Symposia on Child Psychology, Volume 7

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY, VOLUME 7

This page intentionally left blank

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY Volume 7

ANNE D. PICK, EDITOR

THE UNIVERSITY OF MINNESOTA PRESS

•

MINNEAPOLIS

©Copyright 1973 by the University of Minnesota. All rights reserved. Printed in the United States of America at Lund Press, Minneapolis.

Library of Congress Catalog Card Number: 67-30520 ISBN 0-8166-0699-4

PUBLISHED IN THE UNITED KINGDOM AND INDIA BY THE OXFORD UNIVERSITY PRESS, LONDON AND DELHI, AND IN CANADA BY THE COPP CLARK PUBLISHING CO. LIMITED, TORONTO

Preface

THE SEVENTH of the annual Minnesota Symposia on Child Psychology was held at the University of Minnesota in October 1972, and the papers in this volume are the contributions of the participants in that symposium. For that occasion, a group of eminent researchers was invited by the members of the Institute of Child Development to present reports of their own research programs and to consider together matters of mutual concern. A variety of topics is represented among the papers of this volume, as among those of earlier volumes. This diversity of contents is intentional, and it reflects the range of interests of those currently engaged in the study of development. Not accidentally, some similarities of emphasis also are revealed among these reports of investigations of quite different problems. Parents and educators share with researchers a desire to identify the effects of socialization practices on children's development. Diana Baumrind's interest is focused on relations between parents' methods of exercising authority and the development of independence and competence in their children. She urges the use of converging strategies; the validity of conceptual and operational definitions of types of parental control can be established by empirical observations of methods of control used by parents and by observations of child behaviors. She has identified patterns of control by parents which are associated with social responsibility and independence in young children, and she suggests specifically that punishment is not necessarily harmful but that it may be an effective means of control under appropriate conditions. C. G. Beer cautions against generalization by analogy from the findings of ethology to questions about human development. Nonetheless, the v

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY strategy used in his own research on vocal communication between parents and young Laughing Gulls can be generalized without modification to the study of development in any species. Having established that young Laughing Gulls recognize by ear their own parents, Beer then studied the development of this individual recognition. He observed its existence in young birds less than 24 hours post-hatching and subsequently documented changes over time in the behavior of the chicks in response to the vocalizations of the parents. He conducted experiments in the laboratory and observations in the settings in which the behaviors under study occur naturally. The use of this procedure allowed him first to validate the existence and course of development of individual recognition and then to interpret it intelligently in the context of social development. A second paper in this volume in which is reflected a concern for identifying relations between socialization practices and child development is that of Norma Feshbach. She hypothesizes that socioethnic differences in socialization practices are functionally related to socioethnic differences in cognitive development. Reinforcement style, the giving of praise and of criticism, is the aspect of socialization studied. It was selected as a general variable, one which can be observed in parents, teachers, and children. First she observed a relation between socioethnic identity and reinforcement style among children and their mothers in one culture. Then she documented the generality of the relation by observing it in two other cultures. Finally, she supported the interpretation of a functional relation between reinforcement style and cognitive performance by finding that mothers of children who had difficulty learning to read used different styles of reinforcement than did mothers of children who read easily. John Hagen and Gordon Hale have collaborated in an investigation of the development of selective attention in children. Two stages of information processing are described. At the first stage, relevant information is identified, and at the second stage, attention to the relevant information is maintained. Hagen and Hale suggest that developmental changes are to be found primarily at the second stage. From the results of a series of studies in which children performed a variety of tasks, it was suggested that, with development, children become more efficient in the use of selective attention. The generality of this account of the development of selective attention and the relation of attention to environmental variables was explored by extending the investigation to other populations. David Klahr uses information-processing models to formulate theories vi

PREFACE

and to test hypotheses about human cognitive development. He constructs models which are specific to an experimental task and which, unlike metaphor models of task performance, are detailed and disprovable by the children whose behavior is being simulated. One goal of this strategy is to propose and to test principles of developmental change based on models containing explicit assumptions about task performance at different times. The tasks for which Klahr has constructed programs for performance include several which derive from the developmental theory of Jean Piaget. Harriet Rheingold proposes a new interpretation of a fact about human infants which is often observed but little noticed. Infants who can locomote leave their mothers to seek out nearby new objects and places. She notes that such separations from the mother are not stressful, at least not for the infant, and she suggests that they be viewed not simply in the context of the dependence of the child on the mother, but as reflections of the emergence of independence in the child. After observing behavior rightfully termed independent during the first year of life, she studied systematically one class of independent behavior during the second year. She recorded children's explorations in a free play situation, and she describes active, eager children who, upon finding new nearby rooms and new toys, spent more time with the toys than with their mothers. The children also shared their discoveries with their mothers, suggesting that "Show and Tell" as well as other components of independent behavior develop much earlier than commonly has been assumed. Financial support for this seventh symposium was provided again by a Public Health Service grant from the National Institute of Child Health and Human Development (HD-01765), by a grant from the Graduate School of the University of Minnesota, and by the Institute of Child Development. In addition, the work of the editor was carried out at the Center for Advanced Study in the Behavioral Sciences, and the support from that institution and from its staff is acknowledged with appreciation. A number of individuals bore responsibility for conducting this sympo sium, a task made more complicated for them by the editor's absence from the scene before the symposium. Helen Dickison was director-inresidence, and she was assisted by John Drozdal, Virginia Eaton, Elizabeth Haugen, and Douglas Sawin among others. The capable staff of the University of Minnesota Press have guided the publication process from manuscripts to book with maximum efficiency. vii

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY Finally, gratitude is extended to the investigators who conducted the research and prepared the papers which are collected here. The talent, conscientiousness, and enthusiasm of these individuals made the editorial task a pleasure. ANNE D. PICK Stanford, California May 1973

viii

Table of Contents

The Development of Instrumental Competence through Socialization BY DIANA BAUMRIND

3

A View of Birds BY c. G. BEER

47

Cross-Cultural Studies of Teaching Styles in Four-Year-Olds and Their Mothers BY NORMA D. FESHBACH

87

The Development of Attention in Children BY JOHN W. HAGEN AND GORDON H. HALE

117

An Information-Processing Approach to the Study of Cognitive Development BY DAVID KLAHR

141

Independent Behavior of the Human Infant BY HARRIET L. RHEINGOLD

178

List of Contributors

205

Index

209

This page intentionally left blank

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY, VOLUME 7

This page intentionally left blank

DIANA BAUMRIND

The Development of Instrumental Competence through Socialization

THE major objective of the program of research to be described here is to identify the effects of alternative patterns of parental authority on the development of instrumental competence in the child. Emphasis will be placed on the upbringing of girls to encourage independence. The program of research has been in progress for over a decade. (Detailed presentations of the research data are found in Baumrind [1967, 197la] and Baumrind & Black [1967].) The young child's development is the result neither of spontaneous maturing of inborn capacities nor of automatic adaptation to programed stimuli. It is, rather, the result of increasingly complex interactions with socializing adults, primarily parents, who, during the early years, have the power to control these interactions. Children are not the originators of their own actions in the sense that adults should be. An adult can contribute to his own development by altering the stimuli which impinge upon him and by defining objectives for himself which, once formulated, then structure his actions. A child, on the other hand, will be presented with stimuli and asked to accomplish goals formulated for him by his upbringers. Innate and maturational predispositions, present at birth, and mediated by neurophysiological processes, interact throughout the individual's life with environmental factors to determine the course of development. Although maturation of the child's nervous system provides opportunities NOTE: The program of research discussed in this paper was supported by the National Institute of Child Health and Development under Research Grant HD02228. 3

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY for development, these opportunities can be realized only in a facilitating social environment designed by knowledgeable adults. Socialization is the process by which the young person, through education, training, and imitation, acquires his culture as well as the habits and values congruent with adaptation to that culture; thus, he attains skill in instrumental and expressive functions. In the studies reported here, instrumental competence is defined by social responsibility, independence, achievement orientation, and vitality. By social responsibility is meant behavior which is friendly rather than hostile to peers, facilitative rather than disruptive of others' work, and cooperative rather than resistive of adult-led activity. By late childhood, the qualities of objectivity and self-control are important correlates of social responsibility. By independence is meant behavior which is ascendant rather than submissive, purposive rather than aimless, and self-determining rather than conforming. By achievement orientation is meant behavior in which the child seeks rather than avoids intellectual challenge and problem solves persistently and efficiently rather than inefficiently and impulsively. Vitality refers to the child's level of biological energy and vigorous appearance. Authoritarian, Permissive, and Authoritative Models of Child Training In 1961,I began to study child-rearing practices associated with instrumental competence in children. In this section, the two studies based upon a typological approach to child rearing will be discussed. The first study, with a small sample, was a pilot study. The second, longitudinal study is still in progress. FIRST STUDY

Methods. Subjects were 32 three- and four-year-olds selected from among all the children enrolled at the Child Study Center, Institute of Human Development, University of California, Berkeley, during the fall semester of 1961. The selection procedures began with the assessment of all the children on five dimensions intended to measure instrumental competence at ages three and four: self-control, approach-avoidance tendency, self-reliance, vitality (from buoyant to dysphoric), and peer affiliation. Each dimension was illustrated and given concrete meaning for the nursery school teachers by reference to relevant time sample categories and by 4

DIANA BAUMRIND

instances of actual observed behavior. After being observed for fourteen weeks, the children were ranked on each dimension both by their nursery school teacher and by the observing psychologist. The 52 children who received one of the five highest or the five lowest rankings on at least two of the five dimensions were observed further, individually, in a laboratory setting where they were given some standardized tasks. For example, one task included three puzzles graded in difficulty so that each child experienced easy success, probable success, and certain failure. Their responses to success and failure were observed and rated on the five dimensions by the testing psychologist and by the observing psychologist. In order for a child to remain in the study, the observing and the testing psychologists' ratings of the child in the two settings had to concur. Using these multiple assessment procedures, three contrasting groups of children were obtained, each with a clear-cut, stable pattern of interpersonal attributes. The three groups of children were selected in order to test a set of hypotheses concerning the interacting effects on child behavior patterns of parental control, parental maturity demands, parent-child communication, and parental nurturance. Pattern I contained all children who were ranked high on Vitality (from Buoyant-Dysphoric), Self-Reliance, Approach-Avoidance Tendency, and Self-Control (6 girls, 7 boys). Pattern II contained all children who ranked low on Peer Affiliation and Vitality and did not rank high on Approach-Avoidance Tendency (7 girls, 4 boys). Pattern III contained all children who ranked low on Self-Reliance, Self-Control, and Approach-Avoidance Tendency (3 girls, 5 boys) (Baumrind, 1967). Each mother-child pair was observed in a two-hour structured teaching experience followed by a play experience in the laboratory setting (see Baumrind, 1967, pp. 68-70 for description of the structured observation). Also, two home visits were made to each family by a psychologist who had not previously rated the child's behavior. The home visits were structured identically for each family, and they occurred during a period from shortly before the dinner hour until just after the child's bedtime. This two- to three-hour period is commonly known to produce instances of parent-child divergence and was selected for observation in order to elicit a wide range of critical control interactions under maximum stress. Each mother and father was interviewed separately and the interviews were tape recorded. These interviews were rated using a fifty-six-item scale based on the scales used by Sears, Maccoby, and Levin (1957). 5

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY Families were rated on a twenty-four-item Parent Behavior Rating Scale (PBRS) based in part on the Fels Parent Behavior Rating Scales (Baldwin, Kalhorn, & Breese, 1949). These observations and interviews were used to rate parent's early activities on four dimensions of child-rearing practices selected for their theoretical importance as possible predictors of competence in preschool children. At the time this study began, considerable concern about the negative effects of strict discipline on children was being expressed, particularly in the clinical and educational literature (Becker, Peterson, Luria, Shoemaker, & Hellmer, 1962; Goodman, 1964; Kagan & Moss, 1962; Maslow, 1954; Neill, 1964; Rogers, 1960). In the study reported here, parental control was defined so that punitiveness and arbitrariness were not components of it. Thus, the effects on the child of strict discipline which was punitive could be distinguished from the effects of equally strict discipline which was neither punitive nor arbitrary. The operational definition of the four dimensions of parent-child interaction derive from observations made in both laboratory and home settings and consist of Summary Ratings for the Structured Observation (SRSO) and Home Visit Sequence Analysis (HVSA). The dimensions are defined as follows: Parental control refers to those parental acts intended by the parent to shape the child's goal-oriented activity; to modify his expression of dependent, aggressive, and playful behavior; and to promote internalization of parental standards. Parental control as defined here is not a measure of restrictiveness, punitive attitudes, or intrusiveness, but is a measure of strict discipline. The behavior of the mother in the teaching and play situations was rated on the following variables from the SRSO: (a) mother consistently enforced house rules (see Baumrind, 1967, p. 69, for description of house rules), (b) mother gave structure to child's activities, (c) mother (apparently) felt in control of the child's behavior, and (d) child acted in accord with mother's stated wishes. Both parents were rated on five HVSA variables. Two examples from the five HVSA variables are as follows (see Baumrind [1967] for a complete description of the variables): Positive Outcome is the percentage of parent-initiated control sequences where the child complies. The purpose of this measure is to assess the parent's ability to enforce directives. Positive Outcome by Persistence is the percentage of total parent-initiated control sequences where the parent achieves compliance after repeating the directive or increasing the use of 6

DIANA B A U M R I N D power, minus those parent-initiated control sequences where the parent does not persist and the child does not comply. The purpose of this measure is to assess the parent's ability to enforce directives when the child initially does not obey. Maturity demands refers primarily to the pressures put upon the child by the parents to perform up to his ability intellectually, socially, and emotionally (independence-training) and secondarily to the leeway given the child to make his own decisions (independence-granting). SRSO variables rated were (a) mother's expectation of child's intellectual attainment, (b) mother's demand for self-reliant child behavior, and (c) mother's demand for self-control on part of child. One example from the four relevant HVSA variables is: Independence Training, Control, the percentage of parentinitiated control sequences where the message concerns cognitive insight into cause-and-effect relations or factual knowledge about the world. The purpose of this measure is to assess the extent to which the parent's control efforts are directed at teaching the child more about natural and social reality. Clarity of parent-child communication means the extent to which the parent uses reason to obtain compliance, solicits the child's opinions and feelings, and uses overt rather than manipulative techniques of control. The SRSO variable items rated were (a) ease and spontaneity of verbal communication and (b) clarity of directives that the mother used. One of the three HVSA variables is Uses Reason to Obtain Compliance, the percentage of parent-initiated control sequences where the parent uses reason with directive. This measures the extent to which the parent offers a reason for a directive before the child objects to the directive. Nurturance refers to caretaking; to those parental acts and attitudes that express love and are directed at guaranteeing the child's physical and emotional well-being. Nurturance is expressed by warmth and involvement. By warmth is meant the parent's love and compassion for the child, expressed by sensory stimulation, verbal approval, and tenderness of expression and touch. By involvement is meant pride and pleasure in the child's accomplishments, manifested by words of praise and interest, and by conscientious protection of the child's welfare. The SRSO variables rated were (a) attentiveness to child; (b) warmth in the form of support, reassurance, nurturance; (c) absence of hostile behavior (such as belittling and sarcasm); and (d) solicitousness in spending time with the child and being involved with his performance and pleasure. One of the three HVSA 7

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY variables rated is Uses Positive Incentive and Reinforcement, the percentage of parent-initiated sequences involving either positive or negative incentives in which the positive reinforcements are used. This score measures the relative use of positive versus negative reinforcement. Results. The results derived from all these measures were as follows: Parents of Pattern I children (children designated mature), by comparison with other parents studied, were controlling and warm. They were rated on all measures as communicating more clearly with their children than did parents of children in either Pattern II or Pattern III. Despite parent behavior ratings indicating high readiness of reinforcement, especially by comparison with parents of Pattern III children, the homes of Pattern I children, according to the ratings, lacked discord and disciplinary friction. According to the interview, these parents used corporal punishment more often (persisting until compliance was obtained), than parents of Pattern III children, but ridicule, frightening the child, and withdrawal of love less frequently (n.s.). However, the parents of Pattern I children used positive reinforcement more than negative reinforcement to obtain compliance. Pattern I children subjected to consistent pressure for mature and obedient behavior were both socially responsible and assertive. This combination of high control and positive encouragement of the child's independent strivings was called Authoritative parental control. Parents of Pattern II children (children designated dysphoric and disaffiliated) were rated as lower on use of rational rather than coercive methods of control and as less nurturant and sympathetic with their children, but not as less controlling, than were parents of Pattern I children. According to interview data (significant only for mothers), the parents were more inclined to give respect for parental authority and a religious belief as reasons for their demands than were parents of Pattern I children. Parents of Pattern II children were rated as more controlling than were parents of Pattern III children. They did not attempt to convince the child through use of reason to obey a directive, nor did they encourage the child to express himself when he disagreed. Their expressed attitudes were less sympathetic and approving, and they more often admitted to frightening the child. These parents who, relative to other parents studied, were detached and controlling and somewhat less warm were called Authoritarian. By comparison with parents of Pattern I children, the parents of Pattern III children (designated immature) behaved in a markedly less controlling manner and were not so well organized or so effective in running their 8

DIANA B A U M R I N D households. According to the interviews, they did not feel in control of their child's behavior or appraise their influence on the child as high. Neither parent demanded much of the child, and fathers were lax reinforcing agents. Parents engaged in less independence training, although they granted the child's demands for independence and, according to ratings, babied their children more. By comparison with mothers of Pattern I (mature) children, mothers of Pattern III (immature) children used withdrawal of love and ridicule rather than overt power, physical punishment, or reason to obtain compliance. The most significant difference between parents of children who were dysphoric and disaffiliated (Pattern II) and parents of children who were immature (Pattern III) is that the controlnurturance ratios were in opposite directions: parents of the dysphoric and disaffiliated children (Pattern II) were more controlling and less warm, whereas parents of the immature children (Pattern III) were less controlling and warmer, although not so warm as parents of Pattern I children. These parents of Pattern III children were called Permissive. SECOND STUDY

In order to replicate and to extend the findings of this first exploratory study, a second study using similar methods and variables was initiated (Baumrind, 197la). The design of Study II differed from the design of Study I in that: (a) Parent-child relationships in Study II were examined for boys and girls separately, (b) Study II, still in progress, is longitudinal. The children are now eight and nine years of age and are being seen a second time. It is hoped to observe them again during adolescence. (c) The subjects in Study II were selected from thirteen nursery schools, privatecooperative, public school—cooperative, as well as university-operated facilities, and thus the sample is more varied than that of Study I. (d) Patterns in Study II were defined by parent scores rather than by child scores. (e) An attempt was made in Study II to identify patterns of parental authority in addition to the three identified in Study I. The distinction between two patterns of parental authority high in control but differing in encouragement of independence and individuality, Authoritarian and Authoritative, was maintained in Study II (Baumrind, 1966; 1968). In addition, a search was made for patterns low in control which would differ in whether lack of control reflected laxness and neglect or an ideologically motivated belief in giving children maximum freedom. Subjects in the second study were enrolled in the fall of 1967 and in the 9

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY spring of 1968 in one of the thirteen nursery schools. Of the 246 families who consented to observation of their children and completed a lengthy Parent Attitude Inquiry, there were 150 who were willing to participate in the home visit phase of the study, and whose nursery school age child obtained a Stanford-Binet IQ score of at least 95 and had no diagnosed developmental anomaly. The final sample consisted of 60 white girls, 74 white boys, and their families and 16 black children and their families.* By comparison with the population from which it was drawn, the sample contained children who were more cooperative and fathers who were less authoritarian. Child Behavior Clusters. During a period of three to five months, an observer recorded the interpersonal and social behavior of the children as they engaged in activities in nursery school. In addition, each child was rated while taking the Stanford-Binet. The entire protocol describing the child's behavior over the school semester and while taking the StanfordBinet was used to make ratings. In a previous study (Baumrind & Black, 1967), a two-dimensional, eight-cluster model of preschool behavior was developed. Analyses of the behaviors described in the protocols of this study were directed at determining the dimensionality of the behavior space covered by the items and its similarity to the previous model. As in the previous study, the first two clusters from a BC TRY (Tryon & Bailey, 1966) cluster analysis were uncorrelated. They accounted for 89 per cent of the mean of the squared original correlations for both sexes and for over 65 per cent of the initial estimate of communality. This more than met the criteria for a two-dimensional model. A principal-components solution was used to provide the most stable two-factor solution. Then all Q-sort items were plotted in this two-factor space with their factor coefficients used as coordinates. The items were formed into clusters on the basis of position on the circular plot, pattern of intercorrelation of contiguous items, and similarity of pattern for both sexes. The actual ordering of the six empirical clusters and a seventh overlapping cluster of theoretical interest is illustrated in Figure 1. Parent Behavior Clusters. Information about family interaction was obtained from observations and interviews in the home as in Study I (BaumThe data for the black children and their families were analyzed separately because the parent-child relationships were, as expected, not the same as for whites.

10

DIANA B A U M R I N D

rind, 1967). Fifteen constructs, rather than four as in Study I, described the relevant parental behaviors. Fifty Parent Behavior Rating (PER) scales were devised to assess the behavior of mother and father separately; twenty-five additional scales were devised to measure the joint influence of the parents. Each of the fifteen constructs was itself defined as a dimension so that the observers could summarize their impressions of the family by rating the family on the dimension. The items defining the constructs were subjected to the BC TRY cluster analysis procedures. The major empirical clusters which emerged are described as follows in terms of the initially conceived constructs. a. Firm Enforcement. This cluster included items which had been constructed to measure Firm versus Lax Enforcement Policy, and Obedience

Figure 1. Child behavior model, sexes combined, nursery school setting. Dashed lines inside circle represent principal axes from previous study (Baumrind & Black, 1967). 11

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY as a Salient Positive Value versus Obedience as a Nonsalient Negative Value. The mother and father solutions were closely comparable. b. Encourages Independence and Individuality. This second cluster was designated Encourages Independence and Individuality for both parents, although more than half of the defining items differ for the mother and the father. For the mother, all but two defining items had been constructed to measure three related constructs — Encourages versus Discourages Independence, Encourages versus Discourages Verbal Exchange and Use of Reason, and Promotes Individuality versus Social Acceptability. For the father, items defining Encourages versus Discourages Verbal Exchange and Use of Reason were important. In addition, the Flexibility and Clarity versus Inflexibility and Lack of Clarity of Parent's Views, and Confidence versus Lack of Confidence in Self as a Parent were prominent components of Father Cluster 2. c. Passive-Acceptant. For both parents, the majority of the items defining the Passive-Acceptant cluster were drawn from items devised to measure Willing versus Reluctant to Express Anger or Displeasure to Child. These items were intended to measure parental inhibition of aggression and to reflect passivity and mildness in the parent. d. Rejecting. Clusters designated Rejecting measured for both parents Expresses Punitive versus Nurturant Behavior. e. Father Promotes Nonconformity; f. Father A uthoritarianism. For the father, two additional clusters emerged which did not have their counterparts in clusters for mothers. The cluster designated Promotes Nonconformity was composed almost entirely of items designed to measure Promotes Individuality versus Social Acceptability. The cluster designated Authoritarianism was defined primarily by items designed to measure Encourages versus Discourages Independence, and Promotes Respect for Established Authority versus Seeks to Develop a Cooperative Working Relationship with the Child. g. Mother Cluster: Self-Confident, Secure, Potent Parental Behavior. Items in this cluster were designed to assess Flexibility and Clarity versus Inflexibility and Lack of Clarity of the Parent's Views, and Confidence versus Lack of Confidence in Self as a Parent. h. Five Joint PBR Clusters. An additional cluster analysis was performed on the twenty-five items devised to define five constructs describing the parents' joint conduct. The items intended to define operationally the five theoretical constructs emerged almost intact in the empirical clus12

DIANA BAUMRIND

ter analyses, except that Discourage Emotional Dependency was defined by only two of the items and was therefore quite limited in its meaning. These five joint clusters were designated Expect Participation in Household Chores; Enrichment of Child's Environment; Directive; Discourage Emotional Dependency; and Discourage Infantile Behavior. Pattern Definitions. Families were typed on the basis of their patterns of scores on these Parent Behavior Rating clusters: 54 families of white boys and 48 families of white girls were assigned to patterns. Most of the families not assigned had cluster scores which resembled one or another pattern in shape, but failed to meet the criteria for magnitude of scores. These patterns of parental authority were defined to produce contrast groups of families corresponding to more refined definitions of the patterns described in Study I. The focus here is on four theoretically interesting patterns, two high on control and two low on control. The two high on control are designated Authoritarian and Authoritative. The two low on control are designated Permissive and Nonconforming. Conceptual and operational definitions of the terms Authoritarian, Authoritative, and Permissive follow. The fourth term, Nonconforming, is defined operationally but not conceptually because it was originally conceived as a variant of Permissive upbringing. The Authoritarian parent values obedience as a virtue and believes in restricting the child's autonomy. This parent values the preservation of order and traditional structure as an end in itself. He or she does not encourage verbal give and take, believing that the child should accept the parent's word for what is right. In defining this pattern operationally, it was required that parents have scores above the median on Firm Enforcement, below the median in Passive Acceptant, and below the median in Encourages Independence and Individuality, and that the father score in the bottom third on Promotes Nonconformity or the top third on Authoritarianism. The Authoritative parent attempts to direct the child's activities in a rational, issue-oriented manner. Both autonomous self-will and disciplined conformity are valued by Authoritative parents; they affirm the child's present qualities but also set standards for future conduct. They use reason, power, and shaping by regime and reinforcement to achieve objectives. In defining this pattern operationally, it was required that Authoritative parents have scores above the median in Firm Enforcement, below the 13

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY median in Passive-Acceptant, and above the median in Encourages Independence and Individuality. The Permissive parent behaves in an affirmative, acceptant, and benign manner toward the child's impulses and actions. The aim of the ideologically aware Permissive parent is to give the child as much freedom as is consistent with the child's physical survival. Freedom to the Permissive parent means absence of restraint. As in the previous study, it was not possible to find a group of parents who corresponded precisely to the prototypic Permissive parent described above because many noncontrolling, passive-acceptant parents were also cool or uninvolved. The criteria were: scores below the median on Firm Enforcement, above the median on Passive-Acceptant, below the median on Expect Participation in Household Chores, and below the median on Directive. The criteria for assignment to the category Nonconforming were that both parents score in the top third of the distribution on Encourages Independence and Individuality or father scores in the top third on Promotes Nonconformity and in the bottom third on Authoritarianism. These parents were anti-authoritarian and some were anti-authority, but they did make demands on their children. The data for these parents are presented separately because Nonconforming parents differed from Permissive parents in that the former were less passive and exerted firmer control than the latter. Results. Comparisons among the four patterns on the fifteen constructs are illustrated in Table 1 — in Part A for parents of girls, and in Part B for parents of boys. Numbers refer to mean scores with a possible range of from 1 to 5 (see Baumrind [197la], pp. 82-83, for Ns and SDs). In Table 2, relations between patterns of parent behavior and child behavior are summarized — in Part A for girls and in Part B for boys. Numbers refer to cluster scores obtained from a sample with a mean of 50 and a standard deviation of 10 (see Baumrind [1971a], pp. 56-58, for Ns and SZ)s).Six comparisons of child-rearing practices and the related differences in child behavior for girls and boys will be discussed: (a) Authoritarian versus Authoritative; (b) Authoritarian versus Permissive; (c) Authoritarian versus Nonconforming; (d) Authoritative versus Permissive; (e) Authoritative versus Nonconforming; and (/) Permissive versus Nonconforming. a. A uthoritarian versus A uthoritative. It can be seen in Part A of Table 14

DIANA B A U M R I N D 1 (A versus B) that Authoritarian parents of daughters in comparison with Authoritative parents did not enrich their child's environment or present her with a flexible, clear position. The Authoritarian parents discouraged independence and verbal exchange, and did not promote individuality. They were relatively punitive. It can be seen in Part A of Table 2 (A versus B) that daughters of Authoritarian parents were significantly less Dominant and Independent, and were somewhat less Domineering, Purposive, and Achievement Oriented than were' the daughters of Authoritative parents. It can be seen in Part B of Table 1 (A versus B) that Authoritarian parents of sons by comparison with Authoritative parents did not enrich their child's environment or present him with a flexible, clear position. The Authoritarian parents were less firm in enforcing directives, and they promoted greater respect for established authority. They lacked confidence in themselves as parents, discouraged independence and verbal exchange in their sons, and did not promote individuality. They were relatively more punitive. In Part B of Table 2 (A versus B) it is seen that the sons of Authoritarian parents were significantly more Hostile, Resistive, and less Achievement Oriented than were sons of Authoritative parents. (Because sons of Authoritarian parents had significantly lower, although also above average IQ'S, and IQ scores were positively correlated with Achievement Orientation in this sample, intelligence cannot be ruled out as a significant source of the differences in these attributes defining competence.) b. Authoritarian versus Permissive. In Part A of Table 1 (A versus C) it is seen that Authoritarian parents of girls by comparison with Permissive parents were more directive, more likely to discourage emotional dependency, firmer in enforcing directives, valued obedience more, and promoted respect for established authority. The Authoritarian parents discouraged independence and verbal exchange. They were more willing to express anger, did not promote individuality, and demonstrated relatively punitive behavior. From Part A of Table 2 it is seen that these numerous differences in child-rearing practices showed no reliable relations with behaviors of the preschool girls studied. Authoritarian parents of boys by comparison with Permissive parents (Table 1, Part B, A versus C) expected more participation in household chores, were more directive, and were firmer in enforcing directives. They valued obedience more and promoted respect for established authority. They discouraged independence and verbal exchange. They were more 15

Table 1. Pattern Comparisons for Fifteen Parent Behavior Rating (PER) Constructs Pattern Mean Scores A. Authoritarian B. Authoritative C. Permissive IV. Nonconforming H. Harmonious A vs. others" A vs. B A vs. C A vs. IV A vs. H B vs. others0 B vs. C B vs. IV B vs. H C vs. others0 C vs. IV C vs. H IV vs. others0 H vs. others0

I

II

III

IV

V

34 3.6 2.6 3.4 3.2

1.6 2.9 2.0 3.2 2.6

3.1 3.2 2.1 2.8 2.0

3.1 3.1 2.6 3.0 3.0

2.8 3.1 2.1 2.5 3.0

10

.05

. .

.05

.01 .01 .01 .05 .05 .05

.05 .05

.10 .01

.05

.05 .05 .01

.10

.01 .05

.05

.05

VI

PER Constructs" VII VIII IX PART A. GIRLS

X

2.4 3.6 3.9 2.9 3.3 3.5 3.6 3.4 2.7 3.6 2.6 1.9 2.4 1.6 2.7 4.0 2.6 2.6 1.2 3.6 3.3 1.8 1.2 3.5 Significant Pattern Differences* .05 .05 .01 .01 .05 .01 .01 .01 .05 .05 .01 .01 .10 .01 .01 .01 .05 .10 .10 .01 .01 .01 .01 .01 .05 .01 .01 .05 .05 .01 .05 .05 .01 .10 .10 .10 .10 .05 .01 .05

XI

XII

XIII XIV

XV

2.1 3.6 3.7 3.8 3.7

2.3 3.8 3.8 4.4 4.3

3.3 3.1 2.1 3.3 2.5

3.3 2.5 2.5 2.0 2.3

.01 .01 .01 .01 .01

.01 .01 .01 .01 .01

.05 .01 .10

2.1 3.1 3.1 3.4 4.0 .01 .01 .05 .05 .01

.01 .01 .01 .01 .01

.01 .01 .05 .10 .10

.05 .05 .01

.10

Table 1 — Continued PER Items'1 I

Pattern

II

III

IV

V

VI

A. Authoritarian B. Authoritative C. Permissive IV Nonconforming

3.9 4.4 2.7 3.0

0

A vs. others A vs. B A vs. C A vs. IV B vs. others0 B vs C B vs. IV C vs others0 C vs. IV IV vs others0

VII

VIII

IX

X

XI

XII

XIII XIV

XV

3.3 3.9 2.6 3.5

2.4 3.2 3.3 3.6

2.6 3.8 3.5 3.6

3.1 3.4 2.2 3.0

3.6 2.4 3.0 2.0

PART B. BOYS

Mean Scores

.01 .10 .01 .01 .05 .01

1.6 2.8 1.9 2.7 .01 .01 .01 .01 .01 .05 .10

3.0 3.3 2.5 2.8

3.1 3.1 2.9 3.0

2.7 3.2 2.0 2.9

.10 .05 .01 .01 .05 .01 .10

.05 .01 .01 .05

2.5 3.6 2.5 3.5

3.9 4.6 2.1 3.0

3.8 3.6 2.5 1.8

3.2 2.8 2.1 1.7

Significant Pattern Differences13 .05 .05 .01 .01 .01 .05 .05 .01 .01 .01 .10 .05 .01 .01 .01 .01 .01 .01 .01 .01 .05 .05 .01 .01 .01 .01 .10 .01 .05 .05 .01 .05 .10 .05 .01 .01

.01 .05 .05 .01

.01 .01 .01 .01 .05

.05 .01 .01 .10 .01 .05

2.2 3.2 3.5 3.8 .01 .01 .01 .01

.01 .01 .10 .01 .05 .10 .10 .01

"PBR items are: I, expect participation in household chores; II, enrichment of child's environment; III, directive; IV, discourage emotional dependency; V, discourage infantile behavior; VI, flexibility and clarity of the parent's views; VII, firm enforcement; VIII, obedience as salient positive value; IX, promotes respect for established authority; X, confidence in self as parent; XI, encourages independence; XII, encourages verbal exchange; XIII, willing to express anger; XIV, promotes individuality; XV, expresses punitive behavior. b There were no significant differences for IV vs. H. c Others refers to all subjects of the same sex whose families were visited except those in the pattern under consideration.

Table 2. Pattern Comparisons for Q-Sorl Clusters and IQ Scores"

IQ

Q-Sort Cluster Pattern

I

III

II

IV

V

VI

Score VII Means

PART A. GIRLS A. Authoritarian (N = 10) . B. Authoritative (N = 11) . C. Permissive (N = 11) ... IV., Nonconforming (AT = 5) H. Harmonious (N = 6)

A vs. others" A vs. B A vs. H B vs. others'1 B vs. C B vs. IV B vs. H C vs. othersb C vs. H IV vs. others" IV vs. H H vs. others'5

-

46.8 50.2 50.4 52.5 40.2

47.6 52.4 50.6 45.7 44.5

46.0 48.,6 49.1 47.6 44.7 54.8 56..6 55.0 54.3 56.7 48.1 46.,2 45.0 50.4 48.5 42.3 40,.2 44.3 47.1 41.0 48.1 54.,1 56.2 58.6 56.3 Significant Pattern Differences

10

.10

.05

.10

.05

.01

.05

.01

.05 .05 .05

.05

01 .05 .01

05

.05

.10 .05

.10 .05

.10

.10 .10

.10 .05

.10 .01 .01 .05 .10 .01

122.6 132.7 128.3 129.8 135.8 .10 .10

.05 .01

PART B. BOYS A. Authoritarian (N ~ 16) . B. Authoritative (N =14) . C. Permissive (N = 11) . . . IV. Nonconforming (N = 8) A vs. others" A vs. B A vs. IV B vs. others" B vs. C B vs. IV C vs. others" C vs. IV IV vs. others

52.7 43.1 52.4 50.8

50.6 49,.4 50.7 47..6 47.4 46.0 51..9 54.2 56.,1 50.3 51.3 48..0 47.1 44..3 45.6 48.8 52,.8 51.1 57.,3 57.2 Significant Pattern Differences .10

5.1..1 43.,7 52,.1 46.,3

05

.05

01 05 10

.05 .05

.10

.01 .05 .05

.01

115.9 128.9 121.0 131.4 .05 .05 .05

.01

.01 .01 .05

.05 .05

.10

NOTE: 0-Sort Clusters are: I, Hostile-Friendly; II, Resistive-Cooperative; III, Domineering-Tractable; IV, Dominant-Submissive; V, Purposive-Aimless; VI, Achievement Oriented; VII, Independent-Suggestible. " Pattern comparisons which were not significant have been omitted. b Others refers to all subjects of the same sex whose families were visited except those in the pattern under consideration.

18

DIANA BAUMRIND

willing to express anger and did not promote individuality. As with the girls, these numerous differences in child-rearing practices showed no significant relations with the boys' behavior. Such differences for boys as did exist were in the opposite direction from that for girls — that is, sons of Permissive parents were less Achievement Oriented and Independent (despite their higher IQ'S) than were sons of Authoritarian parents. c. Authoritarian versus Nonconforming. Authoritarian parents of girls by comparison with Nonconforming parents (Table 1, Part A, A versus IV) did not enrich the child's environment or present their daughters with a flexible, clear position. The Authoritarian parents were firmer in enforcing directives, valued obedience more, and promoted respect for established authority. They discouraged independence and verbal exchange, and did not promote individuality. They were more punitive. There were no significant differences between the two groups in their daughters' behavior at this age. However, it is of interest that the girls reared by Nonconforming parents were actually less Dominant and Purposive than daughters of Authoritarian parents. If the aim of Nonconforming parents was to encourage independence and individuality by their methods of upbringing, they apparently failed to achieve this objective. As can be noted from Table 1 (Part B, A versus IV), Authoritarian parents compared with Nonconforming parents of boys differed significantly along the same dimensions of child rearing as did the respective parents of girls. Unlike daughters, sons of Authoritarian when compared with Nonconforming parents (Table 2, Part B, A versus IV) were significantly less Achievement Oriented and Independent. (Again, IQ differences cannot be ruled out as a source of these differences.) d. Authoritative versus Permissive. Authoritative parents of girls by comparison with Permissive parents (Table 1, Part A, B versus C) expected more participation in household chores, enriched the child's environment, and were more directive. They were firmer in enforcing directives, valued obedience more, were more likely to promote respect for established authority, and had more confidence in themselves as parents. They were more willing to express anger. The daughters of Authoritative parents (Table 2, Part A, B versus C) were significantly more Dominant and Purposive and somewhat more Independent than daughters of Permissive parents. Authoritative parents of boys differed significantly from Permissive 19

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY parents of boys (Table 1, Part B, B versus C) in the same way as the respective parents of girls. In addition, the Authoritative parents of boys discouraged infantile behavior and presented the child with a position which was clear and flexible — both to a greater degree than Permissive parents of boys. Sons of Authoritative families (Table 2, Part B, B versus C) were significantly less Hostile and Resistive and were more Achievement Oriented than sons of Permissive parents. Also, the sons of Authoritative parents were somewhat more Purposive than sons of Permissive parents. e. Authoritative versus Nonconforming. Authoritative parents of girls by comparison with Nonconforming parents (Table 1, Part A, B versus IV) were firmer in enforcing directives and were more likely to value obedience and to promote respect for established authority. Daughters of Authoritative parents (Table 2, Part A, B versus IV) were significantly more Domineering, Dominant, Purposive, and Independent than were daughters of Nonconforming parents. Authoritative parents of boys differed significantly from Nonconforming parents of boys (Table 1, Part B, B versus IV) in all the ways indicated for girls. In addition, Authoritative parents expected more participation in household chores and were more directive. The sons of Nonconforming parents were somewhat less Friendly than sons of Authoritative parents (Table 2, Part B, B versus IV), but their scores were near the mean for the total sample. The differences were due to the very low scores of the sons of Authoritative parents on the Hostile-Friendly cluster. /. Permissive versus Nonconforming. Permissive parents of girls by comparison with Nonconforming parents (Table 1, Part A, C versus IV) did not enrich their daughters' environment and were less willing to express anger. These differences between the two groups of parents both low in control were not related to differences in their daughters' behaviors. Permissive parents of boys, by comparison with Nonconforming parents (Table 1, Part B, C versus IV) did not enrich their sons' environment or discourage infantile behavior. The Permissive parents failed to present their sons with a flexible, clear position; lacked confidence in themselves as parents; and were less willing to express anger, although somewhat more punitive. The sons of Permissive parents, in comparison with sons of Nonconforming parents, were significantly less Achievement Oriented and Independent (Table 2, Part B, C versus IV). 20

DIANA B A U M R I N D EFFECTS OF AUTHORITARIAN, AUTHORITATIVE, PERMISSIVE, AND NONCONFORMING UPBRINGING

In both studies, the direction of the effects of Authoritative child rearing when compared with Permissive or Authoritarian upbringing on the development of competence denned by social responsibility and independence was generally positive. In Study I, boys and girls who were socially responsible (i.e., nondisruptive with adults and affiliative with peers) and independent (i.e., approach-oriented, self-reliant, and buoyant) had parents who were classified as Authoritative. In Study II, Authoritative parental behavior was associated with independent, purposive, dominant, and achievement-oriented behavior in girls and with all indices of social responsibility in boys. There was some indication that the extremely firm control of Authoritative parents, even when compared with that of Authoritarian parents, impaired the development of independence in otherwise highly competent boys — namely, sons of Authoritative parents did not have above average scores on Independence. In both studies, the differences were more marked between children reared authoritatively and those reared either permissively or in an authoritarian manner than were the differences between children reared in a permissive and those reared in an authoritarian manner. Permissive and Authoritarian parents differed in the control-nurturance ratio (with Permissive parents higher in nurturance and Authoritarian parents higher in control). But both differed significantly from Authoritative parents in that the Permissive and Authoritarian parents lacked confidence in their childrearing practices, did not enrich their children's environment, and, for boys, did not have a clearly defined child-rearing policy. Both Permissive and Authoritarian parents lacked balance between what was offered to the child in the way of support and what was demanded of him in terms of obedience. True, the imbalance was in opposite directions, but it was difficult to distinguish between the effects of these two kinds of imbalance, at least in the preschool years. Authoritative parents, by contrast, balanced what they offered with what they demanded. They balanced high control with high independence-granting, high standards for maturity with much support and nurturance. It will be of interest to see whether this early experience with reciprocity in human relations is associated at later time periods with accelerated attainment of post-conventional morality. The distinction made in Study II, but not in Study I, between Permissive and Nonconforming parents, both relatively noncontrolling, proved pro21

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY ductive with boys. Sons of Nonconforming parents were significantly more achievement oriented and independent than were sons of Permissive parents. For boys, the firmer control, higher maturity demands, and clearer philosophy of the Nonconforming parents resulted in achievement orientation and independence. By contrast, Nonconforming parents produced daughters who were less rather than more achievement oriented and independent than daughters of Permissive parents, although not to a significant degree. While Nonconforming mothers of boys did not see themselves as victimized by society, these particular Nonconforming mothers of girls saw themselves as pawns of forces they could not control (attitudes expressed during interview about their sex roles). Because of their considerable reluctance to either punish or place high demands upon their daughters, it is possible that Nonconforming mothers did not provide a strong model or train their daughters in instrumental functions and that these were reasons for their daughters' relative incompetence.

Socialization Practices Associated with Dimensions of Competence in Preschool Girls and Boys The objective of Study III was to identify parent dimensions and variables associated with instrumental competence in preschool children. In Studies I and II, a typological approach to data reduction was used in order to reveal the relations between contrasting configurations of parent variables and child behaviors. That the relation with child behavior of a particular parent behavior depends upon the total configuration of variables has been demonstrated. For example, it was shown that the relation of high parental control to social responsibility and independence in the child depends upon the extent to which the parent also encourages individuality and independence; thus, the distinction between the effects on the child of Authoritarian versus Authoritative control. A correlational study can specify the general effect on the child of a theoretically interesting parent dimension. If there is no effect seen for a parent variable thought to have a universal linear effect, or if an effect is seen but the direction is opposite to that which would be postulated as universal by a currently popular child-rearing belief or theory, the validity of that belief or theory may properly be questioned. In Study III, subjects were 95 new sets of parents and their preschool children. Data were analyzed separately for boys and girls. Behavioral 22

DIANA BAUMRIND

and interview data on parents were derived first from home visits and are in the form of discrete HVSA variables as in Study I (only 9 of the 18 variables used in Study I were computed for Study III) and second from PARENT INTERVIEW DIMENSIONS arrived at through cluster-analytic techniques. Data on children were derived from prolonged observations in nursery school and structured settings and consist of g-sort ratings. A child-behavior model (similar in structure to models presented by Schaefer [1961] and Becker & Krug [1964]) was developed and its relation to these parent measures was assessed. The Q-sort clusters in Figure 1 to which they correspond will be listed in parentheses after the name. The names given the Q-sort clusters in the four-cluster solution described in Baumrind and Black (1967, p. 297) were Disafnliative-Affiliative (I), Resistive-Cooperative (II, III), Independent-Dependent (IV, VII), and Assertive-Withdrawn (V, VI). The following relationships (significant at W* B>W** B>W*

B>W**

SOURCE: Reprinted by permission from D. Baumrind, "An Exploratory Study of Socialization Effects on Black Children: Some Black-White Comparisons," Child Development, 1972, 43, 264 (Table 1). b *N = 5. N=10. *p value VALOF (object, attribute) -» value/nil ATTOF (value) -> attribute Secondary SAMEANY (object x, object y) -» value/nil DIFANY (object x, object y) -> attribute/nil FINDONE (value, set) -> object/nil Tertiary FINDALL (value, set) -» list of objects PAIRSAME (set) -> object x, object y, value/nil PAIRDIF (set) -> object x, object y, attribute/nil COUNT (set, value) -> number NOTE: Reprinted by permission of Academic Press, Inc., from D. Klahr and I. G. Wallace, "An Information Processing Analysis of Some Piagetian Experimental Tasks," Cognitive Psychology, 1970, 1, 367.

We postulated a basic set of these fundamental processes in a paper dealing with several of Kofsky's classification tasks (Klahr & Wallace, 1970). They are listed below in terms of their input-output relationships. These fundamental processes can be used as the building blocks in writing the task-specific routines as computer programs. The verbal model 147

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY for exhaustive sorting can be more precisely stated in the form shown in the second accompanying list. The routine, called EC, is written in an ALGOL-like language called POP-2 (Burstall, Collins, & Popplestone, 1968), and consists almost entirely of calls upon the fundamental process. All that remains indigenous to EC are the control statements that determine the sequence of events and the variables needed to store information about the results of the subprocesses. function EC set = > olst; vars obx valx attl; NOTICE (set) -» obx; PLACE (obx, olst); NOTICE (obx) -»valx; FINDALL (valx, set) -» olst; ATTOF (valx) -> attl; loop: NOTICE (set) -* obx; PLACE (obx, olst); //obx = nil then exit; VALOF (obx, attl) -> valx; FINDALL (valx, S6t) -> olst;

goto loop end; NOTE: Reprinted by permission of Academic Press, Inc., from D. Klahr and J. G. Wallace, "An Information Processing Analysis of Some Piagetian Experimental Tasks," Cognitive Psychology, 1970, 1, 374.

There are three classes of fundamental processes shown in the first list. The primary processes represent the lowest level of explanation: they are defined in terms of the functional relations between input and output, but no model for their actual operation is presented. These are processes which are not yet analyzed but which, presumably, are analyzable. The other fundamental processes are defined in terms of the primary processes. For example, in the accompanying list FINDALL consists of repeated calls upon FINDONE, which in turn calls NOTICE and is. The list also illustrates a crude attempt to include motivational mechanisms in our performance models. The DRIVE and LIMIT represent an extremely simple means of accounting for the fact that children's performance is partly a function of their motivation to do the task presented to them. We have described the specifics of their operation (Klahr & Wallace, 1970a); here we simply note the fact that information-processing theories can include such variables (see also Simon, 1967). function FINDONE val set -» obj; loop: NOTICE (set) -» obj; /'/ is (obj, val) then exit; if. DRIVE then goto loop else LIMIT (obj) exit end; function FINDALL val set —> olst; vars ob; loop: FINDONE (val, set) -» ob; PLACE (ob, olst); // ob -> nil then exit; if. DRIVE then goto loop else exit end; NOTE: Reprinted by permission of Academic Press, Inc., from D. Klahr and J. G. 148

DAVID KLAHR Wallace, "An Information Processing Analysis of Some Piagetian Experimental Tasks," Cognitive Psychology, 1970, 1, 370.

A Basic Model. Although it seems implausible to assume that children have stored in long-term memory task-specific processes such as EC, it does seem plausible to assume that by the time they reach the age range under consideration, they have some functional equivalent of at least the primary processes. The child has a twofold problem when novel tasks are presented. First he must assemble, from his repertoire of fundamental processes, a task-specific routine that is sufficient to pass the task at hand; then he must execute that routine. A schematic view of this basic model is presented in Figure 1. Failure can be attributed to any of three causes: the absence of the appropriate fundamental process, the inability of the assembler to put together the appropriate fundamental processes, or failure to correctly execute the task-specific routine. Determination of the adequacy of the fundamental process repertoire suggests a logical and empirical analysis similar to the tradition of task analysis (Gagne, 1970; Glaser & Resnick, 1972; Resnick, Wang, & Kaplan, 1970). However, our approach places greater emphasis upon the dynamic processing demands of task components than upon the purely

Figure 1. An assembler model of task performance. (Reprinted by permission from D. Klahr and I. G. Wallace, "An Information Processing Analysis of Some Piagetian Experimental Tasks," Cognitive Psychology, 1970, 1, 362.) 149

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY logical components. For example, the analysis yields predictions about the effects upon the response times of the number of objects in the stimulus display. Failures in cognitive synthesis (Farnham-Diggory, 1970) provide striking examples of situations where, although requisite subprocesses exist, the full task cannot be successfully performed. Whether to attribute this to assembler failures or to the limited capacity of the system to execute the (correctly assembled) routine is an unresolved issue (FarnhamDiggory, 1972; Simon, 1972). Furthermore, the level of generality of both the assembler and the fundamental processes with which the assembler works is itself a complex issue. Several possible dichotomies between what the subject brings to the experiment and what he constructs at "runtime" have been suggested by Newell (1972a). Failures to execute appropriately assembled task-specific routines can be attributed to at least two sources. The inclusion of some simple motivational mechanisms allows us to sweep many performance failures under this general heading of motivation. The unsatisfactory nature of this category can be improved only by elaborating the current mechanisms into an information-processing motivational model (Simon, 1967). The second source of failures of execution lies in the processing demands made by the routines. It is possible for a computer program that controls a real-time device to be logically correct, but to fail to run because of speed or storage limitations of the machine. Similarly, the programs in the human information processor, in conjunction with certain task environments, may exceed his processing capacity. Assumptions about longterm memory, short-term memory, and the control of attention must be made more explicit if we are to determine the effects of these kinds of reasons for task failure. The "closed subroutine" representation described thus far has some severe shortcomings as a means for attacking these problems. First, there is an overly restrictive distinction between control and computation, a distinction that seems to have no psychological basis. Second, there is no straightforward manner in which relatively local and minor changes in the system can produce apparently qualitative improvements in performance. A third problem with the subroutine approach is the lack of constraint it imposes on short-term memory. Finally, the model requires that task-specific routines be assembled from the fundamental processes by an assembler of considerable power and scope. In the next section we intro150

DAVID KLAHR duce a form of process model that provides a partial resolution for each of these difficulties.

Production Systems: A Language for Process Models In the past few years a new form for describing information-processing models of cognition has been proposed and successfully applied to a modest range of complex problem-solving activities (Newell, 1966; Newell & Simon, 1972). The models are posed in the form of a collection of independent rules, called productions, that together form a production system. The rules are stated in the form of a condition and an action: C—> A. The condition refers to the symbols in short-term memory (STM) that represent goals and knowledge elements existing in the system's knowledge state; the action consists of transformations on STM including the generation, interruption, and satisfaction of goals; modification of existing elements; and addition of new elements. A production system obeys simple operating rules. a. The productions are considered in sequence, starting with the first. b. Each condition is compared with the current state of knowledge in the system, as represented by the symbols in STM. If all of the elements in a condition can be matched with elements (in any order) in STM, then the condition is satisfied. c. If a condition is not satisfied, the next production rule in the ordered list of production rules is considered. d. If a condition is satisfied, the actions to the right of the arrow are taken. Then the production system is re-entered from the top (Step a). e. When a condition is satisfied, all those STM elements that were matched are moved to the front of STM. This provides a form of automatic rehearsal. f. Actions can change the state of goals, replace elements, apply operators, or add elements to STM. g. The STM is a stack in which a new element appears at the top, pushing all else in the stack down one position. Since STM is limited in size, elements may be lost. These rules operate within the framework of a theory of human problem solving described in Newell and Simon (1972) and briefly summarized by Newell (1972b, pp. 375-376). Structurally, the subject is an information processing system (IPS) consisting of a processor containing a short-term memory which has access to a long-term memory (LTM). The processor also has access to the 151

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY external environment, which may be viewed as an external memory (EM). All action of the system takes place via the execution of elementary processes, which take their operands in STM. The only information available upon which to base behavior is that in STM; other information (either in LTM or EM) must be brought into STM before it can effect behavior. At this level the system is serial in nature: only one elementary information process is executed at a time and has available to it the contents of STM as produced by prior elementary processes. Seriality here does not imply seriality either of perception or of accessing in LTM. This general model and the verbal rules listed above have been precisely specified in a special programing language created by Newell (1972b) called PSG (for Production System, version G). Production systems written in PSG can be run on the PSG interpreter in a time-sharing mode under user (i.e., model builder) control. The user can observe the sequential consequences of his model, and can provide inputs for as yet unspecified subprocesses. An Example of PSG. The example to be presented in this section is intended not as a psychological model, but rather as a demonstration of some of the features of PSG qua programing language. Figure 2 shows a production system that represents the hammering of a nail into a board (a) and a trace of the system as it is executed (b). First, we shall list some PSG conventions. Everything to the right of a semicolon is ignored: line 100 is merely a title. The last line (1000) contains information used by the loading routines, and is not part of the model, per se. Everything else is in the form of a label, followed by a colon, followed by a structure enclosed in parentheses. The first four of these structures (lines 200-500) are production rules. These rules consist of a condition written as a conjunction of elements, an arrow ( >) and a series of actions. The details of these productions differ, but they are all of this same general form. We shall return to the meaning of their particulars when we describe their execution. Line 600 contains a special structure, named LOOK, which requests input from the terminal. That is, LOOK represents a part of the model that has not yet been programed, and whose operation must therefore be simulated by the model builder. When LOOK is evoked as an action, the model builder must decide what information to provide before the system can continue to function. Line 700 contains the information that the system needs to get started: when PSG initializes the interpretation of a production system, it inserts TOP.152

DAVID KLAHR GOAL into the top of STM. The structure named BUILD (line 800) determines the sequence in which the productions will be considered: thus, P4 will be tried first, then PI, etc. Finally, the size of STM is determined by the number of NIL'S allocated to it. As for the dynamic behavior of the system (Fig. 2b), everything in lower-case letters is typed by the model builder, everything in upper case is typed out by the system. The command build start! initializes the production system interpreter: STM is cleared to all NIL'S, the count of ac00100 00200 00300 OOUOO 00500 00600 00700 00800 00900 01000

;DEMO OF PSG USING SIMPLE EXAMPLE PI:((GOAL * JOIN) AND (UP HAMMER) AND (NAIL UP) --> (UP ===> DOWN)) P2:((GOAL * JOIN) AND (DOWN HAMMER) —> (DOWN ===> UP) LOOK) P3:((GOAL * JOIN) —> (DOWN HAMMER)) PU:((GOAL * JOIN) AND (NAIL FLUSH) —> (* ==> +)) LOOK:(OPR CALL) TOP.GOAL:(GOAL * JOIN) BUILD:(PI* PI P2 P3) STM:(NIL NIL NIL) ("BUILD LOADED. DO BUILD START!") RETURN.TO.TTY!

•build start! 0. STM: ((GOAL * JOIN) NIL NIL) P3 TRUE 1. STM: ((DOWN HAMMER) (GOAL * JOIN) N I L ) P2 TRUE (GOAL * JOIN) () OUTPUT FOR LOOK = *(naM up) *|z ,z U. STM: ((NAIL UP) (GOAL * JOIN) (UP HAMMER)) PI TRUE 5. STM: ((GOAL * JOIN) (DOWN HAMMER) (NAIL UP)) P2 TRUE (GOAL * JOIN) () OUTPUT FOR LOOK = **(nail up) *lz ,z 8. STM: ((NAIL UP) (GOAL * JOIN) (UP HAMMER)) PI TRUE 9. STM: ((GOAL * JOIN) (DOWN HAMMER) (NAIL UP)) P2 TRUE (GOAL * JOIN) () OUTPUT FOR LOOK = **(nail flush) *|z /z 12. STM: ((NAIL FLUSH) (GOAL * JOIN) (UP HAMMER)) PI* TRUE 13. STM: ((GOAL + JOIN) (NAIL FLUSH) (UP HAMMER)) END: NO PO TRUE

**

Figure 2. A simple production system and its trace. 153

MINNESOTA S Y M P O S I A ON CHILD P S Y C H O L O G Y

tions is set to zero, the structure named TOP.GOAL is put into STM, and a scan of the list of productions in BUILD commences. The first production to be considered is PI. It scans STM for the three elements: (GOAL * JOIN), (UP HAMMER), and (NAIL UP). Only the first of these is currently in STM, so P4 is not satisfied. Next PI looks for the two elements in its condition, and fails. P2 also fails. Finally, P3 finds a match between its condition and the elements in STM. Since P3's condition is satisfied, the actions associated with it are taken. In this case the action consists of simply adding a new element (DOWN HAMMER) to the front of STM, and pushing everything else in STM down one notch. The current state of STM is printed out in Figure 2b after 1 (to indicate that one action has been taken since the system started). After a production has "fired" — that is, after its condition has been matched and its associated actions have been taken, the production system is re-entered at the top. Thus, after P3 has completed its actions, the sequence of productions, as listed in BUILD, is tested sequentially once again. P4 and PI fail again, but this time P2 is satisfied. The two actions in P2 are (DOWN = — = > UP) and LOOK. The first of these is an action that modifies an element already in STM: the second element in STM is scanned for DOWN, and it is changed to UP. The action LOOK is, as described above, a call upon the terminal for the output of an as yet unprogramed routine that is supposed to determine whether the nail is up or flush. At this point, the modeler decided that it was still up, entered (nail up), and returned control to the system. The state of STM after four actions is now printed out. The same basic control cycle is repeated, with the determination of which production will fire being entirely dependent upon the contents of STM. Further explanations of the details of PSG will be given in the following descriptions of some psychological models. A Model for Quantitative Comparison: PSQC1. In experimental studies of class inclusion, conservation, transitivity, and many other tasks, the child is asked to make judgments of the relative amounts of two or more quantities. In this section we will describe a model, written in PSG, for quantitative comparison. Once the model has been presented, it will be used as the point of departure for extensions in three directions: upward, into two contexts in which quantitative comparison takes place: class inclusion and conservation; downward, to more specific models of the subprocesses utilized by quantitative comparison; and forward, to models of development ally later versions of quantitative comparison. 154

DAVID KLAHR PSQC1 is a running program for quantitative comparison written in PSG. Figure 3 shows the complete set of productions for PSQC1. The system consists mainly of goal manipulations and operator calls that provide a precise model of the following view of quantitative comparison. The question More x or more y? is intended to mean Are there more things with value x than there are things with value y? In order to determine the answer to this question the system must compare the quantitative symbols corresponding to the amount of the things that are Jt, and the things that are y. In order to compare the symbols, it must first generate them, using some quantification operator. PSQC1 works in a relatively simple problem space. In addition to the various goals and their states, it needs only the information listed in lines 600-800 (Fig. 3) concerning the classes of elements for values, relations, and quantitative symbols. The productions on lines 2100-3500 constitute the core of the psychological model. The order in which they are scanned is determined by PSQC1 (4400), in this case much the order in which they are listed, with the exception of PA, PSTART, and PZ. PA ensures that only one goal at a time is active (indicated by *). Whenever it finds two active goals, it sets the older of the two to interrupted (% ). Since it has top priority (being the first production in PSQC1), it will repeatedly fire until only a single goal is active. PZ serves the opposite function: reactivating interrupted goals in the absence ( ABS) of an active one. The main productions will be described in the order in which they are actually satisfied. P3 converts the word MORE into an active goal. It represents the process whereby the semantics of the term more establish, in this context, an active goal that will trigger further actions. The action in P3 contains a special symbol, = = >, that scans the first element in STM for the symbol on the left of the arrow, and replaces it with the symbols on the right: thus (WORD MORE) gets transformed to (GOAL*MORE). P4 simply adds the active goal COMPARE to STM whenever it finds an active goal MORE. P9 says, in effect, if the goal COMPARE is active and a value exists, then create the goal of quantifying that value. The condition element (VAL) searches for an element that has two components: the tag VAL and a member of the class . As defined in line 600, any of the terms RED, BLUE, etc., could satisfy the search for a . Within the local domain of P9, is assigned whatever member of the class it finds, and retains this value for the action side of 155

00100 00200 00300 00*00 00500 00600 00700

;PSQC1 ; PSG VERSION OF PSMORE, KLAHR AND WALLACE (1972). ;CALLS TERMINAL FOR QUANTIFICATION OPERATORS AND ;FOR COMPARISON OF MAGNITUDES ; :(CLASS RED BLUE SQUARE ROUND WOOD) :(CLASS < > =)

00800 :(CLASS QS) 00900 X1:(VAR) 01000 X2:(VAR) 01100

;

01300 01*00

QUANT I FY:(OPR CALL); INPUT QUANTITATIVE VALUE: ( Q S N < V A L » . RELATE:(OPR CALL); RELATE TWO SYMBOLS. «VAL> (* =«> *)) PZ:((GOAL *) ABS AND (GOAL %) ~> (% *)) ; ;MAIN PRODUCTIONS PI:((GOAL + MORE) AND (XI X2) —> SAY) P3:((WORD MORE) —> (WORD ==> GOAL *)) P*:((GOAL * MORE) —> (GOAL * COMPARE)) P5:((GOAL + COMPARE) AND (GOAL % MORE) —> (? ===> +))

02800 02900 03000 03100 03200 03300 03UOO 03500 03600

; P9:((GOAL * COMPARE) AND (VAL (VAL ===> OLD VAL) (GOAL * QUANTIFY + )) ; P11:((GOAL * QUANTIFY QUANTIFY) ; PDVO:((WORD (WORD «> VAL)) ;

03800 03900

; ;

02500 02600 02700

03700

P7:(X1 « «QS» AND X2 =- «QS» AND (GCftL * COMPARE) —> «QS> «*=> OLD «=> OLD (* ==> +))

SAY:(ACTION (OPR XI PRVL) (OPR PRVL) (OPR X2 PRVD)

01(000 OUOO 0*200

TOP.GOAL: (GOAL * ATTEND) PSTART:((GOAL * ATTEND) --> PROBLEM) PROBLEM:(OPR CALL); INPUT (MORE) (VAL1) (VAL2).

0**00

PSQC1:(PA PDVO PI P3 P* P5 P7 P6 P9 P10 Pll PZ PSTART)

0*300

;

0*500 ; 0*600 STM:(NIL NIL NIL NIL NIL NIL NIL NIL NIL) 0*700 ; 0*800

("MOR.AP1 LOADED. DO PSQC1 START!") RETURN.TO.TTY!

Figure 3. A production system for quantitative comparison: PSQC1.

156

DAVID KLAHR the production. P9 also ensures that it does not fire repeatedly, by changing the tag VAL to OLD VAL. Figure 4 shows the trace of PSQC1 operations for the task of subclass comparison, to determine whether in an array of red and blue squares, there are more reds or more blues. The trace consists of a printout of STM each time that a production is satisfied and its associated actions have been •psqcl start I

0. STM: ((GOAL • ATTEND) NIL NIL NIL NIL NIL NIL NIL NIL) PSTAKT TRUE (GOAL • ATTEND)

()

•|z

OUTPUT FOR PROBLEM - '(word noreKword blue)(word red)

h. STM: ((WORD RED) (WORD BLUE) (WORD MORE) (GOAL • ATTEND) NIL NIL NIL NIL NIL) PDVO TRUE 5. STM: ((VAL RED) (WORD BLUE) (WORD KDRE) (GOAL * ATTEND) NIL NIL NIL NIL NIL) POVO TRUE 6. STM: ((VAL BLUE) (VAL RED) (WORD MORE) (GOAL * ATTEND) NIL NIL NIL NIL NIL)

n TRUE

7. STM: ((GOAL • MORE) (VAL BLUE) (VAL RED) (GOAL * ATTEND) NIL NIL NIL NIL NIL) PA TRUE 8. STM: «fiOAL • MORE) (GOAL * ATTEND) (VAL BLUE) (VAL RED) NIL NIL NIL NIL NIL) Pk TRUE 9. STM: ((GOAL • COMPARE) (GOAL • MORE) (GOAL t ATTEND) (VAL BLUE) (VAL RED) NIL NIL NIL NIL) PA TRUE 10. STM: ((GOAL • COMPARE) (GOAL 4 MORE) (GOAL 1 ATTEND) (VAL BLUE) (VAL RED) NIL ML NIL NIL) P9 TRUE 12. STM: ((GOAL * QUANTIFY BLUE) (GOAL • COMPARE) (OLD VAL BLUE) (GOAL : MORE) (GOAL 4 ATTEND) (VAL RED) NIL NIL NIL) PA TRUE 13. STM: ((GOAL • QUANTIFY BLUE) (GOAL % COMPARE) (OLD VAL BLUE) (GOAL i MORE) (GOAL % ATTEND) (VAL RED) NIL NIL NIL) Pll TRUE (GOAL • QUANTIFY BLUE) «VAL> BLUE) OUTPUT FOR QUANTIFY • *«(qs 2 blue) •U ,z 15. STM: ((OS 2 BLUE) (GOAL • QUANTIFY BLUE) (GOAL ". COMPARE) (OLD VAL BLUE) (GOAL » MORE) (GOAL * ATTEND) (VAL RED) NIL NIL)

P10 TRUE 16. STM: ((GOAL * QUANTIFY BLUE) (OS 2 BLUE) (GOAL % COMPARE) (OLD VAL BLUE) (GOAL } MORE) (GOAL % ATTEND) (VAL RED) NIL NIL)

n TRUE

17.

STM: {(GOAL • COMPARE) (GOAL » QUANTIFY BLUE) (QS 2 BLUE) (OLD VAL BLUE) (GOAL » MORE) (GOAL \ ATTEND) (VAL RED) NIL

NIL)

P9 TRUE 19. STM: ((GOAL • QUANTIFY RED) (GOAL • COMPARE) (OLD VAL RED) (GOAL * QUANTIFY BLUE) (OS 2 BLUE) (OLD VAL BLUE) (GOAL * MORE) (GOAL \ ATTEND) N I L ) PA TRUE 20. STM: ((GOAL * QUANTIFY RED) (GOAL t COMPARE) (OLD VAL RED) (GOAL + QUANTIFY BLUE) (QS 2 BLUE) (OLD VAL BLUE) (GOAL I MORE) (GOAL i ATTEND) NIL) Pll TRUE (GOAL • QUANTIFY RED) «VAL> RED) OUTPJT FOR QUANTIFY • *«(qs 1 red) •U ,z 22. STM: ((OS 1 RED) (GOAL * QUANTIFY RED) (GOAL * COMPARE) (OLD VAL RED) (GOAL * QUANTIFY BLUE) (QS 2 BLUE) (OLD VAL BL E) (GOAL t MORE) (GOAL t ATTEND)) P10 TRUE 23. STM: ((GOAL * QUANTIFY RED) (QS 1 RED) (GOAL t COMPARE) (OLD VAL RED) (GOAL * QUANTIFY BLUE) (QS 2 BLUE) (OLD VAL BLU E) (GOAL * MORE) (GOAL t ATTEND))

n TRUE

2k. STM: ((GOAL • COMPARE) (GOAL + QUANTIFY RED) (QS 1 RED) (OLD VAL RED) (GOAL » QUANTIFY BLUE) (QS 2 BLUE) (OLD VAL BLU E) (GOAL t MORE) (GOAL I ATTEND)) P7 TRUE (OLD OS 1 RED) (NIL NIL X2 (OLD OS 2 BLUE) XI (OLD QS 1 RED)) OUTPUT FOR RELATE • "(blue > red) •U 28. STM: ((BLUE > RED) (OLD QS 1 RED) (OLD QS 2 BLUE) (GOAL « COMPARE) (GOAL » QUANTIFY RED) (OLD VAL RED) (GOAL * QUANT FY BLUE) (OLD VAL BLUE) (GOAL ? MORE)) PE TRUE 29. STM: ((GOAL « COMPARE) (BLUE > RED) (OLD QS 1 RED) (OLD QS 2 BLUE) (GOAL « QUANTIFY RED) (OLD VAL RED) (GOAL * QUANTI FY BLUE) (OLD VAL BLUE) (GOAL % MORE)) P5 TRUE 30. STM: ((GOAL » COMPARE) (GOAL « MORE) (BLUE > RED) (OLD QS 1 RED) (OLD QS 2 BLUE) (GOAL « QUANTIFY RED) (OLD VAL RED) (GOAL » QUANTIFY BLUE) (OLD VAL BLUE)) PI TRUE XI: BLUE : >

X2: RED

3U. STM: ((GOAL * MORE) (BLUE > RED) (GOAL » COMPARE) (OLD QS 1 RED) (OLD QS 2 BLUE) (GOAL » QUANTIFY RED) (OLD VAL RED) (GOAL « QUANTIFY BLUE) (OLD VAL BLUE))

Figure 4. A trace of PSQC1 on subclass comparison. 157

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY taken. The numbers that precede each STM display indicate the total number of actions that have been taken since the system started. As described above, in several cases the system calls upon the terminal for the output of operators that are not included, in programed form, in this production system. These outputs, indicated by lower-case letters, are typed in by the model builder. The command PSQC1 start! inserts the TOP.GOAL into STM and initiates PSQC1. The only production whose condition side is matched by STM elements is PSTART. PSTART has an action named PROBLEM which calls upon the terminal for an input (in Fig. 3, see lines 4000-4200). The input for quantitative comparison is then provided (in lower case). This input can be viewed as the result of preliminary linguistic processing of the experimental instructions. The state of STM after PSTART has completed its actions is shown in Figure 4 at (4.). Then the simple verbal encoder, PDVO, changes the WORD tag, having detected that both RED and BLUE are members of the class . Next, P3 converts the verbal term (MORE) to the active goal (GOAL*MORE). Notice that this goal appears (8.) at the front of STM. PSG includes a mechanism that automatically moves all the matched elements in a condition up to the front of STM. This represents a psychological assertion about automatic rehearsal in STM for those elements that evoke a production. As new elements are added, any elements in STM that are not matched by condition elements get pushed farther down until they eventually drop out of STM. For example, a scan of Figure 4 shows the element (GOAL % ATTEND) being pushed down and out of STM. The interrupted goal (GOAL % MORE) is just about to drop out of STM (29.) whenPS matches (and modifies) it (30.). Returning to (8.), P3 moves (WORD MORE) to the front of STM and modifies it to (GOAL*MORE). Since this is a modification of an existing element, there are as many elements in STM at (7.) as at (6.). P4 adds a new element to STM, (GOAL*COMPARE), and PSG operates such that new elements are added to the front of STM, pushing all else down one notch. A t ( 1 3 . ) P l l i s satisfied, resulting in the action QUANTIFY, an operator that calls on the terminal for the hypothesized output from a quantification operator. The call is made in a local context, (listed after PI 1 TRUE) just as it would be if QUANTIFY were itself a production system. The element (QS 2 BLUE) is the result of a human simulation of a quantifier that scans the hypothetical display for blue things and creates a quantitative 158

DAVID KLAHR symbol for two blue things. (Notice that at this level we have no model of quantification per se, although we have indicated the necessity for quantification operators of some sort. We shall return to this issue in detail at a later point.) The tag QS is the notation for a quantitative symbol, and the numeral 2 is an arbitrary (but obviously convenient) symbol for a specific value. The tag will be used directly by other productions, while the value will be used by another terminal call for a quantitative relational operator. The behavior of PSQC1 between (8.) and (16.) can be summarized: Given a goal of determining which of two values is MORE, a subgoal of COMPARE is generated; this, together with a VAL, generates a subsub goal of QUANTIFY for that value; this fires the quantification operator, which produces a quantitative symbol, which in turn satisfies the quantification goal. But two quantitative symbols are required for a comparison, and at this point only one exists, thus the sequence is repeated (17.)-(24.). Now P7 detects that the relationship between the two quantitative symbols can be determined by the operator RELATE. Since this is also a terminal call, the local context is provided and the system asks for the result of the relational operator. Once this relationship is provided, the comparison goal is satisfied (29.), and then the goal of determining more is satisfied (30.). Finally the system produces the result (following PI TRUE), and stops (34.). Class Inclusion. A slight alteration in the question which stimulated the trace just presented yields the familiar Class Inclusion (ci) question, More blues or more squares? (Let us assume for the remainder of this discussion that the array consists of two blue squares and one red square.) The prominence accorded to class inclusion by Piaget (1952) has stimulated a wide variety of ci studies. However, an analysis of the empirical results generated by these studies yields widely disparate pictures of the developmental course of ci (Klahr & Wallace, 1972a). The age of 50 per cent failure has been found to be as high as 11 years (Inhelder & Piaget, 1964) and as low as 6 years (Smedslund, 1964). The explanations offered for failure on ci can be divided into two categories: perceptual encoding failures and processing failures. An example of the former is Wohlwill's (1968) hypothesis that "the perception of two contrasting subclasses, unbalanced as to number, creates a strong tendency to translate a class inclusion question into a subclass comparison question" (p. 462). Inhelder and Piaget (1964), in contrast, attrib159

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY lite failure to the child's inability to think of the superset B while thinking of one of its parts A. It is only later that the child develops the requisite representations and processing capacity such that "the whole B continues to exist even while its components A and A' are separated in thought" (pp. 103-104). How can the model of quantitative comparison further our understanding of these issues? Initially, we (Klahr & Wallace, 1972a) placed the burden of explanation for failure on ci upon the unspecified (at that time) quantification operators. We argued that when the quantification operator was evoked for the first value to be quantified, it marked the internal representation of the collection; upon the second attempt the marked items were bypassed, thus giving the classic erroneous response. (For example, during the "blue" pass for "more blue or more square" — where squares are the superset — all blue squares are marked, so that on the "square" pass only the red squares are quantified.) In the context of PSQC1 such a mechanism could account for a system that can pass the subclass comparison task (more reds or blues), but fail ci. With development, the quantification operators were postulated either to remove old marks before processing or to make a copy of the representation for the collection. One of the benefits of specifying a process model in an unambiguous form is that it becomes highly falsifiable (Popper, 1959), both logically and empirically, and thus the model is amenable to extension, to modification, and if necessary, to abandonment. Hayes (1972) noted what he believed to be a logical flaw in our model, based upon the observation that if the superset happens to be quantified first, then on the second pass the system would find nothing at all to quantify. We subsequently demonstrated (Klahr & Wallace, 1972b) that this was not a logical error, in the sense of inconsistency, contradiction, or incompleteness. The system would in fact produce the correct answer, but for the "wrong" reason. However, the predicted frequency of such serendipity far exceeded the empirical facts, and on this basis PSQC1 can be considered only as a partial explanation of the ci phenomena.

Quantification Operators Three features of PSQC1 are candidates for revision, two that lie on the system-environment interface and one that lies totally within the system. The latter concerns changes in the existing production rules or their 160

DAVID K L A H R sequence. Such modifications are, as we shall demonstrate, unnecessary. The two areas where changes will be made are in the verbal encoding rules — about which we have said very little thus far — and in the quantification operators. In this section we shall summarize the empirical evidence concerning the nature of quantification operators, and then describe the form of the PSG models for such operators. These models will then be linked to the quantitative comparison model presented earlier. What was initially an undefined process "simulated" by the model builder, will become a programed model evoked in the context of a higher level task. A quantification operator is an organized collection of elementary processes that takes, as input, the stimulus to be quantified (e.g., a collection of blocks) as well as specified constraints (e.g., red only) and produces, as output, a quantitative symbol. Quantitative symbols are labeled internal representations (e.g., "two," "long," "tiny") that can be used in quantitative comparisons. Given two such symbols, the system can determine their relative magnitudes, whereas given two nonquantitative symbols, it can determine only whether or not they are identical. Evidence suggesting the existence of three quantification operators — subitizing, counting, and estimation — comes from analyses of reaction times (RT) and of errors in tasks requiring adult subjects to report the number of items in a display (Jensen, Reese, & Reese, 1950; Kaufman, Lord, Reese, & Volkman, 1949; Saltzman & Garner, 1948; Taves, 1941; Woodworth & Schlosberg, 1954, pp. 90-105). A reanalysis of the results of these studies and some new evidence is provided in Klahr (1973a). The earlier investigations were addressed to the question of whether the time required to quantify a collection is independent of the number of items viewed (n). The answer appears to be negative. A plot of RT versus n yields a monotone increasing curve in the range from 1 to 30 items. However, around n = 5 the slope abruptly changes from approximately 40 to approximately 300 miliseconds (ms) per item. There are corresponding discontinuities in error rates and in reported self-confidence. Finally, there is a subjectively different experience for n above and below 5. We have retained the term subitizing (Kaufman et al., 1949) for the operator used to quantify small collections. The parameters that define subitizing are a slope of 40 ms and a maximum range of 4 or 5 items. These parameters are similar to short-term memory (STM) scanning 161

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY rates (Steinberg, 1969) and to capacity limits (Miller, 1956). Thus, the parameters suggest that subitizing occurs in an interaction between STM and the environment. Our initial hypothesis was that the quantification operators utilize a complete internal representation of the stimulus (Klahr & Wallace, 1972a). One of the models we proposed as an explanation for successful functioning in the ci context actually made a copy of this representation before processing it. However, two lines of evidence appear to refute this hypothesis. First, the results of our studies with adults (Klahr, 1973a) indicate that the rapid rate of quantification (at least for small amounts) precludes LTM storage of the entire display. Second, the results of studies of the response latencies of children on ci (Wallace, 1972a) indicate that they respond much too rapidly to have created such an internal representation. In addition, Wallace (1972a) found that providing an external "copy" of the display did not substantially reduce the frequency of ci failures. All of this weakens the case for both the plausibility and the efficacy of an internally created copy of the entire display. A Process Model for Subitizing. The foregoing analysis has led us to the creation of some plausible models of quantification. A series of models for subitizing and counting have been written in PSG (Klahr, 1972). In this section we shall describe only one such variant in order to provide an example of the fine-grained analysis that is possible with this type of model. We shall then utilize the quantification model in the context of the quantitative comparsion model. The subitizing subsystem, PSUBIT, is shown in Figure 5, and a trace of the system running on a display of two elements is shown in Figure 6. The productions serve three general functions: the PDT'S (1000-1300) are part of a template matching system, PSTMP; the PDB'S (2000-2200) correspond roughly to the notion of moving sequentially along a list of stored quantitative symbols; and the PDS'S provide the control for initiating and terminating the subitizing process. PSUBIT is initialized when the goal SUBIT becomes active. The first production to be fired is PDS1: it ATTENDS to the environment and then sets up the first possible response in STM. PDS2, the last production to be satisfied, detects a satisfied subitizing goal and creates a quantitative symbol (QS) by concatenating the target value with the symbol name. Subitizing is viewed as a combination of template matching and of a 162

DAVID KLAHR 00100 00200 00300 00UOO 00500 OOGOO 00700 00800 00900 01000 01100 01200 01300

;SUB.E03 ; SANE AS SUB.E02, MIDIFIED TO WORK WITH HOR. SERIES. ; :(CLASS ISA ELM) XO:(VAR) X1:(VAR) :(CLASS RED BLUE SOJARE CIRCLE) ATTEND: (ACT I ON (Kit (OMO) (MTC(«VAL>») NOTICE) ; POn:((G«L • SUBIT) AW) (ELM) AW (TSA) AND «TD) ABS —> (• =*> «)) PDT2:((QOAL • SUBIT) AW (ELM) AND (TSA) AND (ELM) AND (TSA) AND «TE» ABS —> (• >=> *)) PBT5:((GOAL • SUBIT) AND (ELM) AMD (TSA) AND (ELM) AMI (TSA) AND (ELM) AND (TSA) AND «TE» ABS --> (• '=> »)) POTIi:((GOAL • SUBIT) AND (ELM) AND (TSA) AND (ELM) AND (TSA) AND(ELM) AND (TSA) AND (ELM) AND (TSA) AiJ) «TL» A

BS --> (* «> »»

01UOO PSTMP:(PDT1 POT2 PDT3 TOTU ) 01500 ; 01600 PDS1:((GOAL • SUBIT) —> ATTEND (SUB 1HTSA )) 01700 POS2:((QOAL * SUBIT) AM) (SUB XO) —> (SUB -—> OLD SUB) 01100 (NTC («VAL»)) (XI ==•> OS XO XD) 01900 ; 02000 POB2:((GOAL • SUBIT) AND (SUB 1) --> (1 •>==> 2)(TSA)> 02100 B)B3:((GQAL • SUBIT) AND (SUB 2) —> (2 ===> 3HTSA)) 02200 POBli:((GOAL • SUBIT) AM) (SUB 3) —> (3 ===> UXTSA)) 02300 ; 021.00 PSNB:(PDB2 PDB3 POB RED) *lz ,z 8. PDB2 10. POT2 11. PDS2 I1K END:

**

OUTPUT FOR NOTICE = *(elm red squareXelm red square)

STM: ((TSA) TRUE STM: ((TSA) TRUE STM: ((GOAL TRUE STM: ((QS 2 NO TO TRUE

(SUB 1) (ELM RED SQUARE)

(ELM RED SQUARE) ((RED)) (GOAL * SUBIT) NIL)

(GOAL * SUBIT) (SUB 2) (TSA) (ELM RED SQUARE) (FLM RED SQUARE) ((RED))) + SUBIT) (ELM RED SQUARE) (TSA) (ELM RED SQUARE) (TSA) (SUB 2) (RED)) (GOAL + SUBIT) (OLD SUB 2)

((RED)))

(ELM RED SQUARE) (TSA) (ELM RED SQUARE) (TSA))

Figure 6. A trace of PSUBIT on a two-element display. 163

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY Such models are attempts to account for certain developmental data about the onset of cardinality prior to ordinality (Gelman, 1972). The general flow of PSUBIT is: a. NOTICE the stimulus. This is a call upon the terminal for input of the entire stimulus as a set of independent elements. A local context is provided (RED in Fig. 6). Note that we have pushed down the level of undefined processes toward the perceptual end of the system. b. Transfer the name of the first possible response (SUB 1) and a single piece of the template (ISA) from LTM to STM. c. If there are as many (TSA'S) as (ELM'S), then satisfy the SUBIT goal and produce a quantitative symbol containing the name of the current response. d. Otherwise, modify the response name to its next value and add another template piece to STM. Figure 6 shows a trace of this general scheme on a two-element display. In the range l^n^.4, PSUBIT takes 3 additional actions per additional element. The actions are: the input of an additional ELM, the addition of an extra TSA, and the modification of a response symbol. One may equate this to the 40 ms slope for subitizing reported earlier, by assuming that these actions take on the average 15 ms each, and by assuming also that no other activity in the interpretation of the production system contributed appreciably to the time. The most important specific assumption is that all conditions are tested in parallel: the sequential nature of both the testing of conditions and the STM scan for a particular condition is to be viewed as a serial simulation of a parallel process (on this issue see Newell, 1972b).Notice that this is quite a different view of the function of STM than is to be found in most other contemporary STM scanning models. A PSG model of the results of typical STM experiments (Newell, 1973) suggests an interpretation that bears little resemblance to the well-known flow-chart models (e.g., Norman, 1969;Sternberg, 1969). A REVISED MODEL FOR QUANTITATIVE COMPARISON

In this section we will describe PSQC2, a modified version of PSQC1 that includes PSUBIT as its explicit quantifier, and a rudimentary verbal encoder that accounts for ci failures. Both of these extensions require programing modifications which, in turn, require additional psychological assumptions. The model for PSQC2 (Fig. 7) can be compared with PSQC1 (Fig. 3). The main productions for goal manipulation (lines 5200-6400) are 164

DAVID KLAHR essentially unchanged. The major changes are the addition of productions for chunking and unchunking (2200-3900), a modified verbal encoder (4500-4700), and the change in QUANTIFY from a terminal call to a sequence of actions that includes subitizing (1900). STM Capacity. One major distinction between production system models and most other forms of information-processing models is the presence or absence of unconstrained local memories. In models using conventional programing languages, memory space is created simply by naming variables, and distinctions between short- and long-term memory are uncommon. In PSG, all productions take their inputs from and place their outputs in a common workspace: STM. The model builder must decide what constitutes a reasonable size for this workspace. A lower limit appears to be Miller's (1956) well-known estimate of 7 ± 2. However, our models must include room for control information as well as for the chunks that are typically measured in experimental situations. The original model, PSQC1, requires only 9 slots in STM. PSUBIT requires about the same STM capacity. However, when PSUBIT operates in the context of PSQC2, enough new elements are introduced to cause crucial information to be lost from STM. Thus we face a design choice: either increase STM capacity, almost doubling it, or find some way to save information temporarily. The former alternative would, in this instance, violate only an aesthetic sense, an STM capacity of 20 being inelegant, but in general expansion is completely unsatisfactory, for if PSQC2 were itself operating in the context of a higher level routine, we would need an even larger STM capacity. Furthermore even a small increase in capacity is not always desirable: some systems actually depend upon the loss of information from STM. If such systems are imbedded in larger systems with associated STM increases, they cease to function properly. We have chosen the second alternative for dealing with a limited STM capacity. PSQC2 contains a set of productions for creating a single chunk of up to 5 elements from a class of items that are worth saving. Just before subitizing, the action (ps.l PSCHNK) in the action chain QUANTIFY (1900) ensures that one pass through PSCHNK will occur. If there are any elements of the class <SAV> (1100) — that is, if there are any active or interrupted goals, quantitative symbols, or value names — then the first five of them will be packed together into a single element by PSCHNK (3000-3900). It seems reasonable that before initiating an encoding process that will flood STM with temporary information, the system col165

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY 00100 00200 00300 OOltOO 00500 00600 00700 00800 00900 01000 01100 01200 01300 01UOO 01500 01600

;PSQC2 ; XO:(VAR) Xlr(VAR) X2:(VAR) X3:(VAR) XU:(VAR) X5:(VAR) ; ; <SAV>:(CLASS * % VAL :(CLASS RED BLUE SQUARE ROUND WOOD) : (CLASS «WVAL1> NOT <WVAL2» <WVAL» <WVAL1>:(CLASS <WVAL» <WVAL2>:(CLASS <WVAL» :(CLASS < > =)

01700 01800 01900 02000

:(CLASS QS) RELATE:(OPR CALL); RELATE TWO SYMBOLS. «VAL> (CHNK ==> OLD CHNK) XI) PDUC2:((CHNK XI X2) —> (CHNK ==> OLD CHNK) X2 XI) PDUC3:(( CHNK XI X2 X3) —> (CHNK ==> OLD CHNK) X3 X2 XI) PDUCii:((CHNK XI X2 X3 X«0 —> (CHNK ==> OLD CHNK) Xl» X3 X2 XI) PDUC5:((CHNK XI X2 X3 XU X5) --> (CHNK ==> OLD CHNK) X5 Xi» X3 X2 XI) ;

03100 03200 03300 03UOO 03500 03600 03700 03800

PDCH2:(X1 == «SAV» AND X2 == «SAV» —> (CHNK XI X2)) PDCH3:(X1 = «SAV» AND X2 == «SAV» AND X3 == «SAV» — > (CHNK XI X2 X3)) PDCHI»:(X1 — «SAV» AND X2 «• «SAV» AND X3 == «SAV» AND XU == «SAV» —> (CHNK XI X2 X3 X«0) PDCH5:(X1 — «SAV» AND X2 =« «SAV» AND X3 =» «SAV» AND X«t « «SAV» AND X5 == «SAV» — > (CHNK XI X2 X3 X (CHNK XI))

Figure 7. A production system for quantitative comparsion including a call on PSUBIT and an object-oriented verbal encoder: PSQC2.

lects a small number of items with high saliency and puts them together for reference even while performing the encoding subtask. The chunk itself is rehearsed by the quantifier. In PSUBIT (Fig. 5, line 800), just before the environmental input, CHNK is brought to the front of STM by NTC (a PSG command). Those rules that deal with the environment must keep from being swamped by incoming information, and one way to avoid this is to rehearse important items before admitting such inputs. In summary, the effect of the decision not to increase STM capacity is, first, to cause one of the chunking productions (Fig. 7, 3000-3700) to fire before quantification takes place; second, to rehearse the chunk before noticing the display (Fig. 5, line 800), and third, to unpack the 166

DAVID K L A H R OdOOO 01(100 OU200 01(300 OliUOO 01(500 OU600 OU700 01*800 OU900 05000 05100 05200 05300 05400 05500 05600 05700 05800 05900 06000 06100 06200 06300 061(00 06500 06600 06700 06800 06900 07000 07100 07200 07300 071(00 07500 07600 07700 07800

;GOAL MANIPULATION PA:((* GOAL) AND (* GOAL) --> (* ===> %)) PZ:((* GOAL) ABS AND (% GOAL) --> (% -=> *)) •VERBAL ENCODING PDV1:((MORE) AND «WVAL1» AND «WVAL2» --> (XO =«> OLD XO) (XI «—> OLD X1XVAL «WVAL1> NOT <WVAL2») (VAL «WVAL2> NOT <WVAL1»)) /

PSVERB:(PDV1) ;MAIN PRODUCTIONS Pl:((+ GOAL MORE) AND (XO XI ) —> ( + ==> OLD) SAY)

P3:((MORE) --> (MORE -«> * GOAL MORE)) PU:((* GOAL MORE) ~> (* GOAL COMPARE)) P5:((+ GOAL COMPARE) AND (% GOAL MORE) --> (% -«> + ) ) P7:(X1 — «QS» AND X2 « «QS» AND (* GOAL COMPARE) —> «QS> ==> OLD «=> OLD +)) P9:((* GOAL COMPARE) AND (VAL XO) --> (VAL «-> OLD VAL) (* GOAL QUANTIFY XO)) P10:((* GOAL QUANTIFY XO) AND «OjS> XO) —> (* »-> -O) Pll:((* GOAL QUANTIFY XO) —> (XO) QUANTIFY) SAY: (ACTION (OPR XO PRVL) (OPR PRVL) (OPR XI PRVD) TOP.GOAL:(ACTION PROBLEM) PROBLEM:(OPR CALL); INPUT (MORE) (VAL1) (VAL2). PSM2:(P1 P3 Pi( P5 P7 P6 P9 P10 PSEXEC:(PA PSVERB PSQC2) PSQC2:(PSUC PSM2 PZ)

Pll)

STM:(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL) ("MOR.B02 LOADED.

DO 'PSEXEC START! 1 ") RETURN.TO.TTY!

chunk upon return to PSQC2 by firing one of the unchunking productions (Fig. 7, 2200-2700). The effects of these productions will be indicated in the discussion of the trace below (see Fig. 8). Verbal Encoding. In both PSQC1 and PSQC2 we assume that an unspecified linguistic processor operates upon the input question and leaves three items in STM, the word MORE and the names of two values. We have postulated a rudimentary verbal encoder. In PSQC1 it was a simple rule that identified the value names and gave them appropriate tags for subsequent processing (PDVO in Fig. 3). The rule also translated the word MORE into a goal (P3). In PSQC2 we have a verbal encoder, PDV1, that operates as follows. Given the input from a ci question (MORE, BLUE, SQUARE) the system generates symbols for objects, not values: (BLUE NOT SQUARE) and (SQUARE NOT BLUE). These symbols are maintained in STM, ultimately providing a context 167

MINNESOTA SYMPOSIA ON CHILD PSYCHOLOGY pw«ec start I

NIL

«VAL> SQUARE) OUTPUT FOR PROBLEM - •(m>re)(blue)(square)

,1 0. STM: ((SQUARE) (SLUE) (MORE) NIL NIL NIL NIL NIL NIL N I L ) PDV1 TRUE k. STM: ((VAL (BLUE NOT SQUARE)) (VAL (SQUARE NOT BLUE)) (MORE) (OLD SQUARE) (OLO BLUF) ML ML NIL NIL ML) P3 TRUE 5. STM: ((• GOAL MORE) (VAL (BLUE NOT SQJARE)) (VAL (SQUARE NOT BLUE)) (OLD SQUARE) (OLD BLUE) NIL NIL ML NIL N I L ) P* TRIE 6. STM: ({• OOAL COMPARE) (• GOAL MORE) (VAL (BLUE NOT SQUARE)) (VAL (SQUARE NOT BLUE)) (OLD SQUARE) (OLD BLUE) NIL ML N IL NIL) PA TRUE 7. STM: ((• GOAL COMPARE) C GOAL MORE) (VAL (BLUE NOT SQUARE)) (VAL (SQUARE NOT BLUE)) (OLD SQUARE) (OLD BLUE) NIL NIL N IL NIL) P9 TRUE 9. STM: ((• GOAL QUANTIFY (BLUE NOT SQUARE)) (• GOAL COMPARE) (OLO VAL (BLUE NOT SQUARE)) (% GOAL MORE) (VAL (SQUARE NOT BLUE)) (OLD SQUARE) (OLD BLUE) NIL NIL NIL) PA TRUE 10. STM: ((• GOAL QUANTIFY (BLUE NOT SQUARE)) (i GOAL COMPARE) (OLD VAL (BLUE NOT SQUARE)) It GOAL MORE) (VAL (SQUARE NOT BLUE}) (OLD SQUARE) (OLD BLUE) NIL NIL NIL) Pll TRUE POO* TRUE 16. STM: ((GOAL • SUBIT) (CHMK (• GOAL QUANTIFY (BLUE NOT SQUARE)) (? GOAL COMPARE) (? GOAL MORE) (VAL (SQUARE NOT BLUE)) ) (• GOAL QUANTIFY (BLUE NOT SQUARE)) (t GOAL COMPARE) . GOAL MORE) (VAL (SQUARE NOT BLUE)) ((BLUE NOT SQUARE)) (OLD VAL ( BLUE NOT SQUARE)) (OLD SQUARE) (OLD BLUE)) PDS1 TRUE ((BLUE NOT SQUARE)) «VAL> BLUE) OUTPUT FOR NOTICE - ••(elm blue squareMelm blue square) •U 2*. STM: GOAL COMPARE ) (t GOAL MORE)) PDB2 TRUE 26. STM: . GOAL C OMPARE)) PDT2 TRUE 27. STM: ((GOAL « SUBIT) (ELM BLUE SQUARE) (TSA) (ELM BLUE SQUARE) (TSA) (SUB 2) ((BLUE NOT SQUARE)) (CHNK (• GOAL QUANTI FY (BLUE NOT SQJARE)) (>. GOAL COMPARE) (t GOAL MORE) (VAL (SQUARE NOT BLUO» (• GOAL QUANTIFY (BLUE NOT SQUARE)) (t GOAL C OMPARE)) POS2 TRUE 30. SIM: ((OS 2 (BLUE NOT SQUARE)) (GOAL « SUBIT) (OLD SUB 2) (ELM BLUE SQUARE) (TSA) (ELM BLUE SQUARE) (TSA) (CHNK (• GO AL QUANTIFY (BLUE NOT SQUARE)) (i GOAL COMPARE) (t GOAL MORE) (VAL (SQUARE NOT BLUE))) (• GOAL QUANTIFY (BLUE NOT SQUARE)) (t OOAL COMPARE)) END: NO PD TRUE 30. STM: ((QS 2 (BLUE NOT SQUARE)) (GOAL * SUBIT) (OLD SUB 2) (ELM BLUE SQUARE) (TSA) (ELM BLUE SQUARE) (TSA) (CHNK (• GO AL QUANTIFY (BLUE NOT SOUARE)) (t GOAL COMPARE) (t GOAL MORE) (VAL (SQUARE NOT BLUE))) (• GOAL QUANTIFY (BLUE NOT SQUARE)) (t GOAL COMPARE)) POX* TRUE 35. STM: ((• GOAL QUANTIFY (BLUE NOT SQUARE)) (>, GOAL COMPARE)