Psychological Review
VOLUME 87 NUMBER 6 NOVEMBER 1980
A Theory of Cognitive Development: The Control and Construction of Hierarchies of Skills
Kurt W. Fischer University of Denver
A theory of cognitive development, called skill theory, attempts to provide tools for the prediction of developmental sequences and synchronies in any domain at any point in development by integrating behavioral and cognitive- developmental concepts. Cognitive development is explained by a series of skill structures called levels together with a set of transformation rules that relate these levels to each other. The levels designate skills of gradually increasing complexity, with a specific skill at one level built directly from specific skills at the preceding level. The transformation rules specify the particular develop- mental steps by which a skill moves gradually from one level to the next. At every step in these developmental sequences, the individual controls a par- ticular skill; that is, he or she controls a structure composed of one or more sources of variation in what he or she does or thinks in a specific context. In development, these skills are gradually transformed from sensory-motor actions to representations and then to abstractions. The transformations pro- duce continuous and gradual behavioral changes; but across the entire profile of a person's skills and within highly practiced task domains, a stagelike shift in skills occurs as the person develops to a new optimal level. The theory sug- gests a common framework for integrating developmental analyses of cognitive skills, social skills, language, and perceptual-motor skills, as well as certain behavioral changes in learning and problem solving.
The development of the theory described in this A newborn baby is mostly helpless and article was supported by a grant from the Spencer unable to deal with much of the world Foundation. I would like to thank the colleagues who around him. Over the years the baby grows provided feedback on earlier drafts of the article: R. into a child, the child into an adult. Ex- Bank, B. Bertenthal, C. Brown, J. Campos, W. Carr, M. Cole, R. Corrigari, F. Dance, J. Flavell, H. Hand, plaining the psychological transformation P. Harris, S. Barter, J. Keenan, R. McCall, P. Mounoud, that the individual undergoes in these 20- R. Roberts, D. Rowe, N. Sahin, L. Silvern, D. Thomas, odd years is one of the most challenging J. Tucker, M. Watson, M. Westerman, and S. H. tasks facing psychology. White. Special thanks go to A. Bullinger, M. Haith, A. Lazerson, B. MacWhinney, and S. Pipp for their The theory presented in this article, called help on several phases of the article. The idea that led skill theory, attempts to explain a large part to Figure 2 was suggested by A. McLeod. I would also of this psychological transformation. It like to acknowledge the scholars whose ideas have been focuses primarily on cognition and intelli- most important to the formation of the theory: J. Bruner, J. Dewey, D. Hebb, J. Kagan, J. Piaget, B. F. gence, and it deals with aspects of learning Skinner, H. Werner, S. H. White, and P. H. Wolff. and problem solving. Skill theory treats The help of G. Anderson, B. Richardson, and K. Sulli- cognitive development as the construction van in preparation of the manuscript is also much appre- of hierarchically ordered collections of ciated. Requests for reprints should be sent to Kurt W. specific skills, which are defined formally Fischer, Department of Psychology, University of by means of a set-theory description. Denver, Denver, Colorado 80208. Of course, other psychologists have dealt
Copyright 1980 by the American Psychological Association, Inc. 0033-295X/80/8706-0477S00.75
477 478 KURT W. FISCHER with these same general issues before, and find that stimulation facilitates physical skill theory builds on their ideas, including development in premature infants. concepts from the work of Piaget (1936/ Despite the general agreement on the 1952, 1970; Piaget, Grize, Szeminska, & interaction of organism and environment, Vinh Bang, 1968; Piaget & Inhelder, 1966/ developmental psychologists have had dif- 1969), Bruner (1971, 1973), Werner (1948, ficulty incorporating both organism and 1957), and Skinner (1938, 1969), informa- environment into their theories. When tion-processing psychology (Case, 1974; attempting to include both, they have ef- Pascual-Leone, 1970, Note 1; Schaeffer, fectively emphasized one side or the other. 1975), and the study of skill learning (Baron, For instance, Piaget is perhaps the de- 1973; Gagne, 1968, 1970; Reed, 1968). The velopmental psychologist best known for intent of skill theory is to integrate ideas his interactional approach (1936/1952, 1947/ from these various approaches to produce 1950, 1975), yet his explanatory constructs a tool for explaining and predicting the de- have focused primarily on the organism. velopment of behavior and thought. It is the organism that changes from one Before describing skill theory in detail, stage to the next, with the environment I will discuss several of the key issues that playing only a minimal role (see Beilin, it attempts to deal with; the relation between 1971, and Flavell, 197la). Piaget himself organism and environment in cognitive de- has recognized this problem: Faced with a velopment and the issues of sequence and host of environmentally induced instances synchrony. The theory will then be pre- of developmental unevenness in perform- sented quasi-formally in terms of assump- ance (called horizontal decalage; Piaget, tions, definitions, notation rules, and de- 1941), he has said that he simply cannot scriptions of both the hierarchical levels of explain them (Piaget, 1971, p. 11). cognitive control and the transformation At the other extreme are the behaviorists, rules for development from level to level. who, like Piaget, recognize the importance Several experiments testing the theory will of both organism and environment. Their be described, corollaries of the theory will explanatory constructs, however, have ef- be proposed, and general implications and fectively emphasized the environment and limitations of the theory will be discussed. neglected the organism: Concepts such as reinforcement, punishment, practice, and Both Organism and Environment imitation are used to explain behavior and development (Bandura & Walters, 1963; Most psychologists agree that psycho- Reese & Lipsitt, 1970; Skinner, 1938, 1969). logical theories, to be adequate, must Useful as these concepts are, they require reckon with both organism and environ- important modifications to deal adequately ment (e.g., Aebli, 1978, Note 2; Endler & with organism and environment (Catania, Magnuson, 1976; Greenfield, 1976). The 1973, 1978; Herrnstein, 1977; Premack, interaction of organism and environment 1965). is even more obvious in development than To take advantage of the insights of such in most other areas of psychology. Even diverse positions as Piaget's genetic epis- the maturation of the child results from a temology and Skinner's behaviorism, one combination of organismic factors (in- must somehow put organism and environ- cluding genes) and environmental factors. ment together in the working constructs of For example, myelination of nerve fibers a theory. The present theory is based on in the cortex is controlled not only by genes the concept of skill, which itself connotes but also by environmental stimulation a transaction (Sameroff, 1975) of organism (Fischer & Lazerson, in press; Peiper, and environment. The skills in the theory 1963). G. Gottlieb (1976) reports that spe- are always defined jointly by organism and cific experiences are necessary for many environment. Consequently, the skills are aspects of normal physical and behavioral characterized by structures that have prop- development even when the infant is still in erties like those described by organism- the womb, and Cornell and Gottfried (1976) oriented psychologists and that simultane- THEORY OF COGNITIVE DEVELOPMENT 479
ously are subject to the functional laws very core of the study of cognitive develop- outlined by environmentally oriented psy- ment: the issues of sequence and synchrony chologists. The sets that describe the skill in development. Under what circumstances structures are always jointly determined by will skills show invariant developmental the actions of the organism and the environ- sequences, and under what circumstances mental context that supports those actions: will specific skills develop with some de- The organism controls its actions in a par- gree of synchrony? In practice, a theory ticular environmental context. This resolu- of cognitive development must be able to tion of the organism-environment dilemma predict and explain developmental se- allows some progress toward explaining quences and synchronies. This is, I believe, and predicting cognitive development, al- the most essential criterion for evaluating though it also raises some problems of its any theory of cognitive development. own, which will be discussed later. One of the most immediate implica- The Theory tions of defining specific skills in terms of both organism and environment is that rela- Skill theory provides an abstract repre- tively minor alterations in the environ- sentation of the structures of skills that mental context of action will literally emerge in cognitive development, together change the skill being used. That is, the with a set of transformation rules that relate organism's control of a skill depends on a these structures to each other. The struc- particular environmental context. This im- tures and transformation rules comprise a plication should be kept in mind because it tool for explaining and predicting develop- has many important ramifications for the mental sequences and synchronies from theory and its corollaries. birth to young adulthood. As I will demon- strate later, they may also allow for the Sequence and Synchrony explanation and prediction of cognitive Within the context of this proposed development in adulthood. The theory thus resolution of the organism-environment focuses on the organization of behavior; it dilemma, skill theory attempts to provide is primarily a structural theory, although it a precise answer—or at least a framework is in no way incompatible with functional that will allow the pursuit of a precise analyses (see Catania, 1973, 1978; Fischer, answer—to five interrelated questions. On 1972; Piaget, 1968/1970). first reading, several of the five questions Here is a brief overview: Skills develop may seem similar, but as the theory is pre- step by step through a series of 10 hier- sented, the distinctiveness of the questions archical levels divided into three tiers. The should become clear, (a) What is the struc- tiers specify skills of vastly different types: ture of an individual's cognitive skills at any sensory-motor skills, representational one point in development? (b) Which skills skills, and abstract skills. The levels specify develop into which new skills as the child skills of gradually increasing complexity, moves step by step from infancy to adult- with a skill at one level built directly on hood? (c) What is the process by which pres- skills from the preceding level. Each level ent skills develop into new skills? (d) How do is characterized by a reasonably well de- present skills relate to the skills that they fined type of structure that indicates the have developed from? For example, are the kinds of behaviors that a person (child or previous skills included in the present skills, adult) can control at that level. The skills supplanted by the present skills, or what? at each level are constructed by a person (e) Why is cognitive development so often acting on the environment. She performs uneven in different domains? The attempts several actions induced by a specific en- to answer these questions are anchored to vironmental circumstance, and the way specific cognitive skills investigated in the those actions occur in that circumstance developmental research literature. provokes her to combine the actions: The Underlying these five questions are two person thus combines and differentiates central issues that operationally form the skills from one level to form skills at the 480 KURT W. FISCHER next higher level. The movement from one mental sequences has frequently found that level to the next occurs in many micro- certain "logical" sequences do not actually developmental steps specified by a series of occur (e.g., Hooper, Sipple, Goldman, & transformation rules. Notice that the skills Swinton, 1979; Kofsky, 1966). develop through levels, not stages: De- The reciprocal give and take between velopment is relatively continuous and theory and data is, in my opinion, essential gradual, and the person is never at the same for theoretical progress in cognitive-develop- level for all skills. The development of skills mental psychology (Feldman & Toulmin, must be induced by the environment, and 1975; Furby, 1972; Hanson, 1961). The most only the skills induced most consistently important test of the levels and of all other will typically be at the highest level that the predictions from skill theory is empirical. individual is capable of. Unevenness in de- The theory must also be internally consistent, velopment is therefore the rule, not the ex- but internal consistency will be for naught if ception. The level of skills that are strongly the theory cannot describe, predict, and induced by the environment is limited, how- explain the development of actual cognitive ever, by the highest level of which the per- skills. son is capable. As the individual develops, In this article, I do not attempt to provide this highest level increases, and so she can a comprehensive review of the large body be induced to extend these skills to the new, of relevant research. Instead, the primary higher level. goal is to make the concepts of skill theory as clear as possible and to show how these Relation Between the Theory and Its Data concepts can be tied to behavior. Concrete examples of specific skills are used to illus- The formulation of Levels 1 to 7 is based trate most concepts. To demonstrate how on the large empirical literature on cognitive the concepts relate more broadly to the re- development between birth and adoles- search literature, a few instances of research cence. Both the specific structures of the relating to each concept are cited. These levels and the numbers of levels were in- examples have been chosen to represent a ferred from these data. To the best of my wide variety of behaviors, including re- judgment, a larger number of levels did not search from many different laboratories. I seem to be warranted by the data, and a also indicate which concepts or predictions smaller number did not seem sufficient to do not yet have good research documenta- explain the data. The validity of this judg- tion. ment will, of course, be determined by future research. The basis for prediction of developmental Assumptions and Definitions sequences, like the sequence of seven Skill theory is based on a number of levels, has been at issue in the cognitive- specific assumptions and concepts. This developmental literature. A number of de- discussion of them is not exhaustive but velopmental psychologists have argued that focuses on ideas that need to be especially developmental sequences can be predicted clear at the outset. The assumptions and on a purely logical basis, where the term concepts divide roughly into three topics: logical seems to mean internally consistent the concept of cognitive control, the nature (e.g., Brainerd, 1978; Kaplan, 1967; Kohl- of skills, and the characteristics of the levels berg, 1969). According to this way of think- and transformation rules. ing, if a coherent, "logical" argument can be made for a predicted developmental se- quence, that sequence must occur. Al- Concept of Cognitive Control though the sequence of cognitive levels predicted by skill theory is internally con- Cognition is a complicated concept. In sistent, I do not believe that this consis- much of the developmental literature, the tency itself provides an adequate test of the term cognition is used to refer to skills of a sequence (Fischer & Bullock, in press). Also, particular type of content—typically research that has explicitly tested for develop- knowledge of the physical world (as op- THEORY OF COGNITIVE DEVELOPMENT 481 posed to the social, emotional, or linguistic commonly classified as motor, perceptual, worlds) or knowledge as measured by stand- or mental. For example, an infant not only ard Piagetian tasks. But there is confusion grasps a doll or shakes a rattle or kicks a and controversy about how the concept of blanket but also watches the doll, listens to cognition should be used (Chandler, 1977; the rattle, and feels the blanket. According Flavell, 1977; Kessen, 1966). to skill theory, the higher-level cognitions of In skill theory, cognition refers to the pro- childhood and adulthood derive directly cess by which the organism exercises from these sensory-motor actions: Repre- operant control (Catania, 1978; Skinner, sentations are literally built from sensory- 1938, 1969) over sources of variation in its motor actions. own behavior. More specifically, the person The definition of action in skill theory is, can modulate or govern sources of variation however, different from Piaget's use of the in what he or she does or thinks. These term. First of all, within Piaget's frame- sources of variation are denoted in the work, the sense in which cognitions beyond theory by sets: sensory-motor sets, repre- infancy are themselves actions (not merely sentational sets, and abstract sets. As cog- derivative from actions) is not clear: When nitive development progresses, infants a child represents a leaf fluttering in the first control variations in their own sensory- breeze, falling to the ground, having a green motor actions, then children control varia- color, and turning red in the fall, in what tions in their own representations, and sense is the child acting? According to skill finally adolescents or adults control varia- theory, the child is controlling representational tions in their own abstractions. Representa- sets for leaves' fluttering, falling to the tions subsume sensory-motor actions, ground, being green, and turning red. This and abstractions subsume representations. control of variations can be conceived as an According to this conception, cognition action on the part of the child, in that the includes anything that involves the person's child actively controls the variations cog- controlling sources of variation, even when nitively. Also, all representational sets are these sources have conventionally been literally composed of sensory-motor ac- called emotions, social skills, language, or tions, as I will illustrate later. whatever. All these various domains share Second, an action involves a set (rather the same processes of developing more and than merely a point) because it must always more effective cognitive control. be applied to something, and in being ap- plied, it must always be adapted to that Nature of Skills thing. Every time an infant grasps a rattle or every time an adult recognizes a familiar Skill theory assumes that cognitive skills face, the action is adapted to the specific can be described effectively and precisely thing acted upon. Thus, every time an action in terms of elementary intuitive set theory is carried out, even on the same thing, it is (see Suppes, 1957). The general definition of done a little differently. Notice that each a set is a collection of things. Why is it specific realization of an action always in- necessary to talk about collections to ex- cludes both a subject and an object—an plain cognitive development? When people organism and an environment. An action is control sources of variation in what they do therefore a set of similar behaviors on or think, each such source is a collection or things, but not just any such set: In an action, set, since it is a class of variations. This the person can control the relevant varia- quality of cognition can be made more con- tions in the behaviors on things. An infant crete by discussion of how cognition is who can consistently grasp a rattle has a set based in action. for grasping that rattle. An adult who can Cognition and action. All cognition repeatedly recognize a specific familiar face starts with action, in a very broad sense. has a set for recognizing that face. The thing Piaget (1936/1952; Piaget & Inhelder, 1966/ is always included with the behavior in the 1969) has pointed out that cognition is es- definition of a set. In many ways, this defi- sentially what the organism, from its own nition of action is closer to the behavioral point of view, can do, whether the doing is concepts of operant and skill than to Piaget's 482 KURT W. FISCHER
conception. Indeed, the term behavior in documenting new instances, especially class might be superior to the term set, when the unevenness can be attributed to but class is commonly used in psychology environmental causes. Unevenness has to refer to a type of concept, and set has no been found so often and synchrony so such surplus meaning. seldom that many developmental psycholo- Skills, schemes, and operants. Set and gists have begun to suggest that unevenness action are clearly synonyms within the may well be the rule in development, and theory. How do they relate to skills? A synchrony the exception (e.g., Carey, 1973; skill is a unit of behavior composed of one Cole & Bruner, 1971; Feldman & Toulmin, or more sets. The characteristic structure 1975). Unevenness has been demonstrated for each level is a type of skill, varying in repeatedly for every Piagetian period of complexity from a single set at Level 1 to a development.2 very large number of sets at the highest The concept of skill, in contrast to levels. What makes a group of sets into a Piaget's scheme, requires that unevenness skill is the person's control over both each be pervasive in development, because skills individual set and the relations between the are defined in terms of the environment as sets. For example, an infant who can shake a well as the organism. Changes in the en- rattle in order to listen to it has a skill com- vironmental context of action produce posed of two related sets, shaking the rattle changes in a skill. In this regard, skills and listening to the noise it makes. share important similarities with Skinnerian The relation between the concept of skill operants (Skinner, 1938). The term operant in the theory and the concepts of scheme refers to a behavior that is emitted by an and operant from Piaget and Skinner may organism, not elicited by a stimulus. At the help to clarify the meaning of skill. Piaget's same time, the specific form of the behavior general word for cognitive structure is and the probability that the organism will scheme1—a structure for knowing, a pro- emit the behavior are affected by environ- cedure that the child actively applies to mental stimuli. The behavior is therefore things in order to understand them. In broad controlled by both the individual organism conception, there are many similarities be- and environmental stimuli. Hunt (1969) and tween scheme and skill, as already indicated Aebli (1978, Note 2) have pointed out that in the discussion of action, but there are also most of the behaviors studied by Piaget and major differences. One of the most im- his colleagues are in fact operants. portant differences involves the organism- The phenomena of developmental un- environment problem: Piaget's schemes evenness make good sense from a be- allot much less importance to the environ- haviorist perspective. Behavioral research ment than the skills of the present theory has shown repeatedly that task factors have do. Schemes are assumed to have a high potent effects on most kinds of behavior in degree of generality, encapsulated in Piaget's concept of the structure d'ensemble (Piaget, 1957, 1968/1970; Inhelder & Piaget, 1 Many of the English translations of Piaget's works 1955/1958). This powerful generality of use the word schema instead of scheme to translate the French scheme. There is a problem with this schemes should produce a high degree of usage: In recent years Piaget has differentiated scheme synchrony in development. Two tasks that from schema (Furth, 1969; Piaget & Inhelder, 1966/ according to Piagetian analysis require the 1971). Schema refers to an internal image of some- thing, which is very far from the meaning of scheme. same scheme should develop at the same 2 time. Yet rather than synchrony, re- Here are just a few of the relevant references: for the sensory-motor period, Butterworth, 1976; Jack- searchers typically find unevenness in de- son, Campos, & Fischer, 1978; Kopp, O'Connor, velopment (e.g., Flavell, 1971b; Jamison, & Finger, 1975; Uzgiris & Hunt, 1975; for the pre- 1977; Liben, 1977; Toussaint, 1974). operational period, Gelman, 1978; Goldstein & The number of well documented in- Wicklund, 1973; Watson & Fischer, 1980; for the con- crete operational period, Achenbach & Weisz, 1975; stances of unevenness has been increasing Hooper et al., 1971; Jackson, 1965; Smedslund, 1964; astronomically in recent years; American and for the formal operational period, Martarano, psychologists seem to take special delight 1977; Neimark, 1975; Piaget, 1972; Wason, 1977. THEORY OF COGNITIVE DEVELOPMENT 483
Horizontal both animals and people. The effects are so Spring- powerful that a number of analyses of Segment human abilities have been developed that deal primarily with the influences of task on 4 performance (e.g., Fleishman, 1975; Horn, 1976). In addition, specific experience with a .Vertical task has repeatedly been shown to be im- Segment portant. These two factors, task differences and experience, likewise account for many instances of unevenness. For example, the type of task, the materials used in a task, Weight and simple changes in the format of a task have all repeatedly produced unevenness Figure I. The spring-and-cord gadget. (e.g., Barratt, 1975; Jackson et al., 1978; Kopp, O'Conner, & Finger, 1975). Even simple practice with a task affects stage of through the seven levels must occur within a performance (e.g., Jackson et al., 1978; skill domain, not across skill domains. In Wohlwill & Lowe, 1962). other words, the development of cognitive The usefulness of the concept of operant skills occurs in much the way that behav- does not extend, however, to analysis of iorally oriented psychologists have sug- the organization of behavior. Although gested (Baron, 1973; Gagne, 1968, 1970; reinforcement and punishment can be useful Schaeffer, 1975). The child masters specific experimental operations for analyzing or- skills, builds other specific skills upon them, ganization, they are insufficient. What the and transfers skills from one domain to an- concept of operant lacks in behaviorist other. This mastery process involves quali- theory is a system for analyzing the or- tative changes in skills, but the specific ganization of operants and how that or- changes occur gradually, not abruptly. ganization changes with learning and de- Induction of a new skill. An example will velopment. Skill theory is designed to show how development is induced jointly by provide such a system. both the person's skills and the environ- In general, then, scheme and operant are mental circumstances in a particular situation. synonyms for skill within the present The development of conservation of length theory, although of course they have dif- in the gadget shown in Figure 1 (adapted ferent psychological frameworks. The from Piaget et al., 1968, chap. 4) provides a levels of cognition are a hierarchy of skills, simple illustration of this joint induction by schemes, or operants in which each higher- organism and environment. In the gadget, a level skill, scheme, or operant is actually cord is attached to a spring and draped composed of lower-level skills, schemes, over a nail, so that the cord is divided into or operants. The theory thus provides a tool two segments by the nail, a horizontal seg- for analyzing skills, schemes, or operants ment and a vertical segment. Differing into units of widely varying complexity. weights attached to the cord will produce The definition of sets has an important changes in the length of the horizontal seg- implication for the meaning of skill, scheme, ment of the cord and concomitant changes and operant. Because an action always in- in the length of the vertical segment. volves a particular object or thing, a skill Consider a 5- or 6-year-old girl who al- must be specific to particular objects or ready has two skills (or schemes or oper- things. This implication is equivalent to ants) for the length of the cord: (a) She saying that as children develop, they master understands approximately how the length specific cognitive skills; they do not develop of the vertical segment relates to the length uniformly across the entire range of skills. of the horizontal segment; that is, she can Similarly, since cognitive development roughly control the relation between the proceeds by the coordination of specific vertical length and the horizontal length, skills or schemes or operants, development using the vertical to predict the horizontal. 484 KURT W. FISCHER
(b) She also understands approximately sential contribution of the environment to how the horizontal length relates to the skill development requires, of course, that vertical length; that is, she can use the unevenness be the rule in development, but horizontal to roughly predict the vertical. it by no means excludes instances of syn- But she does not yet understand that the chrony. Developmental synchrony in changes in the horizontal length compen- various degrees is predicted by the theory. sate for the changes in the vertical length, Analysis of skill structures plus control of so that the total length of the cord does environmental factors such as practice and not change; she does not yet understand familiarity allow the prediction of special conservation of the length of the cord. instances of near-perfect synchrony, as well To construct an understanding of this con- as predictions of various degrees of syn- servation, she must coordinate her two chrony under differing circumstances. Such skills for predicting the length (vertical predictions will be illustrated later. predicts horizontal, and horizontal predicts Because of the connotation of the word vertical). This combination will occur only skill, the phrase skill domain implies a fairly if (a) the child has the two skills and (b) broad grouping of behaviors. However, she plays with a gadget in which length in methods for determining the developing fact conserves. As she applies the two skills child's groupings of behaviors into skill repeatedly to the gadget, the task itself domains are crude at best (see Beilin, 1971; induces the child to notice a connection be- Flavell, 1971b, 1972; Wohlwill, 1973). So as tween them, because the properties of the not to beg the question of which skills task make the two skills closely related. develop together in a single domain, I will Then the child explores the connection and distinguish task domain from skill domain. gradually constructs a new, higher-level A task domain is a set of behaviors that skill for conservation of the total length involve only minor variations in the same of the cord. task, in contrast to the broad grouping of The importance of the contribution from behaviors across tasks in a skill domain. the gadget (the environment) should not be Within a task domain, there is virtually no underestimated. If the cord were not a cord problem in determining which behaviors but a rubber band, conservation of the belong to that domain. As will be shown length would not obtain, because the differ- later, the theory can predict developmental ent weights that stretch the spring would sequences within a task domain. It may also also stretch the rubber band. More gen- prove useful in determining the nature and erally, the child's possession of two skills scope of skill domains, but that usefulness cannot by itself produce coordination of remains to be demonstrated. those skills. The child must be induced to Task analysis. Because task factors are coordinate them by applying them to some- so important in skill theory, task analysis thing for which they do coordinate.3 The joint action of organism and environ- ment in cognitive development is equally 3 This analysis differs from that of Piaget et al. important for all the skill levels in the (1968) in three major ways: (a) They do not grant the same inductive role to the task, (b) They do not theory. A 1- or 2-month-old infant, for ex- ascribe to the 5-year-old the ability to relate vertical ample, will typically not be able to control to horizontal and vice versa, although they do de- the relation between shaking a mobile and scribe an ability to relate weight to length of the watching it jiggle. But when she has mas- spring (which is also consistent with skill theory). tered the two individual skills, shaking the These several abilities are both predicted by skill theory and supported by some research (Wilkering, mobile and watching it, she will be induced 1979). (c) They do not explain conservation as arising by the mobile to coordinate the shaking from the coord inationfof skills relating vertical and and the watching. It is a property of mobiles horizontal. Instead, they describe three stages: relating —and of many other things in the world— weight to spring, then understanding conservation, and finally understanding the proportional relation that shaking them produces interesting between weight and amount of displacement. Their changes in their appearance. third stage develops much later than what is dis- Developmental synchronies. This es- cussed in the present example. THEORY OF COGNITIVE DEVELOPMENT 485 is clearly central to using the theory. The Before the levels themselves can be de- central question for task analysis is: What scribed, a number of key concepts must be sources of variation must the person control introduced. to perform a task? That is, what sets must Relations between skills and levels. she or he control, and what relations be- Contrary to the use of stage or period in most tween sets? Guidelines for task analysis cognitive-developmental models, the levels will be described later after the theory are used generally to characterize a child's has been more fully elaborated. skills, not the child in general. A child will Closely related to the problem of specify- normally be at different levels for different ing which sets and relations a person must skills. To characterize a specific child, a control in a task is the problem of defining cognitive profile is required, indicating level the boundaries of a set. Indeed, the most of performance on a wide range of skills useful form of set theory may prove to be (see, for example, Rest, 1976). the theory of fuzzy sets (Negoita & Ralescu, There is, however, one sense in which the 1975), which does not require precise defini- levels are used to characterize the child. tions of set boundaries. The problem of Each child has an optimal level, indicating defining the boundaries of a set is virtually the best performance the child shows, which identical to the problem encountered by is presumably a reflection of both practice behaviorists in defining the boundary of an and the upper limit of his or her processing operant (Schick, 1971). The problem may be ability. Just as in information-processing more serious theoretically than practically theories, this central processing limit in- (Catania, 1978), but it is still a problem. creases with development (Case, 1974; Skill theory at least points in the direction Flavell & Wohlwill, 1969; Halford & Wil- of a solution by specifying a universe of son, 1980; Pascual-Leone, 1970; Scandura, possible skill structures and thus providing a 1973). But skill theory does not require the tool for partially defining behavioral units. homogeneity of performance demanded by Development is analyzed into a hierarchy of many information-processing theories, since operants—skill levels of increasingly com- the optimal level is merely an upper limit, plex cognitive control—plus various transi- not a characteristic of all cognitive behavior tional forms specified by the transformation at a given point in development. Also, the rules. A particular behavior can be related to limit is characterized by a skill structure one of the possible skill structures, and at (one of the cognitive levels) rather than a the minimum, the theory will then imply simple whole number of items in working particular kinds of changes in the cores and memory. boundaries of sets across transformations The postulation of levels instead of con- and levels. tinuous monotonic increases in complexity has implications for the form of the in- Concepts for Defining Levels and crease in optimal level with age: Associated Transformations with the levels, there will be spurts in the Through the joint contributions of the speed of developmental change. That is, as a person and the environment, skills, schemes, child moves into a new level, she will show or operants develop through at least seven rapid change; but once the level has been hierarchical levels. The skills at each level attained, she will show slower change. In are characterized by a structure that this way, the speed of development will vary indicates the kinds of behaviors that the cyclically with the skill levels. Note that this person can control at that level. Also, at hypothesis does not mean that develop- each level, the skills include all the lower mental change is abrupt or discontinuous. levels. For example, when a child is at Level The child moves into a new level gradually 5 for a specific skill, that skill subsumes over a long period, but the speed of change skills at Levels 4 through 1. Note, however, during this period is relatively rapid. that these lower-level skills become more Although I have defined the optimal level differentiated at each higher level to which as a single upper limit, there is a possibility the superordinate skill develops. suggested by ability research that at the 486 KURT W. FISCHER
Table 1 clude much more complexity and detail than The Cycle of Four Levels That Repeats a mapping.4 in Each Tier A third type of structure, called a system Characteristic Set-theory of systems, is a relation between two sys- Level structure description tems, as shown for Level IV in Table 1. The psychological interpretation of a system of I Single set [W] or [X] systems is that people can relate two sys- II Mapping [W — X] tems in a single skill, which allows them to form a new kind of set: the most elementary III System [WA,B <-» XC,D] set M at the next higher tier. In this new IV System of systems rw^xi set, each system is one element, so that the | or [M]simplest set has just two elements. LY ^ zj Note that in all these structures, a set is a source of variations that the person can control—variations in actions, representa- highest levels, a person may have a few dif- tions, or abstractions. In each case, the ferent optimal levels in different broad do- variations involve behaviors-on-things, but mains. For example, an adult's optimal level the level of complexity of the organization in spatial skills may be different from his or of those behaviors increases markedly at the her optimal level in verbal skills (see higher levels. Consequently, I will at times Horn, 1976). use simplified descriptions of higher-level Mappings and systems. The concepts of mapping and system define the possible relations between sets within a skill, and 4 The concepts of mapping and system are both both of these concepts can be described in derived in part from Piaget's and Werner's work. set-theory terms. A mapping is a structure Piaget and his colleagues (Piaget et al., 1968; see also relating two sets: a collection of ordered Flavell, 1977) have analyzed several behaviors of the preschool child in terms of what they call a function, pairs in which the first member in each pair which is similar to a mapping. But they seem to restrict is from one set (W) and the second member their analysis to only a limited group of behaviors is from another set (X). The first set is said and analyze those behaviors in terms of the degree to to be mapped onto the second: [W — X]. which the behaviors match the characteristics of a A system is composed of a relation be- mathematical function. Their conclusion is therefore that preschool children can sometimes show quasi tween two subdivided sets. Each set is functions (called constituent functions) but not real divided into two subsets, which are related functions (called constituted functions). The skill- to the two subsets in the other set. The two theory concept of mapping may be viewed as a re- subdivided sets are said to form a system, definition, generalization, and extension of Piaget's concept of function. The concept of system is not with the subsets noted by subscripts: directly present in Piaget's work, but it derives in part [WA,B
Table 3. What happens after Level 7 is When a mathematician says that one set is primarily conjecture, because there has mapped onto another, he or she means, been so little research on cognitive develop- roughly speaking, that variations in the first ment in adulthood. Yet the predictions of set produce predictable variations in the the theory are clear and direct: The abstract second one. In an analogous way, at Level sets should produce an abstract tier—an- II a child can understand situations where other progression through the cycle of four he or she can relate one set of variations to levels. When the combinations of abstract a second set of variations. sets reach Level 10, they should produce Level III is characterized by a system still another new kind of set. Specification —a relation between two sets each of which of the nature of the new sets at Level 10 is divided into two subsets, indicated by the must await future research on cognitive two-headed horizontal arrow between sets development in adults. in Tables 1 and 3. The child is no longer To distinguish the general cycle of levels limited to the two simple sets in the map- from the specific levels, the Roman nu- pings of the previous level but can control merals I to IV will be used to refer to the relations between two subsets for each set. levels of the cycle, and the Arabic numerals That is, the child can understand situations 1 to 10 will be used to refer to the actual where he or she can systematically relate behaviorally defined cognitive levels. two components of one set of variations to As shown in Table 1, Level I is character- two components of a second set of varia- ized by single sets—single sources of vari- tions. In this way the child can deal with ation that the child can control by them- one subset while still keeping the other in selves but not in relation to each other. That mind and as a result can control much finer is, the child cannot yet coordinate sets into a covariations in the two sets than at Level II. higher-level skill. The characteristic structure for Level IV The characteristic structure for Level II is a system of systems—a relation between is a mapping—a relation between two sets, two systems, indicated by the two-headed indicated by the long line in Tables 1 and 3. vertical arrow in Tables 1 and 3. At this
Table 2 Notation Rules
Type of symbol Examples Meaning
Roman numerals I, II, III, IV Cycle of levels that repeats in each tier Arabic numerals 1, 2, ... 5, . . . 10 The ten hierarchical levels Plain capital letters J, K, and L L, L + 1 Undesignated level Lowercase italic letters b, s, e Skills of unspecified level Boldface capital letters M, G, P Sensory-motor sets Italic capital letters A, F, R Representational sets Script capital letters 3),M Abstract sets Plain capital letters W, X, C Sets of undesignated tier Superscript to the right G", F* Sets designated by the main letter are components of the set designated by the superscript, which is at the next higher tier Superscript to the left LA, 2P Level of set THEORY OF COGNITIVE DEVELOPMENT 489
Table 2 (continued) Type of symbol Examples Meaning
Subscript to the left or right Information of interest about the sets; used to discrim- inate related sets; two letter subscripts indicate the set is composed of two subsets Brackets [A Sets and relations inside brackets constitute a single skill Long line connecting two letters [A — F] Mapping: Relation between two sets Horizontal two-directional arrow [A *-* F} System: Relation between two sets, each composed of two subsets Vertical two-directional arrow [A <-* F System of systems: Relation t between two systems \R
Diff Diff A = AM, AN Differentiation of the set or Diff [A <-» F] = [AG,H skill on the left into the sets or skills on the right
level, a person can control the relation be- cess by which Level IV of one tier be- tween two systems, keeping in mind one comes Level I of the next tier. Level I can system while dealing with the other. This co- be thought of as a simple building block. ordination of two systems produces a new Level II is then a combination of those kind of set, the most elementary set M at the building blocks in one dimension to form next tier, as shown in Table 1. lines. At Level III, lines are combined to The metaphor drawn in Figure 2 illus- make two-dimensional objects, such as the trates the cycle of four levels and the pro- square in the figure. Finally, at Level IV, 490 KURT W. FISCHER
LEVEL representational, and abstract tiers will help to clarify the general picture of cognitive development presented by the theory. The I child's potential skills with the spring-and- cord gadget in Figure 1 will be traced n through the levels as a continuing example. Sensory-Motor Tier: Levels I to 4 The first four levels constitute the sensory- m motor tier, as shown in Table 3. In this tier, all skills are composed of sensory-motor sets—actions (including perceptions) on objects, events, or people in the world. Skills at this tier have most of the charac- teristics that have been called "sensory- motor" by a long and distinguished line of psychologists (e.g., Baldwin, 1925; Dewey, 1896; Hobhouse, 1915; Lashley, 1950; Piaget, 1936/1952; Werner, 1948): Both Figure 2. A metaphor for the cycle of four levels. sensory and motor components are integral parts of the skills and for most purposes planes are combined to form three dimen- cannot be genuinely separated. Because the sional objects, such as a cube—a new type infants can control only sensory-motor of building block. In this way the cycle actions, their skills are purely practical: begins over again, with Level IV of one tier They understand how to act on specific serving as Level I of the next tier. things in the world but cannot think about An elaboration of how this cycle of Levels those things independently of acting on I to IV applies in the sensory-motor, them. They understand what they can do
Table 3 Sensory -Motor and Representational Levels of Skills Sensory-motor Representa- Abstract Level Name of structure sets" tional sets sets" 1 Single sensory- motor set CA] or ['B] 2 Sensory -motor mapping [2A — 2B] 3 3 3 Sensory-motor system [ AG,H <•» BG>U] 4 System of sensory-motor systems, which is a A 4B 4 single representational set r "T» " I = t /?] ["C" <~> "D"] 5 Representational mapping 6 Representational system 7 System of representational systems, which is a single abstract set
a Sensory-motor sets continue after Level 4, but the formulas become so complex that they have been omitted. To fill them in, simply replace each representational set with the sensory-motor formula for Level 4. b Development through the abstract tier shows the same cycle as development through the sensory-motor and representational tiers. Abstractions are built from representational and sensory-motor sets in the same way that representations are built from sensory-motor sets. THEORY OF COGNITIVE DEVELOPMENT 491
and what they make happen. They do not gadget, one set, 1S, involves the infant's understand that objects, events, and people looking at the gadget when it crosses her have their own characteristics independent field of vision and maintaining it in her sight. of what the infants themselves do; that Another set, 'G, involves her grasping the ability awaits the development of repre- spring when it touches her hand and main- sentational sets.at Level 4. Consequently, taining her grasp on it. Most of Piaget's a child does not realize, for example, that (1936/1952) primary circular reactions seem her favorite rattle has properties like hard- to be Level 1 single sensory-motor actions. ness and the capacity to make noise that The infant can control many such single sets are independent of her own actions on it. at Level 1, but she cannot control the rela- Nor does she understand that people and tions between sets. many other things can act by themselves Single sensory-motor sets are not limited independently of her actions. To emphasize to adult-defined modalities in perception the domination of this world by action and and action. The young infant does not know, to avoid confusion from terms like object for example, that seeing is different from or person, I will refer to objects, people, listening. When she is attempting to look at and other things in the infant's experience the doll swinging in front of her, any sounds as tableaux.5 For example, an infant grasps it makes can be incorporated into her set a tableau, not an object, and listens to a 'D. So long as she does not have to relate the tableau, not an object. sights and sounds independently, sight and Several independent investigators have sound can be mixed together in the same recently reported data that generally sup- Level 1 skill. This lack of differentiation at port the pattern of developmental changes Level 1 contrasts with Piaget's (1936/1952) predicted by the four sensory-motor levels argument that young infants have differ- (Emde, Gaensbauer, & Harmon, 1976; entiated schemes for seeing, hearing, grasp- Kagan, 1979; McCall, Eichorn, & Hogarty, ing, and so forth, which must be coordinated 1977; Uzgiris, 1976). McCaH's analyses are together. The undifferentiated and unco- especially relevant: In examining patterns of ordinated status of Level 1 skills in the correlations among items in infant tests, present theory fits Werner's (1948,1957) he found changes in correlation patterns characterization of a developmentally prim- that suggested four successive periods of itive state. Many of the studies of classical change and consolidation in the first two and operant conditioning in young infants years of life—times of instability in cor- may involve such undifferentiated multi- relations followed by times of stability. If modality sets (see Papousek, 1967; Samer- infants are in fact developing through Levels off, 1971). 1 to 4 in an age-related progression, one Although infants cannot control any rela- would expect periods of change and con- tions between sets at Level 1, they do solidation in correlations exactly like those readily drift from one set to another, usually that McCall found. Further research to test led by some tableau. Consequently, even the relation between McCall's findings and though they cannot yet coordinate two sets, the levels clearly needs to be done. they do not become stuck on one set for The characteristic structure of Level 1 is long. Indeed, their drifting from set to set the single sensory-motor set (shown in eventually leads them to explore the relation the top row of Table 3), a set, 'D, of acting between two sets and so to intercoordinate on tableaus, such as looking at a doll. A them into a Level 2 skill, simultaneously 12-week-old infant may look for long differentiating them from each other. periods at the tableau produced by a doll The characteristic structure of Level 2 is hanging on a string in front of her. Even
when the doll swings back and forth in a 5 wide arc, she can keep her gaze on it. This is For the same reasons, Piaget occasionally used this term in his works on infancy (Piaget, 1936/1952, a single sensory-motor set or action, the 1937/1954). He did not, however, use it consistently in set 'D of adaptations of looking at the doll these works, and he has not used it in subsequent tableaus. Similarly with the spring-and-cord works. 492 KURT W. FISCHER the sensory-motor mapping, in which one considered at every level and especially at sensory-motor set, 2A, is mapped onto a the earliest levels within a tier, where dif- second sensory-motor set, 2B, as shown in ferentiation is always poor. Table 3. One type of sensory-mo tor map- Level 3 is characterized by the sensory- ping is a means-end mapping, in which a motor system, in which two components of 3 child can use one action in order to bring one sensory-motor set, AG,H, are related to about a second action. For example, a 7- two components of a second sensory- 3 month-old infant looks at a tableau of a doll motor set, BG,H, as shown in Table 3. The and uses what she sees to guide her attempts most investigated type of sensory-motor to grasp the tableau (Field, 1976; Lasky, system is the means-end system. Unlike the 1977; Ruff, 1976). She has combined two means-end mapping of Level 2, the means- simple actions, looking at the doll and grasp- end system allows the infant to control ing it, into one means-end mapping in complex variations in means and ends which looking is used as a means to bring (Fischer, Note 4). For example, Piaget's about grasping. That is, she has mapped the 10.5-month-old son Laurent drops a piece of sensory-motor set 2D of looking at the doll bread, watches it fall, breaks off a crumb onto the sensory-motor set 2H of grasping and drops it, watches it fall, and so forth it, as shown in Table 3. She may also have (Piaget, 1936/1952, Observation 141). He a separate, complementary mapping, in constantly varies the means (the way in which she maps grasping the doll onto look- which he drops the bread) and watches ing at it. For example, she grasps the tableau closely the variations in the end (seeing the of the doll and brings it before her eyes so bread fall). that she can look at it. Similarly, with the At Level 2, he was unable to perform spring-and-cord gadget, an infant pulls on such a complicated experiment in action; he the spring, 2G, so that she can watch it could learn little more than that dropping stretch, 2S. Many of Piaget's (1936/1952) produced falling. The reason for this limita- secondary circular reactions are means - tion was that he could relate only one aspect end actions of this sort, although a number of dropping the bread to one aspect of seeing of the behaviors that he classifies in this the bread fall. category seem to be complex forms of Level At Level 3, he can relate two aspects of 1 actions. each action, and therefore he can build skills Sensory-motor mappings should include that coordinate and differentiate types of many types of skills besides means-end variations in dropping with types of varia- mappings, especially skills involving two tions in falling. Similar kinds of skills can be components within the same modality. built with the spring-and-cord gadget—for Bertenthal, Campos, and Haith (in press) example, learning not only that pulling the describe one such skill: By 7 months, infants string makes it stretch but that pulling it in can apparently relate several visual com- different ways makes it stretch differently. ponents such as angles to form a line (see Examples of such means-end systems Level II in Figure 2). Presumably many abound in the research literature (e.g., more such mapping skills develop within Bryant, 1974, p. 162 ff.; Koslowski & modalities such as looking, grasping, and the Bruner, 1973; Fischer & Roberts, Note 3). like in infants. As with earlier levels, researchers have Just as with Level 1, however, Level 2 neglected other types of Level 3 skills, such skills cannot be subdivided according to as those within a modality (see Fischer & adult conceptions of modalities. If stimuli Corrigan, in press). from two different adult-defined sensory Despite all the sensory-motor sophistica- modalities, for instance, co-occur in such a tion of Level 3, the skills are still definitely way that the infant can treat them as one limited: The infant is only able to control source of variation, then at Level 2 the one sensory-motor system at a time, and infant can treat them as a single set that she therefore he cannot yet deal with many of can relate to a second set. The same kind of the complexities of acting on objects, nor concern about the definition of sets must be can he understand objects independently THEORY OF COGNITIVE DEVELOPMENT 493 of his own actions. In the world, every vertical or horizontal segment. Tasks can be object is in fact the focus of a number of designed that will help him to separate such different sensory-motor systems; that is, factors in one situation, but when the factors every object can be made to participate in covary in a task, the child will treat them or produce many different types of actions. in a single representation. The ability to understand objects in this way Many different types of representational (as independent agents of action) first de- sets should develop at Level 4, according to velops at Level 4 (Watson & Fischer, 1977). the theory; and Piaget (1946/1951, Observa- tion 64) described a behavior that demon- Representational Tier: Levels 4 to 7 strates a second type, a set of objects or events that all share a single action or Level 4 is the culmination of the sensory- characteristic. His daughter Jacqueline used motor tier, and so it produces a new type the word bimbam to mean swaying or flutter- of set and begins a new tier, the representa- ing. She combined her sensory-motor tional tier. In terms of the repetitive cycle of system for rocking back and forth on a piece levels, the characteristic structure for Level of wood with her system for making a leaf 4 is the system of sensory-motor systems flutter and used "bimbam" to refer to both. (sensory-motor Level IV), which is the Then she gradually extended this repre- same as the single representational set sentational set to a wide range of objects.6 (representational Level I). This type of skill Other examples of the construction of single is a relation between two sensory-motor representational sets from sensory-motor systems, as shown in Table 3. The combina- systems have been described by Bertenthal tion of these systems generates the single and Fischer (1980), Watson and Fischer representational set in which children can (1977), Fischer and Corrigan (in press), represent simple properties of objects, Fischer and Roberts (Note 3), and Fischer events, and people independently of their and Jennings (in press). own immediate actions. A word of caution may be helpful at this With the spring-and-cord gadget, the child point about the meaning of representation. can combine Level 3 systems for the gadget The term is often used as a virtual synonym into a single Level 4 representation. One for recall memory or for symbol use. But in such skill involves the child's understanding skill theory, representation is different from that the spring itself stretches. For example, both of these meanings. It refers to the co- the following two systems can be co- ordination of two or more sensory-motor ordinated at Level 4: When he pulls the systems to form a single representational spring, it stretches; when he sees someone set, not to recall memory or symbolization else pull the spring, it stretches. Therefore, per se. Skills involving both recall memory a characteristic of the spring is that it and symbol use can develop before Level 4, stretches; the child controls a representa- and in addition skills can be constructed at tional set 4L for the spring's stretching. In Level 4 that do not centrally involve either the same way, he constructs a set *W repre- recall or symbol (Fischer & Corrigan, in senting that the weight itself can "pull," press). A single representation is defined by independently of his feeling it; and he con- its structure, not by its function as recall, structs a set *C representing that the cord symbol, or any other such psychological can be big, independently of his making category. it move. The characteristic structure for Level 5 is With these single representations, the the representational mapping, in which one child shows a lack of differentiation anal- representational set, 5/?, is mapped onto a ogous to that with Level 1 single sensory- second representational set, 5r, as shown motor actions. In the gadget, he will confuse the pressure exerted by the weights with 8 The rules of compounding, substitution, dif- their size, mixing them both together as ferentiation, and intercoordination nicely account for "big." Similarly, he will confuse the total the sequence by which this skill developed, as de- length of the cord with the length of the scribed by Piaget (1946/1951). 494 KURT W. FISCHER in Table 3. With this kind of skill, the child combines the vertical and horizontal lengths can relate variations in one representation to of the cord when one weight is used with the variations in a second representation.7 same length when another weight is used, and Consider a 4- or 5-year-old who is given the thus he knows how the lengths vary together spring and several weights of different sizes and compensate for each other (Piaget et al., from the gadget in Figure 1. If he has had 1968; Verge & Bogartz, 1978). With the sufficient experience with the task, he can gadget, he can also construct several other roughly use the size of the weight (one set) to Level 6 systems, each involving the relation control the length of the spring (the other of two concrete variables to each other. set), thus understanding in an approximate Other representational systems that have way that large weights will make the spring been studied in the research literature in- stretch farther than small weights. clude most of Piaget's concrete opera- Notice in Table 3 that this structure (like tional tasks (e.g., Inhelder & Piaget, 1959/ all representational structures) can be de- 1964) and a number of other tasks (e.g., scribed either in terms of representational Watson & Fischer, 1980; Winner, Rosen- sets without visible reference to their sen- stiel, & Gardner, 1976). sory-motor origins or in terms of the Despite all this sophistication, however, sensory-motor sets on which the repre- the skills of Level 6 are still definitely sentational sets are based. For example, limited. The child can only deal with one the child's understanding of the relation Level 6 system at a time. He cannot relate between weight and spring ties directly to various systems to one another. Even if he his overt actions of manipulating and seeing understands every one of the possible Level the weight and spring, because the repre- 6 systems in the gadget, for example, he sentational sets are actually composed of cannot integrate them into a single higher- sensory-motor systems specifying what the level skill. More generally, he cannot yet child can do with the gadget. understand objects independently of their Besides the representations for weight overt characteristics, because he is limited and length of spring, the child could also to dealing with one Level 6 system at a time. construct representations for the length of That is, he cannot think of objects in the the vertical segment of the cord and the abstract. length of the horizontal segment (or depend- ing on the nature of the specific gadget, a Abstract Tier: Levels 7 to 10 representation for the total length of the Level 7 is the culmination of representa- cord). A child who is very familiar with the tional development, generating a new kind gadget could conceivably possess at least 12 of set and starting a new tier, the abstract different mappings, all possible pairings of tier. In the recurring cycle of four levels, the four sets—weight, spring length, ver- the characteristic structure for Level 7 is tical and horizontal lengths of cord (see the system of representational systems Wilkering, 1979). Despite all this knowl- (representational Level IV), which is the edge, the child's understanding of the gadget same as the single abstract set (abstract would be peculiarly disjointed because of Level I). In an abstract set, the person his inability to consider two aspects of each abstracts an intangible attribute that charac- set simultaneously. That is why, for ex- ample, he has difficulty treating the vertical and horizontal lengths as segments of a 7 Piaget does not postulate the existence of a major single cord of constant length. cognitive-developmental change in the middle pre- school years, but some of his own research suggests Level 6 is characterized by a representa- that there might be such a change (Piaget et al., 1968), tional system, in which the child relates two and many studies over the last two decades have 6 subsets of one representation, /?J>K, to two documented that preschool children's abilities are far subsets of a second representation, 6r , greater than prior research had indicated (Gelman, JjK 1978). Also, two developmental theories that are not as as shown in Table 3. For example, he can well known as Piaget's posit a major developmental understand conservation of length of the shift at about age 4 (Bickhard, 1978; Isaac & O'Connor, cord in the gadget, as described earlier. He 1975). THEORY OF COGNITIVE DEVELOPMENT 495
terizes broad categories of objects, events, length and width compensate for each other. or people. (Note that, as with representa- The coordination of these two concrete tion, abstraction has many different mean- conservation skills produces the abstract ings in psychology; see Pikas, 1965. These concept of conservation, which can then be various meanings should not be confused generalized to other tasks. Other instances with the specific meaning used here.) of Level 7 skills include most analogies In a Level 7 skill, the person can control (Lunzer, 1965), political concepts like law the relation between two representational and society (Adelson, 1972), and a few of systems, as indicated by the Level 7 struc- Piaget's simpler formal operational tasks ture in Table 3. Consider a 15-year-old boy (Inhelder & Piaget, 1955/1958). who can control a system of systems for the Following the recurring cycle, abstrac- sets in the spring-and-cord gadget. He can tions should develop through Levels 7 to 10, integrate several of the systems from the For example, with the spring-and-cord previous level into a single Level 7 system gadget, the individual will start with single that controls the relations among the weight, abstractions such as conservation, then the vertical length of the cord, the hori- relate two such abstractions in a mapping, zontal length of the cord, and the length and so forth. Because so little research of the spring. When he is thinking, for has been done on cognitive development example, about how the changes in weight beyond adolescence, however, no data are produce changes in the length of the spring, available to provide a strong test of such he can simultaneously consider how those predictions. To illustrate the kind of de- changes relate to the changes in the vertical velopmental progression that is predicted and horizontal lengths of the cord. He can and to emphasize the applicability of the thus understand how all the changes covary. theory to things other than cold cognition, This skill not only allows him to control I will present a hypothesized sequence in the gadget effectively, but it also gives him the development of a person's identity an abstract set for the general state of the (Erikson, 1963)—one's sense of the kind gadget. of person one is. Many different kinds of abstractions can At Level 7, single abstract sets, a person be constructed at Level 7. For example, a can for the first time construct abstract person can for the first time understand the identity skills (see Erikson, 1974). These abstract concept of conservation—varia- identity concepts result from the coordina- tions in two related quantities compensate tion of two representational systems about for each other so as to produce no change the self. For instance, a certain 9-year-old in some superordinate quantity. With only may have a Level 6 system for identification Level 6 skills, the person can understand with his father's career as a psychologist. most of the individual kinds of conserva- He relates his representation of himself to tion that Piaget and his colleagues have his representation of his father as a psychol- documented (Piaget & Inhelder, 1941/1974; ogist (Kagan, 1958). Likewise, he has an- Piaget & Szeminska, 1941/1952), but cannot other system relating his representation of integrate those separate conservations into himself as both skilled with other people and an abstract concept of conservation. good at science to his representation of For instance, the person combines the what psychologists do: They are people- skill for conservation of the length of the oriented scientists. Most 9-year-olds are not cord in the gadget with the skill for con- yet capable of coordinating two such Level 6 servation of amount of clay (where the same systems into a Level 7 skill. piece of clay is squeezed into different A few years later, when the child can shapes, such as from a ball to a sausage). coordinate the two systems, he can thus In the conservation-of-length task, the two construct his first abstract set for his career lengths are equal because the vertical and identity. With the addition of a few other horizontal lengths compensate for each representational systems to the Level 7 skill other. In the conservation-of-clay task the via microdevelopmental transformations, two amounts are equal because changes in he can build a complex abstract set relating 496 KURT W. FISCHER various of his own characteristics to various progression from pre-operational to formal aspects of the career that he is considering. operational thought, according to skill At LevelS, abstract mappings, the person theory, because both the Piagetian periods can relate one abstract identity concept with and the scientific progressions involve another. For example, he can coarsely development within a tier from Levels I relate his own career identity with his con- to IV.8 Oddly, Piaget too (1970; Piaget in ception of his potential spouse's career Beth & Piaget, 1961/1966) has suggested identity: Perhaps he sees his own career that there may be general parallels between identity as requiring that his spouse be in a the development of scientific theories and closely related career or perhaps as re- the development of cognition in the child. quiring that his spouse be primarily a home- I say "oddly" because his position on maker. formal operations seems to preclude such Level 9 abstract systems produce a much parallels. more flexible, differentiated relation be- Within Piaget's framework, cognitive de- tween two identity concepts. For instance, velopment virtually ends with formal opera- the person can relate two aspects of his tions: Adolescents entering the formal own and his spouse's identity, such as operational period have achieved fully career and parental identities, and thus con- logical thinking, and there is little more for sider in a more differentiated way what his them to do, except perhaps to extend their own identity requires of his spouse's logical thinking to new content areas (Piaget, identity and what his spouse's identity 1972). Many people have been dissatisfied requires of his own identity. with this conception of formal operations Finally, at Level 10, systems of abstract (e.g., Arlin, 1975; Gruber & Voneche, 1976; systems, this person can coordinate two or Riegel, 1975; Wason, 1977), but there has more abstract identity systems. He might been no alternative position for analyzing relate his own and his spouse's career and development beyond early adolescence. parental identities now (one Level 9 system) Consequently, major age differences in the with their career and parental identities acquisition of various of Piaget's formal 10 years ago when they were first married operational tasks have been interpreted pri- (a second Level 9 system). The result is a marily as resulting from performance higher-level conception of what their joint factors, not from developmental changes career and parental identities have been like (Inhelder & Piaget, 1955/1958; Martarano, during their marriage. 1977; Neimark, 1975). According to skill Although I know of no rigorous tests of theory, many of these age differences may this or any other developmental sequences well arise because the tasks requirev dif- in abstract skills during adolescence and ferent levels of abstraction. adulthood, several investigators have re- Piagetian scientific tasks and the rarefied ported data that generally support the pre- atmosphere of theory construction are not dictions of development from Levels 7 to 10. the only places that skills should develop Some of the most detailed findings involve through Levels 7 to 10. Most adults prob- developments in the history of science. Both ably master at least a few skills beyond Miller (Note 5) and Gruber (1973; Gruber & Level 7, like the hypothesized identity con- Barrett, 1974) have described developments cepts. Other skills that probably belong to of scientific theory that seemed to them to Levels 7 to 10 include moral judgment, the roughly follow Piaget's description of cog- managerial skills of the director of a corpora- nitive development from the pre-operational tion or a school system, the skills required period to the formal operational period. to write an effective essay or novel, and the Miller illustrates this parallel for the de- skills involved in programming and operat- velopment of quantum mechanics, and Gruber for the development of Darwin's theory of evolution. If these scientific 8 Within the present theory, Piaget's pre-operational, theories were developing through Levels 7 concrete operational, and formal operational periods to 10, their progression would resemble the are explained by Levels 4 to 7. THEORY OF COGNITIVE DEVELOPMENT 497 ing a computer (Fischer & Lazerson, in sets when one of the other four transforma- press, chap. 13). tions occurs, but it can also be used sepa- rately to predict microdevelopmental steps. Transformation Rules The microdevelopmental transformations of differentiation, substitution, focusing, Now that the structures of the levels have and compounding eventually produce the been described, the operation of the five macrodevelopmental transformation of transformation rules can be illustrated with intercoordination. These five transforma- some precision. The five rules specify how tion rules are probably not exhaustive; a skill is transformed into a new, more ad- future research will indicate whether ad- vanced skill. These rules are thus the heart ditional transformation rules are required. of the mechanism for predicting specific All the transformations are defined sequences of development. The need for structurally. Two or more skills with given such a set of transition rules to account structures are transformed into one or more for developmental change has been recog- skills with a new type of structure. The nized for a long time by many develop- induction of a specific structural transforma- mental psychologists (e.g., Beilin, 1971; tion always involves both organismic and Brainerd, 1976; Flavell, 1963; Kessen, 1966; environmental factors. At least two or- Van den Daele, 1976). The rules are also ganismic factors are involved: The person intended to apply to changes in the organiza- must initially have the skills required for tion of behavior during learning or problem application of the transformation and must solving (Fischer, 1975, 1980; Leiser, 1977). be capable of applying the transformation The transformation rules and the skill rules to those skills. For example, if a per- structures of the levels should be able to son has the necessary initial skills but they explain most of the developmental se- are already at her optimal level, then she will quences documented in the research litera- not be able to apply the transformation for ture. In addition, many new sequences can combining those skills to reach the next be predicted that have not yet been investi- higher level. gated. In this section on the transformation Likewise, at least two environmental rules, however, I will refrain from reviewing properties are necessary. First, the environ- empirical support for the rules, so that I ment must have properties such that if the can present the concepts briefly and directly. initial skills are transformed, the resulting In a later section, several studies testing new skill will work. Second, the specific predictions based on the rules will be de- environmental situation must have prop- scribed. erties such that it will induce the person to The five transformation rules are inter- use the initially separate skills in juxtaposi- coordination, compounding, focusing, sub- tion, thus leading her to explore the relations stitution, and differentiation. Intercoordina- between the initial skills and construct the tion and compounding specify how skills transformed skill (see also Schaeffer, 1975). are combined to produce new skills. Inter- The transformation therefore requires both coordination describes combinations that organism and environment; transformations produce development from one level to the cannot be attributed to either organism or next (macrodevelopment), and com- environment alone. pounding describes combinations that Two of the transformation rules, inter- produce development within a level (micro- coordination and compounding, involve development). Focusing and substitution combinations of two skills to produce a new, specify smaller microdevelopmental steps more complex skill. Many psychologists than compounding. Focusing deals with have talked about combinations of skills as moment-to-moment shifts from one skill to a mechanism to explain the development of another, and substitution designates certain more complex skills, especially in the litera- cases of generalization of a skill. The fifth ture on skill acquisition (e.g., Bruner, 1971, rule, differentiation, indicates how sets be- 1973; Fitts & Posner, 1967) and the Piagetian come separated into potentially distinct sub- literature (e.g., Cunningham, 1972; Hunt, 498 KURT W. FISCHER
1975; Piaget, 1936/1952). The first two trans- ments. When her skills with the gadget are formation rules attempt to specify exactly only at Level 5, she can understand two how such skill combinations occur. separate representational mappings in- volving the vertical and horizontal segments of the cord. She can understand the mapping Intercoordination 5 from the horizontal segment, CH, to the 5 Intercoordination specifies how the vertical segment, CV, using the horizontal person combines skills to develop from level length to predict the vertical length; and she to level, all the way from Level 1 to Level can understand the mapping from the ver- 3 10. The process is analogous to the com- tical segment, CV, to the horizontal seg- 5 bination of atoms to form a molecule. At ment, CH, using the vertical length to pre- the beginning of the process of interco- dict the horizontal. As a result, the child's ordination, the child has two well-formed behavior with the cord at Level 5 seems skills, a and b, at a specific Level 1. The paradoxical to an adult. The child seems to two skills are functioning separately from understand how the horizontal and vertical each other until some object or event in the segments of the cord change and how the environment induces the child to relate the changes relate to each other, yet she does two skills to each other. The child then not recognize that the total length of the cord works out the relationship between the two must always remain the same because the skills with that object or event and so changes compensate for each other (Wil- gradually intercoordinates the skills. When kering, 1979). the intercoordination is complete, the two The paradox is resolved when the child skills, a and b, from Level L have been intercoordinates the two mappings to transformed into a new skill, d, at Level produce the Level 6 skill for conservation L+ 1, which includes them. The process of length in the gadget, as follows: is diagramed as follows: 5 5 5 5 [ CH — CvH Cv — CH] = a-b=d. (D BCH.v+» SCH.v]. (2) The multiplication symbol signifies inter- The child with this Level 6 skill can under- coordination (Table 2). stand how vertical and horizontal length The essence of the process of interco- interrelate, instead of merely how vertical ordination lies in what seems to most adults relates to horizontal and how horizontal to be a paradox. A child is given a task relates to vertical (Verge & Bogartz, 1978). that normally requires a Level L under- That is, she has constructed a skill for the standing, but her skill for that task is only at total length of the cord (composed of hori- Level L- 1. Consequently, she seems to zontal and vertical components), and that have all the knowledge that is needed to skill allows her not only to predict how perform the task, yet cannot do it. Only horizontal and vertical vary but also how when she intercoordinates the relevant skills their covariations sum to a constant length. at Level L - 1 to form the new skill at The formal descriptions of Levels 1 to 7 Level L will she be able to perform the task. in Table 3 indicate graphically how inter- Note, however, that this process of inter- coordination occurs at each level. Re- coordination is gradual and continuous. The peatedly as one moves down the table, the fact that it involves qualitative change does combination of two skills at one level pro- not in any way imply that the change is duces a new kind of skill at the next level. abrupt or discontinuous. The diagrams in Table 3 also show how each The development of conservation of skill at one level still includes the two skills length in the gadget (Piaget et al., 1968) from the previous level. The formal de- provides a clear illustration of this paradox. scriptions thus show both the origin of each As stated before, the child must have a higher-level skill in the lower-level skills Level 6 skill to understand that the length of and the emergence of a new type of skill at the cord conserves despite changes in the the higher level. lengths of the vertical and horizontal seg- I chose the term intercoordination be- THEORY OF COGNITIVE DEVELOPMENT 499 cause it provides a specifically appropriate 3H] + [3H <-» 3S] = description of the process of combination 3 of two skills at one level to form a new skill 3H S]. (4) at the next level. Intercoordination means She thus produces a more complex Level 3 reciprocal coordination. Two lower-level skill that allows her to control the relations skills become coordinated with each other among all three actions. and thereby produce a new higher-level What behavioral consequences does such skill. In this article, the term inter coordina- a skill have? When the child is actually in tion is reserved explicitly for this process. bed, it is difficult to assess whether she has The term coordination is used to refer in the skill, because the context alone pro- general to all instances of a person's relating duces all three components. As a result, she two or more actions whether or not he or she can show all three actions together without is going through the process of interco- controlling the relations among them. The ordination. existence of this environmentally elicited conjunction of the three actions, on the Compounding other hand, shows how the environment can induce combination of the actions into a The second rule for combination of skills, complex skill. At least once or twice every compounding, specifies the most important day, the child is faced with a situation microdevelopmental transformation. In where the three actions go together. Almost compounding, two skills, a andb, at Level L inevitably, then, she will explore the rela- are combined to form a more complex skill, tions among the actions and ultimately c, at the same Level L.9 The process is produce the compounded skill in Equation 4. diagramed as follows: For assessment of this compounded skill, pretend play provides a better situation b =c. (3) than going to bed, because in pretend play the child must actively put the three actions The addition symbol signifies compounding. together. When she can control all three Just as with intercoordination, compound- actions in a single system, then she can ing is induced by both organismic and en- pretend to go to sleep — holding the pillow, vironmental factors. First, the person must placing her head on it, and closing her eyes possess skills a and b, and second, some (Watson & Fischer, 1977). Other develop- object or event in the environment must in- mental sequences involving compounding duce him or her to combine them. have been tested and supported by Berten- An example will clarify the compounding thal and Fischer (1978), Watson and Fischer process. Consider an 18-month-old who has (1980), Hand (1980), and Fischer and one Level 3 skill relating holding a pillow, Roberts (Note 3). 3P, to placing her head on the pillow, 3H, and The process of compounding is not neces- a second Level 3 skill relating placing her sarily limited to combining just two simple head on the pillow, 3H, to going to sleep, 3S. skills. It also has more complex forms, with (Going to sleep is originally an involuntary combinations of larger numbers of skills. response, but like blinking and breathing, it For example, the child might compound can be brought under partial voluntary the Level 3 skill in Equation 4 so that it control. Many children at this age expend a included four or five actions instead of only lot of effort trying to control sleeping and the three.10 Indeed, such successive compound- circumstances that accompany it. Usually, 3 the specific response that is signified by S is 9 Compounding of another sort might also occur. The voluntarily closing the eyes or saying skill d at Level L + 1 might be combined with skill c "sleep.") With these two skills, the child at Level L to form the more complex skill e at Level still cannot control all three actions at once: L + 1. Research is required to determine whether both types of compounding exist. holding the pillow, placing her head on the "' Two points should be noted about this complex pillow, and going to sleep. To do so, she kind of compounding. First, the number of skills must compound the two Level 3 skills: compounded cannot be endless because compounding 500 KURT W. FISCHER ing may ultimately account for much of the task determine the limit of what the person process of intercoordination, as I will illus- can handle cognitively in that task. At any trate later. one moment, she cannot bring to bear all of Compounding describes relatively large her skills; normally, she can deal with only microdevelopmental steps. The next two one skill at a time. Focusing describes the transformation rules, focusing and sub- person's shifts from one skill to another stitution, describe smaller microdevelop- within the level or levels at. which she is mental changes. functioning in the task. For instance, the hypothetical child knows a lot about the Focusing: Moment-to-Moment Behavior gadget, because she has mastered all 12 mappings. Nevertheless, her understanding Focusing deals with one kind of shift in of the gadget is severely limited by the fact what is commonly called attention. It that she can focus on only one mapping at describes not only a type of developmental a time. change but also a type of moment-to- Say that at a certain moment she is con- moment change in behavior. In a specific sidering the set, 5W, of weights. She cannot task or context, a person will normally deal with all six of the mappings for weight have a collection of skills available, and but must focus on just one, such as the those skills will generally be related to each mapping of weight, 5W, onto length of the other because subgroups of them will share spring, 5L. A few moments later, she shifts one or more sets. For example, recall the focus to a second, related skill, the mapping hypothetical child who has a complete Level 5 of horizontal length of the cord, CH, onto 5 understanding of the gadget (without length of the spring, 5L, and then she shifts compounding): She understands 12 dif- focus to the mapping of length of the ferent two-set mappings, all possible pair- spring, 5L, onto horizontal length of the ings of the four sets involving the gadget. 5 cord, CH. These changes in focus are In this collection of skills, each set is in- diagramed as followc: cluded in six of the mappings. At a given 5 5 moment with the gadget, the child will be — L] > [ CH — using one of the mappings. When she shifts focus, she shifts from one specific mapping (7) to a second closely related mapping that Clearly, changes in focus can produce shares at least one set with the first map- 11 very complicated sequences of behavior. In ping. A shift in focus from skill e to skill/ assessing a person's skills with a task, care is represented symbolically as follows: must be taken to separate mere changes in e>f. (5) focus from the actual control of relations between sets. The shifts in focus indicated The symbol for "greater than" thus signifies in Formula 7 do not demonstrate control by a shift in focus. When a shift in focus can the child of the compounded skill [5W — 5 5 5 5 be consistently controlled by the child, the L — CH — L — Ca|, although under transformation is diagramed: the proper environmental circumstances Foe (6) they can be transitional to the formation of such a compounded skill. The levels of the collection of skills that a Focusing is not, however, merely a person has available to her on a specific statement of a methodological difficulty. is probably seriously limited by memory. Limitations " Notice that according to this definition, focusing should be much less severe when the skills are inter- could not happen at Level 1, because skills at Level 1 coordinated into a higher-level skill. Second, a mere each include only one set. However, the theory pre- string of behavior, occurring once or twice, does not dicts that Level 1 sensory-motor sets are generated indicate that the person has compounded all the by a prior reflex tier, which specifies the components behaviors in the sequence into a single skill. Just as of a Level 1 set and thereby indicates how focusing with the little girl in bed, one must be certain that applies to Level 1. The nature of this tier will be the person actually controls the relations between sets. suggested later. THEORY OF COGNITIVE DEVELOPMENT 501
5 It allows predictions of certain kinds of CV— (12) developmental orderings. Consider a task that can be solved with, at a minimum, which involves control of all three variables two skills at Level L and a shift in focus at once instead of only two. from one of the skills to the other. This task According to this analysis, then, the child is more complex than a task that can be will show the following microdevelopmental solved with, at a minimum, one skill at Level sequence of skills: first Formula 8 or 9, then L. If the two tasks are within the same Formula 10, then Formula 11, and finally task domain, then the first, more complex Formula 12. Similarly, the focusing rule task is predicted to develop after the second predicts many microdevelopmental se- task. quences, such as transitional steps between For example, suppose that the gadget is acquisition of the simple Level 3 skills on partially covered, so that only two variables the left-hand side of Equation 4 and acquisi- are visible at a time. The child first deals tion of the compounded Level 3 skill on the with only the weight, 5W, and the vertical right-hand side of Equation 4. See Hand segment, 5C , using the skill (1980) and Watson (1978) for tests of ad- V ditional sequences involving focusing. 5 — CV]. (8) Substitution Once she has used this skill, the cover is changed so that she can see only the vertical The transformation rule of substitution segment and the spring, which requires the deals with one type of generalization: A skill skill at Level L is mastered with one task,
[5Cy_5L] (9) and then the person attempts to transfer it to a second, similar task. The rule applies By shifting what is covered, the experi- when all components but one in the first task menter can thus control the child's change are identical with those in the second task in focus: and when that one different component can 5 5 5 be generalized to the second task. At [ W — Cv ] > [ C v — (10) Levels II and III, the component must be a For the child to do this task as described set; at Level IV (which is Level I of the next in Formula 10, she must have both Level 5 tier), it can be a set or a system. The skill skills. The focusing rule therefore predicts with the substitute component will be that the skills in Formulas 8 and 9 will mastered after the original skill and before develop before the change in focus in any skills of greater complexity in the same Formula 10. A developmental sequence of task domain. Substitution is diagramed as this type has been demonstrated by Gottlieb, follows: Taylor, and Ruderman (1977). Sub d = dlt (13) With the covering procedure, the experi- menter can teach the child to change focus or for a specific level, consistently. The child will thus learn a new Sub [5A — 5fi] = [5A (14) skill involving a change of focus: 5 The set Bt is the substitute set. 5 5 5 5 Foc([ W CV],[ CV — L]) The skill for pretending to go to sleep 5Cv)>(sC — (11) provides an example of the application of v this rule. After the child develops the skill which will allow her to do the task even in Equation 4, she extends that skill to a when all three variables are uncovered. substitute object. Instead of holding her This controlled-focusing skill is slightly pillow and pretending to go to sleep, she more advanced developmentally than the substitutes a piece of cloth for the pillow: simple change in focus in Formula 10. It is Sub [3P <-» 3H <-» 3S] also transitional to the compounded Level 3 3 3 5 skill = [ Pt <-> H «-» S]. (15) 502 KURT W. FISCHER
3 The set Pj, holding the cloth, is substituted Diff A = AM, AN. (17) for the original set 3P, holding the pillow. The extension of the pretending skill to the The development of conservation of cloth develops after the original skill (on the length in the gadget illustrates how dif- left-hand side of Equation 15) and before ferentiation occurs when a new skill is any more complex skills (Watson & Fischer, formed. A child with Level 5 mappings for 1977). the gadget understands generally how the length of the vertical segment relates to the length of the horizontal segment and vice Differentiation versa but does not yet understand conserva- The final transformation rule for explain- tion of the total length of the cord. Another ing development is differentiation, in which way of stating this confusion is that in this what was initially a single set becomes task, the child has not adequately differ- separated into distinct subsets. Differentia- entiated the total length of the cord from the tion is probably always a product of one of lengths of the horizontal and vertical seg- the other transformations, especially inter- ments. When asked about the total length coordination or compounding. As Werner of the cord, the child confuses it with the (1948, 1957) has argued, differentiation and length of the horizontal or vertical segment. integration always occur together. In skill Although this kind-of lack of differentiation theory, differentiation and integration (com- may seem odd to an adult, it occurs com- bination) are thus complementary, whereas monly in children and indeed is charac- in many other approaches they are opposed teristic of earlier cognitive levels (Smith & (e.g., Kaye, 1979; McGurk & MacDonald, Kemler, 1977; Werner, 1948). 1978). The lack of differentiation in the gadget is Differentiation can therefore be either resolved when the child intercoordinates the microdevelopmental or macrodevelop- two Level 5 mappings to form the Level 6 mental, depending on which other trans- system for conservation of the total length formation is involved. For macrodevelop- of the cord, as shown in Equation 2. The intercoordination produces differentiation ment, the degree of differentiation is so great 6 of the set for total length, CV,H, from the that a set at Level L should be considered 6 sets for vertical length, CV, and horizontal a different set when it reaches Level L + 1. 6 At higher levels, earlier global sets are length, CH: divided into distinct new sets that serve Diff (5C , 5C ) = 6C , 6C , 6C , . (18) in place of the earlier sets. (The superscripts V H V H V H to the left of the capital letters designating In the set for total length, the child com- sets—see Tables 2 and 3—indicate the bines covariations in vertical and horizontal level of the set and thereby serve as a lengths into a concept of total length. Note reminder that a set differentiates as it de- also that the sets for vertical and horizontal velops to higher levels). Because of the lengths can be differentiated more finely at formation of these new sets, the person Level 6 than at Level 5: The child can deal controls an ever larger repertoire of sets as with smaller variations in length in each of development proceeds. The expansion of the sets. the number of sets leads to a corresponding The specific variables that are separated increase in the number of skills, since the in a child's behavior are a function not only newly differentiated sets can become of the level but also of the particular task. separate components in new skills. For a child with skills at a given level, The process of differentiation is dia- changes in the task alone can produce gramed as follows: separation. For example, if the cord in the Diff d=d* (16) gadget (Figure 1) were straightened out, a child with the Level 5 skills in Equations 2 where the subscripts indicate subsets in the and 18 could easily control the set for the skill d. Differentiation of a specific set A is total length of the cord in the modified designated: gadget, since it would be only a single set. THEORY OF COGNITIVE DEVELOPMENT 503
At the same time, with a gadget like the tion of the cord, but because of fatigue or original one, in which the cord is still emotional upset is now functioning at Level divided into vertical and .horizontal seg- 5. She can use a skill that would not be pos- ments, he or she could tell that the vertical sible for someone who has never developed and horizontal segments were each different this skill to Level 6. She might use the from the total cord in the modified gadget. coordinated lengths of the two segments of Likewise, certain experimental training pro- the cord to make coarse, qualitative Level 5 cedures can produce such separation or dis- predictions about the length of the spring: crimination (Denney, Zeytinoglu, & Selzer, 6 1977). [ CV,H — (19) The interaction of task and level helps to So far, I have emphasized general issues resolve a paradox in the developmental about differentiation because they are im- literature. In some experiments, young chil- portant for understanding how differentia- dren confuse variables like the several types tion and combination work together in skill of cord length in the gadget, but in other theory. But differentiation can also be used experiments children of the same age easily as a developmental transformation rule. separate variables that seem at first to be the That is, it can be used to predict steps in a same as the ones they confused (Kemler & developmental sequence. In the spring- Smith, 1978; Smith & Kemler, 1978). In- and-cord gadget, a skill for coarsely pre- deed, the same child can show both kinds of dicting vertical length from horizontal skills—ones demonstrating a global, syn- length is less differentiated than a skill for cretic whole that confounds several vari- predicting the same thing more exactly; and ables and ones using virtually the same vari- the coarser skill will develop earlier than the ables separately (Peters, 1977). In the tasks more differentiated one. In a sorting task, where she uses the variables syncretically, the skill for putting different shades of red the child must deal with a number of related into a single category is more differentiated variables at the same time, and her skill level than the skill for putting identical shades of is not sufficiently advanced for her to sepa- red into a single category, and the more dif- rate the variables. But in the tasks where ferentiated skill will develop later (Fischer she separates them, she does not need to & Roberts, Note 3). deal with all of them simultaneously; able to work with first one variable and then an- Ordering the Results of Transformations other, she can easily separate them. This separation is, of course, not the same With five different transformation rules, as the differentiation that is required to co- some principles are needed for ordering the ordinate all the variables in a single skill. results of the different transformations into For instance, with the Level 6 conservation developmental sequences. First of all, for a skill in the gadget, the child must differ- clear-cut prediction of a sequence to obtain, entiate covariations in vertical and hori- all skills must be in the same task domain. zontal lengths and combine them into a con- Given that they are in the same domain, cept of total length. The three types of length the following principles allow ordering of are not merely separated; they are also steps: integrated. 1. If one of the transformations is applied The relation between differentiation and to a skill or skills, the skill resulting from cognitive level has many other implications the transformation will develop after the for analyzing development, according to initial skills. skill theory. For example, when a person 2. Starting with specific skills at Level L, has at some point developed a skill to Level a skill resulting from an intercoordination L but is now using the skill or some of its transformation will develop after a skill components at a lower level, the sets will resulting from microdevelopmental trans- still show the effects of the earlier differ- formations, because the skill resulting from entiation at Level L. Suppose that a child intercoordination will be at Level L + 1. has developed the Level 6 skill for conserva- 3. When Principles 1 and 2 do not provide 504 KURT W. FISCHER an ordering, then for skills at the same level, Guidelines for Task Analysis those with more sets will develop later. 4. If more than one skill is involved in a Use of the theory to explain development behavior (e.g., because of the focusing requires a behavioral analysis of perform- transformation), that behavior will develop ance on the specific task or tasks in ques- later than the behaviors specified by each tion: What exactly must a person do to per- skill separately (by Principle 1). A skill that form each task? compounds the several skills into one will This kind of behavioral analysis is not as develop later than the same skills connected simple as it may seem. The situation is by a change in focus. If the focusing skills analogous to that of a behaviorist trying to involve a greater number of distinct com- determine which specific operants or re- ponents than the compounded skill, then as sponses comprise performance on a given a rule of thumb the focusing skills will task. Finding the operants is no easy develop later. matter (Breland & Breland, 1961; Schick, Notice that by these principles, many 1971). pairs of skills cannot be ordered develop- On the other hand, many investigators mentally. Of course, skills that have the have been highly successful in analyzing same type of structure but different com- behavior into its natural units (see de Villiers ponents cannot be ordered because they are & Herrnstein, 1976; Marler & Hamilton, in different task domains. But in addition, 1966). Premack (1965), for instance, found many skills within the same domain can- that simple observation of the actions that not be ordered—for example, two skills tend to recur regularly in an animal's be- that are the same except that one has a havior allowed him to infer a long list of substituted set and one has a differentiated natural operants that formed a hierarchy of set. reinforcers. And Fischer (1970, 1980) found With the descriptions of the transforma- that changes in patterns of responding over tion rules, all the major concepts of the trials in common learning situations demon- theory have been presented. The next step strated the formation of new, higher-level is to demonstrate how the theory functions behavioral units. as a tool for explaining and predict- The skill structures specified in the theory ing development. After describing a set are intended to reflect the natural units of of guidelines for analyzing tasks and relating behavior (both thought and action), in- them to the constructs of the theory, I will cluding its hierarchical character, with present several experiments that have used higher-level units subsuming lower-level the theory to predict specific developmental ones. Determination of the validity of these sequences and synchronies and will then structures will, of course, require extensive explain a few of the many possible general research. deductions from the theory. Use of the theory to analyze behavior into skill structures necessitates, first of all, Using the Theory to Predict Development a thorough knowledge of the available uni- verse of skill structures defined by the levels The theory can be used to predict and and transformation rules. Given that one explain various developmental phenomena, has this knowledge, then task analysis can including developmental sequences and be facilitated by using a set of guidelines synchronies, certain effects of the environ- that have been helpful for me and my col- ment on developing skills, individual dif- leagues. To illustrate the use of these guide- ferences in development, the nature of lines, I will show how each one applies to developmental unevenness, and structural an analysis of the development of an under- relations among developing skills. But all of standing of a social role during childhood these predictions and explanations depend (Watson, 1978; Watson & Fischer, 1980). on a prior step—task analysis (Brown & For a social category to be a social role, French, 1979; Gollin & Saravo, 1970; Klahr according to role theory, it must involve at & Wallace, 1976). least two social categories in relation to each THEORY OF COGNITIVE DEVELOPMENT 505
other (Brown, 1965; Mead, 1934). For systems are essentially role-specific be- instance, the social role of mother requires haviors or characteristics. For example, a the complementary role of child, and the doctor gives a patient inoculations (one social role of doctor requires the comple- sensory-motor system) and examines her mentary role of patient. Which skill struc- ears (a second system), and a patient takes ture is required, then, for a child to under- the inoculation and poses for the ear ex- stand a social role, such as a doctor ex- amination. amining a patient? 3. What are the relations between sets The guidelines for task analysis fall within that the child must control (among the two general categories: guidelines for deter- various possible relations shown in Table 3)? mining what the person must control and Once the first two questions have been guidelines for designing and interpreting answered, determination of the relations particular tasks. between sets is often simple. For the doctor role, the set for doctor must have at least Control a mapping relation with the set for patient: [5/? —55 ]. (20) At least three major questions are in- D P volved in analyzing what the person must With a mapping, the child can relate the control. doctor role to the patient role, which is all 1. Does the skill require sensory-motor, that is necessary to meet the minimal cri- representational, or abstract sets? For terion of relating a social role to its comple- understanding a social role, sensory-motor ment. sets are clearly not sufficient, since the role involves more than the child's own actions. Tasks Representational sets are necessary, be- Thus far, the skill analysis for the role of cause the role involves the characteristics doctor has proceeded as if the skill could be and actions of people independent of the considered independently of a particular child. Abstract sets are not needed, since task. But in fact, the analysis must take the social roles as defined here require only particular task into account. At least three concrete characteristics and actions of major issues are involved in designing and specific people (a doctor relating to a pa- interpreting specific tasks. tient) rather than intangible attributes. 4. What is the particular task, and what Understanding the general definition of a must the person control to perform it? For social role as involving one social category the role example, Watson and I devised a and its complement would necessitate the task for assessing the child's understanding control of intangible attributes, that is, of the role of doctor (Watson & Fischer, abstract sets. 1980). Seated at a table, a child was shown 2. What are the sources of variation that two rigid-cardboard, stand-up dolls (a the person must control in the skill? For the doctor and a child patient) and a few doctor's doctor role, the child would have to control instruments. The experimenter acted out two representational sets, not only the set the doctor's examination of the patient and for a person acting as doctor, ^?D, but also then asked the child to act out a similar the set for a person filling the complementary story. The child was not asked to copy the role of patient, SP. Both of these sets are story precisely, so that no requirement of required because according to the definition exact imitation would interfere with the of social role, a role must be related to its child's demonstrating her knowledge. To complement. show the role of doctor, the child had to Also, note that, by definition, at least have the doctor doll carry out at least two two sensory-motor action systems must appropriate actions in relation to the patient comprise each representational set, because doll. The doctor might, for example, give representational sets are formed from com- the patient a shot and look in her ears or binations of sensory-motor systems. For take the patient's temperature and examine the roles of doctor and patient, the action her throat. 506 KURT W. FISCHER
In analysis of a particular task, sources assess that ability or concept (Bertenthal of variation will often become apparent & Fischer, 1978; Opaluch, 1979). that are not evident if one erroneously For the doctor role, the definition is that attempts to consider the skill independently one agent must show doctorlike behaviors of a task. In the present case, the task in relation to a second agent, which must brings no change in the basic mapping skill show reciprocal patientlike behaviors. A as diagramed in Formula 20. But the com- minimal task for this concept is the doll-play ponents of the representational sets are a task, with just two dolls, the doctor and the little more complicated than they appeared patient. Many children who can demon- in the analysis of Question 2. Because the strate the doctor role in this task will not child must manipulate the dolls, each repre- show it in a more complex task: If the sentational set must include a minimum of experimenter's story involves, for instance, not just two but three sensory-motor a mother bringing her child patient to the systems. For each representational set, the doctor's office and consulting with the child must manipulate the appropriate doll doctor and nurse while the patient is being in addition to performing at least two role- examined, many of the children will demon- specific actions, such as giving an inocula- strate an apparent inability to understand tion and an ear examination. the role of doctor (Watson & Fischer, 1980). One problem that can arise in interpreting 6. To go beyond an analysis of an in- particular tasks is that incorrect task analy- dividual task and predict a developmental ses in the developmental literature may sequence, one must keep all tasks in the interfere with determination of what a per- sequence within the same task domain. With son actually must do to perform a task. For the doctor role, for example, the levels and instance, for Piaget's final object-perman- transformation rules can be used to produce ence task, where the child must find an an ordering of developmental complexity, object that has been put through a series of with tasks more (or less) complex than the invisible displacements, most investigators basic doctor-role task. But if those tasks use have assumed that the task requires the different procedures or varying roles (such as cognitive recreation of the invisible dis- mother-child), the theory cannot predict a placements by the child (Piaget, 1937/1954; precise developmental sequence. The many Uzgiris & Hunt, 1975). Recently, this inter- environmental and organismic factors that pretation has been questioned (Jennings, produce unevenness mean that develop- 1975; Harris, Note 6), and several investi- mental sequences can only be predicted gators have shown that the task does not produce cognitive manipulation of rep- unambiguously when as many sets as pos- resentations of invisible displacements sible are kept the same from one develop- (Bertenthal & Fischer, in press; Corrigan, mental step to the next. To make clear pre- in press). dictions from the task analysis of the doctor 5. What is the minimal task that would role, the same demonstration procedure demonstrate the skill in question? If the should be used at every step, the same dolls skill is a specific concept, for example, should be included, and the doctor-patient one must first specify exactly what is meant relation should remain the basis of every by the concept and then determine the step. The more microdevelopmental the easiest task that would demonstrate it. predicted sequence, the more essential Without specification of a minimal task, it is that the content and procedure remain erroneous inferences may be made about the same from one step to the next. the child's ability (Shatz, 1977). Task com- Even with these six guidelines, doing a plexities that are basically irrelevant to the task analysis is no trivial matter. Unfortu- ability in question will overload the child nately, it still involves a degree more art than cognitively and prevent him from showing I would like. Yet once a task analysis is in his ability. The skill level at which a person hand, predictions based upon it follow fairly can control an ability or concept is a func- easily from the levels and transformation tion of the complexity of the task used to rules. THEORY OF COGNITIVE DEVELOPMENT 507
Predicting Developmental Sequences doctor, nurse, and patient (Step 3) but more advanced than the doctor- role skill (Step 2): Beginning from a task analysis, one can S 5 S Foe D — SP], [ /?D — TN]) = use the transformation rules to predict a 5 developmental sequence. The sequence can — »sp) >(*/?„ — rN)j. be either macrodevelopmental or micro- developmental or both, and it can have The child can make the doctor deal with the virtually any number of steps, depending on patient and then make the doctor deal with the number of transformations that are used. the nurse, but does not integrate doctor, There is no one true sequence that all nurse, and patient all together in the appro- children will always show, because the priate role relations. This behavior is more exact sequence that a child demonstrates advanced developmentally than the doctor will be determined to a great extent by the role at Step 2 because the child must possess particular tasks that he or she experiences. two complete Level 5 skills. The behavior Previous studies attempting to test detailed is less advanced than the compounded skill developmental sequences (mostly predicted at Step 3 because although it contains the from Piaget's work) have shown a singular same components, they are not unified into lack of success (e.g., Hooper, et al., 1979; a single skill. Kofsky, 1966). Tests of sequences predicted Another microdevelopmental step can be from skill theory, however, have been predicted by use of the substitution rule: 5 5 5 highly successful (Bertenthal & Fischer, Sub[ /?D— 7N — 5P] = 1978; Hand, 1980; Tucker, 1979; Watson & 5 Fischer, 1977, 1980; Fischer & Roberts, [ /?D — (22) Note 3). The child shows the same behaviors as for Starting from the task analysis for the Step 3 but replaces the nurse doll with a doctor-role skill, one can predict many substitute object that does not normally fit developmental steps (Watson & Fischer, the nurse role, such as a plain adult male 1980). Table 4 shows just a few of them. doll. This skill is more advanced develop- Application of the compounding rule to the mentally than the skill on the left of Equa- doctor-role skill (Step 2) expands the doctor tion 22. role to include a second complementary 5 Thus, Equations 20, 21, and 22 lead to role, that of nurse, JN, thus producing a prediction of a four-step developmental more complex Level 5 skill (Step 3). The sequence. First, the child develops the basic child starts out with the two simple Level 5 doctor-role skill in Equation 20 (shown as skills on the left of the transformation Step 2 in Table 4), then the skills resulting equation in Table 4: one relating the doctor from the indicated transformations in the role to the complementary patient role and following order: Equation 21, Step 3 in the other relating the doctor role to the Table 4, and Equation 22. complementary nurse role. When those 12 Besides these and many other micro- two skills are combined by compounding, developmental predictions, macrodevelop- they produce the skill on the right of the mental predictions can be made, of course. equation: The child can make the doctor The intercoordination rule specifies trans- deal with both the nurse and the patient in formations from level to level. Reversal such a way that the doctor takes into ac- of the intercoordination rule decomposes count the nurse's role relation to the patient 5 the doctor-role skill (Step 2 in Table 4) into (symbolized by the mapping of 7N and its two component Level 4 skills: the simple 55 in the compounded skill). 4 P representational sets for doctor, /?D, and Besides the steps shown in Table 4, many other microdevelopmental steps can be pre- 12 dicted. With application of the focusing rule, Several alternative pairs of simple Level 5 skills could be combined to produce the same compounded for instance, an intermediate step can be Level 5 skill relating doctor, nurse, and patient roles. s 5 predicted that is less developmentally ad- For example, [ Rn TN] could be compounded vanced than the compounded skill relating withprN — *$,,]. Table 4 o A Developmental Sequence of Social Role Playing 00
Cognitive Role-playing Step level skill Example of behavior Skill structure Transformation rule
4 1 4: Representa- Behavioral role The child pretends that a doctor [ «D] Intercoordination: tional sets doll uses a thermometer and 4 4 a syringe. [ KDH SP] = Step!
5 5 5: Representa- Social role The child pretends that a doctor [ RD - 5P] Compounding: tional doll examines a patient doll, 5 5 mappings and the patient doll makes p«D 5P] + pRD TN] = Step 3 appropriate responses during the examination.
Social role with The child pretends that a doctor 5S ] Focusing: P I two compli- doll examines a patient doll 5 mentary roles and is aided by a nurse doll. Foc(pRF 5C], Both patient and nurse P« 3r 55 ]) = Step 4 respond appropriately. D ;V P 5«3 o K w 5 5 5 5 Shifting between The child pretends that a doctor SC) > ( «D rN — Sp)] Intercoordination: family role and doll is the father of the patient 5 5 5 5 doctor role doll, and then he or she [ RD — 5P] • [ tf F — 5C] = Step 5 switches to having the doctor doll fill only the doctor role — examining the patient doll with the help of the nurse doll, as in Step 3.
6: Representa- Intersection of The child pretends that a doctor Compounding:3
tional two roles and doll examines a patient doll 6 systems their comple- and also acts as a father to [ RD,r <-» «5P,C] + ["«„,„ ** «VM,W] ments the patient, who is his son or + PV , ^ 65 , ] = Step 6 daughter. The patient doll M W P C acts appropriately as both patient and offspring. (Table continues) THEORY OF COGNITIVE DEVELOPMENT 509
4 patient, 5P. Thus, the theory predicts that at Level 4 the child will be able to handle behavioral roles—behaviors relating to the doctor role alone or the patient role alone. *fc o !>- He or she will know, for example, that a SSJ« . j i M O JO doctor uses a thermometer or a syringe,
|*3 but will not include the patient as a partici- O U CM en c « 2 -fi pant in these actions by the doctor. U I 1~" Going in the other direction—up the de- a u ll I o g velopmental scale—the skill for the doctor J8 role can be intercoordinated with the related skill for the father role, in which the adult 5 male plays the role of father, /?F, in relation 5 w to the role of child (son or daughter), 5C. H•rt »\ W1 J3 ill Since an adult male can be both a doctor and a father, and a young person can be both a patient and a son or daughter, the child can intercoordinate the two skills as shown 6 for Step 5. The symbol /?D,F stands for the representation for the behavior of a man who is both doctor and father to his child, 'fi § is 8 jaO and the symbol 5P)C stands for the repre- °*'" u" ° sentation for the behavior of a young person "osi* i u ._ who is both a patient and a son or daughter § -c u 2 iI |O ^(r to the father. Each new Level 6 representa- tion is thus a combination of two of the
£ U Level 5 representations on the left of the 1 w transformation equation in Table 4. With the 8 new Level 6 skill, the subject takes the per- OOO felrai .•3 _ 2 spective of a man who is a doctor and is ^>13 2 treating his son or daughter and simul- taneously takes the perspective of the son or
l e o f beha v daughter who is a patient of the doctor father. That is, at Level 6, the subject can act out this kind of social-role intersection E x u with the doctor and patient dolls. This type fS of social-role intersection is what the child ilsl needs to understand how one of his parents •a -a o • i«s •S •« ( ! sf 11 can fill two roles, such as parent and job "° E1^ cue u holder or parent and spouse (Fischer & 3.1 .2o I •§ '^"" .* ^ ^ Watson, in press). A Given any careful task analysis, the levels 1 ia n i and transformation rules thus make direct predictions about developmental se- quences. Application of the microdevelop- f 3 mental rules to the analysis for the gadget R 1| Predicting Developmental Synchronies the object-permanence tasks, it was pre- Across Task Domains dicted that he would also begin to use words to ask about or refer to objects that were Because of the importance of environ- not present, especially in the object-per- mental factors, precise predictions of micro- manence tasks.13 For example, he would developmental sequences can be made only start using "all gone" and "more" appropri- within a task domain, where most of the ately for the absent objects. This corres- components are the same or very similar pondence was predicted from skill theory for adjacent steps in a sequence. The pre- because with Level 4 skills, the child con- diction of synchronies across task domains trols representational sets and therefore can is much more complicated, because few or understand that objects are agents of action no components are shared across domains. independent of him: He can control the Yet predictions about synchrony are clear. representational set or sets for objects in First, because unevenness is the rule in those tasks even when he cannot perceive development, the degree of developmental the objects. He should, therefore, be able synchrony between two task domains will to speak spontaneously about objects that seldom be high. It will usually be moderate disappear in those tasks or in similar situa- for familiar domains, because each inde- tions. Corrigan's findings supported this pendent skill develops with age and this prediction of precise correspondence relation with age produces some correlation between object permanence and use of "all between the two skills. gone" and "more." Second, manipulation of environmental Testing for developmental synchronies factors such as degree of practice will between task domains is unfortunately more drastically alter the degree of synchrony. complex methodologically than it at first For instance, sequences in two highly appears. The correlation produced by age practiced domains should show nearly per- alone is a difficulty that is too often ignored. fect synchrony, as will be explained later. If the age range tested is wide, the cor- Third, whenever developmental se- relations can be substantial. The develop- quences in two different domains intersect ment of classification skills between 1 and so that a skill in one domain becomes part 7 years, for example, correlates highly with of a skill in the other, the development of shoe size, r(68) = .85, p < .001 (Fischer & the skill in the first domain will predict Roberts, Note 3). the development of the skill in the second. Skill theory suggests several ways of This correspondence will be precise, with overcoming this problem in testing for de- virtually every child that develops through velopmental synchronies. First, when the two intersecting sequences snowing the precise predictions can be made about predicted correspondence. exactly which developmental steps in the Corrigan (1977, 1978, 1979, 1980) has different domains should coincide, then found support for these predictions about correspondence between domains can be synchrony between task domains for the tested directly rather than indirectly through relationship between the development of correlations. object permanence (finding hidden objects) Second, predictions about relative de- and the development of language. First, the general correlation between object perma- nence and language development in a group 13 This hypothesis may seem at first to contradict the earlier discussion of the problems with the Piagetian of infants between 10 and 26 months of age task analysis of the invisible-displacements tasks. was only moderate, r (29) = .36, p < .01. There is no contradiction for two reasons: First, Further analyses indicated that this correla- Corrigan used a more complex testing procedure that tion was produced entirely by the relation seemed to provide a better assessment of the use of of performance in each task domain to age. representation in object-permanence tasks than the Piagetian procedure. Second, an object-permanence Second, one point of precise correspond- task can require representation for reasons other ence between the two skills could be pre- than those embodied in the Piagetian task analysis dicted. When the child reached Level 4 for (Fischer & Jennings, in press). THEORY OF COGNITIVE DEVELOPMENT 511 grees of synchrony can be tested. Consider Longitudinal testing should therefore developmental sequences x, y, and z, where produce faster movement through a de- x and y are hypothesized to involve virtually velopmental sequence than cross-sectional the same skills, and z is hypothesized to testing. Jackson, Campos, and Fischer involve different skills. Within a given age (1978) tested this prediction by comparing range, sequences x and y should correlate the effects of longitudinal and cross-sec- together more highly than either of them tional procedures on development through correlates with sequence z. Similarly, if a an eight-step sequence of object perma- particular environmental condition such as nence. Longitudinal testing produced a large practice is hypothesized to increase the practice effect, as predicted: two to three synchrony between two developmental se- steps in the eight-step sequence. quences, then the correlation between the Because of this practice effect, longi- sequences under that condition should be tudinal testing should produce an inflated higher than the correlation under other en- estimate of the synchrony between develop- vironmental conditions. Indeed, according ment in two different task domains. Usually, to skill theory, an experimenter should be in a group of children who have not experi- able to control the degree of synchrony enced longitudinal testing, most of the that he or she will obtain by simple en- children will have differential experience vironmental manipulations. with the skills in any two domains. Conse- quently, in cross-sectional testing, the Role of the Environment synchrony between the two developmental sequences will not be high, except in the According to skill theory, environmental case where the sequences actually belong factors play a central role in determining to the same skill domain. (Recall that a skill the relative degree of synchrony between domain is composed of a group of task developmental sequences, and they also domains that develop in close synchrony.) affect the specific developmental sequences On the other hand, the extensive practice that people show. Some of these predictions that occurs in much longitudinal testing are presented below, primarily for the virtually eliminates this differential experi- effects of specific testing procedures, in- ence and elevates the skills in both task cluding the differences between longitudinal domains to the person's optimal level. Con- and cross-sectional procedures and the sequently, even when the skills are in fact effects of the specific tasks used to test from independent skill domains, longi- developing skills. tudinal testing will usually produce a high synchrony between them—and a high Effects of Testing correlation. Corrigan's study of language develop- Longitudinal and cross-sectional pro- ment and object-permanence development cedures should produce very different tested this prediction (Corrigan, 1977, 1978). patterns of synchrony across task domains, As I reported above, she found that for a as a function of the effects of practice. group of infants tested cross-sectionally, Because skills must be practiced to be the correlation between the developmental mastered, a skill that is practiced regularly sequences was only .36. But for three should develop faster than a skill that is infants who were tested longitudinally over practiced less often. In most longitudinal the same age range, the correlations were studies, children are effectively given re- much higher: .75, .78, and .89 for the in- peated practice with the skills being in- dividual infants. Liben's (1977) study of the vestigated, because they perform the same effects of training and practice on memory or similar tasks session after session. In improvement and Jackson et al.'s (1978) most cross-sectional studies, on the other comparison of cross-sectional and longi- hand, children are not given regular practice tudinal procedures also corroborate the with the skills being investigated, because prediction. they are tested on each task only once. These findings thus support the argument 512 KURT W. FISCHER that cross-sectional testing in general pro- volving focusing, compounding, or differ- vides a better test of the naturally occurring entiation will not appear in their behavior synchrony between task domains than if they are not exposed to the specific tasks longitudinal testing. Developmental psy- or situations that will induce those par- chologists commonly disparage the useful- ticular skills. ness of cross-sectional methodology in Even macrodevelopmental steps in- developmental research, but the ability to volving intercoordination may be skipped predict developmental sequences makes for particular sequences. Recall, for in- cross-sectional testing a powerful develop- stance, the Level 7 skill for the abstract mental tool (Fischer, Note 7): Specific concept of conservation, that is, the concept parallel sequences can be predicted in differ- of quantities that do not change because ent task domains, and a separate task can be they are composed of two constituent devised for each step in each sequence. quantities that compensate for each other. Then, with cross-sectional testing of every Suppose that a person develops this con- person on every task, scalogram analysis cept of conservation without ever having can be used to test the validity of the se- developed the Level 6 skill for conservation quences, and the synchrony between se- of length. Perhaps he coordinates a Level 6 quences can be compared step by step skill for conservation of amount of clay with (Bertenthal & Fischer, 1978; Watson, 1978; another Level 6 skill for conservation of Watson & Fischer, 1977). number and so generates the abstract con- Variations in testing procedure will affect cept of conservation without ever dealing not only the degree of synchrony but also with conservation of length. When he is the particular developmental sequences then tested for conservation of length in that people show. Many developmental the spring-and-cord gadget, he can gen- psychologists assume that every skill eralize the Level 7 skill for abstract con- domain shows only one true developmental servation to conservation of length in the sequence, one set of stages of a fixed num- gadget, and thus he will have developed the ber (e.g., Kohlberg, 1969). Skill theory skill for conservation of length without predicts, to the contrary, that the develop- ever having gone through Level 6 for that mental sequence that a person progresses particular skill. He will have effectively through will vary depending upon the as- skipped Level 6 in the developmental se- sessment tasks and procedures used, as well quence for conservation of length. as analogous environmental factors that Many of these irregularities and varia- occur naturally, outside the experimental tions in developmental sequences will be re- context (Fischer & Corrigan, in press). duced or eliminated by repeated testing with The variation in sequences as a function similar tasks. Suppose, for example, that an of testing is especially obvious for micro- 8-year-old child has many other Level 6 developmental sequences. The develop- skills but has not been induced to develop mental transformation rules can be used to conservation of length. Exposure to the task predict a large number of microdevelop- for conservation of length with the gadget mental steps. For example, use of the sub- will normally induce him to develop con- stitution rule on Steps 2,3, and 4 in Table 4 servation of length (Hooper, Goldman, would have produced six microdevelop- Storck, & Burke, 1971). Because of effects mental steps instead of three. Yet if chil- like this, performance in later testing ses- dren are not exposed to the specific tasks sions will commonly fit a sequence better corresponding to each predicted step, many than performance in the initial session of the steps will not appear in their behavior. (Tucker, 1979). If their environment never induces the use The effects of specific tasks and testing of a substitute object, for example, they procedures may explain many of the dis- will never show these three new substitution agreements in the developmental literature steps for Table 4, nor any of the other pos- about sequences in a given skill domain. sible substitution steps in the development For example, different investigators, using of social role playing. Likewise, steps in- different procedures, have found different THEORY OF COGNITIVE DEVELOPMENT 513 microdevelopmental sequences for object ences, the environment would induce large permanence (compare for example, Cor- individual differences in development. rigan, 1977, 1978; Opaluch, 1979; Uzgiris Individual differences can take several & Hunt, 1975; Wise, Wise, & Zimmerman, forms. People differ in rate of development: 1974). Some move through the hierarchy of levels These effects of testing procedures on much faster than others. People differ in variations in sequences and on synchronies their profiles of cognitive skills—catalogues across sequences are more than a mere of which skills have attained which levels. methodological nuisance. They are a reflec- And most interestingly, people differ in the tion of the general importance of environ- paths through which they develop. mental factors as determinants of cognitive Many cognitive-developmental psychol- development. ogists have assumed that all people nor- mally develop through the same develop- Why Unevenness Must be The Rule mental path in any single domain, but re- cently a large number of researchers have If environmental factors are as important begun to argue that individual differences in as I have argued in determining sequence some or all developmental paths are the and synchrony, then indeed unevenness norm (e.g., Braine, 1976; Nelson, 1973; must be the rule in development. The level, Rest, 1976). or step within a level, that an individual Skill theory predicts that individuals will attains on a task is affected by so many frequently follow different paths of develop- environmental factors that he or she could ment and that these differences will take at not possibly perform at the same level or least two forms. First, different individuals step on all tasks. Jackson et al. (1978), in will develop in different skill domains. One their study of object permanence, examined person will develop basket-making skills but three different potential sources of uneven- not reading skills; another will develop both ness: practice, task, and content. All three basket-making skills and reading skills, but sources produced unevenness. As de- not skills for drawing maps. scribed earlier, the difference between the Second, different individuals will follow longitudinal and cross-sectional groups different developmental paths in the same shewed strong unevenness due to practice: skill domain (Fischer & Corrigan, in press). two to three steps in an eight-step sequence. The developmental transformation rules Similarly, the specific task used to assess predict a large number of different possible object permanence created substantial un- paths in any single domain. The spring- evenness: two steps in the eight-step se- and-cord gadget illustrates how individuals quence. Finally, the content (the type of can take different paths within the same stimulus searched for) often produced small domain. The way that an individual moves but reliable unevenness, especially with the from Level 6 skills for the gadget to a Level 7 cross-sectional procedure: Both the type of skill integrating all four variables of the object and the familiarity of the object pro- gadget (weight, length of spring, vertical duced unevenness ranging up to one step in length of cord, and horizontal length) will the eight-step sequence. vary depending upon the particular Level 6 skills that he combines. The results of two Individual Differences possible alternative paths are shown in Table 5. In the first path, an individual Just as environmental factors make un- begins with two Level 6 skills: the system evenness the rule within an individual, so relating weight, 6W, to the length of the they ensure that different individuals will spring, 6L, and the system for conservation, show different patterns of cognitive de- relating total length of the cord at two dif- velopment. Of course, hereditary factors ferent times, iCv,H and iCV,H- As shown in also contribute to individual differences in Table 5, the individual forms a Level 7 skill development (as well as to unevenness); for the entire gadget by intercoordinating but even without those hereditary differ- these two Level 6 skills. 514 KURT W. FISCHER In the second path, a different individual allows direct access to the concept of con- begins with a different group of Level 6 servation of the total length of the cord, systems, each involving weight 6W; weight whereas the second skill requires that the and length of the spring, 8L; weight and conservation be inferred from the coordina- 6 vertical length of the cord, CV; and weight tion of two representational systems. 8 and horizontal length of the cord, CH. He On the other hand, the two final Level 7 too combines these skills to form a Level 7 skills are equivalent for most purposes. skill for the entire gadget; but to do so, he Both of them interrelate the same four vari- must go through more developmental trans- ables, and both of them reflect accurately formations, as shown in Table 5, and he the relations among the variables in the real ends up with a different skill from the in- gadget. Individuals using the two skills will dividual who followed the first path. come to mostly the same conclusions about The first path is more efficient than the the variables in the gadget. second one: It requires fewer transforma- Similarly, for virtually every skill at every tions, and the final skill (Step 2 of Path 1 one of the levels, different individuals can in Table 5) relates the four variables to- take different developmental paths within a gether without redundancy. The second skill domain, and usually the end products path not only goes through more trans- of the different paths will be skills that are formations but also produces a skill (Step 3 equivalent for most purposes. That is not to of Path 2 in Table 5) that is full of redun- say, however, that individual differences dancy, with the weight variable reappearing are minimal. The different paths within a in every representational system. The skills domain are often significant; and more im- also differ somewhat in the behaviors that portant, individuals normally develop in they control. For example, the first skill different skill domains and to different skill Table 5 Alternative Developmental Paths to a Level 7 Skill for All Four Variables in the Gadget Cognitive level Path Path 2" e 6 6 8 8 6: Representational Step 1: [ W <-> "L] and Step 1: [ W <-> L], [ W <-> CV], and 6 systems fiCv,n <-* |CVlH] ['W <-» CH] 7: Systems of repre- Transformation: Transformation: 6 6 S 6 6 sentational systems [ W «•» L] • [?CV,H ** |Cv.H] = Step 2 \?W <-» L] • \ W «-»• CV] = Step 2a Step 2: Step 2a: [' 7 cv Transformation: 6 [«VV <-» "Cvl • ['W <-> CH] = Step 2b 7 7 Step 2b: f CV 7C,, Transformation: 7 7 <-* L CV = Step 3 t 7 7 <-» CV 'W CH Step 3: 7 I 7 W <-> CV \!/ 7Ci. . a Steps 2a and 2b form separate skills, but they do not develop in sequence with respect to each other, according to this skill analysis. THEORY OF COGNITIVE DEVELOPMENT 515 levels in the same domains. The environ- usually by 7 or 8 years of age, that the mental diversity of human experience, as amount of clay does not change when a ball well as the genetic diversity of the human of clay is elongated into a sausage, flattened species, ensures the occurrence of major into a pancake, or changed into some other individual differences in development. shape. At the same age, however, they still Skill theory thus makes several general believe that the weight of the clay ball does predictions about the effects of environ- change when the shape changes. Typically, mental factors on sequence and synchrony they will not develop the skill for conserva- in development and provides tools for ana- tion of weight until 9 or 10 years of age. lyzing some of these effects. In addition, Within Piaget's framework, this consistent the structures defined by the theory suggest sequence is puzzling because both types of a number of general corollaries about struc- conservation are said to require exactly the tural relations and how they determine se- same kind of concrete operational scheme: quence and synchrony. Two factors (height and length) covary in such a way that changes in one compensate Structural Corollaries for changes in the other. According to skill theory, conservation of I shall not attempt to provide an ex- weight develops after conservation of sub- haustive list of structural corollaries but in- stance because it requires a compounded stead will present a few illustrations of Level 6 skill that subsumes the skill for con- potentially useful ones. servation of substance. In conservation of substance, the child must coordinate the Consistent Decalage Within a Task Domain length and width of the original piece of clay, ?BL,W» with the length and width of the Unevenness in skills across domains transformed piece, i#Lw (Halford, 1970; seems to be a fact of development. But Peill, 1975; Verge & Bogartz, 1978).15 In according to the theory, many phenomena conservation of weight, on the other hand, that are commonly classified as instances of the child must go beyond mere amount of unevenness are in fact microdevelopmental clay and think about weight of clay. That is, sequences: The unevenness follows the he must relate the changes in the length and same pattern in virtually all children in a width of the clay to a third factor, such as given social group, and it seems actually to the weight readings on a scale or the amount arise from differences in the complexity of offeree that he feels when he holds the clay the skills. Most of the instances of horizon- in his hand, 6F. To coordinate all three sets tal decalage (unevenness within a stage or together in a single skill, he must compound period) studied by Piaget and his colleagues the skill for conservation of the substance show such microdevelopmental sequences. clay with a skill involving the weight of the The skill theory explanation is simplest in clay, such as the skill in which the child cases where the skills belong to the same relates the length of pieces of clay (for task domain. The skill that develops later instance, sausage-shaped pieces) to their can be derived by the transformation rules from the skill that develops earlier. 14 Note that this type of conservation is properly Among the best documented cases of called conservation of substance. It has often been consistent decalage within a task domain is erroneously translated as conservation of matter or the development of conservation of sub- conservation of volume. Both matter and volume are much more abstract and difficult concepts than amount stance and conservation of weight. Re- of a substance such as clay, and they develop at search has repeatedly shown that school later ages. children develop conservation of substance 15 A precise measure of the amount of clay, of 1 to 3 years before conservation of weight course, requires three dimensions (height, length, and (e.g., Hooper et al., 1971; Piaget & Inhelder, thickness), not just two; but with early Level 6 skills the child does not yet understand true volume—that is, 1941/1974, especially in the introduction to three-dimensional volume. His understanding of the 2nd edition; Uzgiris, 1964). In conserva- amount of clay is based on a relatively crude coordina- tion of substance,14 children understand, tion of just two dimensions. 516 KURT W. FISCHER Table 6 A Few Examples of Mimicking Actual cognitive levels Mimicking skill at Level L Mimicked skill at Level L + 1 2 2 2 2 3 3 Levels 2 and 3 [% — M2 — G2 — M, — S,] PS <-»• M <-» G] 2 2 2 3 3 Levels 2 and 3 [% — M2 — G2] > PG, — M, — %] PS <-» M <-»• G] Levels 6 and 7 PM weight: mimicking skill at Level L is by no means 8 identical with the mimicked skill at Level F] = L + 1. In general, the skill at Level L + 1 [l^L.W *~* l^L.W **'/*']• (23) will be much more flexible and differentiated than the skill at Level L, and the child will Consequently, the child will develop con- have much better control over the relations servation of the weight of clay after con- among sets. But there will still be many servation of the substance of clay. similarities between the mimicking skill and This same kind of analysis should be able the higher-level skill. to explain most cases of consistent decalage An example from the sensory-motor within a skill domain, including cases where the differences in complexity are not ob- tier will illustrate how mimicking occurs. vious, as when differences in stimulus sali- By compounding Level 2 mappings, the ence produce decalage (Odom, 1978; child can mimic the flexibility and com- Fischer & Roberts, Note 3). The skills in plexity of a Level 3 system, as shown in each case actually differ in complexity, but Table 6. Consider the actions of grasping a psychologists have previously categorized doll, G, looking at the doll, S, and moving them as showing unevenness simply be- the arm, M. When a child has a Level 3 cause there has been no tool for analyzing system controlling all three of these actions, the skills and thus recognizing the dif- he can combine several aspects of each of ferences in complexity. the three actions in a great variety of ways. For example, he can look at the doll and Mimicking use what he sees to guide the movement of his arms to grasp the doll, and then once he Besides explaining phenomena like the has grasped it, he can move it in front of his lag between the development of conserva- face and visually examine it. More generally, tion of substance and conservation of he can carry out plans that require him to weight, microdevelopmental transforma- consider the relations among several as- tions also predict another phenomenon: pects of all three actions simultaneously. mimicking, in which a complex skill or He can use his looking to guide his moving series of skills at Level L produces behavior all along the path of movement; he can place that seems at first to require a skill at Level the doll at any point in space within his L+ 1. reach; he can remember where he saw the A person can mimic a skill at Level L + 1 doll a few seconds before and reach there by acquiring a complex skill or series of to grasp it. And he can do all these complex skills at Level L that includes all the sets things smoothly and planfully, without trial that comprise the higher-level skill. The and error. mimicking skill will usually result from the At Level 2, the infant can mimic this transformations of compounding or focus- Level 3 system by compounding the three ing (or both), as illustrated in Table 6.1 use actions (Table 6). First suppose that he has the word mimic intentionally because the a sensory-motor mapping relating grasping THEORY OF COGNITIVE DEVELOPMENT 517 the doll, 2G, moving it, 2M, and looking at that it mimics. For example, Bryant and it, 2S: When he happens to grasp the doll, Trabasso (1971) carefully trained preschool he can move it in front of his eyes and look children to correctly judge the larger of at it. He also has the related mapping of every pair of sticks in a five-stick series. looking, moving, and grasping: When he When the children were asked about non- happens to look at the doll, he can move his adjacent parts from the series without being hand to where he sees it and then grasp it. shown the specific lengths again, many of By compounding these two skills, he can them correctly inferred the longer stick— construct a complex Level 2 skill that mimics thus apparently demonstrating transitive in- the Level 3 skill, as follows: ference, which for their series of sticks 2 2 would seem to be a Level 6 skill. How- M2 — G2] + pG, ever, the training procedure was perfectly — 2M — 2G — ! — 2S,]. (24) designed to teach a compounded Level 5 2 2 skill that would mimick the Level 6 skill With this mimicking skill, the child can for transitive inference. demonstrate a complexity and recombina- If the children had only been taught a tion in his actions that mimics the com- mimicking skill, their correct performance plexity and recombination of Level 3. When should have been limited. For example, he happens to look at the doll, he can move they should not have been able to solve a his hand to it, grasp it, move his hand in transitivity problem that required them to front of his body, and look at the doll there. organize the needed information about non- The sequence of actions is thus physically adjacent sticks on their own. In a follow-up reversed and looks superficially like the re- study, Bryant (1974, pp. 54-56; 1977) found combination of looking, moving, and grasp- exactly that: Children who after training ing that occurs so fluidly in the Level 3 skill. could consistently solve the original transi- But in fact it is still only a chaining of actions. tivity problems could not solve similar new The infant can carry out the sequence, but transitivity problems that required them to he cannot reorder it into the many flexible seek out the needed information on their combinations that typify Level 3. own. According to the mimicking corollary, A more primitive form of mimicking can all instances of mimicking should show also occur in this situation, as shown in similar kinds of limitations. Table 6. When the child has only the two When one uses skill theory to analyze simpler Level 2 skills shown in Equation 24, behaviors that Piaget has studied, it is the stimulus context can lead him to change important to be aware of mimicking, es- focus from the first skill to the second: He pecially for many of his infant observations. happens to look at the doll, moves his hand Most cases of primary, secondary, and to where he sees it, and grasps it. As he tertiary circular reactions, for instance, holds it in his hand, he then loses sight of seem at first to require sensory-motor it and so changes focus to the second skill: skills at Levels 1, 2, and 3, respectively. He maintains his grasp on the doll, moves But closer examination shows that many his hand in front of his face, and looks. of these reactions are probably complex Thus, the context produces behavior that skills at the previous levels. superficially appears to show the mimicking Mimicking is not just a laboratory curios- Level 2 skill or the mimicked Level 3 skill, ity or a measurement problem, however. but the child cannot actually control either of It occurs normally when the child con- these complex skills. structs transitional steps in the spontane- Mimicking has been produced in the ous development of a skill. Indeed, mimick- laboratory by a number of ingenious experi- ing skills probably lay the foundation for mental psychologists (e.g., Case, 1974; the child's development to the next level. Harris & Bassett, 1975; Siegler, 1976), and some of these studies nicely support Parallels Between Tiers the skill-theory argument that the mimicking A third corollary involves the relations skill is different from the higher-level skill between tiers. Because the general Levels I 518 KURT W. FISCHER to IV (Table 1) repeat at every tier, behavior More tests of the predicted parallel be- should show structural parallels between tween Levels 1 to 4 and Levels 4 to 7 are tiers. If a specific developmental sequence clearly necessary, but besides generating occurs at the sensory-motor tier, for tests of skill theory, the parallel serves example, then in the proper environment a another important function in research. It similar sequence should appear at the repre- offers a source for new hypotheses. For sentational tier, but it should of course in- every phenomenon that is discovered in volve changes in the structure of representa- sensory-motor development, a similar tions rather than changes in the structure of phenomenon can be searched for in repre- sensory-motor actions. sentational development, and vice versa. I know of only two sets of studies that Likewise, developments at the sensory- provide data relating to precise parallels motor and representational tiers suggest between tiers. One shows a parallel in the similar developments at the abstract tier. representational tier to a sensory-motor Other investigators have proposed a sequence; conversely, the other shows a general parallel between sensory-motor parallel in the sensory-motor tier to a development and later development (Piaget, representational sequence. 1937/1954, 1967/1971; Mounoud, 1976; In the sensory-motor tier, the infant Siegel & White, 1975; Werner, 1948). Piaget develops skills for finding hidden objects. (1'941) even gave a special name to parallels By Level III of the sensory-motor tier, across his developmental periods: vertical he can follow the visible displacements of decalages (distinguished from horizontal an object and look for it where it last disap- decalages, which are "parallel" develop- peared (see Piaget, 1937/1954, Stage 5 in ments within the same period). Greenfield chapter 1). Because of the parallel between and her colleagues have searched for struc- tiers, a similar skill for search should de- tural parallels between language and manip- velop at Level III of the representational ulative play (Goodson & Greenfield, 1975; tier. Drozdal and Flavell (1975) have de- Greenfield, Saltzman, & Nelson, 1972; scribed exactly such a behavior, which they Greenfield & Schneider, 1977). None of call "logical search behavior." By 7 or 8 these investigators, however, has provided years of age, most children could represent a system for analyzing and predicting the the probable displacements of a lost object parallel structures, and consequently it has and so look for it where it had probably been impossible to test the validity of sug- been lost. (See also Wellman, Somerville, gested parallels. Skill theory, with its sys- & Haake, 1979.) tem for analyzing the structure of skills, Mounoud and Bower (1974/1975) report a may allow more precise tests of proposed parallel in the opposite direction: from the structural parallels. representational tier to the sensory-motor Besides specific structural parallels be- tier. At Level III of the sensory-motor tween tiers, skill theory also predicts new tier, infants developed a skill that was ap- tiers, because Level IV of each tier pro- parently parallel to the skill for conservation duces a new kind of set. Both before and of weight at Level III of the representational after the three specified tiers, the cycle of tier: When a familiar object made of a four levels can occur again with different malleable substance like clay was altered types of sets. There must, of course, be from its usual shape, the infants grasped it as some limit on the recurrence of the cycle, if its weight remained the same, even though since it cannot go on infinitely; but that in other situations they routinely adjusted limit will have to be determined by future their grasp to fit the differing weights of research. various objects. That is, they seemed to assume that the familiar object's weight re- Reflex Tier mained the same even though its shape had changed. This sensory-motor conserva- The tier before the sensory-motor tier tion was not present in young infants and could be called the reflex tier and might well emerged by about 18 months of age. provide the starting point for skill develop- THEORY OF COGNITIVE DEVELOPMENT 519 ment: The infantile reflexes seem to be directly to the prediction of a reflex tier— reasonable candidates for the initial units a study by Bullinger (1977, Note 8). Much of from which skills are constructed. Un- the large quantity of other research on the fortunately, almost no research has been newborn (Haith & Campos, 1977) could be done that can be used to test the existence interpreted in terms of such a tier, but none of these levels, and consequently I have of it seems to provide a direct test of the treated this tier as a corollary rather than predicted four levels of reflex development. as a more firmly established part of the Bullinger describes how the tonic neck re- theory. flex becomes gradually coordinated with the The infant or fetus begins with single looking reflex and eventually develops into a reflexes, combines the single reflexes into looking skill that is independent of the tonic reflex mappings, then combines the map- neck reflex. pings into reflex systems, and finally com- In a sense, there are really two tonic bines the reflex systems to form systems of neck reflexes. In one, the infant turns his reflex systems, which are single sensory- head to the right and raises his left hand, motor sets (Level 1 in Table 3). and in the other, he turns his head to the The term reflex is used in a number of left and raises his right hand. The tonic different ways in the psychological litera- neck reflexes and various looking reflexes ture. Some psychologists reserve the term show a significant physical dependency: for behaviors that are not subject to operant When the young infant is producing a given control and that are often assumed to be tonic neck reflex, he can look only to the controlled by the peripheral nervous sys- side of his midline where his head is turned. tem, like the knee-jerk reflex. I use the term For example, when his head is turned to the instead in the sense that it is used by ethol- right, he can look at stimuli within his ogists (e.g., Hinde, 1970) and many psychol- visual field to the right of his midline, but he ogists (e.g., Piaget, 1936/1952): It refers to cannot look at stimuli to the left of midline. what might be called preprogramed be- To look at stimuli to the left, he must pro- havior— species-specific activities that duce the other tonic neck reflex, in which seem to be biologically programed into the his head is turned to the left. Bullinger nervous system (Teitelbaum, 1977). For describes how the infant gains control of example, Zelazo, Zelazo, and Kolb (1972) this relation. My description of Bullinger's have worked with the stepping reflex, a results includes an interpretation in terms of complex response that can be elicited in the the four reflex levels. newborn infant and that seems to be or- At Level I, single reflex sets, the infant ganically related to the voluntarily con- produces single reflexes, like each of the trolled walking that develops toward the tonic neck reflexes and each of the various end of the first year after birth. Other ex- looking reflexes; but he cannot control amples would be the sucking reflex, which is any relations between reflexes. Bullinger elicited by stimulation of the lips, and the found that infants from 15 to 45 days of age tonic neck reflex, in which the infant turns produced the tonic neck reflexes and various his head to one side and raises his arm on looking reflexes, but usually could not con- the opposite side. Even complex behaviors trol any relation between tonic neck reflex like looking are reflexes within this meaning: and looking. The sophisticated rules for visual scanning At Level II, reflex mappings, the infant described by Haith (1978) seem to be pre- maps one reflex onto another and thus programed properties of the looking reflex begins to control relations between reflexes. or reflexes. To distinguish these reflex be- For example, he should be able to produce haviors from peripherally controlled re- the head-right tonic neck reflex in order to flexes like the knee jerk, I will call them look at a stimulus to his right. At Level III, reflex skills or sets, because skill theory reflex systems, the infant relates two map- predicts that they normally develop into pings to each other, integrating the two sensory-motor skills. tonic neck reflexes with the two looking I know of only one study that relates reflexes (left and right) in a reflex system. 520 KURT W. FISCHER He should therefore be able to shift from structural corollaries, as well as other one tonic neck reflex to the other as neces- general effects of the environment on skill sary to look anywhere within his left and development and, of course, many other right visual fields. Bullinger describes the specific developmental sequences and syn- development of control by the infant over chronies. Rather than enumerating more the relation between the tonic neck reflexes such predictions, however, I would like to and the looking reflexes, but he does not turn to some general implications of skill discriminate between the predicted Level II theory for conceptions of cognition, learn- and Level III skills. Infants usually showed ing, and development. some control of relations between the two types of reflexes at 45 to 80 days of age. A Few Implications of the Theory At Level IV, systems of reflex systems, the infant coordinates two Level III sys- Any theory worth its salt should do more tems into a higher-order system and thus than answer the original questions it was generates a single sensory-motor set devised to answer. It should have implica- (sensory-motor Level 1). He should be tions for other important questions. Several able, for example, to relate the tonic-neck- of the most interesting implications of skill reflex-and-looking system with another theory involve central topics in cognitive reflex system involving posture and looking, psychology: the nature of the big picture of thus showing highly flexible looking be- cognitive development, the analysis of havior that is relatively independent of cognitive development and learning across specific postures: He has generated a new skills, and the relation between behavior kind of set, the single sensory-motor and thought. action of looking. Bullinger found such The Big Picture of Development flexible looking behavior commonly in infants 80 to 120 days old. Skill theory emphasizes careful analyses In this way, development through the of specific tasks and predictions of specific reflex tier produces a single sensory-motor sequences and synchronies in circum- set. Note, however, that such a set involves scribed task domains. But it also goes be- not only one reflex system but two or more, yond these specifics to predict the general because a Level IV skill involves the co- nature of major shifts in cognitive develop- ordination of at least two Level III systems. ment—how skills are changing across the In the Bullinger example, the child co- board as the person develops. ordinates the tonic-neck-reflex system with Although particular skills do not show another postural system in such a way that abrupt or discontinuous change, major the postural adjustments go almost un- statistical shifts in populations of skills do noticed, but in other cases the two systems occur (Feldman & Toulmin, 1975). In skill are more obvious. For example, an infant theory, the child's optimal level increases can coordinate a reflex system for sucking with age, and the speed of the increase is with a reflex system for looking, and thereby faster when the child is moving into a new he can look while he is sucking. This kind level (Fischer & Bullock, in press; Fischer, of analysis can provide a mechanism for Note 7). Together with environmental in- predicting and explaining the composition duction, these spurts at each level will of sensory-motor sets, especially the types produce major changes in the profile of skill of co-occurring behaviors that can be levels. Transition periods between "stages" globally combined in the single, poorly dif- can therefore be defined as times when an ferentiated sensory-motor sets described increase in optimal level is producing a earlier. major shift in the population of skills, with Skill theory produces, then, at least these many skills gradually moving to the new four structural corollaries: the reflex tier, optimal level. To the extent that the new parallels between tiers, mimicking, and con- optimal level applies broadly across a wide sistent decalage within a task domain. The range of skills, the shift in the skill profile theory should also be able to predict other should be dramatic and easy to detect. THEORY OF COGNITIVE DEVELOPMENT 521 The study by McCall et al. (1977) on shifts in patterns of skills with development. shifts in the profiles of infant skills shows These general shifts allow one to predict one method for inferring such transition not only broad statistical changes but also points. These researchers found instabilities many other general skill patterns, such as in the correlation patterns of infant tests the probability of possession of a specific that correspond generally to what is pre- skill in all people in a large, culturally dicted by skill theory. When a shift to a new homogeneous population. One can predict, optimal level occurs, an increased uneven- for example, the average age at which ness in the levels of performance will virtually all children of a given culture will appear in the individual child. The reason have attained a specific level of a skill that for this greater unevenness is that the speed is important for that culture: Virtually all of increase in optimal level becomes larger American middle-class children will have at these times and the child can initially attained an understanding of the social role apply this new capacity to only a few skill of doctor (Level 5: Step 2 in Table 4) by domains. Consequently, many correlations 5 years of age. One can specify the normal across domains decrease. The periods of range in which American middle-class correlational instability thus reflect times of children will normally be moving onto a new maximal change. McCall et al. found four cognitive level for skills that are important such periods of instability during the first to them, as shown in Table 7. Also, tests 2 years of life, exactly as is predicted from can be made of the levels predicted by skill the four sensory-motor levels. (They theory versus those predicted by other found these periods of instability before theories (e.g., Bickhard, 1978; Case, 1978; they knew about skill theory.) Halford & Wilson, 1980; Isaac & O'Connor, Presumably, similar instabilities could 1975; Mounoud, 1980; Mounoud & Hauert, be found for all the higher levels as well. Note 9). For example, Kuhn (1976) finds instabilities in ability-test correlations in early adoles- Application to Other Skill Domains cence, when people are presumably moving to optimal Level 7, single abstractions. As the social-role example implies, the Epstein (1974a, 1974b, 1978) reports spurts "big picture" to which skill theory applies in mental age and brain growth that seem to is not limited to the standard cognitive- correspond with the emergence of Levels 5, developmental tasks (mostly Piagetian tasks 6, 7, and 8. and IQ-type tasks). It has the promise of There is a difficulty, however, with using applicability across many different skill age as the dimension along which one looks domains and consequently the potential for for instability. After infancy, developmental integrating theoretical analyses in areas that canalization decreases (McCall, 1979; have usually been treated as theoretically Scarr-Salapatek, 1976), and consequently distinct. Skill theory may be applicable to people probably no longer change to a new areas as diverse as language development, optimal level at the same approximate age. social development, and learning. This variability in the age of shifting should The skill levels should apply to any skills increase dramatically at higher levels. Also, that develop, since they characterize the at higher levels, the prevalence of uneven- general information-processing system of ness within an individual should become human beings. Applying the theory to a new much greater. This problem with age can skill domain will not be an easy matter, of be eliminated if good measures of skill course, because it will require careful de- levels are used. Then people can be grouped scriptive analysis of the specific skills that not by age but by their optimal level, and develop in that domain. This kind of careful the distribution of optimal levels within a analytic research has only recently become sample will demonstrate whether spurts and common in cognitive-developmental instabilities exist (Fischer & Bullock, in psychology. press; Fischer, Note 7). The first step in applying skill theory to Skill theory thus predicts general types of new spheres such as language develop- 522 KURT W. FISCHER Table 7 Age Periods at Which Levels First Develop Cognitive level Age period" 1: Single sensory-motor sets Several months after birth 2: Sensory-motor mappings Middle of first year 3: Sensory-motor systems End of first year and start of second year 4: Systems of sensory-motor systems, which are single representational sets Early preschool years 5: Representational mappings Late preschool years 6: Representational systems Grade school years 7: Systems of representational systems, which are single abstract sets Early high school years 8: Abstract mappings Late high school years 9: Abstract systems Early adulthood 10: Systems of abstract systems Early adulthood a These periods are merely estimates for middle-class Americans. For Levels 9 and 10, existing data do not allow accurate estimation. ment or social development must therefore only thing special about these Piagetian be an analysis of some of the specific cognitive skills is that their development skills that develop in language and in social was investigated first—before the develop- relationships (see, e.g., Harter, 1977). ment of the language skills or social skills Starting with these specific skills, the theory that they are supposed to explain. Interac- can be used to predict how they will de- tions between some Piagetian skills and velop through the skill levels, as was demon- some language skills or some social skills strated earlier by the prediction of a de- will undoubtedly occur in development, velopmental sequence for social-role skills but they will be highly specific interactions, (Table 4). not general relationships in which one type Notice that language skills, social skills, of skill will be a general prerequisite for and skills in Piagetian tasks are all "equal" the other. And interactions will occur in in skill theory (as they are in the approach both directions, not just from Piagetian of Vygotsky, 1962). Many recent ap- skills to language or social skills, but also proaches to language development and vice versa. The earlier discussion of syn- social development have postulated that cog- chrony explained the kinds of relationships nitive skills are somehow more fundamental that should be expected: (a) a low general than language skills or social skills. For synchrony across domains, (b) high general example, the development of some Piagetian synchrony only when the skills in the measure of cognitive development, such as specific domains being tested are all main- object permanence, is hypothesized to be tained at the children's optimal level, and the one prerequisite for the appearance of (c) specific interactions only when a par- language (see Corrigan, 1979; Fischer & ticular skill in one domain becomes a com- Corrigan, in press). Similarly, researchers ponent of a particular skill in the other in social development use conservation or domain. Note that the kind of specific some other Piagetian measure to explain the interaction to be expected is what be- emergence of important social skills, such as havioral analyses of transfer have always perspective-taking and morality. The predicted: Specific components of one skill Piagetian skill is again elevated to a special become components of a second skill status, as if it were more fundamental (e.g., Baron, 1973; Mandler, 1962; Reed, than the social skills. Ernst, & Banerji, 1974). According to skill theory, there is nothing In addition to large-scale developmental particularly fundamental about object changes, skill theory is also applicable to permanence, conservation, or any other changes in behavioral organization that are Piagetian measure of development. The usually categorized under learning or prob- THEORY OF COGNITIVE DEVELOPMENT 523 lem solving. These changes should be pre- action, since thought is literally built from dictable by the microdevelopmental trans- sensory-motor skills. Also, sensory- formation rules of the theory. For example, motor development does not cease at the in the microdevelopmental sequence in end of the sensory-motor tier but con- which children pretend about going to sleep, tinues at higher levels.16 the successive steps in the sequence are Representational and abstract skills pro- essentially steps in the generalization of duce and direct sensory-motor actions. an action: Children pretend to go to sleep, This relation between representation and then pretend to put a doll to sleep, then action is illustrated by the example of the pretend to put a block to sleep, and so forth child's understanding of the spring-and-cord (Watson & Fischer, 1977). Similarly, many gadget at Level 5. When the child under- microdevelopmental sequences typically stands the mapping of weight (representa- categorized under cognitive development tional set 5W) onto the length of the spring could equally well be categorized under (representational set 5L), her control of learning or problem solving (e.g., Fischer each representational set is based on sen- & Roberts, Note 3). sory-motor sets. With her Level 5 skill, Likewise, adults solving a complex she can therefore directly control the problem or rats learning to run a maze show various weights to manipulate the length of systematic changes in the organization of the spring. She is not left sitting in a corner their behavior (Duncker, 1935/1945; merely thinking about how weight relates Fischer, 1975; Siegel & White, 1975). These to length. Behaviors studied in our labora- changes can be treated as microdevelop- tory also illustrate this relationship between mental sequences, and therefore skill theory representational and sensory-motor sets should be able to predict and explain them (Bertenthal & Fischer, 1978; Watson & (Fischer, 1974, 1980). Fischer, 1977, 1980; Fischer & Roberts, Skill theory, then, may help to integrate Note 3). such apparently diverse research areas as The inclusion of sensory-motor skills learning, problem solving, social develop- in representational skills is especially evi- ment, language development, and cognitive dent in language. Speech and gesture, which development. It also has important implica- are both sensory-motor skills, are essential tions for another major research problem— components of the representational skills of the relation between behavior and thought. language (e.g., Fischer & Corrigan, in press; MacWhinney, 1977). Behavior and Thought In addition, the control of sensory-motor skills by representational skills extends be- A classic problem for most cognitive yond the direction of sensory-motor skills approaches has been that their constructs that are already present. Higher-level skills typically do not explain how thought is also direct the acquisition of new lower- turned into action (see Hebb, 1974). As level skills. Jacqueline's "bimbam" skill, some wit said, they leave the organism described earlier, provides an example sitting in a corner thinking. (Piaget, 1946/1951, Observation 64). When Skill theory provides a possible way out she first combined two Level 3 sensory- of this dilemma. Thought (representation motor systems into the Level 4 bimbam and abstraction) develops out of behavior representation for fluttering, her skill con- (sensory-motor action), and the skills of trolled just two things that fluttered: herself, thought hierarchically incorporate the skills when she rocked back and forth on a piece of action that they have developed from. of wood, and leaves, when she made them That is, representational skills are actually composed of sensory-motor skills; and 16 likewise, abstract skills are actually com- In Piaget's theory, the nature of the relation be- tween sensory-motor action and representation is less posed of representational skills and there- clear, but it seems that sensory-motor development fore sensory-motor skills. Consequently, stops at the end of the sensory-motor period (e.g., there is no separation between thought and Piaget, 1946/1951, p. 75). 524 KURT W. FISCHER flutter. Then, through compounding and at this time it does not deal adequately substitution, she extended the skill to new with skill domains. objects, such as curtains, that she could A task domain involves a series of tasks make flutter or that fluttered in the breeze. that are all very similar to each other, For each object to which she extended the typically sharing a basic group of com- skill, she constructed or included a new ponents but differing in the additional com- Level 3 sensory-motor system involving ponents that are required to perform the the fluttering of the new object, and this tasks. A skill domain, on the other hand, skill thus became a new sensory-motor involves a number of task domains that component of the Level 4 "bimbam" skill. share similar skills and therefore develop In the same way, representational skills in approximate synchrony. at higher levels are constantly used to con- At present, skill theory determines skill struct new sensory-motor skills. Develop- domains in a primarily empirical way. When ment from Levels 4 to 7 produces skills developments in two task domains show a that subsume more and more sensory- degree of synchrony that cannot be ac- motor actions and at the same time control counted for by environmental factors such finer and finer differentiations of sensory- as practice effects, then the two task do- motor actions. Consequently, skill theory mains are said to belong to the same skill should be able to predict the development domain. To deal with skill domains in a more of complex sensory-motor skills like satisfactory way, skill theory will ultimately driving a car, using a lathe, or operating require concepts for specifying the glues a balance scale—skills that develop after that tie task domains together. These con- the first 2 years of life. Research does sup- cepts will presumably lead to a graduated port the argument that orderly develop- notion of skill domain rather than an all- mental changes occur in sensory-motor or-none notion: Task domains will vary in skills during both childhood (e.g., Green- terms of the proportions of skills that they field & Schneider, 1977; Ninio & Lieblich, share. 1976) and adulthood (e.g., Hatano, Miyake, & Binks, 1977). In addition to making numerous specific Accessing Skills developmental predictions, then, skill The second limitation involves a matter theory has significant implications for the that skill theory says little about. No pro- nature of changes in populations of skills in cesses are designated to deal explicitly with development, the integration of theoretical the way in which skills are accessed. A analyses of skill development and learning person may have available the skill needed in spheres that have been traditionally to perform a particular task or to show a treated as distinct, and the relation between specific behavior and yet in the appropriate behavior and thought. But skill theory also context may fail to use that skill. Skill has several limitations. theory does not deal directly with phe- nomena of this type, which are commonly Limitations of Skill Theory classed under the rubric of motivation. Two limitations of skill theory are the What makes a person do one thing instead need for a more powerful definition of skill of another when she is capable of doing domains and the need to deal with the either? processes by which skills are accessed. The omission of accessing also means that skill theory neglects many of the phenomena Defining Skill Domains of memory and attention that are such central concerns within the information- Skill theory provides a mechanism for processing framework (see Estes, 1976). predicting and explaining the development Skill theory should be able to predict the of skills in specific task domains, and it development of memory skills, and it has also gives a general portrait of how popula- already been used as a tool for uncovering tions of skills change with development. But some new memory phenomena, such as a THEORY OF COGNITIVE DEVELOPMENT 525 relation between recall success and skill competence versus performance. Although level (see Watson & Fischer, 1977). It does there is some overlap between the two not specify, however, how the process of issues, they are not the same. The extreme accessing skills relates to individual differ- formulation of the competence-perform- ences and task differences in memory per- ance model assumes that a structure is formance. present but that there is some performance Skill theory in its present formulation limitation that prevents it from being fully does not use the information-processing realized in behavior (Chomsky, 1965). The framework. It is a structural theory that access question, on the other hand, entails has its roots in the classical tradition of no such assumption, because skill theory cognitive psychology (see Catania, 1973; does not posit powerful structures that have Fischer, 1975). In recent years many psy- difficulty eventuating in behavior. The chologists have come to equate cognitive access question is simply: What are the psychology with the information-processing processes that determine which skill an approach. This equation ignores the fact individual will use in a particular task at a that a long and venerable tradition of cog- given moment? nitive psychology existed decades before the information-processing approach was Concluding Comment invented. On the other hand, skill theory is not Whatever their form, theories are tools inconsistent with the information-pro- for thought (Hanson, 1961). The essential cessing approach. Indeed, I would hope that test of a theory is whether it is a good tool. some parts of it could be reformulated in This theory is intended to be a useful tool information-processing terms. Such a for- for understanding cognitive development mulation might provide more precision in and facilitating the process of theoretical some parts of the theory and thereby help integration that is essential to progress in to overcome some of the theory's limita- psychology (Elkind & Sameroff, 1970; tions, including the treatment of accessing Haith & Campos, 1977). The theory prom- skills. ises to provide a system for predicting and Any attempt to provide an information- explaining developmental sequences and processing formulation, however, should synchronies in any skill domain throughout avoid a major pitfall that has plagued many the life span, and it also promises to inte- information-processing analyses of cog- grate analyses of development with treat- nitive development: They neglect the adap- ments of learning and problem solving. tive process that is the very basis of cog- Time and research will tell whether this nition according to skill theory. The cog- promise becomes fact. nitive organism is constantly adapting skills to the world, and this adaptation provides Reference Notes the foundation for cognitive development 1. Pascual-Leone, J. A theory of constructive and learning (see MacWhinney, 1978). Any operators, a neo-Piagetian model of conservation, information-processing formulation of the and the problems of horizontal decalages. 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