of disjointed skills and senescent information and hinders students from critically examining their personal (alternative) scientific conceptions. This is exactly the point made in Section 6.3.5: ‘Students’ epistemologies are problem driven. So they do not have a picture of a science as having an overall coherent structure’. The main problem to be solved in getting students to undergo conceptual change is to get them to change their epistemology.
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Appendix: Peer Evaluation of Group Members PEER EVALUATION OF GROUP MEMBERS TEAM PURPOSE: To ensure that the “team component” of each individual’s grade reflects each person’s contributions to the group project. ASSUMPTION: When a member has in total, contributed to the overall work of the team about the same as the average team member, he/she should receive 100% of the “overall team grade” for the team component of the course. When a member has made exceptional contributions to the work of the team (e.g. analytical, organizational. written, investigative, verbal) he/she should receive a higher grade (e.g. 110%, 120% of the team grade). Similarly, when a member has been contributing less than other members, he/she should receive a lower grade (e.g. 90%, 80% of the team grade). There is no requirement that the overall percentage average 100%. For example, it is possible for one member to receive 110% and the rest of the group to receive 100%. INSTRUCTIONS: List below the members of your team and indicate what percentage of the team grade you recommend for yourself and for each other team member. If you have listed a percentage other than 100% for any team member please indicate underneath the evaluations or on back of the form an explanation for the evaluation. For example group member x did extra research, summarizing the material of a number of relevant chapters for the group. NAME 1. (Yourself 2. 3. 4. 5.
PERCENTAGE
Chapter 7
Educational Models Based upon Philosophy of Science
Developing a Scientific mindset thus may not simply be a conceptual change from personal scientific concepts to scientifically accepted concepts. It may also be a change in attitude from a view that study in science is a matter of solving problems using an independent set of tools, classified according to problem type, to a view that a science subject consists of a web of interconnected concepts.
7.1
7.1.1
Students Coming into a Gateway Course Do Not Have a Coherent Well Defined Knowledge of the World Changing Students’ Epistemologies
Pintrich et al. (1993) point out the modern theory of conceptual change assumes that bringing about changes in an individual student is analogous to the manner in which change occurs in scientific paradigms. These theories are usually based upon the descriptions of changes in scientific paradigms proposed by philosophers of science, particularly Kuhn (1970, 1992) and Lakatos (1970). A major obstacle in such an effort is that the students do not conceive of the subject in terms of a coherent theoretical framework. Kalman et al. (1999), explain that “Up until midway through high school, students can be successful at courses by memorizing templates for every situation encountered on an examination. Thus it is natural for students to compartmentalize their knowledge. That is applying different templates to different knowledge subsets”. Thus students coming into the course are likely not to have a coherent well defined knowledge of the world. Elby (2001) has said “students’ epistemological beliefs-their view about the nature of knowledge and learning affect their mindset; metacognitive practice, and study habits in a physics course”. According to Paul Hewitt, their actual epistemology is quite different from that of their teachers; “The professor classifies the problems in terms of physics concepts, while the students classify them by situations” (Hewitt, 1995). Indeed it has been shown in
C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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studies on the subject that some students view physics as weakly connected pieces of information to be separately learned in contrast to the web of interconnections perceived by their instructors (Hammer, 1989, 1994). This former notion is confirmed by Huffman and Heller (1995). They suggest that an explanation of a factor analysis that they performed on an administration of the Force Concept Inventory (abbreviated as FCI devised by Hestenes et al. (1992) based on the original Halloun and Hestenes (1985a) Mechanics Diagnostic Test) to 750 university students in a calculus-based introductory physics course is that such students personal (alternative) scientific conceptions “are best characterized as loosely organized, ill-defined bits and pieces of knowledge that are dependent upon the specific circumstances in question”. Developing a Scientific mindset thus may not simply be a conceptual change from personal scientific concepts to scientifically accepted concepts. It may also be a change in attitude from a view that study in science is a matter of solving problems using an independent set of tools, classified according to problem type, to a view that a science subject consists of a web of interconnected concepts. Paul Hewitt, the author of several college and high school textbooks including the best selling Conceptual Physics (Harper Collins) has said: “The professor classifies the problems in terms of physics concepts, while the students classify them by situations” (Hewitt, 1995).
7.1.2
Framework Theories
Although Vosniadou’s (1994) postulates that students’ viewpoints about nature are contained in framework theories in addition to various specific theories are ontologically and epistemologically based, they are still based upon the notion that students enter introductory courses with a coherent knowledge structure and thus share the difficulty with one of the two basic assumptions of Posner et al. (1982).
7.1.3
Weakly Organized Knowledge Systems
A framework for describing and correlating characteristics of weakly organized knowledge systems is given in the detailed paper of diSessa (1993). DiSessa postulates that the students’ knowledge system is composed of phenomenological primitives (p-prims) which are abstracted from common experiences. P-prims are the smallest unit of particular knowledge elements and form the basis upon which the student sees and explains the world. P-prims are not concepts themselves, but combinations of p-prims are involved in the creation of structures called causal nets. “Causal nets are, roughly, our replacement for the ‘theories that lie behind observations’. Or the theories implicated in theory-based notions of categories” (diSessa and Sherin, 1998, p. 1174). Hence, causal nets may be described as the inference-based explanations used to make sense of the world, which in turn form the basis of theories. DiSessa and Sherin link these mechanisms to concept acquisi-
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tion through a structural component called a coordination class. These coordination classes in turn are made of structural components that perform two distinct activities, for example centered on gathering information through selecting what to ‘see’ (referred to as “readout strategies). DiSessa and Sherin (1998) define conceptual change as involving both the separate changes in readout strategies and in the causal net. On the causal net side, the construction of a whole new causal net may be required, or an existing one may need to be developed and reorganized.
7.1.4
Structuralist Approach
7.1.4.1
Naïve Theories
Rather than beginning with the views of philosophy of science on how scientific theories change, Chi and her collaborators focus on the general conceptual framework that makes a theory “scientific”. Thus, Chi’s approach even more than that of diSessa is a structuralist approach. Students as Hewitt (1995) pointed out do not classify problems in terms of physics concepts, and instead classify them by situations. They do not understand the commonality of concepts between the different situations. Chi et al. (1981) and Chi et al. (1994) theorize that this is precisely why many science concepts are difficult for the novice to grasp. Novice learners tend to build explanations (mental models) based on surface features. Chi and collaborators assert that the many underlying structural and process attributes required to understand scientific concepts are not consistent with the surface features that they generate. Consequently, students’ intuitive naïve interpretations, lead to incorrect conclusions and misconceptions. Slotta and Chi (1999) state, “once an ontological commitment is made with respect to a concept, it is difficult for this to be undone” The student in the introductory course builds learning on surface features and it is this facet that causes them to classify problems by situation instead of commonality of concepts. The students’ alternative scientific conceptions are rooted in these surface features that are based upon their observations of the world.
7.1.4.2
Incommensurability of Naïve Theories and Scientific Theories
Chi et al. (1994) define conceptual change as learning that changes a preexisting conception. This definition holds a basic assumption that the learner has some prior idea, knowledge, of the concept. This of course suffers from the same defect noted already with all earlier ideas of conceptual change; focusing on the individual alternative scientific conceptions. Recently (See for example Chi and Roscoe, 2002), Chi clarifies her stance on the structures of concepts as embedded in naïve theories. She explicitly claims that naïve theories and scientific theories are often incommensurate. The idea of incommensurability stems from philosophy of science, specifically Kuhn and Feyerabend. This then harkens back to the idea of Posner et al. (1982) that conceptual change is analogous to theory change in
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science. In this sense, the work of structuralists such as Chi et al. suffers from the same defect as Posner et al. with the assumption that students initially possess some form of primitive theory. As noted earlier this feature is contradicted by the work of Hammer (1989, 1994) that some students view physics as weakly connected pieces of information to be separately learned, whereas others view physics as a coherent web of ideas to be tied together; a notion confirmed by Huffman and Heller (1995). Acquiring a scientific mindset is not simply a conceptual change from alternative personal scientific concepts to scientifically accepted concepts, but rather along the lines suggested by Elby (2001) that the students need to change their epistemology, before they are ready to make wholesale conceptual changes. We will explore methods of changing students’ epistemologies later in this book.
7.1.5
Posner, Strike, Hewson and Gertzog (1982)
7.1.5.1
The Model
Posner et al. (1982) divide the question into two parts: 1. Under what conditions does one central concept come to be replaced by another? 2. What are the features of a conceptual ecology which govern the selection of new concepts? Their answer is basically that: 1. Students must know of problems with their personal (alternative) scientific conceptions. 2. The replacement (current textbook) concept must be intelligible. Students must be able to understand how to apply the replacement conception to qualitative and quantitative problems presented to them. 3. The replacement concept must be plausible. It must be possible for the student to use the replacement concept to solve all problems that were previously understood in terms of the previously held personal concept. 4. There should be some advantages to using the replacement concept. This could for example be wider applicability of the new concept.
7.1.5.2
Critique
Tao and Gunstone (1997) have noted the widespread use of the framework of Posner et al. (1982). They note that “The criticisms are mainly leveled at its rational level— that it neglects non–cognitive factors (e.g. motivational and classroom contextual factors) which may also affect conceptual change”. Indeed Strike and Posner (1992) discuss “several implicit assumptions that now seem to us to be questionable”.
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However, Tao and Gunstone (1997) go on to note that although more elaborate models have been proposed, so far none have gained wide acceptance.
7.1.5.3
‘Hard Core’ of a Research Program
Strike and Posner (1992) view their program as “the ‘hard core’ of a research program (Lakatos, 1970, 1976) that could be extended by further work”. In this context, they note “Research programs suggest directions for further inquiry…. We have always regarded attempts to turn our four components of conceptual change into four instructions as misinterpretations of our intent”. In this context note that even if the last three components are satisfied, students will cling to their personal concepts if the first desired characteristic for conceptual change, problems with the students’ personal scientific conception, do not occur. This is because these beliefs make sense in explaining observations they have made about the physical world, and having taken the effort to construct their private understanding, these same students will not easily relinquish their original viewpoints. Halloun and Hestenes (1985a) use the picture of a balloon to describe this feature. The students’ assimilation of the replacement concept pushes in the balloon somewhat leaving the student’s personal concept fundamentally intact. Sufficient pressure must be applied to actually break the balloon. Support for this idea is found in an experiment reported in Kalman et al. (1999).
7.2 7.2.1
Conceptual Conflict Hewson and Hewson (1984)
Hewson and Hewson (1984) suggest that if a student holds a personal scientific concept, he or she does so because the student finds it to be plausible. Thus instruction must not only be aimed at showing that the replacement concept is intelligible, but must also first seek to reduce the plausibility of the personal scientific concept. Although this may be a reasonable strategy with younger students who cannot become fully developed critical thinkers within the confines of the course, it is a rather cumbersome procedure. It is far better to get the student to critically analyze the two concepts and come to the realization that the personal scientific concept needs to be replaced.
7.3
Tseitlin and Galili (2005)
This chapter concludes with a long excerpt from Tseitlin and Galili (2005). This excerpt relates in an important way to the previous chapter, to the work Kalman (2002) just considered and to the next chapter.
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7.3.1
A Model for Education
7.3.1.1
Implications
Tseitlin and Galili (2005) consider: [H]ow, pursuing this goal, they are different from the attempts of philosophers of science1 who usually try to represent science as it is, and not as it is to be consumed (that is studied). Thus, for instance, the model suggested by Tseitlin & Galili (2005) is less inclusive than the scientific programs of Lakatos (1970). They point out a close similarity of their approach to that of Duhem (1906/1954), who in his celebrated work addressed the nature of science in a perspective of physics teaching. Their model promises to be convenient for education, at least because it is useful and can represent other “common places” of science education, by organizing them in a similar manner (this makes common places compatible and producing a system). At the same time the model they suggest is not trivial, possessing a high potential for the description of fine features of scientific discourse: a dialogue between different theories, their competition, crises of discourses, scientific revolutions etc. Among the implications of the approach they suggest (1) a new representation of the scientific revolution, (2) a new representation of conceptual change of the learner (3) a new guiding principle in construction of physics curricula; and (4) a new characteristic of physics students, currently considered in a simple dichotomy of either able or unable to learn physics.
7.3.1.2 Physics is Taught as a Compendium of Factual Knowledge Even a brief review of contemporary textbooks used in universities, colleges and high schools shows that physics is taught as a compendium of factual knowledge delivered in a sequence of disciplines (mechanics, hydrodynamics, thermodynamics, electricity, and so on). The subject matter is presented in the form of rules, laws and principles, mathematically elaborated by formulas and equations, and illustrated with experiments and representative examples. Well-structured mathematical formalism is used to train the application of the theory to problems. It therefore should not surprise us that many physics educators consider the mastering of mathematics as an indisputable premise of physics education. In many universities the type of physics course is determined according to the mathematics used: “calculus”, “algebra” and “conceptual” (without mathematics). Furthermore, in most universities prospective physicists and engineers study in the same classes, and are instructed in the same manner. This is reflected in the titles of the textbooks. 7.3.1.3
Center of the Model
The center includes the ideas, which determine frames and angles of consideration, applied by the discipline explicitly or tacitly. Such are, for instance, the ideas of absolute space and time
1
In this sense Tseitlin and Galili note that one may illustrate the pursuit to reveal the nature of science, “what science is”, as a subject of study, by reference to such philosophers of science as Koyré, Toulmin, Popper, Lakatos, Kuhn, Feyerabend. This of course is exactly what is done in Kalman (2002).
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in Newtonian physics. They identify this unique and, in a sense, a priori unity as the nucleus of the discipline. Regarding the criteria of belongingness to the nucleus, this apparently nonsimple decision might be pragmatic. Indeed, our model is suggested, first of all for the goals of teaching. It is the simplest model which however succeeds in catching the important aspect of science, namely its being a culture. For example, keeping as a goal school teaching of physics, we could identify mechanics of 18th and 19th centuries with Newtonian mechanics, which is an obvious simplification. The theories by Hertz, Kirchhoff and Mach were all in critical opposition to the Newtonian theory. Even Galileo’s mechanics did not coincide with Newtonian mechanics. To include these interesting and important approaches one should upgrade the initially simple idea of nucleus. One might distinguish in it a core, shared by all mentioned theories, and segments that specify each from the theories. Thus, absolute time and space, rigid bodies (or point masses), would belong to the core, whereas Newton’s first law could be located in a nuclear segment, also incorporating Mach’s principle, etc. To remain within a reasonable education format, one would refrain from introducing a different nucleus for each theory. Such a step might be unavoidable with regard to the theories essentially incompatible with the Newtonian one. Such were, for instance, the vortex theory of Descartes, Prigogine’s theory including irreversibility, Vlasov’s theory of statistical nature, etc. They, however, preserve their discussion within a simple model, since it appears to be sufficiently beneficial for the considered goal.
7.3.1.4
Periphery of the Structure
For a given nucleus, all those scientific statements that are consistent with its statements constitute the body knowledge of the discipline, while the others (which genealogically, by subject or in other way) could be related to the nucleus, but conflict with it, belong to the horizon, or periphery of the structure. There is thus formed a super-disciplinary world which is consistent and ordered in itself, although conflicts with the point of view of other “super-disciplines”. This leads us to state that: Any fundamental physical theory arranges all statements in a centralized structure, a sort of quasi-culture, with its own values, language, conceptions, norms, etc. This structure, like a cell, has a nucleus, body, and periphery.
Our perspective essentially extends the “living space” of physics, enabling us to examine and accumulate a variety of conceptions; it provides a tool for formulating in a simple way what constitutes physics. Within this perspective it becomes clear that the common method of instruction in physics focuses mainly, if not solely, on the body-knowledge.
7.3.2
Relationship Between All Discipline-Cultures Comprising Physics
7.3.3
Pictures of Nature
Physics as a whole, therefore, does not allow codification into a single triadic structure. The relationship between all discipline-cultures comprising physics is complex
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and complementary in nature because they all represent different, and equally essential, aspects of nature. One may call them “Pictures of Nature”, reflecting the cultural sense of their interpretations. However, at the same time, and by the very virtue of this lack of rigidity, domains of physical science could be seen as having the human feature of “family similarity” (to use Wittgenstein’s terminology (1968, pp. 65–71). Many practitioners identify physics with its body-knowledge, displaying beliefs that philosophers regard as naïve (Bunge, 1973, p. 4). Actually, Thomas Kuhn’s notion of normal science and normal scientists (Kuhn, 1957) represents this phenomenon. Some prominent physicists, such as Niels Bohr and his colleagues, held another perspective. They considered the nucleus to be the most important subject for research activity in physics. In fact, considering science in its development the philosophy of science usually addresses the nuclear contents. Thus for Karl Popper it is the paradigm of a nucleus which presents a subject for permanent analysis, testing and refutation.
7.3.4
A Dialogic Interaction
The structure introduced by us might cause misinterpretation that we follow the structuralist framework of thought with regard to science. In fact, their model does not fit the structuralist dogma. Thus, the periphery zone of the organization, which incorporates texts representing “other” views, essentially destroys the order prescribed by structuralism. They do not argue for science as a systemized wholeness, which is formed and develops by virtue of some intrinsic laws. The development of a scientific theory, in their view, might be rather due to the dialogic interaction with the theories of the periphery, not only (and might be even less) by virtue of the dogma of the nucleus. Lacan could say that the development of science is performed against the background of the “beliefs” of the “other”. Science cannot exist without the “other”. Any scientific theory projects its beliefs on the other view and vice versa; this is a dialogic interaction, instead of juxtaposition or succession of two monologues. It may resemble an argument, debate between incompatible theories. In fact, being isolated, any of the competing pair would be unable for self-expression and production of the correspondent bulk of the normal knowledge. Moreover, such normal knowledge, which results from the competition, appears highly disordered (also at odds with structuralism), making it impossible to assume an ordered knowledge even as an initial state. This endless interaction between competitive and essentially different theories cannot be restricted to a mere external disturbance of one for the other, but it is just their incompatibility that presents a pledge for the permanent existence and development of science, incorporating both competitors. By analogy, our discipline-culture is in relation to structuralist views on science (Piaget, 1968) similarly to the relation between the dialogic theory of personality of Lacan (1973) and the anthropocentric theory of individual development of Piaget.
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In their view, it is physics as a quasi-culture that should constitute a subject of education. Students will study physics within the horizon of the texts (knowledge) “observed” by physics, while realizing their status within the particular perspective. The new approach makes explicit those indispensable elements that determine physical knowledge but often remain implicit and deprived of attention they deserve. Studying physics begins to transform itself to a study of a culture. What makes us closer to culture is the presence of the “Other” (other knowledge). What allows us to talk about teaching physics as a Culture will be that we will present physics not only as Knowledge, but also as a space of statements (views, theories) of physicists, a discourse, and that is, as a Text.
7.3.5
Physics Not Only as Knowledge, But Also as a Space of Statements
Although the same term is applied when both the scientist and the learner construct knowledge, it has different meanings. 1. In any introductory course, a learner aims to familiarize him/herself with a whole area of knowledge established by the scientific community. In this activity a teacher guides either explicitly or implicitly, making him/her way as direct as possible, suppressing all kind of difficulties and uncertainties. A researcher, on the other hand, constructs the previously unknown, although based on the known. This discovery essentially includes contingency. It is apparent that the most important scientific discoveries were adventures, not recipe applications. An essential difference is the belonging of scientists to the scientific discourse, without which discoveries are impossible. To the same extent, to which it is impossible to reduce discursiveness to disciplinarily, contingency into determinicity, it is impossible to represent a scientific discovery by the learning activity. The study-discovery relationship is understood here as addressing the goals rather than processes. 2. The learner must acquaint him/herself with different theories, metaphysical conceptualizations, forms of presentation, and cultural styles. In a rather short time the student must familiarize themselves with at least four fundamental physical disciplines: (i) classical mechanics, (ii) electrodynamics and the special theory of relativity, (iii) thermodynamics, and (iv) quantum theory. In contrast, a researcher usually practices a specific method and focuses on a problem in a particular area. 3. School studies are short in time, and aim to foster a broad interest in knowledge accumulated over a long time. The learner can afford (and normally is expected) to construct a superficial knowledge of a range of topics, “to catch the ideas” of a variety of conceptions. Unlike the researcher, he/she cannot afford time and energy for a comprehensive exploration. Therefore, learning does not presume a discovery, although it represents the first step to it.
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This perception matches the vision of Bibler (1999, pp. 12–14) who sees human activity in three categories: Shared Labor (as in an industrial plant), Common Labor (as in the activity of a spread community of scientists), and Learning (as an individual activity within an educational institution). The unique feature of the latter is that it does not aim to produce any social commodity. Moreover, being only on the edge of productive activity, it is normal even to refrain from such in the course of learning. To guide the learner in this way is among the most important functions of the teacher.
7.3.6
The Discipline-Culture
7.3.6.1
Structure
A discipline-culture has a structure resembling that of a biological cell. We have already suggested that a discipline-culture can be structurally represented by an organization, which might resemble a biological cell that is made up of three domains (Fig. 7.1): I nucleus – defines the identity of the discipline-culture, includes its fundamental principles, paradigm and claims of meta-disciplinary nature. II body – incorporates all normal disciplinary knowledge. This is established knowledge, each item of which is based on the principles contained in the nucleus. III periphery – contains the knowledge that conflicts with the principles of the particular nucleus. This knowledge presents a challenge for the fundamental claims of the nucleus and possibly a mechanism for its change and reconstruction. The rest of knowledge, outside the periphery, is not within the horizon of the discipline culture, as it does not address the subject matter or is identified as nonscientific in nature. Such a rigid organization implies a mature culture defined as a culture-of-rules (Lotman and Uspensky, 1978). Its nucleus includes the rules of self-reproduction, according to which new texts should be constructed. The opposite type of culture,
Fig. 7.1 The cell structure of discipline-culture
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according to Lothman and Uspensky, is the culture-of-text, which contains samples of texts, but not rules of text production. The cultures thus differ in their attitude to a newly introduced text. The culture of-rules tests whether the new text conforms to the nucleus. If it does, it is included in the normal disciplinary knowledge. If not, it is assigned to the peripheral area (conflicting, but still scientific) or ignored (when identified as non-scientific). The culture-of-texts, on the other hand, is much less restrictive and therefore is more accumulative in nature. It might represent a new area of knowledge (such as science before the scientific revolution of the seventeenth century), or knowledge of the humanities (such as politics, art, literature, etc.).
7.3.6.2
Relationship of Two Fundamental Theories
Each basic discipline within physics (we have mentioned four) originates in a disciplinary culture which allows its representation in the mentioned triadic form. Each such culture considering itself at the center, often ignores or disparagingly refers to the theories of other cultures, assigning them to its periphery. Even a brief review of standard physics textbooks reveals that fundamental claims, belonging to the nucleus receive little, if any, attention. As to peripheral knowledge, this is either ignored or presented as though it belonged to the norm (i.e. ignoring its conflict with the nucleus). Moreover, some textbooks present a harmonious view between different physical disciplines. This belief can be expressed as a principle of correspondence. For example, relativistic physics gradually transforms into classical mechanics by going to the limit of low velocities, quantum mechanics gradually transforms into macroscopic classical physics in the limit of big quantum numbers (or nullifying Plank constant), reversible classical mechanics gradually transforms into irreversible thermodynamics and so on. The fact that some physical results can be obtained by two fundamental theories (only in a certain area of parameters) might cause a belief that one theory is included in the other. Using the discipline-culture model introduced by us we can easily represent the relationship between the two theories: the body areas of two theories may overlay. However, the important thing is that the nuclei do not overlap. Peripheral zones can overlay. All together we arrive at the representation of Fig. 7.2. They emphasize that we consider here physics as knowledge. Were we seeking representation of physics as a discourse, we could obtain a diagram in which body areas would also be separated (Fig. 7.3). Indeed even the statements that sound similarly might have a totally different meaning for in different discourses. All together, the nucleus and the body of theory T2 may belong to the periphery of T1 and vice versa. We see that the tripartite organization as a model of discipline-culture is able explicitly represent specific types of conceptual relationship between the different domains of physics.
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Fig. 7.2 The relationship of two fundamental theories perceived as discipline-cultures (somewhat simplified case, for the periphery is shown)
Fig. 7.3 The relationship of two fundamental theories perceived as scientific discourses. (The simplest case is shown)
7.3.6.3
Classical Mechanics
In the case of classical mechanics, the periphery holds the items of knowledge at variance with the nucleus. Such are: relativistic deviations from Newton’s account at high speeds, the Michelson-Morley experiment, the Mercury trajectory anomaly, the wave behavior of mass particles (electron diffraction, tunneling), interaction for charged particles (field mediation, vector interaction of electrical charges), thermodynamic irreversibility of a many body system, etc. These phenomena were explained in terms of the disciplines historically subsequent to Classical Mechanics such as the Theory of Relativity, the Quantum Theory, and Classical Electromagnetism. Although contradicting the nucleus, all they are within the vision of Classical Mechanics as a discipline-culture, and in this sense belong to it. Moreover, the periphery of Classical Mechanics also includes alternative theories from the past that have been surpassed by Newtonian theory: the Aristotelian theory of motion, the impetus theory of Philoponus and Buridan, Descartes’ theory of vortices, Prigogine’s dynamic theory, etc. Thus a characteristic of the marginal, peripheral domain in this discipline-culture is that it includes both historically precedent and subsequent, more advanced, physical knowledge. Classical Mechanics as a discipline-culture thus remembers its past (what was believed and why, how it was reconsidered and replaced) and it foresees its future defeat (pointing at the phenomena, which were difficult to explain and were account for by succeeding theories). They argue that such organization is appropriate and necessary for a cultural perception of the discipline, even if seems at the first glance as complex or unnecessary
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for an introductory course. The holistic image of mechanics, its meaning, scope of validity and extent of reliability could emerge in the learner only from the acquaintance with the principal ideas and claims, and with the conditions, presumptions, and limitations of this knowledge. This kind of knowledge is not fostered by assessing students in manipulation with complex formalism (the body knowledge). The alternative approach is conceptually rich and less complex formally, which could make it comprehensive and wished by many of the students of the introductory physics course. It should be noted that their model does not conflict with either Kuhn’s (1956), or Lakatos’ (1970) interpretation of scientific revolution, but refines them by an explicit scenario of the process. The efficacy of the discipline-culture approach is due to the articulated peripheral knowledge zone. The latter appear neither in Kuhn’s nor, explicitly, in Lakatos’ models. Their model easily adopts such features as protective belts (our normal zone), scientific research program, hard core, and paradigms (parts of the nucleus in our triadic model), thus exposing the fine structure and functioning of science.
7.3.7
Conceptual Change
7.3.7.1
Initial Knowledge of the Learner
The tripartite model of discipline-culture can assist in interpreting the learning process. The rationale of this approach is in the attempt to conceive human cognition as organized in a manner similar to that of the culture, in which the learner is immersed (Vigotsky, 1994). Consider for example learning the topic of motion in mechanics. As many researchers report (e.g. Viennot, 1979; Halloun and Hesteness, 1985b; Galili and Bar, 1992), the spontaneous ideas of the learner regarding motion are often close to those of Aristotle, who asserted: “motion implies force”. Force is considered to be the cause of movement, and movement is considered to be a process of transition between two states, rather than continuous sequence of states replacing each other. The similarity between the initial knowledge of the learner and the views of Aristotle suggests to the physics instructor to imitate the scientific revolution of the seventeenth century, in order to bring the learner to the adoption of the Newtonian conception of motion – a strong conceptual change.
7.3.7.2
Learning Process
Similar to the account for a scientific revolution, the learning process can be regarded as involving a change in the contents of the nucleus, this time of the individual knowledge. The conceptual change necessarily involves the peripheral domain. Initially, it is the periphery that adopts the new ideas in the course of learning. Gradually, the tension arises between the new ideas (periphery) and the
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pre-instructional conceptions (“schemes of knowledge”, Galili and Hazan, 2000) located in the nucleus. Eventually, and following dissatisfaction with the old knowledge, as opposed to the intelligibility, plausibility and fruitfulness of the new knowledge (Posner et al., 1982; Strike and Posner, 1992), this tension (termed “cognitive conflict” in psychology (e.g. Nussbaum, and Novick, 1982; Dreyfus et al., 1990; Limon, 2001), and “difference of potential”, in physics terms) reaches breaking point – and conceptual change starts. At this stage of breaking, the body area of normal knowledge cannot protect and isolate the nucleus any more, and the knowledge “flows” into and out from the nucleus. The latter is reconstructed and its old content finds itself in the periphery, “waiting” for the opportunity to challenge the nucleus again. This scenario might imply that the process of conceptual change requires activities beyond solving standard problems using memorized algorithms. The teaching that aims to induce conceptual change begins by supplying new contents and fortifying the peripheral knowledge. The increase of tension with the nucleus could be encouraged through focusing on the new concepts, comparing them with those initially held, and emphasizing their incompatible nature – this is basically the constructivist strategy. Obviously, the more developed the peripheral knowledge and the less developed the normal knowledge, the easier it is to bring about conceptual change in the learner. Therefore, it is easier to teach the novice and young (possessing a thin normal domain), than to “re-educate” the experienced and adult (those with a well-developed normal domain). The importance of meta-cognition in the process of conceptual change, the self appreciation of the learning process has been discussed in educational research (e.g. White and Gunstone, 1989; Hewson and Thorley, 1989). The triadic model interprets this aspect as following. If the deficiency of the individual knowledge is not self-recognized, the new knowledge element might be mistakenly placed in the normal area (not in the periphery). Then, instead of promoting conceptual change, the new knowledge may even obstruct the conceptual change.
7.3.8
Physics Curriculum
Discipline-culture approach suggests physics curriculum to attain the features of science itself, to be hierarchical and discursive.
Explaining the failure of many students to learn physics, researchers point to the difficulty of facing a great number of facts, procedures, rules and theories without the guidance regarding their relative importance and validity status. Learners often develop their own organization of knowledge (diSessa, 1993; Minstrell, 1992; Galili and Hazan, 2000) and its spontaneous hierarchy. This might be interpreted as the unsatisfactory nucleus of students’ knowledge organization. Seemingly, the common emphasis of training in normal knowledge (problem solving) does not touch much on nuclei. Moreover, students become disenchanted and lose interest in the subject, divorced from the grand scientific picture – the worldview dimension of life.
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A discipline-culture based curriculum emphasizes the connection between the elements of the normal knowledge with the nucleus, as well as with the periphery. The former represents the metaphysics of the discipline and the latter challenges the presented “order of things”. Together both aspects stabilize every piece of the normal knowledge within the general hierarchy. This approach makes the normal disciplinary knowledge more intelligible and plausible, increasing the chances for successful assimilation. A discipline-culture based curriculum incorporates carefully chosen elements of the history and philosophy of science, as the contents of the nucleus and periphery. This knowledge becomes inherent in the subject matter, instead of being relegated to the sidelines as “non-scientific”, or merely a “cultural debt”. This curriculum regards the discarded theories not as historical curiosities, but as alternative interpretations, contrasting the meaning of the adopted models and principles, and therefore fostering adequate understanding. Thus, by contrast (and paradoxically for many), learning about the Aristotelian paradigm of forcemotion relationship fortifies understanding of its Newtonian counterpart, the Cartesian interpretation of weight helps students to understand Newtonian gravitation, the idea of the absolute space-time reveals the meaning of the relativistic conception, the geocentric world system facilitates understanding of the heliocentric model, and so on and so forth. Historical models remain relevant. The concept of field revived contact interaction. Light photons revived the particle theory of light. The new theory of vacuum revived the idea of aether. By facilitating dialogue of ideas the new curriculum provides wider scope and multiple perspective of knowledge, encouraging students to precede physics enterprise as a living project.
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Chapter 8
Changing Student’s Epistemologies
Kalman and Aulls (2003) note that the students do not conceive of the subject in terms of a coherent theoretical framework. The student’s paradigm in the Kuhnian sense (Kuhn, 1970, 1992), is that the subject consists of solving problems using a tool kit of assorted practices. The historical approach embodied in the course design can be used to affect a change in the mindset of the students. Students change from a view that science is a matter of solving problems using an independent set of tools, classified according to problem type, to a view that a science subject consists of a web of interconnected concepts.
8.1
Constructing an Epistemology
Epistemology should play a more important role both in contemporary research in science and in the teaching of science. If we as educators emphasized the need to change students epistemologies more in our teaching, than there may not only be more success in the understanding of the subject by our students, but also be dividends in the future in more directed research by future graduate students.
8.1.1
Students Do Not Conceive of the Subject in Terms of a Coherent Theoretical Framework
8.1.1.1
View of the Course Almost in a Theatrical Sense as a View of a Drama Involving a Conflict of Actors; Aristotle, Galileo, Newton and Others
Kalman and Aulls (2003) examine a course that attempts to provide an opportunity for students to see the subject as interconnected not only to accommodate scientific concepts, but also to be effective problem solvers. Kalman and Aulls note that the students do not conceive of the subject in terms of a coherent theoretical framework. The student’s paradigm in the Kuhnian sense (Kuhn, 1970, 1992), is that the subject C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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consists of solving problems using a tool kit of assorted practices. Hence, they do not conceive of the course content in terms of a theoretical framework. In their course design, students are presented with two alternative frameworks; pre-Galilean Physics and Newtonian Physics. The idea of their course design is that students would at first view the frameworks almost in a theatrical sense as a view of a drama involving a conflict of actors; Aristotle, Galileo, Newton and others occurring a long time ago. Based upon the final interviews, they concluded that students gradually identify with the conceptual positions taken by the proponents of the alternative frameworks and become themselves a part of the action. As participants passing through a series of interventions, the students become aware that the frameworks relate concepts from different parts of the course and learn to evaluate the two alternative frameworks.
8.1.1.2
Learning About the Aristotelian Paradigm Fortifies Understanding of Its Newtonian Counterpart
Additional support comes from Tseitlin and Galili (2005). Recall from the end of Chapter 7 their remark: Thus, by contrast (and paradoxically for many), learning about the Aristotelian paradigm of force-motion relationship fortifies understanding of its Newtonian counterpart, the Cartesian interpretation of weight helps students to understand Newtonian gravitation, the idea of the absolute space-time reveals the meaning of the relativistic conception, the geocentric world system facilitates understanding of the heliocentric model, and so on and so forth. Historical models remain relevant.
8.1.1.3
Feyerabend’s Principle of Counter Induction
Epistemological change is at the root of major shifts in science. Feyerabend (1993) has pointed out that evaluation of a theoretical framework doesn’t occur until there is an alternative (principle of counter induction). A scientist who is interested in maximal empirical content, and who wants to understand as many aspects of his theory as possible, will adopt a pluralistic methodology, he will compare theories with other theories rather than with ‘experience’, ‘data’, or ‘facts’ ” An example of a discovery that arises in this way is Galileo’s discovery of inertia. Galileo is one of those rare thinkers who want neither forever to retain natural interpretations nor altogether to eliminate them. Wholesale judgments of this kind are quite alien to his way of thinking. He insists on a critical discussion to decide which natural interpretations can be kept and which must be replaced. This is not always clear from his writings. Quite the contrary. The methods of reminiscence, to which he appeals so freely, are designed to create the impression that nothing has changed and that we continue expressing our observations in the same old and familiar ways. Yet his attitude is relatively easy to ascertain: natural interpretations are necessary. The senses alone, without the help of reason, cannot give us a true account of nature.
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What is needed for arriving at such a true account are ‘the … senses, accompanied by reasoning’ (Galileo, 1967); Italics supplied by Feyerabend (1993). Feyerabend notes that Galileo in his early works had been a follower of Ptolemy. He argued against the motion of the earth; “… objects which one lets fall from high places to the ground such as a stone from the top of a tower would not fall towards the foot of the tower; for during the time which the stone coming rectilinearly towards the ground spends in the air, the earth escaping it, and moving towards the east would receive it in a part far removed from the foot of the tower in exactly the same manner in which a stone that is dropped from the mast of a rapidly moving ship will not fall towards its foot, but move towards the stern” (Galileo, 1953). Only later did he take the Copernican point of view and assume that the stone dropped from the mast would fall toward its foot. Feyerabend’s conclusion is that Galileo only arrives at the modern theory of inertia by a critical examination of the tower experiment in the light of two alternative frameworks; that of Ptolemy and that of Copernicus. Feyerabend summarizes: The argument is inverted in order to discover the natural interpretations which are responsible for the contradiction … The new natural interpretations, which are also formulated explicitly, as auxiliary hypotheses, are established partly by the support they give to Copernicus and partly by plausibility considerations and ad hoc hypotheses. An entirely new ‘experience’ arises in this way. There is as yet no independent evidence. (Feyerabend, 1963)
The idea that examining alternatives will enhance critical thinking skills and help to produce conceptual change is put to the test by work such as that of Eliason (1996). His work involves “confronting students with two very plausible ideas that they would normally accept uncritically, and then showing that the two ideas are apparently not compatible with each other”. 8.1.1.4
Plato and Aristotle
The philosophies of science of Plato and Aristotle were both concerned about actual cases. Plato in the Timaeus and Aristotle in the Physics examined questions about nature. These discussions were neither purely metaphysical nor purely empirical in character though they had a methodological aspect akin to that of modern philosophy of science. Thus their philosophies rested on the same mixture of ontological, epistemological, and empirical considerations. Plato rested his philosophy on a basic principle enunciated by the pre-Socratic philosopher Parmenides. Parmenides deduced the nature of reality from logical arguments. He rejected the idea of what is not, as inconceivable. He said the universe is uniform, immovable, and unchanging, with no generation or destruction. Change and motion, are unreal because they require the existence of what is not. In response to Parmenides, Leucippus, and Democritus developed the idea of atomism. The universe consists of tiny, solid, indivisible atoms, which move about in space and cluster together to form the larger objects of common experience. Plato argued that the world had to be based on mathematics, because only mathematics has the eternal nature that
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reflects Parmenides requirement of an unchanging nature. Aristotle was wary of generalizations, but Plato’s theory of the ideal fits in perfectly with mathematics. The ideals: the truly permanent structures and relationships behind the apparent everchanging world could only be found in a physical theory built on a numerical and geometrical framework. Astronomy and the theory of matter were, in Plato’s view, fields in which such a mathematical framework within which this mathematical methodology could be immediately applied. The movements of the planets and the stars could be explained by constructions drawn from three-dimensional geometry and the physics of matter could be described by atoms with shapes reflecting the geometry of the five regular solids (the tetrahedron, dodecahedron, etc.). Since Aristotle’s scientific preoccupations were centered on marine biology rather than astronomy and motion, he developed a very different scientific methodology. He felt that the many particular real situations could not be covered by mathematical entities and relations. The ultimate elements of nature had to be specific entities, recognizable within the familiar sequences of experience. Basic prototypes could be discovered in the typical life cycles of different creatures. Thus, for example, the morphogenesis of a seed exemplifies the “coming into being” of the corresponding type of animal or plant, of which the mature specific form – as defined by its prototype – is the natural destination of its development. Having recognized the natural destinations toward which natural processes of different kinds were directed, it was then possible to construct a comprehensive classification of prototypes, in terms of which, the whole natural world could, in principle, be understood. Such a classification scheme, which resembles the Baconian regularities in nature, would also account directly for the specific qualitative characters of different observed substances and processes.
8.1.1.5
Galileo
There were no experimental facts available to Galileo for him to postulate that the solar system is sun-centered (as suggested by Copernicus) rather than earth-centered (as set forth by Ptolemy). The obvious experimental data favoured Ptolemy rather than Copernicus. Kuhn (1957) has argued that the early supporters of the sun-centered solar system were motivated by a change in orientation from Aristotle to Plato. Plato was a sun worshipper and believed in the primacy of the sun rather than a stationary Earth. Certainly that would seem to be the case with Keplar. This was not good enough for Galileo. He had to have experimental backing for his hypothesis. To reinterpret the high tower experiment in terms of an Earth that rotates around its North South axis, bodies had to have the property of inertia. Once the body is dropped from the high tower, it had to continue moving with the same rotational speed as the rotating Earth even though it is moving freely in the air. This property, inertia of the body had to be general. Thus a body moving on an infinite perfectly smooth plane must move forever at the same speed. Such an ideal would be acceptable to Plato, but rejected by Aristotle. Only observable situations were acceptable to Aristotle and such a plane is an idealization. This hypothesis had
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consequences, which Galileo could test. To Galileo once you have a working theory, all possible developments based on the theory must be correct. Once the law is sufficiently well established, all predictions based on the law are assumed to be correct. Galileo reasoned that objects rolling down an inclined plane behave exactly like a freely falling body, but with the effect of gravity greatly reduced. Thus the value of the demonstration is to open the mind to further possibilities (facts) “without the need of recourse to experiment” Start a ball rolling up a highly polished inclined plane If the plane is tilted up, the ball while rolling uphill, will go more and more slowly. If it is tilted down, the ball will go faster and faster. If the plane is perfect and horizontal, the ball will neither slow down nor speed up but continue forever. Since Galileo’s hypothesis did not arise from experimental data, it did not fit Bacon’s idea of science. It is grounded in the high tower experiment, but the obvious solution to the high tower experiment is the Aristotelian solution. The invention of inertia requires an examination of what would be needed to have the Earth to rotate around its axis and a ball fall straight down beside the high tower. Such a notion requires a high order of critical thinking. Hardly the abilities found in most students entering an introductory course. Galileo’s further use of the abstraction of an infinitely smooth plane is inconceivable to the 50% of students who are still at the concrete operational stage (Piaget – see Chapter 2). The themes stated by Plato and Aristotle are still represented today by two rival approaches to the philosophy of science – one (Platonic) based in ideals such as the infinite perfectly smooth plane used by Galileo to examine inertia, and the other (Aristotelian) based on the idea that science must be grounded in particular observations. As Aristotle put it: “How can an idealization of nature help a weaver or a carpenter in the practice of his craft, or how can anyone, by contemplating the pure archetype, become a better physician or a better general? The physician studies the health of some particular man, for it is individuals that he has to cure”.
8.1.2
Course Design (Kalman and Aulls, 2003)
We have seen in Chapter 3 that students enter introductory (“gateway”) science courses with concepts (“personal scientific concepts”) that are different from those found in the course. In Chapter 7, there has been a discussion of many attempts to get students to change these concepts. It was, however, argued in Section 7.1.1 of that chapter, that most students cannot develop a Scientific mindset by a simple conceptual change from personal scientific concepts to scientifically accepted concepts. It may also be a change in attitude from a view that study in science is a matter of solving problems using an independent set of tools, classified according to problem type, to a view that a science subject consists of a web of interconnected concepts. Kalman and Aulls examine a course that attempts to provide an opportunity for students to see the subject as interconnected not only to accommodate scientific concepts, but also to be effective problem solvers.
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Lelana: It was a different physics class. It was different from all the other physics classes I had before. It was a good change. In every other class, which you go to; you sit down and the teacher just writes a whole bunch of formulas and it’s ‘memorize these’. So it was a good experience. If it was memorizing I just wouldn’t go to class, I wouldn’t do anything, I’d just go write the exam at the end. It has to do with learning.
Students come to see connections between the concepts in the course. In this sense the curriculum is constructed with the students: Ahmad: I would make new links between things, and I would also think about more reasons why that would be true, and possibly at other times, I would think of more reasons why something else would be false.
The course (mechanics) is the first one-semester course in a sequence of three courses covering an introduction to physics. Typically, there are approximately 100 students in each section. The student population in the course is multicultural and multilingual and ranges from freshman in university to graduate students. Students in this course include science majors, humanities majors and engineers. At my university, there are typically many foreign students including at least 20% from Middle Eastern countries. Additionally a significant fraction of the students is returning to school often after having completed a degree in another discipline.
Fig. 8.1 Timeline for course
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Students’ exploration of the concepts in the course occurs through six different activities as shown in the timeline found in Fig. 8.1 for the course events. It shows the course includes four components. Each component will be briefly sketched and the sketch will be followed by a detailed elaboration. 1. Before class, each week students begin by reading material in the text and performing reflective writing as described in Chapter 4 about the concepts found in this material. The intention of this component is to involve students in a metacognitive examination of their perception of Physics concepts. 2. Within the class, there are six related activities that are used to set up a conceptual conflict (Hewson and Hewson, 1984). (a) Within the class on certain selected concepts, there will be either a reflective write-pair-share activity or a collaborative-group exercise. (b) This will be followed by a discussion in class moderated by the professor. At this stage, the professor does not give his/her own interpretation of the concept, but rather attempts to draw out all the “personal scientific concepts” held by the students. (c) A concluding presentation by the professor elaborates the Newtonian point of view with the aid of demonstrations. 3. As discussed in Chapter 5, collaborative-group exercises alone may not be effective. Nelson (1964) points out that “for collaborative learning to be most effective, it is not sufficient simply to have students work together. … Left alone, they often simply create a collage of opinions”. For this reason, the collaborative-group exercises are followed up to 2 weeks later by students handing in a written work, called a “critique” (as described in Section 5.2.3). 4. Lastly, students prepare for the essay question on the examination. The midterm is held 1 week after the relevant conceptual conflict exercise in class (critique week 5 is handed in at same time as the midterm). Students don’t know what to expect in terms of formatting an essay question until they have done the midterm and had in-class feedback. The final examination occurs up to 2½ months after the relevant conceptual conflict exercises in class (critique week 7 is due roughly 2½ months before the final and the last critique week 9 is handed in up to 1½ months before the final exam). One of five questions on the midterm and on the final consists of an essay type examination of one of the concepts covered by the critiques. All questions on the midterm and the final are of equal value. The midterm and final are each worth 30% of the student’s mark. In the following sample of student writing, Fig. 8.2, the student manages to cover every single point about the differences between Aristotle’s and Galileo’s views on motion and additionally, the actual motion of projectiles within the framework of Newtonian Physics. The answer is not done in any standard essay format, but instead in the form of a comical story. If the student had felt that the instructor was a stickler for formal responses, the student would never have dared to respond in this manner.
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Before class, each week students begin by reading material in the text and performing reflective writing about the concepts found in this material. The reflective writing activity is “workshopped” in class. The intention of this component is to involve students in a metacognitive examination of their perception of Physics concepts. One of the points of the activity is to generate questions in class about what they don’t understand. For more details see Chapter 3, Kalman & Kalman (1997) and Kalman, Aulls, Rohar, & Godley (2006).
Each discussion concerns a short topic (pericope) that is placed on a single sheet of paper or transparency. Students engage metacognitively with this material, by sharing their thoughts with a neighbour.
(continued)
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Through the conceptual conflict exercise, students are introduced to the idea that there can be more than one equally logical way of looking at a phenomenon and only experiment, not logic can decide the issue. During the intervention, many students realize that other students in the class hold different viewpoints about motion. Students are encouraged to explore this point
The collaborative-group exercise is followed up to 2 weeks later by students handing in a written work, called a “critique”, in which they are required to present arguments in favour of both “personal scientific concepts” and the Newtonian explanation. They must clearly indicate which position is verified by experimental evidence (with references to the evidence). The critique exercises were worth 5% of their course marks. In doing the critiques students can come to see connections between the concepts in the course.
In the examinations, everything comes together. If an atmosphere of trust has been established, students may descirbe their views in interesting ways as for example in the sample below.
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A basic component of this course design is the use of writing as an aid to encoding information. Students are given a weekly concept assignment based on the compulsory readings for each class. With the exception of the first class, readings are to be done before the class and the concept assignment is based on these readings. During the class, it is assumed that students have read this material. Some of the material and problems found in these readings are not covered in class but students are told that the exam is
Fig. 8.2 Sample midterm
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Fig. 8.2 (continued)
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Fig. 8.2 (continued)
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Fig. 8.2 (continued)
based on everything found in these readings. In advance of the class students read the assigned material for the next week’s lecture(s). They then do reflective writing about what they read. Suggested length three pages, but there is no page limit. Fulwiler comments that “Some writing activities promote independent thought more than others do. Expressive or self-sponsored writing, for example, seems to advance thought further than note copying” (Fulwiler, 1987). Verner Jensen (p. 330 in Fulwiler, 1987) proposes that “Physics students can use the writing process to clarify their thinking and understandings about physical phenomena through their written articulation of relationships”. The term reflective writing is used in this study to refer to the use of freewriting to interact with material from a textbook before the material has been examined in the classroom in a manner that includes self-monitoring of the understanding of the conceptual underpinnings of each reading. A 1-hour in class “workshop” on the use of reflective writing in this manner is given in the introductory class. In a previous study (Kalman et al., 2008), it was found that reflective writing each week places a demand on even good students that they would not have done on their own. That is being prepared each week to sum up what they are learning and to recognize what they are not learning or what needs to be clarified or further elaborated. Furthermore, students who pass the course considered reflective writing to be a beneficial aid to learning how to relate new course concepts to prior knowledge and new concepts to each other.
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The mechanics course begins with a description of nature in terms of displacement, instantaneous velocity, and acceleration. The first two reflective-write-pair-share (Kalman, 1999, 2002) activities explore these concepts. Students are to see that v = 0 at one particular time does not imply that the body is stopped and a = 0 at one particular time does not imply that a body has constant velocity. The third intervention uses a reflective-write-pair-share exercise to contrast Galileo’s views with that of Aristotle about bodies falling near the earth’s surface in a vacuum. It is pointed out that Aristotle is against idealizations. Since a vacuum doesn’t exist, the speed of a body in a vacuum should not be considered. Students are introduced to Galileo’s viewpoint that it is useful to consider idealizations of phenomenon occurring in the real world. Galileo’s original point of view, enunciated while he was at Pisa, is introduced: He took the ratio of the terminal velocities of objects and took the limit of where the density of the medium goes to zero. This would imply that bodies of different mass would fall at different rates in a vacuum. Students view an experiment from “The Video Encyclopedia of Physics Demonstrations” (Berg, 1992); to illustrate Galileo’s ultimate idealization; that all bodies fall at the same rate in a vacuum. It is pointed out to the students that if even an expert such as Galileo could err initially and needed to carefully examine the framework of his belief system than it is certainly incumbent on the students to carefully examine their own ideas. Through the conceptual conflict exercise, students are introduced to the idea that there can be more than one equally logical way of looking at a phenomenon and only experiment, not logic can decide the issue. Students are encouraged to explore this point. An inducement for this exploration is that it is an essay question on a sample midterm and students are notified that their midterm will be very similar to the sample midterm. The next intervention is the first collaborative group/critique exercise. It focuses on the independence of horizontal and vertical motion (and thus the utility of using vectors in Physics). Students are asked to compare the motion of a dropped object with an object thrown horizontally. It is noted that no information or experiment done up to this point of the course can be used to predict the outcome of this experiment. Students see that bodies fall at the same rate even when they have different (including zero) horizontal velocities. During the intervention, many students realize that other students in the class hold different viewpoints about motion. At the end of the collaborative group exercise, students view two experiments from “The Video Encyclopedia of Physics Demonstrations” (Berg, 1992); simultaneous motion of a dropped ball and a thrown ball from the same initial height and the “monkey gun” experiment. The second collaborative group/critique exercise is an examination of a sandbag dropped from a hot air balloon rising at constant speed. Again, it is emphasized that no information or experiment done to date can predict the outcome of this experiment. Again, the discussion concludes with experiments shown from the “The Video Encyclopedia of Physics Demonstrations” (Berg, 1992). The professor describes how Galileo makes use of ideal situations to theorize about and eventually derive the law of inertia. The professor explains that Galileo felt that this law is necessary to understand the Copernican perspective. The final collaborative group/critique exercise continues the discussion of Galileo’s revolutionary idea of inertia. Students are asked to examine the forces acting on a thrown baseball just after it leaves your hand and when it reaches the top of its motion. This brings out in the open a variety of
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students’ personal scientific conceptions including “force being dependent on velocity” and the “force of the hand” balancing the force. In summing up the professor emphasizes the concept of equilibrium and the role of inertia in keeping the ball moving.
8.1.3
Findings
Semi-structured and structured interviews were used to interview students that repeated central questions at the beginning, middle and end of a 13-week course. Lectures in the course occurred from January 6, 1999 until April 9. Students chosen from those who volunteered to be part of the study participated in two lengthy group interviews February 2 and 7 1999. Follow-up individual interviews were conducted on March 1 or March 2, 1999 and a final individual interview conducted on April 6 through April 9, 1999. 8.1.3.1
Finding 1
See Fig. 8.1. Component 2; the combination of group activities followed by in-class discussions and presentations appears to open the students to considering different conceptual positions. Component 3; the written critique channels the students into making decisions about which position is best. Alexei: [In the final collaborative-group exercise we] had three different opinions and everybody tried to defend his or her own opinion. There was no consensus. We did succeed in identifying those critical points in the problem, why, or why not we don’t agree on it so in this case, I found it very helpful. What really helped was the final explanation by the professor, how it really worked, or how that particular situation was supposed to be looked at. It did help in a way that I could point out more precisely the different ways of looking at that particular problem (April interview). Solomon: I think most people left more confused after those things then, well not all of them, but some of them, the one on force, I left more confused. I think after that class most people walked away not knowing what a force was. I know when I walked away I knew that I had to reexamine it (April interview). Ahmad: The group work bombards you with many ideas, and then for the critique you’re going in the opposite direction, you’re trying to get rid of all the ideas and come to one right idea (April interview).
8.1.3.2
Finding 2
As the course progresses, many students become both socially and cognitively more involved in the activities. Lelana, for example in the March interview takes a “toolkit” approach to the activities, but in the April interview, she adopts a different more conceptual mindset: Lelana: [The collaborative-group activity] clears some things that are really not clear but like helping me actually do physics problems, no it doesn’t, you have formulas and you’ve just got to figure out which formulas to use, you don’t need it (March interview).
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Lelana: In the group work, I asked my friends, so what did you think of it? It wasn’t like ‘okay, look at Chapter 5 and the answers right there’. It wasn’t like that. … The last few times he [referring to Ahmad] was in my group and we usually end up arguing, because he usually thinks differently than I do. It’s good challenging each other (April interview).
In the same interview she notes that she was able to use the critiques to construct her view of the concepts: Lelana: You had to write more than two pages. I had to discuss with this and that person and it didn’t come directly from the book because it wasn’t from the book. It came from what I thought and it came from my own, thoughts and everything. It wasn’t coming from a source, so it was like from my understanding and from my point of view (April interview).
8.1.3.3
Finding 3
As the students progress through the course activities, they reflect upon their belief structures. They eventually see the concepts as being interrelated and undergo a change in their mindset. Ahmad: In the second critique or third critique, I started thinking to a previous critique, so it all builds upon itself. The first critique will help explain the second, and that helps to explain the third (April interview). Solomon: In the final example, we both misunderstood. In the other times, it was always I would have one opinion, and they would have another opinion, and I would convince them of my opinion, so then I could see the two opinions but in this one, basically what I learnt, was that through one’s continual learning and advancement, one will constantly have evolving paradigmatic understandings I was in an archaic sort of understanding or paradigm whereas after I reread it, it evolved and there was this switch (April interview).
8.1.3.4
Finding 4
Not all students benefit from the combined components of the course. Some students become active in particular components of the course. Nabilla primarily developed her own thoughts through component 1 (Fig. 8.1); reflective writing. Nabilla: If there’s a new concept, you’re trying to understand what is it about …and that’s what you freewrite about, what you think about the new concept, and how does it make sense to you. … I’m just trying to make myself understand… if you understand it and write, you can understand it more… but obviously if I read and, if I write it down I’ll be concentrating more on it…so, I’d be double understanding it (April interview).
Coming from the United Arab Emirates, Nabilla hasn’t been exposed to group work before. Nabilla: I’m starting to get used to it little by little (February interview). She seems passive and comfortable with group solidarity: Nabilla: Everyone’s talking and some people are saying their point of views, and the group comes out and says their opinion, it’s fun, you feel more comfortable (February interview).
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Her more active involvement in component 2 (Fig. 8.1); the conceptual conflict exercise, does not lead her to more active cognitive involvement in component 3; the critique. Nabilla: You start thinking which one makes more sense and which one’s logical, and then we just wait, the professor saying which one was right. … I saw which one makes more sense, and the different ways people are thinking, critique is just, you’re just plotting them all down (April interview).
By the end of the course, she finds participation in component 2; the conceptual conflict exercise, more comfortable and as a consequence is more cognitively active. Nabilla: If you have an opinion and someone else disagrees, you’re going to talk about it and talk about it, and argue maybe, and you’re just going to come up to the solution and then see what was the right thing when another group presents it in class and the teacher talks about it …so it helps (April interview).
8.1.3.5
Finding 5
A student who sees physics knowledge as a coherent web of ideas appears to be able to monitor their understanding for consistency. Each time a student monitors their understanding, they appear to have more reasons to see Physics as interrelated. Ahmad: I would make new links between things, and I would also think about more reasons why that would be true as opposed, and possibly at other times, think of more reasons why something else would be false (April interview).
The overall perception of the course by the students in this case study is typified by Lelana’s comment: Lelana: The stuff that we discuss during the critiques I never knew much about them. The questions that were asked I didn’t quite know the answers, I had to sit down, think about it, think about it differently, and then from another point of view, and then ask (April interview).
8.1.4
Conclusions
In the study of Kalman and Aulls (2003), it can be seen that the historical approach embodied in the course design was effective in changing the mindset of the students. Students change from a view that science is a matter of solving problems using an independent set of tools, classified according to problem type, to a view that a science subject consists of a web of interconnected concepts. The qualitative results in the study of Kalman and Aulls (2003), are supported by a quantitative analysis given to an entire class which includes the students interviewed in this study (Kalman et al., 2002). The quantitative results demonstrated a significant change in students’ thinking about two central concepts in the course (independence of horizontal and vertical motion and forces acting on a ball thrown in the air).
Chapter 9
Courses for Non-science Students
The approaches that try to attract students to physics by merely writing in words the mathematical formulas (“physics for poets”), or by step-by-step detailed explanations, appear somewhat naïve. “Physics for humanities” requires mainly different contents beyond the simplified formalism. The cultural contents of physics may trigger the interest of many presently identified as not apt to physics, bringing into physics classes the students often lost within the common educational practice. The courses in this chapter conceptualize and attempt to explore a continuing dialogue between science/engineering and the arts, which has affected life and attitudes throughout history and promises to do so for the future. Scientists and engineers are human and fallible and consequently they and their discoveries are influenced by what might be called their cultural contexts. Conversely artists and their works are influenced by changes in scientific thought.
9.1
Three Types of Learners
“Science for humanities” requires a course that contains different contents compared to a traditional science course beyond a simplified formalism. The cultural contents of science may trigger the interest of many students, who are identified as not having the abilities to succeed in a traditional course, bringing into science classes the students often lost within the common educational practice. The approaches that try to attract students to physics by merely writing in words the mathematical formulas (“physics for poets”), or by step-by-step detailed explanations, appear somewhat naïve. Students learn in different ways leading to a need for different instruction, different emphases and, indeed, a different curriculum for non-science students. As seen in Fig. 9.1, Tseitlin and Galili (2005) anticipate three types of learners. Courses focusing on “normal science” are unlikely to appeal to students of the first and third categories, even when the mathematical contents of such courses are reduced:
C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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Fig. 9.1 Three types of learners
Learners of the first type (“philosophers”) show an interest in the ideas and principles of their subject, they like to philosophize. They like generally ordered knowledge and might lose interest, even have difficulties) in learning particular applications (problem solving), if not related to general principles, organized procedures, etc. They seek a holistic vision of science, gravitating to nucleus in discipline-cultures. Students of the second type (“practitioners”) prefer to apply the knowledge provided by the instructor in the form of well-defined procedures. They enjoy their studies, especially when the goals are concrete. They like to solve “fair” problems, which may vary in the ways of application of rules, but not require invention of new ones. These students gravitate to the normal area, body knowledge of discipline-cultures. Finally, students of the third type (“critics”) are inclined to criticize the presented knowledge, and resist theories authoritatively presented. They are creative and like controversy, they suggest their own ideas and explanations, sometimes paradoxical and inconsistent, which challenge the dogma. These students might appear as weak, stubborn, illogical and inconsistent. Facing rigid and indisputable subject matter and teaching, they feel bored and might be disruptive. Their success in class may vary. These students gravitate to the peripheral knowledge of discipline-cultures.
9.2
Course Dossier
A partial discussion of application of the ideas in this book to non-science students is found in Kalman (1999). One additional activity that has been employed in those courses is the course dossier. Writing in science courses allows students to mediate their own “knowledge” with the new knowledge, which the course presents to them. Writing-to-learn and learning to write explores the student’s own doubts, gaps in knowledge and gropings for the answer; only
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after the student has put something on paper does the professor respond. For more details see Section 5.1.2. The course dossier method takes students beyond the reflective writing on the textbook found in Chapter 4 to the use of writing to critically explore the material presented in the class. I have used it in the most advanced undergraduate physics courses and I have also found it particularly useful in science courses designed for non-science students. A shorter version of the method is called:
9.2.1
Passing the Word to the Student; Transforming Each Lecture into a Mini-research Paper
Students prepare preview sheets prior to the classes of the week. This “reflection” is the equivalent of the planning phase of an essay. The lecture then becomes the research component, the material to be addressed. A one page post-summary, “critique” is the body of the research. Students begin with reflective-writing on the material to be covered that week. After rereading reflective-writing, they write the preview sheet. This begins with two or three mini objectives that they feel should be addressed in class that week. They complete their preview sheet with a summary of all the topics that are to be covered that week. Only the preview sheet is marked. However, if the students do not hand in an adequate amount of reflective writing with their preview sheet, the preview sheet will not be graded. The critique may take various forms. In a regular science course it would likely consists of a short introductory paragraph, followed by a presentation of what was covered in the classes of the week. In a course for non-science students, it would be a one-page essay, written in a manner that someone who knows no science can understand. This essay would begin with a short introductory paragraph concerning some particular concept presented in class that week. The rest of the essay would be a critical analysis of the concept. In either case, students are warned that critiques must be presented in properly written paragraphs using normal writing or 12 pt. font and as few equations as possible. Marks are deducted for unnecessary use of mathematics and extra pages are not read.
9.2.2
End of Semester
In courses for non-science students and in smaller, upper year courses, the set of “mini-research papers” can be enhanced by a fuller recursive and interactive approach to writing. At the end of the course, the students collect all or a sample of their critiques and write a single overview of the course using the following procedure:
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First entries: Second entries: Third entries: Fourth entries:
Fifth entries: Final entries:
Two friends, who are not in the course, read the collected critiques and make comments. The student rereads the collected critiques with the comments and writes reflectively on the collection. The second entries are used to develop some common theme(s) that run through the work. The themes are developed into a draft of an essay of “n” pages. (For an upper year science course, this (n) would probably be three pages. For a non-science course with a final exam, five pages. For such a non-science course where the dossier is in place of a final exam, ten pages.) The essay must be a critical examination “covering” the entire course in terms of the themes based on material discussed in class. The two friends read the draft and record their comments. The draft is rewritten reflecting a reconsideration of the material especially in consideration of the remarks by the two friends. Suggested length “n” pages, but there is no page limit.
Students are informed that if any entry is missing from the dossier, the dossier will not be marked. “In order for reflection to occur, the oral and written forms of language must pass back and forth between persons who both speak and listen or read and write - sharing, expanding and reflecting on each other’s experiences” (Belenkey et al., 1986). Prewriting, drafting, and rewriting are integral to any successful piece of writing; what is so often not taken into account is that one never can “get it right” the first time that one puts pen to paper. Writing is a recursive process, one that goes backward and forward and backward again, from jotting down initial conceptions to drafting the work to regeneration of new ideas and new formats. The course dossier provides many opportunities for all of this. Note that the passing of the draft to the two friends not only provides feedback, but also forces the student to establish distance from the material before writing the final version.
9.3
Constellation Courses
The idea of giving constellation courses goes back to the recommendations for future action of a conference on physics for non science majors held in 1965 (Correll and Strassenburg, 1965). Such courses attempt to relate physics and its developments to history, philosophy, religion, literature, the social sciences and the other natural sciences. This helps students with different learning styles as discussed in Section 9.1 of this chapter. It was noted by Correll and Strassenburg (1965) that such a course “will have maximum relevance to non-scientists”. The courses described in this section of this chapter conceptualize and attempt to explore a continuing dialogue between
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science/engineering and the arts, which has affected life and attitudes throughout history and promises to do so for the future. Scientists and engineers are human and fallible and consequently they and their discoveries are influenced by what might be called their cultural contexts. Conversely artists and their works are influenced by changes in scientific thought. Since it is difficult for one person to be expert in both science and the humanities, most of the courses described in this section are team-taught or make extensive use of guest lecturers. In line with the dialogue theme, the courses are felt to be of equal importance to the science and engineering student. Enrolments are typically 30–50% science students in most cases and one such course is exclusively aimed at physics majors. Since a “poet’s” science approach or any kind of “talking down” to the humanities students could “turn off” the science students and since a watered down approach to the humanities would have a similar adverse effect on the humanities students, the treatment is rigorous and uncompromising. In this chapter, the attempt has been to focus on material that would be of use for a teacher in preparing similar courses. Thus there are examples of subjects taught and the technical problems encountered in giving such a course: credit for teaching a team taught courses, problems of team teaching, amount of preparation required, etc. For a brief review of some other courses that explore the interaction of the sciences and the humanities see; Bailey (1971), Davenport, (1970, 1975), Gork and Arons, (1967), Hallett and Kalman (1975), and Nicholson (1965).
9.3.1
Studies in Physics and Literature
Calvin S. Kalman and Linda Rahm Hallett Concordia University This is a course that is team-taught by a physicist and an English professor, who are both present in the classroom at all times. Classes are in discussion group format with the professors in dialogue with each other as well as with the class. The course can be taken independently or toward fulfillment of a minor called Social Responsibility in Science. Other courses in this minor include “Science and the Cultural Crisis”, team-taught by a chemist and a philosopher. Unfortunately, the rule has been to give the professor and his department only half credit for teaching the course. Since such a course has the same number of contact hours as a regular course and normally an increased preparation time, professors accept a distinct overload. Part of the reason for giving such a course is suggested by Allan Holden (1968): “There is a physics that is a single thing. It is the flesh and bloodless body of understanding, visualized by most young students, which descends like manna from heaven and comes to rest in a textbook”. Similarly, there could be said to exist an
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approach to literature, which makes of it a “single thing”, studied only in terms of its own internal structure and development. Such approaches undeniably have value for the future specialist, but their limited perspectives often yield an inadequate appreciation of the nature of the problems and achievements in either field and foster that mutual isolationism discussed by C.P. Snow (1969) in The Two Cultures. For these reasons, the course was designed with both science and arts students in mind and focuses, not on two separate entities- “pure” science and “pure” art – but on the interaction which shapes both throughout history. Some examples of topics discussed follow. In the Middle Ages, the key problem of science was, “What are the true causes of the physical world”. Men knew that the planetary orbits must be circular, since only circular motion is natural. Calculational schemes such as those of Ptolemy might be necessary to save the appearances or for the use of navigators, but that is purely calculational; that’s not science. The debate between Newton and the Cartesians was on precisely this issue. The Cartesians challenged Newton by asking: What is the cause of gravity – the hand of God? Newton’s public answer, which physicists today accept, is that it isn’t necessary to know. What is needed is a mathematical model in which the future position of the planet can be predicted from our present knowledge. The change in viewpoint can be seen in a cultural context by examining such phenomena as the change in painting from the Middle Ages through the Renaissance and Baroque periods. In the Middle Ages, the subject of St. George and the dragon depicts a cosmic struggle with no indication of a specific locale. The appearances do not matter; or, to be more precise, they matter only to the degree that they transcend themselves, pointing to truths, which are divine and non-material. The later, more familiar versions provide detailed depiction of setting and a greater attention to the physical drama of the battle – anatomical accuracy and the convincing representation of three-dimensional bodies in motion, for example. For literature as for science in the transitional period from the renaissance into the eighteenth century, the major question was, to a large extent, an epistemological one. Literature continued to be regarded as principally didactic in aim but the sense of the nature and methods of the knowledge which literature could impart underwent a shift of emphasis which reflects the rising prestige of the new scientific method. It is not simply that Arcadia gives way to the real-life bustle and squalor of Defoe’s or Fielding’s London; in critical theory the essentially Platonic vocabulary of the Renaissance is replaced in the eighteenth century taste and (in character depiction) general laws of human nature which take on a fundamentally predictive quality. Partially inspired by the colossal achievement of Newton, the eighteenth-century artists looked to the physical scientists for a model of their own authority. However, with the Romantics a parting of the ways occurred. The scientists of the Royal Society in the seventeenth century had felt a need to disassociate themselves from the fictions and ornamental language of poets; now it was the poets who felt a need to declare their separateness. Whether, like Wordsworth, they saw the possibility of
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a co-operation between the scientist and the poet working toward the future betterment of humanity, or whether, like Blake and Keats, they remained essentially hostile toward the scientific mentality, the romantic artists agreed on one thing: that the “truths” of the scientist and the poet, as well as the language for communicating those truths, are, and should be, fundamentally different. Mary Shelley’s Frankenstein reflects this Romantic interpretation of the two modes of knowing as an opposition between the integrated vs. the disintegrative intellect. In addition, Frankenstein focuses the question of the responsibility of he scientist, a topic which plays a large part in the second half of the course. Shelley’s novel, in fact, foreshadows all the problems encountered by the atomic scientists a century later; the early idyllic period of study; the growing fascination; the physical isolation (comparable to Los Alamos) during the work of creation; and, finally, the question of control of the monster. For comparison and insight into the actual situation, Robert Jungk’s (1958) Brighter than a Thousand Suns is also used in the course. The ambiguous role of the scientist as an advisor to government is developed in conjunction with a discussion of Friedrich Durrenmatt’s The Physicists. This work, with its emphasis on paradox and the constant eroding of “rational” cause and effect assumptions, is also valuable in discussing the influence of quantum mechanics on literature. Further analogies between modern physics and the arts can be illustrated by the music of John Cage and his descriptions of indeterminate composition in Silence. The use of music at this point nicely counter-balances earlier discussions of music and the importance of harmonic paradigms in Plato and Renaissance astronomical theory. There are many other examples. As a new feature of the course in its second year, and as a response to suggestions from the students themselves, the last 2 weeks of the second term were devoted to informal reports on end of year projects. These projects are given in lieu of an examination and are intended to allow each student the opportunity to develop a thesis and explore independently some idea or area of particular interest suggested by the course’s main theme of interactions between science and the arts. As examples, papers have been submitted on the philosophic implications of modern physics, on alchemy and its use by Goethe in Faust, and on the reaction of some nineteenth-century English authors to the theory of evolution.
9.3.2
Physics and Society in Historical Perspective
Joseph L. Spradley Wheaton College, Wheaton, Illinois The interaction between science and society is most evident from an historical perspective. The changing conceptual models of physics that have dominated the history of science since early Greek thought have contributed to certain
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philosophical systems in the context of widely accepted world views. Consequently, the ideals of society have been pervasively influenced by various interpretations of these science-related syntheses. Alternatively, the structure of society and the world view that supports it can influence the choice of scientific models. Certain cultural expressions including religion and art also reflect such a mutual influence. Four historical periods will serve to illustrate this science-society relationship according to the following outline which will serve as the basis for the subsequent discussion. 9.3.2.1
Outline
Historical World Views Scientific Ideas Philosophic Syntheses Societal Ideals Cultural Trends 1. Greek Rational Numbers Forms Communalism Classic Arabic 2. Medieval Hierarchical Causes Purposes Feudalism Gothic Art Scientific revolution 3. Enlightenment Mechanical Forces Natural Law Capitalism Baroque Art Romantic Reaction 4. Modern Relational Energy Processes Federalism Abstract Art
9.3.2.2
Pythagoras Plato Harmony Animism Art Transmission Aristotle Aquinas Authority Theism
Newton Locke Equality Deism
Einstein Whitehead Complexity Humanism
Details
I. Greek science was strongly influenced by the Pythagorean concept that all natural phenomena conform to numbers. This hypothesis viewed the integers as embodying geometric forms such as triangles and squares. Application of
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this mathematical approach led to the development of the deductive method as a model for all thought. Platonic philosophy extended the Pythagorean doctrine to explain all of reality in terms of eternal forms or ideas external to nature and apprehended only by logical contemplation rather than by sense experience. This scientific thought contributed to a rational world view, but was also handicapped by a built-in bias against experimentation. The same rational world view found expression in the ideal of harmony especially evident in Hellenic society based on the city-state concept of community. Classic Greek art shows a similar focus on ideal forms, and the concept of an ordered universe found religious expression in an animistic view of the world as a living organism. II. A more empirical approach to science was developed by Aristotle. He viewed Plato’s forms as causes within nature governing the behaviors of matter. Various levels of existence formed a great chain of being down through the concentric spheres of the celestial regions to man and the lower forms of the terrestrial region. Aristotle’s geocentric cosmology was further developed during the period of Arabic science and was later transmitted to Western Europe. Under Aquinas the Aristotelian cosmology was integrated with Christian medieval culture. The Thomistic synthesis identified causes with God’s purposes in a unified hierarchical pattern of order. This dramatic world view supported the authoritarian structure of medieval society, including the hierarchies of church and state. In the feudal system, every person played his part just as everything in the universe played its part in the cosmic drama. Monarchy and Church authority were accepted as being consistent with this hierarchical view of reality. Gothic art and Christian theism express the same vertical orientation. III. The foundations of the medieval synthesis were challenged by the heliocentric hypothesis of Copernicus, but more than a century was required before its breakdown in the scientific revolution. A comprehensive system of the universe, based on the terrestrial mechanics of Galileo and the planetary regularities of Kepler was the signal achievement of Newton with his law of universal gravitation. The world now came to be viewed as a great machine consisting of material particles under the action of forces governed by natural law. John Locke applied this mechanical world view to society, teaching that individuals are the atomic ingredients of the state which should be structured by selfevident natural laws such as equality and the rights of life, liberty, and property. His philosophy provided the theoretical foundation for democracy and capitalism based on the ideas of individualism and tolerance. Thus the Newtonian model became the enlightenment ideal for restructuring society on a secular rather than a religious basis. This secularized outlook can also be seen in baroque art and in the deistic tendency to separate God from the world. IV. In the romantic reaction mechanistic philosophy was rejected and freedom and wholeness were exalted against the unchanging laws of determinism and the tendency toward reductionism. An effort to unify the mechanical laws of Newton with the electromagnetic field equations of Maxwell led Einstein to propose the theory of relativity which radically revised the Newtonian cosmology. Space and time could no longer be considered as independent
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absolutes but instead formed an interdependent space-time continuum. The idea of independent particles consisting of an enduring material substance was replaced by the concept of mass-energy equivalence. The inadequacy of the particle model became especially evident with the development of the quantum theory, which showed that atoms are complex systems of interrelated parts. The deterministic certainty of classical physics gave way to probability and the irreducible margin of uncertainty. Both relativity and quantum theory reveal that every event in nature in integrally related to its environment. An extended discussion of historical parallels in science and culture including additional references is found in Spradley (1989).
9.3.2.3
Overview
The process metaphysics of Whitehead is an attempt to develop a philosophical synthesis reflecting the organic unity in nature suggested by modern physics. He replaces the mechanical model of independent particles by a new view of reality based on the kind of internal relationship, which characterize organisms. The focus is on interrelated dynamic processes rather than independent static substances. These implications of modern physics support a relational world view consistent with many trends in contemporary society. In general there is a growing recognition of greater complexity and interdependence than was true of Locke’s mechanistic social theories. This holistic emphasis is seen in trends toward greater social concern of governments for the interrelated needs of people in a technological society, and the more recent emergence of widespread ecological awareness. Efforts to understand and express the increasing complexity of the contemporary world are also reflected in the development of abstract art and the concern of various kinds of humanism for man in relation to an interdependent world. In each of these historical periods the interaction between science and society can be seen in the context of a prevailing climate of opinion. The ideas of science are reflected in the ideals of society and provide the models for a widespread interpretation and acceptance of societal structures. Scientific revolutions are thus inseparable from philosophical revisions and cultural change. An adequate understanding of trends and issues in society requires a proper evaluation of basic scientific concepts.
9.3.3
Science and Humanities Via Science Fiction
Arlen R. Zander East Texas State University, Commerce, Texas 75428 The respectability and acceptability of science fiction (SF) as a legitimate educational genre is well established. However, courses on SF cited do not attempt to deal with the many facets of SF in the most direct manner – an interdisciplinary (ID) teaching
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team. In this paper a team-taught SF course is discussed in which all members of the ID teaching team meet every class. The team consists of a psychologist, a literary scholar, and a nuclear physicist. As a result, it is possible to cope with almost any turn the discussion takes. Furthermore, the presence of a psychologist on the teaching team enables us to avoid the polarization of scientist versus humanist, which often occurs in “physics for poets” courses. Grades for the course are based on a combination of two papers or projects and two exams. The exams consist of 50% essay questions and 50% short response questions. For their papers or projects, students are allowed to deal with virtually any topic, as long as it is somehow related to the course. Each member of the teaching team responds to each student’s paper or project with written comments and a numerical score. The two papers or projects and the two exams are weighed equally in determining the final course grade.
9.3.3.1
Course Material
The course material is very loosely structured around a number of paperbacks, mostly novels. Due to the diverse nature of the available material and the broad spectrum of interest exhibited by students attracted to our course, no attempt is made to impose a rigid format. Students’ responses to questionnaires are used, as far as is practical, in determining course content. The manner in which the course material is presented also varies considerable. In many instances, topics are simply presented informally by a member of the teaching team. At other times, guest lecturers with expertise outside the area covered by the teaching team are invited to meet with the class. Off-campus experts are also used. Student presentations of their own projects also cover a wide variety of topics. Discussion topics include general relativity and black holes in connection with Stranger in a Strange Land and Sirens of Titan, the scientific method and the literary role of the scientist-hero with The Black Cloud, similarities between poets and theoretical scientists with Science and Human Values, the role of physics in planetary ecology with Dune, Doppler shift when reading The Black Cloud, and the morality of scientific research in connection with A Canticle for Leibowitz. The treatment of A Canticle for Leibowitz is typical of the ID, multimedia approach we take in discussing a particular SF novel. The theme of this book is an indictment and warning to the present that the evolution of civilization is reflected by history repeating itself; the end of an era is marked by atomic warfare, the beginning of a new era occurs in a radioactive world, and throughout it all the church survives as the protector and refuge of scientific knowledge. As background material for this book, class demonstrations are presented on circuit boards and schematics, a St. Louis motor, and polarized light and lenses; lectures are given on radiation units, dosages and effects, the psychology of mutants, and the Legend of the Wandering Jew and the guilt of man; and the films “Discovery of Radioactivity” and “Building of the Bomb” are shown. Discussion topics for Canticle include the role of the poet in interpreting the predicament of science, the conflict between
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scientists and laymen about who must accept responsibility for scientific discoveries, and the necessity for a good scientist to report only what he observes. Spontaneous discussions dealt with the idea that God might be equated with the fundamental universal laws of physics and the validity of the subjective perceptions of the poet versus the strictly objective perceptions of a true scientist. 9.3.3.2
Major Problems
The major problems encountered in developing our course were obtaining teaching credit for all members of the teaching team, an unexpectedly large initial enrolment which stifled meaningful discussion, and lack of experience in teaching a truly ID course. The first problem vanished with the large initial enrolment and subsequent success of the course. The second problem was overcome by simply limiting enrolment, by resorting to a small conference room for class sessions so that students and instructors were physically closer together, and by encouraging an informal atmosphere of questioning and commenting during all classes. The latter technique was initiated by the instructors continually questioning each other, asking for explanations of jargon, and having outright arguments in front of the class. The students soon caught on, and, as a result, had virtually none of the inhibition in the presence of an “authority on the subject” that frequently occurs in more formal situations. The third problem very nearly proved to be our downfall initially. Since there were three of us meeting every class, each of us occasionally shirked our class preparation thinking the other two team members could easily make up for it. On several unfortunate occasions all three of us simultaneously took this approach with disastrous consequence in the classrooms. It also was belatedly discovered in several different instances that the team members had totally divergent ideas about what direction a particular discussion should take. These problems were eventually solved by meeting several times a week to discuss course content and progress, and also by simple trial and error. Consequently the course demanded as much, or more, preparation time than a conventional course. 9.3.3.3
Success of the Course
The course has been a definite success in meeting the practical objective of enrolling more non-science students in physics course. Every time the course has been offered, approximately 70% of the students enrolled are non-science majors. Moreover approximately 10% of the students who enrolled in the course the first time it was offered have subsequently enrolled in some other physics course; most often “Physics for Society” or “Descriptive Astronomy”. It should be noted that since these are not required courses and since both deal with topics also discussed in the SF course, it seems likely that taking the SF course is instrumental in persuading students to take another physics course. Student responses to exam questions demonstrate at least modest success in meeting philosophical objectives. These responses indicate that the students
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learn to identify, compare, and contrast scientific and humanistic ideas. For example, when the class was asked to discuss the similarities and differences between scientists and poets, some of the responses received were: “Scientists and poets are similar in that both constantly question and seek answers, both have a starting point and a method, both theorize and then seek verification, both are free to make their own assumption”. “Scientists and poets differ in that the poet deliberately uses words with many meanings but the scientist uses precisely defined words and will even invent new ones which are more specific if old ones are too ambiguous; the poet points out a problem and the scientist tries to solve it; the poet is concerned with private observations but the scientist is concerned with public observations, the poet is subjective but the scientist is objective. Occasional arguments in the classroom also fulfilled the philosophical objective of demonstrating that scientists are both human and fallible. Among the unexpected benefits of the course are the personal experiences of the teaching team as they interact with one another. A marked increase in understanding of the accomplishments of each other’s disciplines and tolerance for each other’s viewpoints becomes evident as the course progresses. This in turn results in more open-minded approaches to our own classroom encounters with students from other disciplines.
9.3.4
Philosophy in Physics and Physics in Philosophy
Martin Eger Department of Physics, City University of New York, College of Staten Island, Staten Island, NY 10314, USA
9.3.4.1
Purpose
The purpose of this paper is not to belabour the well known historical relationship between philosophy and physics, but to justify, on grounds of educational values, as well as proximate pedagogical and institutional requirements, the proposition that the two subjects can and ought to be studied within the framework of a single course. The simplest argument for the conjunction was given by Phillip Frank: “Everyone who is to get a satisfactory understanding of twentieth-century science will just have to absorb a good deal of philosophical thought”. The connection of physics to philosophy is thus qualitatively different from its relation to literature or socio-political history. Not just cultural broadening is involved here, but a necessary element in the study of physics itself. A course in philosophy and physics restores to the latter that vital component of which it has been deprived during the past century of specialization and compartmentalization of knowledge.
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Intercourse Between Physics and Philosophy
Broadly speaking, there are three avenues through which the intercourse between physics and philosophy take place: (1) the philosophical import and presuppositions of specific high level theories such as quantum mechanics, relativity, and statistical thermodynamics; (2) the more general epistemological questions involved in the validation of theories, and the ontological problems raised by the meaning of the results; and (3) the fact that establishment paradigms do, at times, have a long range influence on philosophies apparently unconnected with natural science, e.g. social thought of various types. The teaching of physical principles and techniques that largely ignores or slights the first two aspects does not do justice either to the subject or to the students; while omission of the third aspect severs an important intellectual link between science and society, thereby strengthening the trend toward what Jurgen Habermas and his school have called the “orientation to instrumental action”. The problem is how to incorporate these aspects in a single course and also do justice to the technical content. Neither facts and formalism without reflection, nor mere reflection without facts and formalism. The subject itself points the way to the solution: A focus on a few appropriately chosen major theories, their treatment in depth – with due attention to all three of the enumerated aspects – should be the modus operandi. Space limitations on this brief summary preclude discussion of anything more than one example, which must serve as the paradigm case: special relativity. It has the merit of the highest “philosophical cost-effectiveness factor”, i.e. the ratio of philosophically interesting questions raised and conclusions reached to the mathematical work required. Inevitably, the relativity of time order of point-events, and other startling features of the subject, have an effect like an awakening from “dogmatic slumber”. When this happens, it is advisable to backtrack over the basic derivations, and show – perhaps by an alternative route – the logical connection between the conclusions and the original, seemingly innocuous and simple-minded of operational definition. The reiteration of this concept, in the study of the usual problems, paradoxes, and experiments, reinforces the connection between the epistemological innovation and the strictly physical predictions and verifications. Thus, the first aspect of the relation of physics to philosophy is dealt with at the beginning, center, and endpoint of an important and well established theory. Now the formulation and its meaning must be analyzed more generally: How justified was the adoption of Einstein’s approach over Lorentz’s? What is the role of operational definitions in physics and science as a whole? Does the development of relativity fit the hypothetico-deductive method, or perhaps Lakatos’ more complex “logic of discovery”? And what is a “theory” anyway? What relation to reality does it bear? At this point, even the most philosophically sensitive textbooks must be supplemented with additional reading: above all, the relevant essays by Einstein himself; then the physicist-philosophers like Mach, Bridgman, and Frank. The last of the questions mentioned above is of special significance,
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forming a continuous thread from the Galileo-Balarmine clash about truth and the limits of science, to what today is called the instrumentalist-realist controversy. Here, Karl Popper’s well-known essay, “Three Views Concerning Human Knowledge”, (in Conjectures and Refutations: The Growth of Scientific Knowledge, Papper 1965) is most enlightening. In regard to the third avenue linking physics and philosophy, historical evidence is quite explicit and good reading easy to provide: William James and John Dewey make numerous references to specific developments in the physics of their time, and use the results to support their pragmatist philosophies. For James, the cardinal fact was the final breakdown of belief in exact, universal laws of nature, which turned him into a staunch supporter of the instrumentalist theory of knowledge (James, 1907/1979). This was even more forcefully expounded, and applied across the board from education to morals, by Dewey – who made extensive use of the emergent quantum mechanics of the late 1920s, in which the operational viewpoint, modeled on Einstein’s, proved its power again (The Quest for Certainty, 1930). In addition to pragmatism, positivism, and kindred twentieth century thought, there is the equally interesting relation to certain theories of psychology: Historical essays such as Sygmund Koch’s fascinating sketch of behaviorism can me combined with primary sources like B.F. Skinner’s paper “The Operational Analysis of Psychological Terms”. The study of these influences should not, however, imply that they are necessarily appropriate or beneficial. Instead, this part of the discussion can make contact with the students’ awareness of recent dissatisfaction with many such adaptations in the social sciences; the question is then raised as to how conceptual and methodological transference is to be usefully carried out and rationally evaluated.
9.3.4.3
Can Such a Course Be Taught Successfully
Can such a course be taught successfully under the conditions of present day institutional reality? If the teacher possesses sufficient experience in both areas, there is no reason why one person could not do the job alone. If it is team-taught, however, problems of faculty credit apportionment may arise: When the financial situation was good at CUNY, both instructors received full credit; now this is unimaginable. Enrolment has not, in general, been a problem, though the figures for my courses varied between 30 and 6. One does have to make an effort to inform and encourage those who could truly benefit. But this effort is the heart of the matter, because many students cannot by themselves imagine how relevant these questions can be to the problems in their own fields. When the course is designed primarily for nonscientific people, the technical content is elementary, and therefore natural science majors may have to be denied credit. If permitted, a relatively small number of physics and philosophy majors enroll. But for these groups, such a course is unusually valuable.
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9.3.5 Contemporary Physics: A Freshman Seminar for Physics Majors E.L. Ferretti and M.A. Ludington Albion College, Albion, Michigan Unlike the traditional introductory courses for science majors, this course looks at concepts and principles in physics from a much wider perspective. Instead of beginning the college physics program with a discussion of measurement, units, vectors, kinematics, etc., the student is asked to study physics as a discipline from a historical viewpoint. This naturally leads to consideration of such questions and issues as: “What is physics?” “How has the science of physics developed through the years”, “What does it mean to be a physicist in 2007?”, “What are the social responsibilities of a scientist?”, “What interaction should there be with the various aspects of society?”
9.3.5.1
Five Basic Reasons for Instituting Such a Course
1. It allows the incoming student to see physics as more than just a collection of facts, formulas and mathematical problems. 2. It gives the student an opportunity to become aware of the impact this scientific discipline has had and continues to have on modern thought and action. At the same time, the student has a chance to gain important insights into other aspects of his liberal education; thus, in a sense, narrowing the gap between the socalled “Two Cultures”. 3. It allows the student to see the social responsibilities that he/she will have as a physicist in the twenty-first century. It gives him/her a chance to consider and discuss some of the issues and problems that he/she will one day have to make decisions about, and it provides him/her an opportunity to evaluate how physics relates to the various problems of contemporary society. 4. The course tries to develop in the student a sense of wonder, which hopefully will remain with him/her for the rest of his life; it serves to encourage him/her to begin a career in physics with an enthusiastic anticipation for all that lies ahead. 5. Finally on a more practical note, it gives the student a chance to become accustomed to college and allow him/her time to obtain the necessary mathematical background he/she will need for the more traditional courses that follow. Too often we have lost prospective majors because they were not able to acquire the calculus skills soon enough to be able to understand the physics. 9.3.5.2
Emphasis of Subject Matter
Though the course begins with a look back into history and the development of physics, the emphasis of subject matter is placed on the modern era from 1900 to the present.
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The theory of quantum mechanics is shown to be based on the concepts of probability and uncertainty, as contrasted with the classical absolutism of Newtonian physics. This leads to a discussion of the philosophical implications of the new theory by considering topics like determinism vs. free will and objective reality vs. subjectivity. Likewise the theory of relativity and its relationship to nuclear energy is presented. At the same time, the social responsibilities of the scientist is discussed so that the student is aware of the tremendous impact the decisions and research endeavors of a scientist has on environment and society.
9.3.5.3
Films Utilized
In line with this type of format, films were used which portrayed different aspects of physics and the world of the physicist. Films Shown in Contemporary Physics: “Time Is” “Time Dilation – An Experiment with Mu-Mesons” “Strangeness Minus Three” “Einstein” “The Mighty Atom” “The Building of the Bomb” A few of the films, like the “Mu-Meson Experiment” and “Strangeness Minus Three”, portrayed scientists at work struggling with various assumptions and successfully applying the scientific method to test their hypotheses. Other films emphasized the social character of the physicist: the film “Einstein” presents him as a man very aware of his responsibilities to society; “Building of the Bomb” allows the students the opportunity to see how scientists have struggled with their consciences and reacted to external pressures from political circles. An attempt to show the relationship of physics to the humanities, the beauty of physics and the order and simplicity of the natural world was also made. The film “Strangeness Minus Three”, introduced and concluded by Richard Feynman, emphasized these aspects very well. The students’ reactions to the films were quite favorable and they felt they served an important function in the course. In addition to film presentations, some of the guest speakers from a monthly colloquium for all our physics majors add depth to the course. For example, E.T.S. Walton spoke about the Cavendish Laboratory and its role in the early days of modern physics. In the format of the course, mathematics was deemphasized. Homework assignments were more subjective in nature, and the students were asked to write a paper on some aspect of the course. Some of the topics were: “Modern physics and Its Impact on modern thought”, “Tachyons and what implications they hold for the future”, and “The Manhattan project and its impact on society”. The students’ final grades were based equally upon the homework assignments, quizzes, paper, and final exam. Questionnaires completed by the students at the end of the course
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brought reactions like; “excellent introductory course”, “serves as a stimulus for interesting you in the subject”, “course gave me many new insights and I am more interested in physics now that if I had not taken the course”, “I took the course because I didn’t like physics in high school, but after the course I will surely take some more physics courses”, “different kind of course”, “new look at physics”.
9.3.6
A Science-Humanities Course Series
Alan J. Friedman San Francisco State University
9.3.6.1
Introduction
San Francisco State University experimented with three interdisciplinary courses collectively titled Major Figures and Their Impact. The Program was directed by Professor Michael Gregory of the Department of English, and was funded by the national Endowment for the Humanities. The courses were a response to a conference of students and faculty that culminated in enthusiastic support for a continuing series of introductory level science-humanities classes to develop subjects of central and enduring significance to both disciplines. The curriculum at San Francisco State already included topical courses (the energy crisis, the environment, etc.) and courses on science especially for humanities students (physics for non-scientists), and these courses continue as valuable tools to reach specific groups of students, or to deal with subjects demanding advocacy. For the new courses, the chosen theme was the influence of a major scientist beyond his own discipline. This approach represented an effort to deal directly with the interfaces between disciplines, to be synthetic rather than sequential, and integrative rather than additive. A major advantage of treating the interfaces as opposed to surveying single disciplines was the opportunity to maximize interactions between students from diverse backgrounds by offering classes that both science and humanities students could take on roughly equal footing. Courses on the work and broad impact of Newton, Darwin, and Einstein were offered at the upperdivision undergraduate level, with no prerequisites and open to all majors. These particular scientists served as specific examples from both physical and life sciences; and although pre-registration publicity was not extensive, they each enrolled 20–40 students from a wide range of both science and non-science departments.
9.3.6.2
Description of Courses
Here are brief summaries of the Darwin and Einstein courses only; a course was also given on Newton: Physics, Philosophy and Literature.
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Both courses introduce the scientific achievements of the major figure studied, at the same level as an introductory “liberal arts” course. Often the science or humanities content, readings, and assignments were identical to those the instructors use in conventional introductory courses within a discipline. The main theme and activity of each class covers the implications of the scientists work. Einstein and Modern Literature, which was taught with guest lecturers, begins with an introduction to special relativity (up to the Lorentz transformation equations), quantum theory (as far as the uncertainty relations) and statistical mechanics (on a hand-waving basis). An equal effort went into discussing the developments of the concepts of time, space, and cosmology as they have occurred in several serious modern novels by Lawrence Durrell, Thomas Pynchon, and Robert Coover. The major part of the class work and assignments focused on the many possible relationships between the experimentation by the physicists and by the novelists. In some cases, the physics (or popularizations of the physics) was an acknowledged source of inspiration for the novelists, and in other examples the parallel may have been more deeply rooted in a general cultural trend toward reassessment of the basic concepts of time and space. Darwin and the History of Ideas, also taught with guest lecturers, presented the cultural importance of Darwin’s contributions to evolutionary theory from four different perspectives: (1) an idea which emerges from a broad context of thought in the nineteenth century, including geology, paleontology, theology, biology, and even political economics; (2) an idea which already had a long history before the birth of Darwin, and which survives after his death in new and ever-changing forms; (3) an idea occurring to the mind of a particular man at a particular time, on the basis of his own experiences, interests, observations, readings and peculiarities of his distinct personality; and (4) an idea that has spread far beyond the bounds of the biology dealt with in Darwin’s 1859 publication, and which now pervades widely dispersed areas of thought, among them literature, philosophy, religion, anthropology, sociology and politics. The focus of these courses, then, is not science itself but rather the history of ideas – how a concept (from science in these cases) may influence the broader matrix of a culture. It has been the intention of these courses to demonstrate that a revolution in science may have its most lasting affect not in our choices of hardware, but in our view of ourselves and our relation to the universe at large.
9.3.6.3
Evaluation
These courses were considered to be successful based on student satisfaction measured statistically by evaluation surveys. That conclusion is not unusual for experimental courses, however, since the novelty of the course, and not the course itself, may be responsible for the satisfaction (the Hawthorne Effect). Pre- and post-testing, and control groups will have to be developed before a rigorous statement of satisfaction with these courses can be made, but at least a
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great deal of excitement and intellectual stimulation was clearly indicated by the anonymous student surveys. Instructors evaluated student achievement by comparing the quality of student writing on essays in these courses with essays in single-discipline courses, and by comparing students’ science tests with tests covering the same material in conventional introductory science courses. More data is available for the Einstein course, which was offered twice, and in that course results for both science and non-science students showed no significant differences in comparison with similar students in other courses taught by the same instructor. These comparisons encourage the conclusion that learning takes place in these interdisciplinary courses as thoroughly as in single discipline courses, but do not evaluate the central aim of this kind of program, which is to stimulate synthesis of thinking in the sciences and the humanities. That must be judged from the quantity and quality of synthetic thinking believed to be seen in the students’ work. From this viewpoint, a majority of the students made substantial efforts in this direction, and a good-sized minority succeeded. Moreover, these efforts appeared o be of a higher quality than those of similar students in topical or science-for-non-scientist courses. The administrative difficulties of interdisciplinary course development and support were eased in our case by National Endowment for the Humanities funding. It is not clear whether long term university expenditures and resources will be available for research, team-teaching, and overall effort required for interdisciplinary courses, beyond the extent necessary for conventional singlediscipline courses. Much was learnt during this 1 year program. It is felt that focusing on a major intellectual figure whose work has an impact on a broad front is indeed a way of convincing both science and non-science students of the value, even necessity, of studying outside their own disciplines.
9.3.7
A Cluster of Science-Humanities Courses for Mixed Audiences of Science and Non-science Majors
Lawrence S. Lerner and Edward A. Gosselin California State University, Long Beach, CA 90840
9.3.7.1
Introduction
While differing in specific subject matter and academic level, the three courses discussed in this paper share the following central features: 1. Taught to mixed audiences of science and non-science majors 2. Taught jointly by a physicist and a historian, who are always present in the classroom, where they interact strongly
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3. Given as general-education credit in either natural or social science 4. Graded on the basis of four or five fairly long essays per semester
9.3.7.2
Evolution of the Course Cluster
A special research seminar for juniors in the General Honours Program entitled “Case studies in the interaction between science and society: The Galileo and Oppenheimer affairs” was offered previously. While the challenge of doing original research at the junior level was too great for some of the students, the atmosphere was exciting and nearly all the participants profited educationally from the experience. Out of the course came several lessons, which have been substantiated by further experience: 1. In approaching students who perceive themselves as standing on one side or the other of the “two-cultures” gap, precept by example is as important as specific instruction in demonstrating that the gap is artificial and surmountable. While the two instructors maintain their professional identities and are often critical of one another’s approach, the fundamental unity of the creative process is made clear by their interaction as well as by their specific comments. 2. Some deep common interest on the part of the instructors, although desirable, is not essential. In our case, it is a common research program, which serves as a direct example to students of the fruitfulness of the syncretic approach. The fact that scholars in different fields can work productively together at an advanced level as well as in the classroom, and can communicate the spirit as well as the content of this collaboration, is the strongest possible demonstration of the unity of knowledge. Out of the first course evolved a senior-level course, described in detail elsewhere. (Lerner and Gosselin, 1975). This is a course in history and science, as distinguished from history of science. They are seen as scholarly disciplines, powerful tools for understanding the interaction of man’s intellect with the natural universe, in the context of the evolution of man’s social environment. Broader in scope than the seminar, this course covers a selection of crucial intellectual issues from the Renaissance to the present. Original research is not required of the students, though they are expected to read well beyond the classroom assignments in preparing their essays. The strong interaction, which takes places between science and non-science majors has been very gratifying, and it has been possible to furnish each group with the necessary elements of the “other” discipline without boring the “other” group. This arises from the rarely – met needs of the senior-level major for an elementary but mature review of and perspective on her/his field. The success of this senior-level course encouraged us to offer a course with similar intent aimed mainly at entering freshmen. It is necessarily broader and less deep than the senior course. Entitled “Introduction to Scientific and Humanistic
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Thought”, it is taught to a rather large class of about 50 students. The approach is through intellectual biography of a small number of noted scientists and humanists, conjoined with an intensive study of the subject area in which each left his creative mark, and of his work. To date the most successful subjects of study have been the following: 1. Albert Schweitzer: Based on his autobiographical Out of my life and thought, together with a variety of sources on the development of biblical exegesis in the science-oriented atmosphere of the late nineteenth and early twentieth centuries; on the philosophical trends which influence his commitment to his medical mission, and on the development of musicology and organ technology in the same period. 2. Albert Einstein: based on Banesh Hoffman’s Albert Einstein, Creator and Rebel, together with notes on relativity and an account of an experimental verification of the time dilatation. 3. James D. Watson: Based on his autobiographical The Double Helix.
9.3.7.3
Administrative Consideration
One difficulty, in carrying out the substantial labors involved in planning and teaching courses of the sort discussed here, is that the instructors are not compensated for full-time participation. Not the least of the burden lies in the fact that each instructor must learn a good deal about the other’s discipline, if the interaction is to be fruitful. Without such compensation, the temptation would be to cut corners, and to show up only half the time. This would severely damage the preceptorial aspect of the approach, and seriously impair the unity of organization and effort essential to the courses. At our university, several devices have been employed so that each instructor receives a full three credits of teaching credit: 1. Listing the courses as separate sections in the two departments. 2. Extra teaching credit added by the Office of the Dean of the School of Letters and Science where necessary. 3. Teaching courses in the General Honours Program, which can be flexible in the assignment of instructional credit; or cross-listing in the Honours Program, which then contributes a pro-rata share of teaching credit. Whatever devices are used, it is very important to enlist the interest, sympathy and cooperation of one’s professional colleagues and administrators. A solid and wellfounded assurance of high academic standards is essential in this regard. 9.3.7.4
Conclusion
The two-cultures gap has been damaging to both the scientific and humanistic aspects of our society and to its educational institutions. Indeed the mutual understanding
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arising from this bifurcation have often diverted the process of social controversy into wild-goose chases which have obscured vital issues, and have created an atmosphere in which pronouncements ex cathedra and emotional harangues on good and evil have replaced the arduous rational discourses which alone can benefit the material and spiritual aspects of human life. Perhaps scientific-humanistic courses of the sort discussed here can be useful in correcting these distortions.
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Chapter 10
Computer Assisted Instruction
For a successful CAI dialogue, you need to use short presentations of material/ questions, many opportunities for interactive activity, careful testing of the questions and plenty of opportunities for “looping”.
10.1
Using Computer Assisted Instruction in Science/Engineering Courses
My first incursion into scientific/engineering educational research in 1971 was to see how computer assisted instruction could be used in science courses. The term “computer assisted instruction” (often abbreviated CAI) describes an instructional situation in which a student works at a computer at a program that instructs the student and which is not simply a tool to assist in the instruction of problems or retrieval of information. Typically, such a system would assess student capabilities with a pre-test, present educational materials in an interactive form with jumps to various programs for remediation or advanced educational experiences depending upon student responses. Normally student scores are recorded. I decided to first implement someone else’s computer assisted instruction program on our computer system and then try my hand on my own dialogue. We also made a comparison with student use of our earlier implementation of a dialogue for deriving energy conservation in one dimension developed by Bork and Sherman (1971). Students taking this energy derivation dialogue complained of being placed in an “observer status”. They felt that the program presented them with large amounts of material and checked now and again to see if they were awake! The wording of the questions in some cases was poor. For a successful CAI dialogue, you need to use short presentations of material/questions, many opportunities for interactive activity, careful testing of the questions and plenty of opportunities for “looping”. The material that I am
C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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presented here is not dated. CAI programs are usually offered by publishers and companies for specific uses. They do not present the opportunity for the instructor to set up their own CAI program for their own courses. In this chapter, a CAI language is described that instructors can use as they wish. To illustrate its use, a specific application is described and the results of the evaluation on students are presented.
10.2
A Computer Language for Computer Assisted Instruction
10.2.1
Noah Sherman’s Templates
10.2.1.1
Lessons
When it came to our own dialogue, it was first decided to develop a computer language (Kalman and Kaufman, 1974) that would make it easy for us to write our dialogue and which could be used by others to write their own dialogues. I decided to adapt Noah Sherman’s templates (Sherman, 1971) as the basis for our language. Two modifications of the basic template were made. Firstly, a special “help” class has been added. Students can ask for assistance in trying to answer the question and then try the question again. Secondly, a student with successive correct responses is continually given more encouraging responses: “ok” for one correct response, “good” for two in a row, “excellent” for three in a row and “excellent, keep up the good work” for four in a row. Finally, the possibility of branching has been added. The student’s response is analyzed and based upon the response, instead of continuing to the next question in sequence, the student is directed to any other question in the entire dialogue. The adaptation is found in Fig. 10.1.
10.2.1.2
Pre-tests
A second modified template is used for pre-tests (Fig. 10.2). The major modification is to channel all no-match questions to the first wrong answer class. Although this template is designed for pre-tests, it could also be used by an inexperienced dialogue programmer for preliminary versions of dialogues. Since all no-match answers are channeled to the first wrong answer class, it is normal to use only one wrong answer with one keyword along with a single correct class with all acceptable keywords. One additional logic class was made: A branch to the same question is permitted. Such a question is used to force an unprepared student out of the program.
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Fig. 10.1 Modification of Sherman’s template: A flow chart of the logic for question QJ (Instructional unit J)
10.3
10.3.1
Tutorial on Calculus for the Introductory Mechanics Course Rationale
The problem that we were trying to deal with was the use of calculus in the first of the three introductory courses. The calculus course always lags behind the physics course and students always have difficulties with the brief explanations given by the physics instructors.
10.3.2
Pre-test for the Calculus Tutorial
In our implementation (Kalman et al., 1974), we preceded the tutorial with a computer assisted instruction pre-test. The purpose of the pre-test is to make certain that students have the background preparation needed for students to understand the material presented in the computer assisted instruction tutorial. The correct answer permits the student to proceed to the next question. An incorrect response could lead
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Fig. 10.2 Adaptation of Noah Sherman’s templates for pre-tests
to the student being ejected from the program. Alternatively, students could proceed through the entire pre-test and receive a report of their deficiencies. No serious attempt at teaching material is made in the pre-test. See Fig. 10.3 for the pre-test that we developed.
10.3.3
Testing of Questions
Careful testing of questions is necessary. We introduced our computer assisted instruction calculus dialogues during a summer session. We tried the dialogues on
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Fig. 10.3 Pre-test
a few students at a time and immediately interviewed the students with respect to the reasons why they chose their answer to each question. The answers provided us with additional keywords, alterations in the language of the questions and the need for logic changes in the programs. We would then change the dialogues before the next few students made their attempt. We also discovered that the
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Fig. 10.4 Lesson 1
original dialogue was too long and needed to be split into the two lessons found in Figs. 10.4 and 10.5. By the end of the summer session we had confidence in our dialogues.
10.3.4
Post-test
Comparisons in the fall on a post-test (see Fig. 10.6) with students in a control group indicated significant improvement in student understanding with the CAI instruction. Evaluation was difficult since the dialogue was intended as a tutorial aid and not to teach the subject matter. Data in Table 10.1 indicates students have an improved understanding of the subject material over normal home study. The control group did not take part in the dialogues. The post-test (Fig. 10.6) was administered before
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Fig. 10.5 Lesson 2
any student took the computer assisted instruction dialogue and re-administered after all the dialogue sessions were concluded.
10.3.5
Conclusion
On every question the fractional improvement of students who had taken the dialogue was larger than that of the control group. This itself is strong statistical support that the dialogue had a positive effect on the computer group. In addition, the Mann-Whitney U test was applied to the change in score of each student in each group. The results of this test demonstrate that it is statistically unlikely that the larger improvement of the computer group had occurred by chance.
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Fig. 10.6 Post-test
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10.4 Using the Calculus Dialogue as a Tool to Investigate
163
Fig. 10.6 (continued)
Table 10.1 Evaluation of CAI calculus lessons (fractional increase in score) Question number 1 2 3 4 5 6a 6b 7a 7b 8 9a 9b 10 Computer 0.46 1.0 0.38 1.08 0 0.08 0.69 0.38 0.54 0.85 0.85 0.53 0.08 group Control 0 0.47 0.17 0.52 0 −0.17 0.09 0.54 0.48 0.13 0.35 0 0 group Probability 0.03 0.11 0.14 0.07 –b 0.05 0.09 0.49 0.46 0.002 0.17 0.06 0.22 of increase occurring by chancea a Analysis by Mann-Whitney U test on each question. A comparison of the original scores of both groups by this test for the six questions with the most significant results indicates that the two groups were identical with a probability of 0.49. b No student in either group had any significant improvement in score on this question.
10.4
10.4.1
Using the Calculus Dialogue as a Tool to Investigate the Effects of Correlational Feedback on Learning and to Examine the Interaction of Correctional Feedback with Selected Learner Characteristics Background
Kaufman et al. (1975) utilized the dialogue developed by Kalman et al. (1974) to investigate the effects of correlational feedback on learning and to examine the interaction of correctional feedback with selected learner characteristics. These characteristics were mathematical ability, prerequisite knowledge and anxiety. A secondary focus involved the examination of the effects of anxiety on learning in order to provide support for the Strait Anxiety Theory (Spielberger, 1966; Spielberger et al. 1970).
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This study considered the effect of various learner characteristics on the learning process and in this way attempts to contribute to research efforts in the area of aptitude (or trait) – treatment interactions. The goal of research in this area is to uncover significant interactions between alternative treatments and individual characteristics of learners. Learner variables in this study included mathematical ability, prerequisite knowledge and state anxiety. The research evidence as well as conventional wisdom suggests that the former two variables certainly have some effect on learning. Prior to this study, O’Neil et al. (1969) and O’Neil (1972) had produced some research based upon computer assisted instruction which exhibited evidence in support of Drive Theory. Drive Theory predicts that the performance of highanxiety students would be inferior to that of low-anxiety students on complex or difficult tasks and superior on easy tasks. He also had found that higher levels of state-anxiety were induced in situations in which stress was induced in the students by presenting more difficult materials.
10.4.2
Sample
The experimental subjects consisted of 63 preservice elementary school teachers in the Faculty of Education at the University of British Columbia, Vancouver, Canada. These students were attending a compulsory course in Methods of Teaching Mathematics and volunteers for the experiment were awarded credit towards their final course grade for participating in the experiment. The study was conducted in the month of March, just prior to the end of the course.
10.4.3
Procedure
The total experimental procedure was carried out in two separate periods: 1. Initial lecture and pre-testing session 2. Task period (pre-lesson and main lesson) on a computer assisted instruction terminal followed by post-test and debriefing The experimental subjects completed the task period in groups ranging in size from three to five persons in an isolated, soundproof room. Subjects from each of the three treatment groups worked simultaneously in order to control for extraneous environmental and time variables.
10.4.4
Design
The 63 subjects were randomly assigned to three treatment groups and balanced design was obtained with 21 students in each group. Each group received the same
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content and instructional logic for the computer assisted instruction lesson. The three treatment groups differed in terms of the instructional strategy employed to achieve the main lesson instructional objectives. The difference was specifically in terms of the type of correctional feedback provided to the learner. All three treatment groups received identical information regarding the correct response together with the explanation at some point during the implementation of the particular instructional strategy. The key independent variable in the experiment was correctional feedback and it was informational content of the feedback that was being varied. The other independent variables represented both cognitive and personality characteristics of the students. The cognitive tasks differed in terms of their relationships to the specific computer assisted instruction task. These were mathematical ability and ability to perform on the pre-lesson. The personality variables were both trait- and state- anxiety. State- anxiety was measured at three points during the experiment and trait-anxiety was measured at the beginning. The dependent or criterion variables in this study were post-test score, proportion of errors during learning and average response latency. The latter two were process variables and the former was a product variable. Unanticipated student responses and the number of times the student asked for help were recorded for post-hoc analysis, as well as means and correlations of selected experimental variables.
10.4.5
Pre-lesson
The pre-test used previously has a different emphasis in this experiment. For this reason it is thought of as a pre-lesson. It is not simply a test of student prerequisites, but also instruction in a concept if the student failed to respond correctly (see Fig. 10.2). After the concept was taught, the student was again tested, but on a different example. The pre-lesson had three functions: (a) To provide a measure of the student’s knowledge or ability to learn this particular domain of content in this particular medium (b) To ensure that the student had attained the necessary prerequisites before proceeding to the main lesson (c) To provide practice in working on the computer assisted instruction terminal
10.4.6
Instructional Logic for Main Lesson
A flowchart of the instructional logic used for the three treatment groups on each instructional unit is shown in Fig. 10.1. This instructional logic is a modified version
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of the template developed by Sherman (1971) as discussed in Section 10.2.1. The student is first asked a question and then the student responds, either by asking for help or by attempting to answer the question. If the student types “help”, a hint is given and the student must respond again. If the student types “help” a second time, the student is given the correct answer with an explanation before proceeding to the next instructional unit. If the student responds incorrectly to the question, the program may branch to another question for remedial assistance or may provide correctional feedback. If the student answers the same question incorrectly twice in the same manner, that is falls into the same wrong answer class twice.
10.4.7
Operational Definitions of Treatments
The first treatment group (T1) was instructed precisely according to the instructional logic shown in Fig. 10.1. The deepest level of interaction was attained between the learner and the computer through the instructional program because the nature of the student’s incorrect response was used as the criterion for providing response-sensitive correctional feedback. This feedback was determined by prior analysis of each question by the instructional designer. The second treatment group (T2) received response-insensitive correctional feedback. Each T2 subject was provided with a hint when he/she responded incorrectly. This hint was predetermined and was provided to each T2 subject regardless of the nature of his/her incorrect response. An important criterion for choosing the hint in T2 was that no more information would be provided than could be obtained from all the hints for the corresponding instructional unit in T1. The comment blocks which followed the wrong answers all contained identical comments for a particular instructional unit. The third treatment group (T3) received no correctional feedback information. Each T3 subject was merely informed about the incorrectness of his response and no remedial information was provided. The comment blocks which followed the wrong answers contained no hints, but contained only information telling the T3 subject that his/her answer was incorrect.
10.4.8
Instructional Materials
The subject matter consisted of the concept of the derivative in elementary Calculus and the relationships between the mathematical concept and the physical concepts of distance, speed and time. The lesson could be characterized as a mathematical derivation supplemented by numerical problems which are solved during the lesson. Cronbach and Snow (1969) have suggested that the ideal treatment-set for ATI
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research is likely to consist in applications of some regular instructional material. This suggestion was followed in this study. The prerequisites for the main lesson are given in Fig. 10.3. If a subject had the required prerequisite objective, he/she proceeded immediately to the following item. If not, he/she was instructed and later retested on this prerequisite. A detailed view of the main lesson is found in Figs. 10.4 and 10.5. A sample listing of a portion of a student session (T1) is given in Fig. 10.7.
Fig. 10.7 Portion of one student’s CAI lesson (T1)
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10.4.9
Measurement Instruments
10.4.9.1
Post-test
The 18-item multiple-choice post-test was designed to measure student performance on the objectives of the lesson. This instrument was intended to serve as a criterionreferenced test. Content validity was assured for this test by generating specific items from the list of instructional objectives with due regard given to the relative emphasis given to these objectives in the main lesson. The overall mean number of items correct on the test was 8.95 with three items having difficulty indices of 0.10 or less.
10.4.9.2
Mathematical Ability Test
The cooperative Sequential Test of Educational Progress, mathematics Form 2A (1957), was administered to all subjects at the beginning of the experiment. The norm sample for this form of the test consisted of students in grades 10, 11 and 12 and the test was found to be of appropriate difficulty level for students participating in this experiment. The test consisted of fifty items and was administered in 70 minutes. For the total sample of 63 students, the mean was 31.1, the standard deviation was 7.6 and the coefficient of internal consistence K-R 20 was.85. A logical analysis of the test items seems to suggest that higher-order mental processes, such as problem solving, were being measured and not simply recall of information or application of algorithms. These simpler mental processes were emphasized in the pre-lesson.
10.4.9.3
State-Trait Anxiety Inventory
The State-Trait Anxiety Inventory (STAI) was utilized in order to measure both A-State and A-Trait (Spielberger et al., 1970). The 20-item A-State and A-Trait four point Likert scales were administered at the beginning of the experiment. In addition, a short form of the A-State scale (O’Neil, 1972), consisting of the five items with the highest item-remainder correlations in the STAI normative sample were given during the pre-lesson and during the main lesson. These five items were administered by the computer during the CAI lesson. The 20-item A-State and A-Trait scales have been shown to have high value of reliability, i.e., Cronbach’s Alpha, and evidence of construct validity has been provided (Spielberger et al., 1970). O’Neil (1972) reported reliability (alpha) coefficients for the five-item scale ranging from 0.83 to 0.93 in 17 administrations. The reliability coefficient (Cronbach Alpha) for this group was 0.92 for the 5item A-state instrument, 0.89 for the full 20-item A-State scale, and 0.88 for the A-Trait form.
10.4 Using the Calculus Dialogue as a Tool to Investigate
10.4.9.4
169
Pre-lesson
The grading scheme used for the pre-lesson was discussed earlier. A student received a grade of 0, 1, or 2 on a single instructional unit and there were nine instructional units in the lesson. The pre-lesson was considered as a test of a student’s knowledge and ability to learn the prerequisites required for the main lesson as taught by the computer. The mean score on the pre-lesson was 14.4 out of a possible total score of 18 with a standard deviation of 1.8.
10.4.9.5
Main Lesson
The main lesson was considered as a measure of a student’s ability to perform on a CAI terminal. The student’s errors and latencies were recorded for subsequent analysis. Each instructional unit was also considered as a test item with possible scores of 0 or 1. The students as assigned a value of 0 for an item if the computer provided the correct answer before he answered correctly. If the student answered correctly before being given the answer, he/she was assigned a grade of 1 for that item. The main lesson regarded as a test was not too difficult for these students. The mean score for the group was 10.9 out of a possible score of 15 with a standard deviation of 2.0. This finding shows that most students were able to produce the correct answer before the computer did so, and the lesson was a relatively effective instructor.
10.4.10
Results
10.4.10.1
Analysis
In this study two phases were involved in the analysis of data. The first phase consisted of a regression analysis designed to test the research hypotheses of major interest. The second phase involved some post hoc analysis of the data in order to gain additional insight into the results of the first phase as well as to examine several alternative questions. This second phase involved the examination of intercorrelations for a variety of measures, which were examined for the total group as well as separately for the three experimental groups. Graphs of latencies and errors for the main lesson were also examined for meaningful information.
10.4.10.2
Findings
Correctional Feedback
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The correctional feedback variable had some effect on learning in this experiment. A significant difference (p < 0.03) in proportion of errors was observed between the group receiving response-insensitive correctional feedback (T2) and the group receiving no correctional feedback (T3). The raw means of three groups on most of the variables examined in the study were ranked in the expected order, i.e., T1 > T2 > T3 (see Table 10.2). However, the differences were not statistically significant. The results suggest that the response-insensitive correctional feedback (T2) may be optimal since some helpful information is provided to the student after an incorrect response but prior analysis of all possible responses (and keywords) is not required. This form of correctional feedback requires far less time to prepare by the instructional programmer and much less computer time and storage is used. More definitive results may have been obtained with a lesson having a higher error rate, but this would have been self-defeating since the aim of the program was to help the student succeed. These results suggest that in terms of using CAI in the schools, programmedinstructional materials can emulate the T2 strategy quite easily and cheaply. 10.4.10.3
Mathematical Ability
The variable of mathematical ability had the most evident effect in the study. This variable was highly significant in predicting immediate learning, proportion of Table 10.2 Means of variables for combined groups and for T1, T2, T3 Variable 1. Posttest 2. Time of experimental session 3. Total errors - main lesson 4. Total responses - main lesson 5. Proportion of errors - main lesson 6. Total correct - main lesson 7. do you understand? - main lesson 8. Time to answer -(7) above main lesson 9. Red limit section - main lesson 10. Average first latency - main leson 11. Average total latency - main lesson 12. Enjoyment - main lesson 13. Prelesson score 14. Prelesson correct on first try 15. Average first latency - prelesson 16. Averagge total latency - prelesson 17. Math atility - first testing 18. Full A-State - first testing 19. A-Trait - first testing 20. Short A-State - first testing 21. A-State - prelesson 22. A-Statte - main lesson
Pooled
T1
T2
T3
8.84 1.76 16.63 27.60 0.58 10.90 0.76 83.7
9.19 1.86 14.71 26.48 0.53 11.62 0.71 84.0
8.74 1.81 17.14 28.10 0.57 10.71 0.76 45.9
8.59 1.62 18.05 28.24 0.63 10.38 0.81 121.1
0.79 116.4 189.0 0.63 14.46 6.25 90.3 119.4 31.08 46.9 41.8 9.6 4.9 11.9
0.62 118.0 177.5 0.67 14.71 6.24 81.9 108.2 30.86 47.3 41.3 8.8 4.6 11.2
0.81 123.7 202.7 0.62 14.28 6.10 99.9 134.0 30.24 46.5 43.1 10.2 4.7 12.0
0.95 107.4 186.9 0.62 14.38 6.43 89.2 115.8 32.14 46.8 41.2 9.8 5.3 12.5
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errors and response latency. However, the hypothesized correctional feedback by mathematical ability interaction was not observed for any of the criterion variables. This finding suggests that mathematical ability may not be a useful variable for individualizing instruction and that more specific abilities known to be important to task performance are required. 10.4.10.4
Prerequisite Knowledge
The variable of prerequisite knowledge, as measured on the pre-lesson, was found to be significant in predicting proportion of errors (p < 0.01) only (see Table 10.3). This finding is logical since it would seem that a good predictor of main lesson performance on a CAI lesson during the main lesson would be the performance on CAI pre-lesson. The hypothesized prerequisite knowledge by correctional feedback interaction was not observed for any of the criterion variables. This finding seems to have been caused by the lack of variance in the pre-lesson scores for subjects in the experiment. Most students already had attained the prerequisite objectives and the prelesson served merely as a warm-up for them. 10.4.10.5
Post Hoc Analysis Results
The post hoc analysis provided some useful information for interpretation of the results and suggested some further questions. The correlational analysis also indicated
Table 10.3 Results of regression analysis for proportion or errors Degrees of freedom
Source of variation
Dx2
x3 x6 x4 x5 x1 x2 (x1, x2) x1x3 x2x3 (x1x3, x2x3) x1x6 x2x6 (x1x6, x2x6) x1x5 x2x5 (x1x5, x2x5)
0.094 0.096 0.008 0.068 0.004 0.059 0.063 0.006 0.007 0.13 0.19 0.007 0.026 0.000 0.008 0.008
1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2
Total Error
0.376 0.624
12 50
Fobs
P
0.55) for the T1 and T2 groups suggests that students who find the correct response themselves during the lesson will perform better on the posttest. This result suggests that correctional feedback information is an important part of this learning process. This finding also raises the question about the motivational
Fig. 10.8 Graph of A-State levels during experiment
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properties of correctional feedback since no significant correlation was found when correctional feedback was not provided (T3). The means reported in Table 10.2 indicates that the three treatment groups differed on nearly all of the important variables in he expected direction, but that effects were not statistically significant. The variables referred to are post-test score, total errors, total responses, proportion of errors, total correct, number of students taking optional limit section, enjoyment and main lesson A-State level. The graphs of errors (Fig. 10.9) show that the program had a low error-rate despite efforts by the experimenter to utilize a sample of students who would make many errors. Only one instructional unit had an average of more than two errors for the total group. This instructional unit produced large differences in the unexpected direction between the three groups suggesting that a more difficult lesson may have produced more definitive results. A more difficult lesson could be designed by dealing with more content in each instructional unit than was dealt with in this study. The graph of latencies (Fig. 10.10) shows that the instructional units were uneven in difficulty and that the T2 group took consistently longer on the units in the second half of the main lesson, thereby producing a fatigue effect that may have affected the other results.
Fig. 10.9 Graph of errors on instructional units for T1, T2, T3
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Fig. 10.10 The graph of latencies
10.4.11
Conclusion
The overall conclusion reached in this study was that CAI is an effective and useful medium in which to study the learning and instructional process.
Chapter 11
Summing Up
This book presents the teaching of Science and Engineering Courses at the postsecondary level, and is designed to read like a course in itself. Indeed it can be used as a textbook for a course or read as a course for faculty self-development. Just as in any Science course, I make no attempt to be complete in the historical development of the subject, covering all the developments in Science Educational Research that have occurred in the twentieth century. It is designed to place the neophyte in a position to fully appreciate the twenty-first century stance on the subject and give a fuller appreciation of the subject to those, who are already familiar with the literature. To set the stage for the book, we began in Chapter 1 with some information on the beginnings of science educational research. These beginnings are expanded upon in Chapter 2 to look at some of the actual research that was done in the beginning that laid a basis for current research. That research on intellectual development helps us understand how Vygotsky’s notion of the zone of proximal development (ZPD) relates to classroom teaching. It would seem from the Vygotskian perspective, that it is a mistake to teach on the concrete level to students, who measure on a concrete level on a Piaget type test. According to Vygotsky; “The only ‘good learning’ is that which is in advance of development”. Activities need to be designed to nurture the growth of the student’s functions. It is important to get students to realize that there are viewpoints that are diametrically opposed to their own views. In later chapters, I bring up such a notion in the context of cognitive conflict. Students need to be assisted to examine concepts and problems that are at a higher level than their actual developmental level, but which are nonetheless consistent with their ZPD. Such problems and concepts may be too difficult for them to cope with on their own. The Vygotskian notion is that such students can be scaffolded to successfully grapple with the concepts and problems in a social setting involving the instructor and/or their peers. In Chapter 3, we looked at some of the problems facing a science/engineering student entering a gateway course. Science students hold views different from or alternative to those that they will be taught in their courses. In 1984, seminal papers by McDermott on the one hand and Halloun and Hestenes on the other underlined the necessity for a theory of conceptual change that would provide the underpinnings
C. S. Kalman, Successful Science and Engineering Teaching. © Springer Science + Business Media B.V. 2008
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of new instructional methodologies that could provide enhancements on the knowledge gains on the mechanics diagnostic test devised by Halloun and Hestenes beyond those made by conventional instruction. Attempts at such theories found in this chapter are based upon notions proposed by philosophers of science about how theories change. For that reason, Chapter 6 considers studying philosophers of science to promote critical thinking. To illustrate the practical application of the material introduced in this chapter, we examined a model proposed by Kalman et al. (1999). This model, described in Chapter 4, is based upon the notion of conceptual conflict. Instruction must not only be aimed at showing that the replacement concept is intelligible, but must also first seek to reduce the plausibility of the personal scientific concept. Kalman, Morris, Cottin and Gordon argue that it is far better to get the student to critically analyze the two concepts and come to the realization that the personal scientific concept needs to be replaced. In Chapter 4, we returned to the issue raised earlier in Chapter 3 of the Zone of Proximal Development. It was argued that in addition to peers and faculty, certain kinds of writing can also provide scaffolding for students by encouraging self-dialogue. The idea of reflective writing is to prod students into reflecting metacognitively on the material found in the textbook. Studying a science textbook for the purpose of understanding is often difficult for students because of the extent of the gap between the student’s prior knowledge and the conceptual knowledge demands of the subject matter domain itself. Other obstacles include the density of concepts presented in the textbook, the typical level of abstraction as one moves away from intuitions, based on personal experience, and the strategic demands it places on students to make sense of the content and solve problems. Consequently students normally don’t read the textbook in conjunction with classroom activities, but rather use it as an adjunct to solve problems, picking out what they perceive to be useful solved problems and to be useful pieces of information. Using Reflective Writing, students develop questions about the material which serves as memory markers so that they pick up information from the class that assists them in constructing their understanding of the conceptual underpinnings of the discipline. An issue raised in Chapter 3 was the need for students to critically analyze concepts. In Chapter 5, we began an analysis of developing critical thinking among students. As a practical utilization of the subject, we examined how Kalman et al. (2004) made modifications to the interventions previously explored in Chapter 3 by Kalman et al. (1999) in which the conceptual conflict model was enhanced by the introduction of a writing-to-learn exercise called a critique. The critique was introduced to critically examine alternative possibilities. It is based upon Feyerabend’s principle of counterinduction, which concerns the process by which one theory or idea is used to effect change in its rival. There are indications that in participating in the conceptual conflict activity followed by the critique writing-to-learn exercise students actually increase their critical thinking skills and that with such an improvement students were led to reevaluate their entire conceptual framework. The study of critical thinking was continued in Chapter 6 in terms of philosophy of science. Students need to test their views to see if they are consistent. If students study different philosophers of science they can see that there are different ways of
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seeing the same material. This is a part of their development of their critical thinking skills. Studying how scientists came to examine their views can help students come to examine their own views. One of the purposes in going through a discussion of philosophy of science was to prepare ourselves to look carefully at models of student development that are based upon philosophy of science found in Chapter 7. Kalman (2002) discusses how very important it is that students become aware of how science works so that they can undergo conceptual change; confront their personal (alternative) scientific conceptions. A course discussed in Kalman (2002) is based upon collaborative group work. Groups of 3–5 students are organized with the task of viewing course material through the eyes of a modern philosopher of science: Karl R. Popper, Thomas Kuhn, Imre Lakatos or Paul Feyerabend. The group work is seen as part of the overall attempt to get students to have a better understanding of science. For students to come to grips with the material, they must develop their critical thinking skills. They must come to understand and critically analyze their own views. Only then can they examine the evolution of science and develop ideas about how science works. This chapter concludes with a long excerpt from Tseitlin and Galili (2005) This excerpt relates in an important way to the previous chapter, to the work Kalman (2002) just considered and to the next chapter. This model is not trivial, possessing a high potential for the description of fine features of scientific discourse: a dialogue between different theories, their competition, crises of discourses, scientific revolutions, etc. The most important issue that we considered in Chapter 8 is that developing a Scientific mindset may not simply be a conceptual change from personal scientific concepts to scientifically accepted concepts. It may also be a change in attitude from a view that study in science is a matter of solving problems using an independent set of tools, classified according to problem type, to a view that a science subject consists of a web of interconnected concepts. Thus in Chapter 8 we confronted the issue of changing student’s epistemologies. As Elby (2001) has said “students’ epistemological beliefs-their view about the nature of knowledge and learning affect their mindset; metacognitive practice, and study habits in a physics course”. A major stumbling block in such an effort is that the students do not conceive of the subject in terms of a coherent theoretical framework. Feyerabend (1993) has pointed out that evaluation of a theoretical framework doesn’t occur until there is an alternative (principle of counter induction). The student’s paradigm in the Kuhnian sense is that the subject consists of solving problems using a tool kit of assorted practices. Hence, they do not conceive of the course content in terms of a theoretical framework. We looked at the examination by Kalman and Aulls (2003) of a course that attempts to provide an opportunity for students to see the subject as interconnected not only to accommodate scientific concepts, but also to be effective problem solvers. In this course design students at first view the frameworks almost in a theatrical sense as a view of a drama involving a conflict of actors; various prestigious scientists occurring a long time ago. As participants passing through a series of interventions, the students become aware that the frameworks relate concepts from different parts of the course and learn to evaluate
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alternative frameworks. Helping students to examine their own conceptual framework and make a conceptual change to the framework underlying the course then involves initiating a growth process, which can easily span the entire course. In Chapter 9, we examined the issue of courses for non-science students. One additional activity that has been employed in those courses is the course dossier. Writing in science courses allows students to mediate their own “knowledge” with the new knowledge which the course presents to them. Writing-to-learn and learning to write explores the student’s own doubts, gaps in knowledge and gropings for the answer; only after the student has put something on paper does the professor respond. The course dossier method takes students beyond the reflective writing on the textbook found in Chapter 3 to the use of writing to critically explore the material presented in the class. It has been used in the most advanced undergraduate physics courses and it is particularly useful in science courses designed for nonscience students. The last part of the chapter concerns constellation courses. Such courses attempt to relate science and its developments to history, philosophy, religion, literature, and the social sciences. The last chapter concerns the very important topic of computer assisted instruction. This chapter is based upon my earliest papers in the domain of science/engineering educational research, but I believe they are even more relevant today.
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Name Index
B Boyle, R., 77 Bruner, J. S., 185
C Chi, M. T. H., 97, 98
G Galili, I., vii, 99–109, 112, 131, 177 Gertzog, W., 26, 98–99 Gunstone, R. F., 108
H Haakkarainen, K., 50 Hand, B., 54 Hewson, M., 31, 99, 117 Hewson, P., 26, 31, 98–99, 117 Hewson, P.W., 108
Prain, V., 54 Prigo, R. B., 9
R Redish, E. F., 59, 66 Renner, J. W., 7–9, 11–13 Rosati, P., 6, 12
S Sherman, N., 155–158, 166 Slotta, J. D., 97 Spielberger, C. D., 163, 168 Spradley, J., 140 Sternberg, R. J., 61 Strike, K., 26, 98–99 Strong, J., 78
T Thomson, W., 184 Tseitlin, M., 99–109, 112, 131, 177
L Lord Kelvin, 81
O O’Neil, H. F., Jr., 164, 168
P Paavola, S., 50 Paul, R., 71 Piaget, J., 4, 5, 7–14, 18, 19, 21–25, 27, 29, 79, 102, 115, 175 Pintrich, P., 26, 95 Popper, K. R., 72, 73, 82–84, 87, 88, 100, 102, 145, 177 Posner, G., 26, 27, 96–99, 108
V Viennot, I., 18, 20, 107 Vigotsky, L., 107 Vosniadou, S., 27, 96 Vygotsky, L. S., 7, 13–14, 43, 44, 50, 175
W White, R. T., 108 Wittgenstein, L., 92, 102 Wood, D. J., 14
Z Zieger, L. B., 70 187
Subject Index
A Ability to apply principles garnered from a problem, 4, 7, 8, 35 Accommodation, 19, 27, 29, 30 Alternative personal scientific concepts, 98 Alternative scientific conceptions, 17–42, 59, 61, 63, 69, 93, 96–98, 177 Annotated bibliography of critical thinking resources, 70–71 Assimilation, 19, 27, 29, 79, 99, 109 Auxiliary hypotheses, 79, 82, 113
B Baconian outlook, 74 Baconian principles, 75 Baconian “scientific method”, 76 BioQUEST Curriculum Consortium, 5 Bloom’s taxonomy, 69–70
C Calculus, 4, 50, 73, 96, 100, 146, 157, 158, 163, 166 Change students epistemologies, 111 Chemistry courses, 18 ChemLinks project, 6 Cognitive conflict, 14, 108, 175 disequilibration, 30 Coherent theoretical framework, 95, 111, 177 Collaborative group, 7, 31, 34, 38, 51, 61–64 exercises, 31–32, 61–64, 117, 119, 125, 126 work, 72–73, 177 learning, 33, 38, 61, 117 Compartmentalization, 32, 35, 143
Computer assisted instruction (CAI), 4, 5, 155–161, 163–165, 168, 169, 171, 172, 174, 178 Concept assignment, 53, 117, 120 Conceptual acquisition, 49 change, 17, 25–30, 32–34, 38, 65, 69–72, 74, 75, 93, 95–100, 107–108, 113, 115, 175, 177, 178 conflict, 31–33, 38, 61, 99, 117, 176 conflict exercise, 61, 63, 64, 117, 119, 125, 127, 128 Concrete learners, 10 Constellation courses, 4, 131, 134–152, 178 Contemporary physics: a freshman seminar for physics majors, 146–148 Content processing, 49 Course dossier, 60, 132–134, 178 Critical thinking, 33, 35, 38, 59, 69–93 Critical thinking skills, 35, 59, 61, 64, 65, 71, 72, 113, 176, 177 Critique exercise, 59, 61, 119, 125 Crucial experiment, 73, 76–82 Cultural constructs, 60
D Darwin, 75, 76, 80, 148, 149 Debate of empiricism vs. realism, 71 Debate on general vs. Domain specific critical thinking skills, 71 Demarcation problem, 88–89 Difference between science and pseudoscience and non-science, 69, 79 Discourse knowledge, 46, 49, 50 processing, 49 Discovery learning, 74, 75 Disequilibration, 29, 30
189
190 E Educational research in mathematics, 5 Empiricist tradition in epistemology, 71 Engineering education, 6, 11, 12, 20, 155, 178 Epistemological change, 112 Epistemology, 4, 7, 8, 71, 73, 79, 80, 83, 91, 93, 95, 98, 111–128
F Falsifiability criterion, 82 Feyerabend’s principle of counterinduction, 59, 61, 176 Flexible memory representations, 11 Force concept inventory (FCI), 21–25, 32–35, 62, 63, 96 Framework theories, 27, 96 Freewrite, 47–49, 127
G Gateway courses, 14, 17–21, 26, 95–99
H Hermeneutical circle, 91, 92 Hypotheses non fingo, 75 Hypothetico-deductive method, 76, 80, 82, 144
I Incommensurability, 90, 97–98 Inductive and deductive reasoning, 8 Inquiry-based course, 7, 11 Introductory astronomy courses, 18 Introductory biology courses, 18 Introductory (“gateway”) science courses, 17, 115
J Jung’s Theory of Psychological Types, 11–12
K Knowledge building, 50 Knowledge Telling Model, 45, 46, 50 Knowledge Transforming Model, 45, 47–50, 92
L Lawson Classroom Test of Scientific Reasoning, 21
Subject Index M Mechanics diagnostic test, 17, 21, 25, 96, 176 Memorizing templates, 4, 95 Metacognitive examination, 117, 118 Meyers Briggs indicator, 11 Mini-research paper, 133 Misconceptions, 8, 19, 33, 97 Modern theory of hermeneutics, 91
P Paradigm, 3, 26, 84–89, 95, 102, 104, 107, 109, 111, 112, 127, 137, 144, 177 Paradigm shift science education, 3, 85, 95 Personality type, 6, 12 Personal scientific concept(s), 17, 19, 31–32, 35, 95, 96, 98, 99, 115, 117, 119, 125, 176, 177 Philosophy in physics, 143–145 Philosophy of science, 26, 59, 72, 75, 85, 90, 91, 97, 102, 109, 113, 115, 176, 177 Physics and literature, 135–137 and society in historical perspective, 137–140 Physics Education Group, 5, 18 Physics in philosophy, 143–145 Piggy–backing, 72 Professor-centered approach, 33, 38
R Reflective-writing, 43, 44, 48, 50–53, 60, 133 Reflective writing techniques, 17 Replacement concept, 31, 32, 35, 98, 99, 176
S Scaffolding, 14, 43, 176 Science and Humanities via Science Fiction, 140–143 Science for humanities, 131 Science-humanities courses, 150 Science-humanities course series, 148–150 Scientific mindset, 15, 95, 96, 98, 115, 177 Scientific research program, 87–88, 107 Self-dialogue, 43–45, 47, 176 Structuralist(s), 98 approach, 97–98 framework, 102 Student alternate scientific conception, 17 Student-centred instruction, 11 Student learning problems, 4 Students’ conceptual understanding, 55 Students’ critical thinking skills, 61, 64
Subject Index Students’ epistemological beliefs, 95, 177 Students’ epistemologies, 80, 93, 95, 98 Students personal (alternative) scientific conceptions, 96 Study skills, 3 Subject as interconnected, 111, 115, 177
T Teacher-centred course, 11 instruction, 11 Templates of problems, 11
U Underdetermination, 91
191 W Web of interconnected concepts, 95, 96, 111, 116, 128, 177 What constitutes a “good” scientific theory, 73–74 “What does the teacher want” game, 61 Whig view of history, 93 Workshop on intellectual development, 4 Writing as an aid to encoding information, 120 Writing to learn, 8, 38, 43–56, 59–61, 65, 132, 176, 178
Z Zone of proximal development (ZPD), 7, 13–14, 43, 44, 50, 175, 176
