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Psychological ReviewV O L U M E 87 N U M B E R 6 N O V E M B E R 1980

A Theory of Cognitive Development: The Controland Construction of Hierarchies of Skills

Kurt W. FischerUniversity of Denver

A theory of cognitive development, called skill theory, attempts to providetools for the prediction of developmental sequences and synchronies in anydomain at any point in development by integrating behavioral and cognitive-developmental concepts. Cognitive development is explained by a series of skillstructures called levels together with a set of transformation rules that relatethese levels to each other. The levels designate skills of gradually increasingcomplexity, with a specific skill at one level built directly from specific skills atthe preceding level. The transformation rules specify the particular develop-mental steps by which a skill moves gradually from one level to the next. Atevery step in these developmental sequences, the individual controls a par-ticular skill; that is, he or she controls a structure composed of one or moresources of variation in what he or she does or thinks in a specific context. Indevelopment, these skills are gradually transformed from sensory-motoractions to representations and then to abstractions. The transformations pro-duce continuous and gradual behavioral changes; but across the entire profileof a person's skills and within highly practiced task domains, a stagelike shiftin skills occurs as the person develops to a new optimal level. The theory sug-gests a common framework for integrating developmental analyses of cognitiveskills, social skills, language, and perceptual-motor skills, as well as certainbehavioral changes in learning and problem solving.

The development of the theory described in thisarticle was supported by a grant from the SpencerFoundation. I would like to thank the colleagues whoprovided feedback on earlier drafts of the article: R.Bank, B. Bertenthal, C. Brown, J. Campos, W. Carr,M. Cole, R. Corrigari, F. Dance, J. Flavell, H. Hand,P. Harris, S. Barter, J. Keenan, R. McCall, P. Mounoud,R. Roberts, D. Rowe, N. Sahin, L. Silvern, D. Thomas,J. Tucker, M. Watson, M. Westerman, and S. H.White. Special thanks go to A. Bullinger, M. Haith,A. Lazerson, B. MacWhinney, and S. Pipp for theirhelp on several phases of the article. The idea that ledto Figure 2 was suggested by A. McLeod. I would alsolike to acknowledge the scholars whose ideas have beenmost important to the formation of the theory: J.Bruner, J. Dewey, D. Hebb, J. Kagan, J. Piaget, B. F.Skinner, H. Werner, S. H. White, and P. H. Wolff.The help of G. Anderson, B. Richardson, and K. Sulli-van in preparation of the manuscript is also much appre-ciated.

Requests for reprints should be sent to Kurt W.Fischer, Department of Psychology, University ofDenver, Denver, Colorado 80208.

A newborn baby is mostly helpless andunable to deal with much of the worldaround him. Over the years the baby growsinto a child, the child into an adult. Ex-plaining the psychological transformationthat the individual undergoes in these 20-odd years is one of the most challengingtasks facing psychology.

The theory presented in this article, calledskill theory, attempts to explain a large partof this psychological transformation. Itfocuses primarily on cognition and intelli-gence, and it deals with aspects of learningand problem solving. Skill theory treatscognitive development as the constructionof hierarchically ordered collections ofspecific skills, which are defined formallyby means of a set-theory description.

Of course, other psychologists have dealt

Copyright 1980 by the American Psychological Association, Inc. 0033-295X/80/8706-0477S00.75

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with these same general issues before, andskill theory builds on their ideas, includingconcepts from the work of Piaget (1936/1952, 1970; Piaget, Grize, Szeminska, &Vinh Bang, 1968; Piaget & Inhelder, 1966/1969), Bruner (1971, 1973), Werner (1948,1957), and Skinner (1938, 1969), informa-tion-processing psychology (Case, 1974;Pascual-Leone, 1970, Note 1; Schaeffer,1975), and the study of skill learning (Baron,1973; Gagne, 1968, 1970; Reed, 1968). Theintent of skill theory is to integrate ideasfrom these various approaches to producea tool for explaining and predicting the de-velopment of behavior and thought.

Before describing skill theory in detail,I will discuss several of the key issues thatit attempts to deal with; the relation betweenorganism and environment in cognitive de-velopment and the issues of sequence andsynchrony. The theory will then be pre-sented quasi-formally in terms of assump-tions, definitions, notation rules, and de-scriptions of both the hierarchical levels ofcognitive control and the transformationrules for development from level to level.Several experiments testing the theory willbe described, corollaries of the theory willbe proposed, and general implications andlimitations of the theory will be discussed.

Both Organism and Environment

Most psychologists agree that psycho-logical theories, to be adequate, mustreckon with both organism and environ-ment (e.g., Aebli, 1978, Note 2; Endler &Magnuson, 1976; Greenfield, 1976). Theinteraction of organism and environmentis even more obvious in development thanin most other areas of psychology. Eventhe maturation of the child results from acombination of organismic factors (in-cluding genes) and environmental factors.For example, myelination of nerve fibersin the cortex is controlled not only by genesbut also by environmental stimulation(Fischer & Lazerson, in press; Peiper,1963). G. Gottlieb (1976) reports that spe-cific experiences are necessary for manyaspects of normal physical and behavioraldevelopment even when the infant is still inthe womb, and Cornell and Gottfried (1976)

find that stimulation facilitates physicaldevelopment in premature infants.

Despite the general agreement on theinteraction of organism and environment,developmental psychologists have had dif-ficulty incorporating both organism andenvironment into their theories. Whenattempting to include both, they have ef-fectively emphasized one side or the other.For instance, Piaget is perhaps the de-velopmental psychologist best known forhis interactional approach (1936/1952, 1947/1950, 1975), yet his explanatory constructshave focused primarily on the organism.It is the organism that changes from onestage to the next, with the environmentplaying only a minimal role (see Beilin,1971, and Flavell, 197la). Piaget himselfhas recognized this problem: Faced with ahost of environmentally induced instancesof developmental unevenness in perform-ance (called horizontal decalage; Piaget,1941), he has said that he simply cannotexplain them (Piaget, 1971, p. 11).

At the other extreme are the behaviorists,who, like Piaget, recognize the importanceof both organism and environment. Theirexplanatory constructs, however, have ef-fectively emphasized the environment andneglected the organism: Concepts such asreinforcement, punishment, practice, andimitation are used to explain behavior anddevelopment (Bandura & Walters, 1963;Reese & Lipsitt, 1970; Skinner, 1938, 1969).Useful as these concepts are, they requireimportant modifications to deal adequatelywith organism and environment (Catania,1973, 1978; Herrnstein, 1977; Premack,1965).

To take advantage of the insights of suchdiverse positions as Piaget's genetic epis-temology and Skinner's behaviorism, onemust somehow put organism and environ-ment together in the working constructs ofa theory. The present theory is based onthe concept of skill, which itself connotesa transaction (Sameroff, 1975) of organismand environment. The skills in the theoryare always defined jointly by organism andenvironment. Consequently, the skills arecharacterized by structures that have prop-erties like those described by organism-oriented psychologists and that simultane-

THEORY OF COGNITIVE DEVELOPMENT 479

ously are subject to the functional lawsoutlined by environmentally oriented psy-chologists. The sets that describe the skillstructures are always jointly determined bythe actions of the organism and the environ-mental context that supports those actions:The organism controls its actions in a par-ticular environmental context. This resolu-tion of the organism-environment dilemmaallows some progress toward explainingand predicting cognitive development, al-though it also raises some problems of itsown, which will be discussed later.

One of the most immediate implica-tions of defining specific skills in terms ofboth organism and environment is that rela-tively minor alterations in the environ-mental context of action will literallychange the skill being used. That is, theorganism's control of a skill depends on aparticular environmental context. This im-plication should be kept in mind because ithas many important ramifications for thetheory and its corollaries.

Sequence and SynchronyWithin the context of this proposed

resolution of the organism-environmentdilemma, skill theory attempts to providea precise answer—or at least a frameworkthat will allow the pursuit of a preciseanswer—to five interrelated questions. Onfirst reading, several of the five questionsmay seem similar, but as the theory is pre-sented, the distinctiveness of the questionsshould become clear, (a) What is the struc-ture of an individual's cognitive skills at anyone point in development? (b) Which skillsdevelop into which new skills as the childmoves step by step from infancy to adult-hood? (c) What is the process by which pres-ent skills develop into new skills? (d) How dopresent skills relate to the skills that theyhave developed from? For example, are theprevious skills included in the present skills,supplanted by the present skills, or what?(e) Why is cognitive development so oftenuneven in different domains? The attemptsto answer these questions are anchored tospecific cognitive skills investigated in thedevelopmental research literature.

Underlying these five questions are twocentral issues that operationally form the

very core of the study of cognitive develop-ment: the issues of sequence and synchronyin development. Under what circumstanceswill skills show invariant developmentalsequences, and under what circumstanceswill specific skills develop with some de-gree of synchrony? In practice, a theoryof cognitive development must be able topredict and explain developmental se-quences and synchronies. This is, I believe,the most essential criterion for evaluatingany theory of cognitive development.

The Theory

Skill theory provides an abstract repre-sentation of the structures of skills thatemerge in cognitive development, togetherwith a set of transformation rules that relatethese structures to each other. The struc-tures and transformation rules comprise atool for explaining and predicting develop-mental sequences and synchronies frombirth to young adulthood. As I will demon-strate later, they may also allow for theexplanation and prediction of cognitivedevelopment in adulthood. The theory thusfocuses on the organization of behavior; itis primarily a structural theory, although itis in no way incompatible with functionalanalyses (see Catania, 1973, 1978; Fischer,1972; Piaget, 1968/1970).

Here is a brief overview: Skills developstep by step through a series of 10 hier-archical levels divided into three tiers. Thetiers specify skills of vastly different types:sensory-motor skills, representationalskills, and abstract skills. The levels specifyskills of gradually increasing complexity,with a skill at one level built directly onskills from the preceding level. Each levelis characterized by a reasonably well de-fined type of structure that indicates thekinds of behaviors that a person (child oradult) can control at that level. The skillsat each level are constructed by a personacting on the environment. She performsseveral actions induced by a specific en-vironmental circumstance, and the waythose actions occur in that circumstanceprovokes her to combine the actions: Theperson thus combines and differentiatesskills from one level to form skills at the

480 KURT W. FISCHER

next higher level. The movement from onelevel to the next occurs in many micro-developmental steps specified by a series oftransformation rules. Notice that the skillsdevelop through levels, not stages: De-velopment is relatively continuous andgradual, and the person is never at the samelevel for all skills. The development of skillsmust be induced by the environment, andonly the skills induced most consistentlywill typically be at the highest level that theindividual is capable of. Unevenness in de-velopment is therefore the rule, not the ex-ception. The level of skills that are stronglyinduced by the environment is limited, how-ever, by the highest level of which the per-son is capable. As the individual develops,this highest level increases, and so she canbe induced to extend these skills to the new,higher level.

Relation Between the Theory and Its Data

The formulation of Levels 1 to 7 is basedon the large empirical literature on cognitivedevelopment between birth and adoles-cence. Both the specific structures of thelevels and the numbers of levels were in-ferred from these data. To the best of myjudgment, a larger number of levels did notseem to be warranted by the data, and asmaller number did not seem sufficient toexplain the data. The validity of this judg-ment will, of course, be determined byfuture research.

The basis for prediction of developmentalsequences, like the sequence of sevenlevels, has been at issue in the cognitive-developmental literature. A number of de-velopmental psychologists have argued thatdevelopmental sequences can be predictedon a purely logical basis, where the termlogical seems to mean internally consistent(e.g., Brainerd, 1978; Kaplan, 1967; Kohl-berg, 1969). According to this way of think-ing, if a coherent, "logical" argument canbe made for a predicted developmental se-quence, that sequence must occur. Al-though the sequence of cognitive levelspredicted by skill theory is internally con-sistent, I do not believe that this consis-tency itself provides an adequate test of thesequence (Fischer & Bullock, in press). Also,research that has explicitly tested for develop-

mental sequences has frequently found thatcertain "logical" sequences do not actuallyoccur (e.g., Hooper, Sipple, Goldman, &Swinton, 1979; Kofsky, 1966).

The reciprocal give and take betweentheory and data is, in my opinion, essentialfor theoretical progress in cognitive-develop-mental psychology (Feldman & Toulmin,1975; Furby, 1972; Hanson, 1961). The mostimportant test of the levels and of all otherpredictions from skill theory is empirical.The theory must also be internally consistent,but internal consistency will be for naught ifthe theory cannot describe, predict, andexplain the development of actual cognitiveskills.

In this article, I do not attempt to providea comprehensive review of the large bodyof relevant research. Instead, the primarygoal is to make the concepts of skill theoryas clear as possible and to show how theseconcepts can be tied to behavior. Concreteexamples of specific skills are used to illus-trate most concepts. To demonstrate howthe concepts relate more broadly to the re-search literature, a few instances of researchrelating to each concept are cited. Theseexamples have been chosen to represent awide variety of behaviors, including re-search from many different laboratories. Ialso indicate which concepts or predictionsdo not yet have good research documenta-tion.

Assumptions and Definitions

Skill theory is based on a number ofspecific assumptions and concepts. Thisdiscussion of them is not exhaustive butfocuses on ideas that need to be especiallyclear at the outset. The assumptions andconcepts divide roughly into three topics:the concept of cognitive control, the natureof skills, and the characteristics of the levelsand transformation rules.

Concept of Cognitive Control

Cognition is a complicated concept. Inmuch of the developmental literature, theterm cognition is used to refer to skills of aparticular type of content—typicallyknowledge of the physical world (as op-


posed to the social, emotional, or linguisticworlds) or knowledge as measured by stand-ard Piagetian tasks. But there is confusionand controversy about how the concept ofcognition should be used (Chandler, 1977;Flavell, 1977; Kessen, 1966).

In skill theory, cognition refers to the pro-cess by which the organism exercisesoperant control (Catania, 1978; Skinner,1938, 1969) over sources of variation in itsown behavior. More specifically, the personcan modulate or govern sources of variationin what he or she does or thinks. Thesesources of variation are denoted in thetheory by sets: sensory-motor sets, repre-sentational sets, and abstract sets. As cog-nitive development progresses, infantsfirst control variations in their own sensory-motor actions, then children control varia-tions in their own representations, andfinally adolescents or adults control varia-tions in their own abstractions. Representa-tions subsume sensory-motor actions,and abstractions subsume representations.

According to this conception, cognitionincludes anything that involves the person'scontrolling sources of variation, even whenthese sources have conventionally beencalled emotions, social skills, language, orwhatever. All these various domains sharethe same processes of developing more andmore effective cognitive control.

Nature of Skills

Skill theory assumes that cognitive skillscan be described effectively and preciselyin terms of elementary intuitive set theory(see Suppes, 1957). The general definition ofa set is a collection of things. Why is itnecessary to talk about collections to ex-plain cognitive development? When peoplecontrol sources of variation in what they door think, each such source is a collection orset, since it is a class of variations. Thisquality of cognition can be made more con-crete by discussion of how cognition isbased in action.

Cognition and action. All cognitionstarts with action, in a very broad sense.Piaget (1936/1952; Piaget & Inhelder, 1966/1969) has pointed out that cognition is es-sentially what the organism, from its ownpoint of view, can do, whether the doing is

commonly classified as motor, perceptual,or mental. For example, an infant not onlygrasps a doll or shakes a rattle or kicks ablanket but also watches the doll, listens tothe rattle, and feels the blanket. Accordingto skill theory, the higher-level cognitions ofchildhood and adulthood derive directlyfrom these sensory-motor actions: Repre-sentations are literally built from sensory-motor actions.

The definition of action in skill theory is,however, different from Piaget's use of theterm. First of all, within Piaget's frame-work, the sense in which cognitions beyondinfancy are themselves actions (not merelyderivative from actions) is not clear: Whena child represents a leaf fluttering in thebreeze, falling to the ground, having a greencolor, and turning red in the fall, in whatsense is the child acting? According to skilltheory, the child is controlling representationalsets for leaves' fluttering, falling to theground, being green, and turning red. Thiscontrol of variations can be conceived as anaction on the part of the child, in that thechild actively controls the variations cog-nitively. Also, all representational sets areliterally composed of sensory-motor ac-tions, as I will illustrate later.

Second, an action involves a set (ratherthan merely a point) because it must alwaysbe applied to something, and in being ap-plied, it must always be adapted to thatthing. Every time an infant grasps a rattleor every time an adult recognizes a familiarface, the action is adapted to the specificthing acted upon. Thus, every time an actionis carried out, even on the same thing, it isdone a little differently. Notice that eachspecific realization of an action always in-cludes both a subject and an object—anorganism and an environment. An action istherefore a set of similar behaviors onthings, but not just any such set: In an action,the person can control the relevant varia-tions in the behaviors on things. An infantwho can consistently grasp a rattle has a setfor grasping that rattle. An adult who canrepeatedly recognize a specific familiar facehas a set for recognizing that face. The thingis always included with the behavior in thedefinition of a set. In many ways, this defi-nition of action is closer to the behavioralconcepts of operant and skill than to Piaget's

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conception. Indeed, the term behaviorclass might be superior to the term set,but class is commonly used in psychologyto refer to a type of concept, and set has nosuch surplus meaning.

Skills, schemes, and operants. Set andaction are clearly synonyms within thetheory. How do they relate to skills? Askill is a unit of behavior composed of oneor more sets. The characteristic structurefor each level is a type of skill, varying incomplexity from a single set at Level 1 to avery large number of sets at the highestlevels. What makes a group of sets into askill is the person's control over both eachindividual set and the relations between thesets. For example, an infant who can shake arattle in order to listen to it has a skill com-posed of two related sets, shaking the rattleand listening to the noise it makes.

The relation between the concept of skillin the theory and the concepts of schemeand operant from Piaget and Skinner mayhelp to clarify the meaning of skill. Piaget'sgeneral word for cognitive structure isscheme1—a structure for knowing, a pro-cedure that the child actively applies tothings in order to understand them. In broadconception, there are many similarities be-tween scheme and skill, as already indicatedin the discussion of action, but there are alsomajor differences. One of the most im-portant differences involves the organism-environment problem: Piaget's schemesallot much less importance to the environ-ment than the skills of the present theorydo. Schemes are assumed to have a highdegree of generality, encapsulated inPiaget's concept of the structure d'ensemble(Piaget, 1957, 1968/1970; Inhelder & Piaget,1955/1958). This powerful generality ofschemes should produce a high degree ofsynchrony in development. Two tasks thataccording to Piagetian analysis require thesame scheme should develop at the sametime. Yet rather than synchrony, re-searchers typically find unevenness in de-velopment (e.g., Flavell, 1971b; Jamison,1977; Liben, 1977; Toussaint, 1974).

The number of well documented in-stances of unevenness has been increasingastronomically in recent years; Americanpsychologists seem to take special delight

in documenting new instances, especiallywhen the unevenness can be attributed toenvironmental causes. Unevenness hasbeen found so often and synchrony soseldom that many developmental psycholo-gists have begun to suggest that unevennessmay well be the rule in development, andsynchrony the exception (e.g., Carey, 1973;Cole & Bruner, 1971; Feldman & Toulmin,1975). Unevenness has been demonstratedrepeatedly for every Piagetian period ofdevelopment.2

The concept of skill, in contrast toPiaget's scheme, requires that unevennessbe pervasive in development, because skillsare defined in terms of the environment aswell as the organism. Changes in the en-vironmental context of action producechanges in a skill. In this regard, skillsshare important similarities with Skinnerianoperants (Skinner, 1938). The term operantrefers to a behavior that is emitted by anorganism, not elicited by a stimulus. At thesame time, the specific form of the behaviorand the probability that the organism willemit the behavior are affected by environ-mental stimuli. The behavior is thereforecontrolled by both the individual organismand environmental stimuli. Hunt (1969) andAebli (1978, Note 2) have pointed out thatmost of the behaviors studied by Piaget andhis colleagues are in fact operants.

The phenomena of developmental un-evenness make good sense from a be-haviorist perspective. Behavioral researchhas shown repeatedly that task factors havepotent effects on most kinds of behavior in

1 Many of the English translations of Piaget's worksuse the word schema instead of scheme to translatethe French scheme. There is a problem with thisusage: In recent years Piaget has differentiated schemefrom schema (Furth, 1969; Piaget & Inhelder, 1966/1971). Schema refers to an internal image of some-thing, which is very far from the meaning of scheme.

2 Here are just a few of the relevant references: forthe sensory-motor period, Butterworth, 1976; Jack-son, Campos, & Fischer, 1978; Kopp, O'Connor,& Finger, 1975; Uzgiris & Hunt, 1975; for the pre-operational period, Gelman, 1978; Goldstein &Wicklund, 1973; Watson & Fischer, 1980; for the con-crete operational period, Achenbach & Weisz, 1975;Hooper et al., 1971; Jackson, 1965; Smedslund, 1964;and for the formal operational period, Martarano,1977; Neimark, 1975; Piaget, 1972; Wason, 1977.


both animals and people. The effects are sopowerful that a number of analyses ofhuman abilities have been developed thatdeal primarily with the influences of task onperformance (e.g., Fleishman, 1975; Horn,1976). In addition, specific experience with atask has repeatedly been shown to be im-portant. These two factors, task differencesand experience, likewise account for manyinstances of unevenness. For example, thetype of task, the materials used in a task,and simple changes in the format of a taskhave all repeatedly produced unevenness(e.g., Barratt, 1975; Jackson et al., 1978;Kopp, O'Conner, & Finger, 1975). Evensimple practice with a task affects stage ofperformance (e.g., Jackson et al., 1978;Wohlwill & Lowe, 1962).

The usefulness of the concept of operantdoes not extend, however, to analysis ofthe organization of behavior. Althoughreinforcement and punishment can be usefulexperimental operations for analyzing or-ganization, they are insufficient. What theconcept of operant lacks in behavioristtheory is a system for analyzing the or-ganization of operants and how that or-ganization changes with learning and de-velopment. Skill theory is designed toprovide such a system.

In general, then, scheme and operant aresynonyms for skill within the presenttheory, although of course they have dif-ferent psychological frameworks. Thelevels of cognition are a hierarchy of skills,schemes, or operants in which each higher-level skill, scheme, or operant is actuallycomposed of lower-level skills, schemes,or operants. The theory thus provides a toolfor analyzing skills, schemes, or operantsinto units of widely varying complexity.

The definition of sets has an importantimplication for the meaning of skill, scheme,and operant. Because an action always in-volves a particular object or thing, a skillmust be specific to particular objects orthings. This implication is equivalent tosaying that as children develop, they masterspecific cognitive skills; they do not developuniformly across the entire range of skills.

Similarly, since cognitive developmentproceeds by the coordination of specificskills or schemes or operants, development

Spring-

4

HorizontalSegment

.VerticalSegment

Weight

Figure I . The spring-and-cord gadget.

through the seven levels must occur within askill domain, not across skill domains. Inother words, the development of cognitiveskills occurs in much the way that behav-iorally oriented psychologists have sug-gested (Baron, 1973; Gagne, 1968, 1970;Schaeffer, 1975). The child masters specificskills, builds other specific skills upon them,and transfers skills from one domain to an-other. This mastery process involves quali-tative changes in skills, but the specificchanges occur gradually, not abruptly.

Induction of a new skill. An example willshow how development is induced jointly byboth the person's skills and the environ-mental circumstances in a particular situation.The development of conservation of lengthin the gadget shown in Figure 1 (adaptedfrom Piaget et al., 1968, chap. 4) provides asimple illustration of this joint induction byorganism and environment. In the gadget, acord is attached to a spring and drapedover a nail, so that the cord is divided intotwo segments by the nail, a horizontal seg-ment and a vertical segment. Differingweights attached to the cord will producechanges in the length of the horizontal seg-ment of the cord and concomitant changesin the length of the vertical segment.

Consider a 5- or 6-year-old girl who al-ready has two skills (or schemes or oper-ants) for the length of the cord: (a) Sheunderstands approximately how the lengthof the vertical segment relates to the lengthof the horizontal segment; that is, she canroughly control the relation between thevertical length and the horizontal length,using the vertical to predict the horizontal.

484 KURT W. FISCHER

(b) She also understands approximatelyhow the horizontal length relates to thevertical length; that is, she can use thehorizontal to roughly predict the vertical.But she does not yet understand that thechanges in the horizontal length compen-sate for the changes in the vertical length,so that the total length of the cord doesnot change; she does not yet understandconservation of the length of the cord.

To construct an understanding of this con-servation, she must coordinate her twoskills for predicting the length (verticalpredicts horizontal, and horizontal predictsvertical). This combination will occur onlyif (a) the child has the two skills and (b)she plays with a gadget in which length infact conserves. As she applies the two skillsrepeatedly to the gadget, the task itselfinduces the child to notice a connection be-tween them, because the properties of thetask make the two skills closely related.Then the child explores the connection andgradually constructs a new, higher-levelskill for conservation of the total lengthof the cord.

The importance of the contribution fromthe gadget (the environment) should not beunderestimated. If the cord were not a cordbut a rubber band, conservation of thelength would not obtain, because the differ-ent weights that stretch the spring wouldalso stretch the rubber band. More gen-erally, the child's possession of two skillscannot by itself produce coordination ofthose skills. The child must be induced tocoordinate them by applying them to some-thing for which they do coordinate.3

The joint action of organism and environ-ment in cognitive development is equallyimportant for all the skill levels in thetheory. A 1- or 2-month-old infant, for ex-ample, will typically not be able to controlthe relation between shaking a mobile andwatching it jiggle. But when she has mas-tered the two individual skills, shaking themobile and watching it, she will be inducedby the mobile to coordinate the shakingand the watching. It is a property of mobiles—and of many other things in the world—that shaking them produces interestingchanges in their appearance.

Developmental synchronies. This es-

sential contribution of the environment toskill development requires, of course, thatunevenness be the rule in development, butit by no means excludes instances of syn-chrony. Developmental synchrony invarious degrees is predicted by the theory.Analysis of skill structures plus control ofenvironmental factors such as practice andfamiliarity allow the prediction of specialinstances of near-perfect synchrony, as wellas predictions of various degrees of syn-chrony under differing circumstances. Suchpredictions will be illustrated later.

Because of the connotation of the wordskill, the phrase skill domain implies a fairlybroad grouping of behaviors. However,methods for determining the developingchild's groupings of behaviors into skilldomains are crude at best (see Beilin, 1971;Flavell, 1971b, 1972; Wohlwill, 1973). So asnot to beg the question of which skillsdevelop together in a single domain, I willdistinguish task domain from skill domain.A task domain is a set of behaviors thatinvolve only minor variations in the sametask, in contrast to the broad grouping ofbehaviors across tasks in a skill domain.Within a task domain, there is virtually noproblem in determining which behaviorsbelong to that domain. As will be shownlater, the theory can predict developmentalsequences within a task domain. It may alsoprove useful in determining the nature andscope of skill domains, but that usefulnessremains to be demonstrated.

Task analysis. Because task factors areso important in skill theory, task analysis

3 This analysis differs from that of Piaget et al.(1968) in three major ways: (a) They do not grant thesame inductive role to the task, (b) They do notascribe to the 5-year-old the ability to relate verticalto horizontal and vice versa, although they do de-scribe an ability to relate weight to length of thespring (which is also consistent with skill theory).These several abilities are both predicted by skilltheory and supported by some research (Wilkering,1979). (c) They do not explain conservation as arisingfrom the coord inationfof skills relating vertical andhorizontal. Instead, they describe three stages: relatingweight to spring, then understanding conservation,and finally understanding the proportional relationbetween weight and amount of displacement. Theirthird stage develops much later than what is dis-cussed in the present example.


is clearly central to using the theory. Thecentral question for task analysis is: Whatsources of variation must the person controlto perform a task? That is, what sets mustshe or he control, and what relations be-tween sets? Guidelines for task analysiswill be described later after the theoryhas been more fully elaborated.

Closely related to the problem of specify-ing which sets and relations a person mustcontrol in a task is the problem of definingthe boundaries of a set. Indeed, the mostuseful form of set theory may prove to bethe theory of fuzzy sets (Negoita & Ralescu,1975), which does not require precise defini-tions of set boundaries. The problem ofdefining the boundaries of a set is virtuallyidentical to the problem encountered bybehaviorists in defining the boundary of anoperant (Schick, 1971). The problem may bemore serious theoretically than practically(Catania, 1978), but it is still a problem.

Skill theory at least points in the directionof a solution by specifying a universe ofpossible skill structures and thus providing atool for partially defining behavioral units.Development is analyzed into a hierarchy ofoperants—skill levels of increasingly com-plex cognitive control—plus various transi-tional forms specified by the transformationrules. A particular behavior can be related toone of the possible skill structures, and atthe minimum, the theory will then implyparticular kinds of changes in the cores andboundaries of sets across transformationsand levels.

Concepts for Defining Levels andTransformations

Through the joint contributions of theperson and the environment, skills, schemes,or operants develop through at least sevenhierarchical levels. The skills at each levelare characterized by a structure thatindicates the kinds of behaviors that theperson can control at that level. Also, ateach level, the skills include all the lowerlevels. For example, when a child is at Level5 for a specific skill, that skill subsumesskills at Levels 4 through 1. Note, however,that these lower-level skills become moredifferentiated at each higher level to whichthe superordinate skill develops.

Before the levels themselves can be de-scribed, a number of key concepts must beintroduced.

Relations between skills and levels.Contrary to the use of stage or period in mostcognitive-developmental models, the levelsare used generally to characterize a child'sskills, not the child in general. A child willnormally be at different levels for differentskills. To characterize a specific child, acognitive profile is required, indicating levelof performance on a wide range of skills(see, for example, Rest, 1976).

There is, however, one sense in which thelevels are used to characterize the child.Each child has an optimal level, indicatingthe best performance the child shows, whichis presumably a reflection of both practiceand the upper limit of his or her processingability. Just as in information-processingtheories, this central processing limit in-creases with development (Case, 1974;Flavell & Wohlwill, 1969; Halford & Wil-son, 1980; Pascual-Leone, 1970; Scandura,1973). But skill theory does not require thehomogeneity of performance demanded bymany information-processing theories, sincethe optimal level is merely an upper limit,not a characteristic of all cognitive behaviorat a given point in development. Also, thelimit is characterized by a skill structure(one of the cognitive levels) rather than asimple whole number of items in workingmemory.

The postulation of levels instead of con-tinuous monotonic increases in complexityhas implications for the form of the in-crease in optimal level with age: Associatedwith the levels, there will be spurts in thespeed of developmental change. That is, as achild moves into a new level, she will showrapid change; but once the level has beenattained, she will show slower change. Inthis way, the speed of development will varycyclically with the skill levels. Note that thishypothesis does not mean that develop-mental change is abrupt or discontinuous.The child moves into a new level graduallyover a long period, but the speed of changeduring this period is relatively rapid.

Although I have defined the optimal levelas a single upper limit, there is a possibilitysuggested by ability research that at the

486 KURT W. FISCHER

Table 1The Cycle of Four Levels That Repeatsin Each Tier

Level

I

II

III

IV

Characteristicstructure

Single set

Mapping

System

System of systems

Set-theorydescription

[W] or [X]

[W — X]

[WA,B <-» XC,D]

r w ^ x i| or [M]

LY ^ zj

highest levels, a person may have a few dif-ferent optimal levels in different broad do-mains. For example, an adult's optimal levelin spatial skills may be different from his orher optimal level in verbal skills (seeHorn, 1976).

Mappings and systems. The conceptsof mapping and system define the possiblerelations between sets within a skill, andboth of these concepts can be described inset-theory terms. A mapping is a structurerelating two sets: a collection of orderedpairs in which the first member in each pairis from one set (W) and the second memberis from another set (X). The first set is saidto be mapped onto the second: [W — X].

A system is composed of a relation be-tween two subdivided sets. Each set isdivided into two subsets, which are relatedto the two subsets in the other set. The twosubdivided sets are said to form a system,with the subsets noted by subscripts:[WA,B <H» XA>B]. The double-headed arrowindicates that the structure is a system evenwhen the subsets are not expressly listed inthe formula: [W <-* X].

The psychological interpretation of map-pings and systems is straightforward. In amapping, a person can relate two sets in asingle skill—two sensory-motor actions,two representations, or two abstractions. Ina system, a person can relate two subsets ofeach of two sets in a single skill—twocomponents of two actions, representa-tions, or abstractions. The ability to dealwith two subsets in each set means that theperson can control two sources of variationin each set. As a result, a system can in-

clude much more complexity and detail thana mapping.4

A third type of structure, called a systemof systems, is a relation between two sys-tems, as shown for Level IV in Table 1. Thepsychological interpretation of a system ofsystems is that people can relate two sys-tems in a single skill, which allows them toform a new kind of set: the most elementaryset M at the next higher tier. In this newset, each system is one element, so that thesimplest set has just two elements.

Note that in all these structures, a set is asource of variations that the person cancontrol—variations in actions, representa-tions, or abstractions. In each case, thevariations involve behaviors-on-things, butthe level of complexity of the organizationof those behaviors increases markedly at thehigher levels. Consequently, I will at timesuse simplified descriptions of higher-level

4 The concepts of mapping and system are bothderived in part from Piaget's and Werner's work.Piaget and his colleagues (Piaget et al., 1968; see alsoFlavell, 1977) have analyzed several behaviors of thepreschool child in terms of what they call a function,which is similar to a mapping. But they seem to restricttheir analysis to only a limited group of behaviorsand analyze those behaviors in terms of the degree towhich the behaviors match the characteristics of amathematical function. Their conclusion is thereforethat preschool children can sometimes show quasifunctions (called constituent functions) but not realfunctions (called constituted functions). The skill-theory concept of mapping may be viewed as a re-definition, generalization, and extension of Piaget'sconcept of function. The concept of system is notdirectly present in Piaget's work, but it derives in partfrom Piaget's concept of concrete operations (Inhelder& Piaget, 1959/1964; Piaget, 1942, 1949). One of themost central aspects of a concrete operation is that itis reversible, but research does not support Piaget'sargument that reversibility is absent in the pre-opera-tional period and first emerges in the concrete opera-tional period (Moore & Harris, 1978; Schmidt &Paris, 1978; Fischer & Roberts, Note 3). The con-cept of system in skill theory is intended to explain thebehaviors that have been documented by Piaget'sresearch on concrete operations but without re-quiring that reversibility be absent from mappings.Both mapping and system also incorporate explicitlyWerner's hypothesis that development proceeds bysimultaneous differentiation and hierarchical integra-tion (coordination). The meanings of mapping andsystem are sufficiently different from Piaget's usagethat attempts to plug Piaget's usage into skill theorywill lead to serious errors.


sets; phrases such as variations in lengthor the doctor role will be used as short-hand in place of longer descriptions such asthe child's representation of variations inthe seen lengths of the cord or the child'srepresentation of variations in what she canmake a doctor doll do in examining a patientdoll.

Transformation rules. The five majortransformation rules specify how a skill canbe transformed in development. Severalrules deal with the ways that skills can becombined to produce more complex skillsand how they change as a result of the com-binations. The other rules indicate altera-tions in skills that are less drastic but thatnevertheless produce clear-cut develop-mental orderings of skills. Although therules specify qualitative changes in skills,these changes occur gradually, not abruptly.

The transformation rules are central tothe theory, for they allow much more de-tailed predictions of sequence and syn-chrony than the cognitive levels alone. Thelevels produce only macrodevelopmentalpredictions (across levels), but the trans-formation rules also provide microdevelop-mental predictions (within a level). By themicrodevelopmental transformations, morecomplex skills can be constructed than theones shown in Tables 1 and 3, which are thesimplest possible at each level. Adequateformal definitions of the transformationrules depend on the formal descriptions ofthe levels, and so the rules will be definedprecisely later.

Notation

The introduction of a notation systemwill allow semiformal description of boththe characteristic structures for the levelsand the transformation rules. It will thusfacilitate use of the theory as a tool foranalyzing development. The notation sys-tem and the structural descriptions are notrigorously formal; they are only as elaborateas is necessary to convey the intendedmeanings.

The notation rules are described in Table2. Numbers and plain capital letters J, K,and L designate skill levels. Lowercaseitalic letters indicate skills of unspecified

level. Uppercase letters designate sets, withdifferent typefaces specifying the tier of theset, as shown in Table 2.

Superscripts and subscripts on a capitalletter give additional information about a set.Lines and arrows indicate relations betweensets, and letters above or next to a line orarrow indicate a particular relation. Brack-ets designate a skill, and certain mathe-matical symbols and abbreviations specifythe application of transformation rules.

Recurring Cycle of Four Levels

The progression of skills through thehierarchical levels shows a repetitive cycle,diagramed in Tables 1 and 3. This kind ofrepetition of structure has been discussed byboth Piaget (1937/1954, 1967/1971) andWerner (1948), although neither of them hasdescribed the exact nature of the proposedparallels. The structures of Levels 1 to 4are parallel to the structures of Levels 4 to7 and 7 to 10, but at each cycle the struc-tures are composed of a different type ofset, as illustrated in Table 3.

Each cycle of four levels is a tier and isnamed for its type of set. For the first tier,Levels 1 to 4, the sets are sensory-motor;they are actions and perceptions of the childon things or events in the world. Within thistier, the combinations of sensory-motorsets grow more and more complex as thechild develops through the first four levels,until at Level 4 the combinations create setsof a new kind, representational sets.

These representational sets designateconcrete characteristics of specific objects,events, or people (including the child her-self). Note that the new sets subsume sen-sory-motor sets, as shown in Table 3; thesets from the earlier tier do not disappear.For Levels 4 to 7, the representationaltier, the new sets are again combined inmore and more complex ways, producing acycle parallel to that for Levels 1 to 4.

At Level 7, the combinations of repre-sentational sets create new sets of anotherkind: abstract sets, which are general,intangible attributes of broad categories ofobjects, events, or people. These new setssubsume the representational and sensory-motor sets from earlier tiers, as shown in

488 KURT W. FISCHER

Table 3. What happens after Level 7 isprimarily conjecture, because there hasbeen so little research on cognitive develop-ment in adulthood. Yet the predictions ofthe theory are clear and direct: The abstractsets should produce an abstract tier—an-other progression through the cycle of fourlevels. When the combinations of abstractsets reach Level 10, they should producestill another new kind of set. Specificationof the nature of the new sets at Level 10must await future research on cognitivedevelopment in adults.

To distinguish the general cycle of levelsfrom the specific levels, the Roman nu-merals I to IV will be used to refer to thelevels of the cycle, and the Arabic numerals1 to 10 will be used to refer to the actualbehaviorally defined cognitive levels.

As shown in Table 1, Level I is character-ized by single sets—single sources of vari-ation that the child can control by them-selves but not in relation to each other. Thatis, the child cannot yet coordinate sets into ahigher-level skill.

The characteristic structure for Level IIis a mapping—a relation between two sets,indicated by the long line in Tables 1 and 3.

When a mathematician says that one set ismapped onto another, he or she means,roughly speaking, that variations in the firstset produce predictable variations in thesecond one. In an analogous way, at LevelII a child can understand situations wherehe or she can relate one set of variations toa second set of variations.

Level III is characterized by a system—a relation between two sets each of whichis divided into two subsets, indicated by thetwo-headed horizontal arrow between setsin Tables 1 and 3. The child is no longerlimited to the two simple sets in the map-pings of the previous level but can controlrelations between two subsets for each set.That is, the child can understand situationswhere he or she can systematically relatetwo components of one set of variations totwo components of a second set of varia-tions. In this way the child can deal withone subset while still keeping the other inmind and as a result can control much finercovariations in the two sets than at Level II.

The characteristic structure for Level IVis a system of systems—a relation betweentwo systems, indicated by the two-headedvertical arrow in Tables 1 and 3. At this

Table 2Notation Rules

Type of symbol Examples Meaning

Roman numerals

Arabic numerals

Plain capital letters J, K, and L

Lowercase italic letters

Boldface capital letters

Italic capital letters

Script capital letters

Plain capital letters

Superscript to the right

Superscript to the left

I, II, III, IV

1, 2, . . . 5, .

L, L + 1

b, s, e

M, G, P

A, F, R

3),M

W, X, C

G", F*

LA, 2P

. . 10

Cycle of levels that repeatsin each tier

The ten hierarchical levels

Undesignated level

Skills of unspecified level

Sensory-motor sets

Representational sets

Abstract sets

Sets of undesignated tier

Sets designated by the mainletter are components ofthe set designated by thesuperscript, which is at thenext higher tier

Level of set


Table 2 (continued)

Type of symbol Examples Meaning

Subscript to the left or right

Brackets [A

Long line connecting two letters [A — F]

Horizontal two-directional arrow [A *-* F}

Vertical two-directional arrow [A <-* Ft

\R <H» 5

b mLowercase letters above or next [A — F], [A — F]

to line or arrow

Multiplication sign

Addition sign

Sign for greater than

Equals sign

Foe

Sub

Diff

[A <-> S]

[A «->F] + [F «->/?]

[A <-»F]> [F <->/?]

[A <-> F] + [F <^ R] = [A <-» F <-» /?]

Foe («•,/) = [e >/]

Sub [A <-» F] = [A <-^ F,]

Diff A = AM, AN

Diff [A <-» F] = [AG,H

Information of interest aboutthe sets; used to discrim-inate related sets; twoletter subscripts indicatethe set is composed oftwo subsets

Sets and relations insidebrackets constitute a singleskill

Mapping: Relation betweentwo sets

System: Relation betweentwo sets, each composedof two subsets

System of systems: Relationbetween two systems

A particular relation

Intercoordination of twoskills

Compounding of two skills

Change in focus from the firstskill to the second

The skill on the right is theresult of the transformationindicated on the left

A change in focus betweenthe two skills on the leftproduces the skill on theright

Substitution of a set in theskill on the left producesthe skill on the right

Differentiation of the set orskill on the left into the setsor skills on the right

level, a person can control the relation be-tween two systems, keeping in mind onesystem while dealing with the other. This co-ordination of two systems produces a newkind of set, the most elementary set M at thenext tier, as shown in Table 1.

The metaphor drawn in Figure 2 illus-trates the cycle of four levels and the pro-

cess by which Level IV of one tier be-comes Level I of the next tier. Level I canbe thought of as a simple building block.Level II is then a combination of thosebuilding blocks in one dimension to formlines. At Level III, lines are combined tomake two-dimensional objects, such as thesquare in the figure. Finally, at Level IV,

490 KURT W. FISCHER

L E V E L

I

n

m

Figure 2. A metaphor for the cycle of four levels.

planes are combined to form three dimen-sional objects, such as a cube—a new typeof building block. In this way the cyclebegins over again, with Level IV of one tierserving as Level I of the next tier.

An elaboration of how this cycle of LevelsI to IV applies in the sensory-motor,

representational, and abstract tiers will helpto clarify the general picture of cognitivedevelopment presented by the theory. Thechild's potential skills with the spring-and-cord gadget in Figure 1 will be tracedthrough the levels as a continuing example.

Sensory-Motor Tier: Levels I to 4

The first four levels constitute the sensory-motor tier, as shown in Table 3. In this tier,all skills are composed of sensory-motorsets—actions (including perceptions) onobjects, 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 ofpsychologists (e.g., Baldwin, 1925; Dewey,1896; Hobhouse, 1915; Lashley, 1950;Piaget, 1936/1952; Werner, 1948): Bothsensory and motor components are integralparts of the skills and for most purposescannot be genuinely separated. Because theinfants can control only sensory-motoractions, their skills are purely practical:They understand how to act on specificthings in the world but cannot think aboutthose things independently of acting onthem. They understand what they can do

Table 3Sensory -Motor and Representational Levels of Skills

Level

1

2

3

4

Name of structure

Single sensory- motor set

Sensory -motor mapping

Sensory-motor system

System of sensory-motor systems, which is asingle representational set

Sensory-motorsets"

CA] or ['B]

[2A — 2B]

[3AG,H <•» 3BG>U]

rA"T4B "I»

["C" <~> "D"]

Representa- Abstracttional sets sets"

= t4/?]

5 Representational mapping

6 Representational system

7 System of representational systems, which is asingle abstract set

a Sensory-motor sets continue after Level 4, but the formulas become so complex that they have beenomitted. 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 andrepresentational tiers. Abstractions are built from representational and sensory-motor sets in the same waythat representations are built from sensory-motor sets.


and what they make happen. They do notunderstand that objects, events, and peoplehave their own characteristics independentof what the infants themselves do; thatability awaits the development of repre-sentational sets.at Level 4. Consequently,a child does not realize, for example, thather favorite rattle has properties like hard-ness and the capacity to make noise thatare independent of her own actions on it.Nor does she understand that people andmany other things can act by themselvesindependently of her actions. To emphasizethe domination of this world by action andto avoid confusion from terms like objector person, I will refer to objects, people,and other things in the infant's experienceas tableaux.5 For example, an infant graspsa tableau, not an object, and listens to atableau, not an object.

Several independent investigators haverecently reported data that generally sup-port the pattern of developmental changespredicted by the four sensory-motor levels(Emde, Gaensbauer, & Harmon, 1976;Kagan, 1979; McCall, Eichorn, & Hogarty,1977; Uzgiris, 1976). McCaH's analyses areespecially relevant: In examining patterns ofcorrelations among items in infant tests,he found changes in correlation patternsthat suggested four successive periods ofchange and consolidation in the first twoyears of life—times of instability in cor-relations followed by times of stability. Ifinfants are in fact developing through Levels1 to 4 in an age-related progression, onewould expect periods of change and con-solidation in correlations exactly like thosethat McCall found. Further research to testthe relation between McCall's findings andthe levels clearly needs to be done.

The characteristic structure of Level 1 isthe single sensory-motor set (shown inthe top row of Table 3), a set, 'D, of actingon tableaus, such as looking at a doll. A12-week-old infant may look for longperiods at the tableau produced by a dollhanging on a string in front of her. Evenwhen the doll swings back and forth in awide arc, she can keep her gaze on it. This isa single sensory-motor set or action, theset 'D of adaptations of looking at the dolltableaus. Similarly with the spring-and-cord

gadget, one set, 1S, involves the infant'slooking at the gadget when it crosses herfield of vision and maintaining it in her sight.Another set, 'G, involves her grasping thespring when it touches her hand and main-taining her grasp on it. Most of Piaget's(1936/1952) primary circular reactions seemto be Level 1 single sensory-motor actions.The infant can control many such single setsat Level 1, but she cannot control the rela-tions between sets.

Single sensory-motor sets are not limitedto adult-defined modalities in perceptionand action. The young infant does not know,for example, that seeing is different fromlistening. When she is attempting to look atthe doll swinging in front of her, any soundsit makes can be incorporated into her set'D. So long as she does not have to relate thesights and sounds independently, sight andsound can be mixed together in the sameLevel 1 skill. This lack of differentiation atLevel 1 contrasts with Piaget's (1936/1952)argument that young infants have differ-entiated schemes for seeing, hearing, grasp-ing, and so forth, which must be coordinatedtogether. The undifferentiated and unco-ordinated status of Level 1 skills in thepresent theory fits Werner's (1948,1957)characterization of a developmentally prim-itive state. Many of the studies of classicaland operant conditioning in young infantsmay involve such undifferentiated multi-modality sets (see Papousek, 1967; Samer-off, 1971).

Although infants cannot control any rela-tions between sets at Level 1, they doreadily drift from one set to another, usuallyled by some tableau. Consequently, eventhough they cannot yet coordinate two sets,they do not become stuck on one set forlong. Indeed, their drifting from set to seteventually leads them to explore the relationbetween two sets and so to intercoordinatethem into a Level 2 skill, simultaneouslydifferentiating them from each other.

The characteristic structure of Level 2 is

5 For the same reasons, Piaget occasionally usedthis term in his works on infancy (Piaget, 1936/1952,1937/1954). He did not, however, use it consistently inthese works, and he has not used it in subsequentworks.

492 KURT W. FISCHER

the sensory-motor mapping, in which onesensory-motor set, 2A, is mapped onto asecond sensory-motor set, 2B, as shown inTable 3. One type of sensory-mo tor map-ping is a means-end mapping, in which achild can use one action in order to bringabout a second action. For example, a 7-month-old infant looks at a tableau of a dolland uses what she sees to guide her attemptsto grasp the tableau (Field, 1976; Lasky,1977; Ruff, 1976). She has combined twosimple actions, looking at the doll and grasp-ing it, into one means-end mapping inwhich looking is used as a means to bringabout grasping. That is, she has mapped thesensory-motor set 2D of looking at the dollonto the sensory-motor set 2H of graspingit, as shown in Table 3. She may also havea separate, complementary mapping, inwhich she maps grasping the doll onto look-ing at it. For example, she grasps the tableauof the doll and brings it before her eyes sothat she can look at it. Similarly, with thespring-and-cord gadget, an infant pulls onthe spring, 2G, so that she can watch itstretch, 2S. Many of Piaget's (1936/1952)secondary circular reactions are means -end actions of this sort, although a numberof the behaviors that he classifies in thiscategory seem to be complex forms of Level1 actions.

Sensory-motor mappings should includemany types of skills besides means-endmappings, especially skills involving twocomponents within the same modality.Bertenthal, Campos, and Haith (in press)describe one such skill: By 7 months, infantscan apparently relate several visual com-ponents such as angles to form a line (seeLevel II in Figure 2). Presumably manymore such mapping skills develop withinmodalities such as looking, grasping, and thelike in infants.

Just as with Level 1, however, Level 2skills cannot be subdivided according toadult conceptions of modalities. If stimulifrom two different adult-defined sensorymodalities, for instance, co-occur in such away that the infant can treat them as onesource of variation, then at Level 2 theinfant can treat them as a single set that shecan relate to a second set. The same kind ofconcern about the definition of sets must be

considered at every level and especially atthe earliest levels within a tier, where dif-ferentiation is always poor.

Level 3 is characterized by the sensory-motor system, in which two components ofone sensory-motor set, 3AG,H, are related totwo components of a second sensory-motor set, 3BG,H, as shown in Table 3. Themost investigated type of sensory-motorsystem is the means-end system. Unlike themeans-end mapping of Level 2, the means-end system allows the infant to controlcomplex variations in means and ends(Fischer, Note 4). For example, Piaget's10.5-month-old son Laurent drops a piece ofbread, watches it fall, breaks off a crumband drops it, watches it fall, and so forth(Piaget, 1936/1952, Observation 141). Heconstantly varies the means (the way inwhich he drops the bread) and watchesclosely the variations in the end (seeing thebread fall).

At Level 2, he was unable to performsuch a complicated experiment in action; hecould learn little more than that droppingproduced falling. The reason for this limita-tion was that he could relate only one aspectof dropping the bread to one aspect of seeingthe bread fall.

At Level 3, he can relate two aspects ofeach action, and therefore he can build skillsthat coordinate and differentiate types ofvariations in dropping with types of varia-tions in falling. Similar kinds of skills can bebuilt with the spring-and-cord gadget—forexample, learning not only that pulling thestring makes it stretch but that pulling it indifferent ways makes it stretch differently.Examples of such means-end systemsabound in the research literature (e.g.,Bryant, 1974, p. 162 ff.; Koslowski &Bruner, 1973; Fischer & Roberts, Note 3).As with earlier levels, researchers haveneglected other types of Level 3 skills, suchas those within a modality (see Fischer &Corrigan, in press).

Despite all the sensory-motor sophistica-tion of Level 3, the skills are still definitelylimited: The infant is only able to controlone sensory-motor system at a time, andtherefore he cannot yet deal with many ofthe complexities of acting on objects, norcan he understand objects independently


of his own actions. In the world, everyobject is in fact the focus of a number ofdifferent sensory-motor systems; that is,every object can be made to participate inor produce many different types of actions.The ability to understand objects in this way(as independent agents of action) first de-velops at Level 4 (Watson & Fischer, 1977).

Representational Tier: Levels 4 to 7

Level 4 is the culmination of the sensory-motor tier, and so it produces a new typeof set and begins a new tier, the representa-tional tier. In terms of the repetitive cycle oflevels, the characteristic structure for Level4 is the system of sensory-motor systems(sensory-motor Level IV), which is thesame as the single representational set(representational Level I). This type of skillis a relation between two sensory-motorsystems, as shown in Table 3. The combina-tion of these systems generates the singlerepresentational set in which children canrepresent simple properties of objects,events, and people independently of theirown immediate actions.

With the spring-and-cord gadget, the childcan combine Level 3 systems for the gadgetinto a single Level 4 representation. Onesuch skill involves the child's understandingthat the spring itself stretches. For example,the following two systems can be co-ordinated at Level 4: When he pulls thespring, it stretches; when he sees someoneelse pull the spring, it stretches. Therefore,a characteristic of the spring is that itstretches; the child controls a representa-tional set 4L for the spring's stretching. Inthe same way, he constructs a set *W repre-senting that the weight itself can "pull,"independently of his feeling it; and he con-structs a set *C representing that the cordcan be big, independently of his makingit move.

With these single representations, thechild shows a lack of differentiation anal-ogous to that with Level 1 single sensory-motor actions. In the gadget, he will confusethe pressure exerted by the weights withtheir size, mixing them both together as"big." Similarly, he will confuse the totallength of the cord with the length of the

vertical or horizontal segment. Tasks can bedesigned that will help him to separate suchfactors in one situation, but when the factorscovary in a task, the child will treat themin a single representation.

Many different types of representationalsets should develop at Level 4, according tothe theory; and Piaget (1946/1951, Observa-tion 64) described a behavior that demon-strates a second type, a set of objects orevents that all share a single action orcharacteristic. His daughter Jacqueline usedthe word bimbam to mean swaying or flutter-ing. She combined her sensory-motorsystem for rocking back and forth on a pieceof wood with her system for making a leafflutter and used "bimbam" to refer to both.Then she gradually extended this repre-sentational set to a wide range of objects.6

Other examples of the construction of singlerepresentational sets from sensory-motorsystems have been described by Bertenthaland Fischer (1980), Watson and Fischer(1977), Fischer and Corrigan (in press),Fischer and Roberts (Note 3), and Fischerand Jennings (in press).

A word of caution may be helpful at thispoint about the meaning of representation.The term is often used as a virtual synonymfor recall memory or for symbol use. But inskill theory, representation is different fromboth of these meanings. It refers to the co-ordination of two or more sensory-motorsystems to form a single representationalset, not to recall memory or symbolizationper se. Skills involving both recall memoryand symbol use can develop before Level 4,and in addition skills can be constructed atLevel 4 that do not centrally involve eitherrecall or symbol (Fischer & Corrigan, inpress). A single representation is defined byits structure, not by its function as recall,symbol, or any other such psychologicalcategory.

The characteristic structure for Level 5 isthe representational mapping, in which onerepresentational set, 5/?, is mapped onto asecond representational set, 5r, as shown

8 The rules of compounding, substitution, dif-ferentiation, and intercoordination nicely account forthe sequence by which this skill developed, as de-scribed by Piaget (1946/1951).

494 KURT W. FISCHER

in Table 3. With this kind of skill, the childcan relate variations in one representation tovariations in a second representation.7

Consider a 4- or 5-year-old who is given thespring and several weights of different sizesfrom the gadget in Figure 1. If he has hadsufficient experience with the task, he canroughly use the size of the weight (one set) tocontrol the length of the spring (the otherset), thus understanding in an approximateway that large weights will make the springstretch farther than small weights.

Notice in Table 3 that this structure (likeall representational structures) can be de-scribed either in terms of representationalsets without visible reference to their sen-sory-motor origins or in terms of thesensory-motor sets on which the repre-sentational sets are based. For example,the child's understanding of the relationbetween weight and spring ties directly tohis overt actions of manipulating and seeingthe weight and spring, because the repre-sentational sets are actually composed ofsensory-motor systems specifying what thechild can do with the gadget.

Besides the representations for weightand length of spring, the child could alsoconstruct representations for the length ofthe vertical segment of the cord and thelength of the horizontal segment (or depend-ing on the nature of the specific gadget, arepresentation for the total length of thecord). A child who is very familiar with thegadget could conceivably possess at least 12different mappings, all possible pairings ofthe four sets—weight, spring length, ver-tical and horizontal lengths of cord (seeWilkering, 1979). Despite all this knowl-edge, the child's understanding of the gadgetwould be peculiarly disjointed because ofhis inability to consider two aspects of eachset simultaneously. That is why, for ex-ample, he has difficulty treating the verticaland horizontal lengths as segments of asingle cord of constant length.

Level 6 is characterized by a representa-tional system, in which the child relates twosubsets of one representation, 6/?J>K, to twosubsets of a second representation, 6rJjK,as shown in Table 3. For example, he canunderstand conservation of length of thecord in the gadget, as described earlier. He

combines the vertical and horizontal lengthsof the cord when one weight is used with thesame length when another weight is used, andthus he knows how the lengths vary togetherand compensate for each other (Piaget et al.,1968; Verge & Bogartz, 1978). With thegadget, he can also construct several otherLevel 6 systems, each involving the relationof two concrete variables to each other.Other representational systems that havebeen studied in the research literature in-clude most of Piaget's concrete opera-tional tasks (e.g., Inhelder & Piaget, 1959/1964) and a number of other tasks (e.g.,Watson & Fischer, 1980; Winner, Rosen-stiel, & Gardner, 1976).

Despite all this sophistication, however,the skills of Level 6 are still definitelylimited. The child can only deal with oneLevel 6 system at a time. He cannot relatevarious systems to one another. Even if heunderstands every one of the possible Level6 systems in the gadget, for example, hecannot integrate them into a single higher-level skill. More generally, he cannot yetunderstand objects independently of theirovert characteristics, because he is limitedto dealing with one Level 6 system at a time.That is, he cannot think of objects in theabstract.

Abstract Tier: Levels 7 to 10

Level 7 is the culmination of representa-tional development, generating a new kindof set and starting a new tier, the abstracttier. In the recurring cycle of four levels,the characteristic structure for Level 7 isthe system of representational systems(representational Level IV), which is thesame as the single abstract set (abstractLevel I). In an abstract set, the personabstracts an intangible attribute that charac-

7 Piaget does not postulate the existence of a majorcognitive-developmental change in the middle pre-school years, but some of his own research suggeststhat there might be such a change (Piaget et al., 1968),and many studies over the last two decades havedocumented that preschool children's abilities are fargreater than prior research had indicated (Gelman,1978). Also, two developmental theories that are not aswell known as Piaget's posit a major developmentalshift at about age 4 (Bickhard, 1978; Isaac & O'Connor,1975).


terizes broad categories of objects, events,or people. (Note that, as with representa-tion, abstraction has many different mean-ings in psychology; see Pikas, 1965. Thesevarious meanings should not be confusedwith the specific meaning used here.)

In a Level 7 skill, the person can controlthe relation between two representationalsystems, as indicated by the Level 7 struc-ture in Table 3. Consider a 15-year-old boywho can control a system of systems for thesets in the spring-and-cord gadget. He canintegrate several of the systems from theprevious level into a single Level 7 systemthat controls the relations among the weight,the vertical length of the cord, the hori-zontal length of the cord, and the lengthof the spring. When he is thinking, forexample, about how the changes in weightproduce changes in the length of the spring,he can simultaneously consider how thosechanges relate to the changes in the verticaland horizontal lengths of the cord. He canthus understand how all the changes covary.This skill not only allows him to controlthe gadget effectively, but it also gives himan abstract set for the general state of thegadget.

Many different kinds of abstractions canbe constructed at Level 7. For example, aperson can for the first time understand theabstract concept of conservation—varia-tions in two related quantities compensatefor each other so as to produce no changein some superordinate quantity. With onlyLevel 6 skills, the person can understandmost of the individual kinds of conserva-tion that Piaget and his colleagues havedocumented (Piaget & Inhelder, 1941/1974;Piaget & Szeminska, 1941/1952), but cannotintegrate those separate conservations intoan abstract concept of conservation.

For instance, the person combines theskill for conservation of the length of thecord in the gadget with the skill for con-servation of amount of clay (where the samepiece of clay is squeezed into differentshapes, such as from a ball to a sausage).In the conservation-of-length task, the twolengths are equal because the vertical andhorizontal lengths compensate for eachother. In the conservation-of-clay task thetwo amounts are equal because changes in

length and width compensate for each other.The coordination of these two concreteconservation skills produces the abstractconcept of conservation, which can then begeneralized to other tasks. Other instancesof Level 7 skills include most analogies(Lunzer, 1965), political concepts like lawand society (Adelson, 1972), and a few ofPiaget's simpler formal operational tasks(Inhelder & Piaget, 1955/1958).

Following the recurring cycle, abstrac-tions should develop through Levels 7 to 10,For example, with the spring-and-cordgadget, the individual will start with singleabstractions such as conservation, thenrelate two such abstractions in a mapping,and so forth. Because so little researchhas been done on cognitive developmentbeyond adolescence, however, no data areavailable to provide a strong test of suchpredictions. To illustrate the kind of de-velopmental progression that is predictedand to emphasize the applicability of thetheory to things other than cold cognition,I will present a hypothesized sequence inthe development of a person's identity(Erikson, 1963)—one's sense of the kindof person one is.

At Level 7, single abstract sets, a personcan for the first time construct abstractidentity skills (see Erikson, 1974). Theseidentity concepts result from the coordina-tion of two representational systems aboutthe self. For instance, a certain 9-year-oldmay have a Level 6 system for identificationwith his father's career as a psychologist.He relates his representation of himself tohis representation of his father as a psychol-ogist (Kagan, 1958). Likewise, he has an-other system relating his representation ofhimself as both skilled with other people andgood at science to his representation ofwhat psychologists do: They are people-oriented scientists. Most 9-year-olds are notyet capable of coordinating two such Level 6systems into a Level 7 skill.

A few years later, when the child cancoordinate the two systems, he can thusconstruct his first abstract set for his careeridentity. With the addition of a few otherrepresentational systems to the Level 7 skillvia microdevelopmental transformations,he can build a complex abstract set relating

496 KURT W. FISCHER

various of his own characteristics to variousaspects of the career that he is considering.

At LevelS, abstract mappings, the personcan relate one abstract identity concept withanother. For example, he can coarselyrelate his own career identity with his con-ception of his potential spouse's careeridentity: Perhaps he sees his own careeridentity as requiring that his spouse be in aclosely related career or perhaps as re-quiring that his spouse be primarily a home-maker.

Level 9 abstract systems produce a muchmore flexible, differentiated relation be-tween two identity concepts. For instance,the person can relate two aspects of hisown and his spouse's identity, such ascareer and parental identities, and thus con-sider in a more differentiated way what hisown identity requires of his spouse'sidentity and what his spouse's identityrequires of his own identity.

Finally, at Level 10, systems of abstractsystems, this person can coordinate two ormore abstract identity systems. He mightrelate his own and his spouse's career andparental identities now (one Level 9 system)with their career and parental identities10 years ago when they were first married(a second Level 9 system). The result is ahigher-level conception of what their jointcareer and parental identities have been likeduring their marriage.

Although I know of no rigorous tests ofthis or any other developmental sequencesin abstract skills during adolescence andadulthood, several investigators have re-ported data that generally support the pre-dictions of development from Levels 7 to 10.Some of the most detailed findings involvedevelopments in the history of science. BothMiller (Note 5) and Gruber (1973; Gruber &Barrett, 1974) have described developmentsof scientific theory that seemed to them toroughly follow Piaget's description of cog-nitive development from the pre-operationalperiod to the formal operational period.Miller illustrates this parallel for the de-velopment of quantum mechanics, andGruber for the development of Darwin'stheory of evolution. If these scientifictheories were developing through Levels 7to 10, their progression would resemble the

progression from pre-operational to formaloperational thought, according to skilltheory, because both the Piagetian periodsand the scientific progressions involvedevelopment within a tier from Levels Ito IV.8 Oddly, Piaget too (1970; Piaget inBeth & Piaget, 1961/1966) has suggestedthat there may be general parallels betweenthe development of scientific theories andthe development of cognition in the child.I say "oddly" because his position onformal operations seems to preclude suchparallels.

Within Piaget's framework, cognitive de-velopment virtually ends with formal opera-tions: Adolescents entering the formaloperational period have achieved fullylogical thinking, and there is little more forthem to do, except perhaps to extend theirlogical thinking to new content areas (Piaget,1972). Many people have been dissatisfiedwith this conception of formal operations(e.g., Arlin, 1975; Gruber & Voneche, 1976;Riegel, 1975; Wason, 1977), but there hasbeen no alternative position for analyzingdevelopment beyond early adolescence.Consequently, major age differences in theacquisition of various of Piaget's formaloperational tasks have been interpreted pri-marily as resulting from performancefactors, not from developmental changes(Inhelder & Piaget, 1955/1958; Martarano,1977; Neimark, 1975). According to skilltheory, many of these age differences maywell arise because the tasks requirev dif-ferent levels of abstraction.

Piagetian scientific tasks and the rarefiedatmosphere of theory construction are notthe only places that skills should developthrough Levels 7 to 10. Most adults prob-ably master at least a few skills beyondLevel 7, like the hypothesized identity con-cepts. Other skills that probably belong toLevels 7 to 10 include moral judgment, themanagerial skills of the director of a corpora-tion or a school system, the skills requiredto write an effective essay or novel, and theskills involved in programming and operat-

8 Within the present theory, Piaget's pre-operational,concrete operational, and formal operational periodsare explained by Levels 4 to 7.


ing a computer (Fischer & Lazerson, inpress, chap. 13).

Transformation Rules

Now that the structures of the levels havebeen described, the operation of the fivetransformation rules can be illustrated withsome precision. The five rules specify howa skill is transformed into a new, more ad-vanced skill. These rules are thus the heartof the mechanism for predicting specificsequences of development. The need forsuch a set of transition rules to accountfor developmental change has been recog-nized for a long time by many develop-mental psychologists (e.g., Beilin, 1971;Brainerd, 1976; Flavell, 1963; Kessen, 1966;Van den Daele, 1976). The rules are alsointended to apply to changes in the organiza-tion of behavior during learning or problemsolving (Fischer, 1975, 1980; Leiser, 1977).

The transformation rules and the skillstructures of the levels should be able toexplain most of the developmental se-quences documented in the research litera-ture. In addition, many new sequences canbe predicted that have not yet been investi-gated. In this section on the transformationrules, however, I will refrain from reviewingempirical support for the rules, so that Ican present the concepts briefly and directly.In a later section, several studies testingpredictions based on the rules will be de-scribed.

The five transformation rules are inter-coordination, compounding, focusing, sub-stitution, and differentiation. Intercoordina-tion and compounding specify how skillsare combined to produce new skills. Inter-coordination describes combinations thatproduce development from one level to thenext (macrodevelopment), and com-pounding describes combinations thatproduce development within a level (micro-development). Focusing and substitutionspecify smaller microdevelopmental stepsthan compounding. Focusing deals withmoment-to-moment shifts from one skill toanother, and substitution designates certaincases of generalization of a skill. The fifthrule, differentiation, indicates how sets be-come separated into potentially distinct sub-

sets when one of the other four transforma-tions occurs, but it can also be used sepa-rately to predict microdevelopmental steps.The microdevelopmental transformationsof differentiation, substitution, focusing,and compounding eventually produce themacrodevelopmental transformation ofintercoordination. These five transforma-tion rules are probably not exhaustive;future research will indicate whether ad-ditional transformation rules are required.

All the transformations are definedstructurally. Two or more skills with givenstructures are transformed into one or moreskills with a new type of structure. Theinduction of a specific structural transforma-tion always involves both organismic andenvironmental factors. At least two or-ganismic factors are involved: The personmust initially have the skills required forapplication of the transformation and mustbe capable of applying the transformationrules to those skills. For example, if a per-son has the necessary initial skills but theyare already at her optimal level, then she willnot be able to apply the transformation forcombining those skills to reach the nexthigher level.

Likewise, at least two environmentalproperties are necessary. First, the environ-ment must have properties such that if theinitial skills are transformed, the resultingnew skill will work. Second, the specificenvironmental situation must have prop-erties such that it will induce the person touse the initially separate skills in juxtaposi-tion, thus leading her to explore the relationsbetween the initial skills and construct thetransformed skill (see also Schaeffer, 1975).The transformation therefore requires bothorganism and environment; transformationscannot be attributed to either organism orenvironment alone.

Two of the transformation rules, inter-coordination and compounding, involvecombinations of two skills to produce a new,more complex skill. Many psychologistshave talked about combinations of skills asa mechanism to explain the development ofmore complex skills, especially in the litera-ture on skill acquisition (e.g., Bruner, 1971,1973; Fitts & Posner, 1967) and the Piagetianliterature (e.g., Cunningham, 1972; Hunt,

498 KURT W. FISCHER

1975; Piaget, 1936/1952). The first two trans-formation rules attempt to specify exactlyhow such skill combinations occur.

Intercoordination

Intercoordination specifies how theperson combines skills to develop from levelto level, all the way from Level 1 to Level10. The process is analogous to the com-bination of atoms to form a molecule. Atthe beginning of the process of interco-ordination, the child has two well-formedskills, a and b, at a specific Level 1. Thetwo skills are functioning separately fromeach other until some object or event in theenvironment induces the child to relate thetwo skills to each other. The child thenworks out the relationship between the twoskills with that object or event and sogradually intercoordinates the skills. Whenthe intercoordination is complete, the twoskills, a and b, from Level L have beentransformed into a new skill, d, at LevelL + 1, which includes them. The processis diagramed as follows:

a-b=d. (D

The multiplication symbol signifies inter-coordination (Table 2).

The essence of the process of interco-ordination lies in what seems to most adultsto be a paradox. A child is given a taskthat normally requires a Level L under-standing, but her skill for that task is only atLevel L- 1. Consequently, she seems tohave all the knowledge that is needed toperform the task, yet cannot do it. Onlywhen she intercoordinates the relevant skillsat Level L - 1 to form the new skill atLevel L will she be able to perform the task.Note, however, that this process of inter-coordination is gradual and continuous. Thefact that it involves qualitative change doesnot in any way imply that the change isabrupt or discontinuous.

The development of conservation oflength in the gadget (Piaget et al., 1968)provides a clear illustration of this paradox.As stated before, the child must have aLevel 6 skill to understand that the length ofthe cord conserves despite changes in thelengths of the vertical and horizontal seg-

ments. When her skills with the gadget areonly at Level 5, she can understand twoseparate representational mappings in-volving the vertical and horizontal segmentsof the cord. She can understand the mappingfrom the horizontal segment, 5CH, to thevertical segment, 5CV, using the horizontallength to predict the vertical length; and shecan understand the mapping from the ver-tical segment, 3CV, to the horizontal seg-ment, 5CH, using the vertical length to pre-dict the horizontal. As a result, the child'sbehavior with the cord at Level 5 seemsparadoxical to an adult. The child seems tounderstand how the horizontal and verticalsegments of the cord change and how thechanges relate to each other, yet she doesnot recognize that the total length of the cordmust always remain the same because thechanges compensate for each other (Wil-kering, 1979).

The paradox is resolved when the childintercoordinates the two mappings toproduce the Level 6 skill for conservationof length in the gadget, as follows:

[5CH — 5CvH5Cv — 5CH] =BCH .v+» SCH.v]. (2)

The child with this Level 6 skill can under-stand how vertical and horizontal lengthinterrelate, instead of merely how verticalrelates to horizontal and how horizontalrelates to vertical (Verge & Bogartz, 1978).That is, she has constructed a skill for thetotal length of the cord (composed of hori-zontal and vertical components), and thatskill allows her not only to predict howhorizontal and vertical vary but also howtheir covariations sum to a constant length.

The formal descriptions of Levels 1 to 7in Table 3 indicate graphically how inter-coordination occurs at each level. Re-peatedly as one moves down the table, thecombination of two skills at one level pro-duces a new kind of skill at the next level.The diagrams in Table 3 also show how eachskill at one level still includes the two skillsfrom the previous level. The formal de-scriptions thus show both the origin of eachhigher-level skill in the lower-level skillsand the emergence of a new type of skill atthe higher level.

I chose the term intercoordination be-


cause it provides a specifically appropriatedescription of the process of combinationof two skills at one level to form a new skillat the next level. Intercoordination meansreciprocal coordination. Two lower-levelskills become coordinated with each otherand thereby produce a new higher-levelskill. In this article, the term inter coordina-tion is reserved explicitly for this process.The term coordination is used to refer ingeneral to all instances of a person's relatingtwo or more actions whether or not he or sheis going through the process of interco-ordination.

Compounding

The second rule for combination of skills,compounding, specifies the most importantmicrodevelopmental transformation. Incompounding, two skills, a andb, at Level Lare combined to form a more complex skill,c, at the same Level L.9 The process isdiagramed as follows:

3H] + [3H <-» 3S] =

3H3S]. (4)

b =c. (3)

The addition symbol signifies compounding.Just as with intercoordination, compound-ing is induced by both organismic and en-vironmental factors. First, the person mustpossess skills a and b, and second, someobject or event in the environment must in-duce him or her to combine them.

An example will clarify the compoundingprocess. Consider an 18-month-old who hasone Level 3 skill relating holding a pillow,3P, to placing her head on the pillow, 3H, anda second Level 3 skill relating placing herhead on the pillow, 3H, to going to sleep, 3S.(Going to sleep is originally an involuntaryresponse, but like blinking and breathing, itcan be brought under partial voluntarycontrol. Many children at this age expend alot of effort trying to control sleeping and thecircumstances that accompany it. Usually,the specific response that is signified by 3S isvoluntarily closing the eyes or saying"sleep.") With these two skills, the childstill cannot control all three actions at once:holding the pillow, placing her head on thepillow, and going to sleep. To do so, shemust compound the two Level 3 skills:

She thus produces a more complex Level 3skill that allows her to control the relationsamong all three actions.

What behavioral consequences does sucha skill have? When the child is actually inbed, it is difficult to assess whether she hasthe skill, because the context alone pro-duces all three components. As a result, shecan show all three actions together withoutcontrolling the relations among them. Theexistence of this environmentally elicitedconjunction of the three actions, on theother hand, shows how the environment caninduce combination of the actions into acomplex skill. At least once or twice everyday, the child is faced with a situationwhere the three actions go together. Almostinevitably, then, she will explore the rela-tions among the actions and ultimatelyproduce the compounded skill in Equation 4.

For assessment of this compounded skill,pretend play provides a better situationthan going to bed, because in pretend playthe child must actively put the three actionstogether. When she can control all threeactions in a single system, then she canpretend to go to sleep — holding the pillow,placing her head on it, and closing her eyes(Watson & Fischer, 1977). Other develop-mental sequences involving compoundinghave been tested and supported by Berten-thal and Fischer (1978), Watson and Fischer(1980), Hand (1980), and Fischer andRoberts (Note 3).

The process of compounding is not neces-sarily limited to combining just two simpleskills. It also has more complex forms, withcombinations of larger numbers of skills.For example, the child might compoundthe Level 3 skill in Equation 4 so that itincluded four or five actions instead of onlythree.10 Indeed, such successive compound-

9 Compounding of another sort might also occur. Theskill d at Level L + 1 might be combined with skill cat Level L to form the more complex skill e at LevelL + 1. Research is required to determine whether bothtypes of compounding exist.

"' Two points should be noted about this complexkind of compounding. First, the number of skillscompounded cannot be endless because compounding

500 KURT W. FISCHER

ing may ultimately account for much of theprocess of intercoordination, as I will illus-trate later.

Compounding describes relatively largemicrodevelopmental steps. The next twotransformation rules, focusing and sub-stitution, describe smaller microdevelop-mental changes.

Focusing: Moment-to-Moment Behavior

Focusing deals with one kind of shift inwhat is commonly called attention. Itdescribes not only a type of developmentalchange but also a type of moment-to-moment change in behavior. In a specifictask or context, a person will normallyhave a collection of skills available, andthose skills will generally be related to eachother because subgroups of them will shareone or more sets. For example, recall thehypothetical child who has a complete Level5 understanding of the gadget (withoutcompounding): She understands 12 dif-ferent two-set mappings, all possible pair-ings of the four sets involving the gadget.In this collection of skills, each set is in-cluded in six of the mappings. At a givenmoment with the gadget, the child will beusing one of the mappings. When she shiftsfocus, she shifts from one specific mappingto a second closely related mapping thatshares at least one set with the first map-ping.11 A shift in focus from skill e to skill/is represented symbolically as follows:

e>f. (5)

The symbol for "greater than" thus signifiesa shift in focus. When a shift in focus canbe consistently controlled by the child, thetransformation is diagramed:

Foe (6)

task determine the limit of what the personcan handle cognitively in that task. At anyone moment, she cannot bring to bear all ofher skills; normally, she can deal with onlyone skill at a time. Focusing describes theperson's shifts from one skill to anotherwithin the level or levels at. which she isfunctioning in the task. For instance, thehypothetical child knows a lot about thegadget, because she has mastered all 12mappings. Nevertheless, her understandingof the gadget is severely limited by the factthat she can focus on only one mapping ata time.

Say that at a certain moment she is con-sidering the set, 5W, of weights. She cannotdeal with all six of the mappings for weightbut must focus on just one, such as themapping of weight, 5W, onto length of thespring, 5L. A few moments later, she shiftsfocus to a second, related skill, the mappingof horizontal length of the cord, 5CH, ontolength of the spring, 5L, and then she shiftsfocus to the mapping of length of thespring, 5L, onto horizontal length of thecord, 5CH. These changes in focus arediagramed as followc:

— 5L] > [5CH —

(7)

The levels of the collection of skills that aperson has available to her on a specific

Clearly, changes in focus can producevery complicated sequences of behavior. Inassessing a person's skills with a task, caremust be taken to separate mere changes infocus from the actual control of relationsbetween sets. The shifts in focus indicatedin Formula 7 do not demonstrate control bythe child of the compounded skill [5W —5L — 5CH — 5L — 5Ca|, although underthe proper environmental circumstancesthey can be transitional to the formation ofsuch a compounded skill.

Focusing is not, however, merely astatement of a methodological difficulty.

is probably seriously limited by memory. Limitationsshould be much less severe when the skills are inter-coordinated into a higher-level skill. Second, a merestring of behavior, occurring once or twice, does notindicate that the person has compounded all thebehaviors in the sequence into a single skill. Just aswith the little girl in bed, one must be certain thatthe person actually controls the relations between sets.

" Notice that according to this definition, focusingcould not happen at Level 1, because skills at Level 1each include only one set. However, the theory pre-dicts that Level 1 sensory-motor sets are generatedby a prior reflex tier, which specifies the componentsof a Level 1 set and thereby indicates how focusingapplies to Level 1. The nature of this tier will besuggested later.


It allows predictions of certain kinds ofdevelopmental orderings. Consider a taskthat can be solved with, at a minimum,two skills at Level L and a shift in focusfrom one of the skills to the other. This taskis more complex than a task that can besolved with, at a minimum, one skill at LevelL. If the two tasks are within the sametask domain, then the first, more complextask is predicted to develop after the secondtask.

For example, suppose that the gadget ispartially covered, so that only two variablesare visible at a time. The child first dealswith only the weight, 5W, and the verticalsegment, 5CV, using the skill

5CV— (12)

— 5CV]. (8)

Once she has used this skill, the cover ischanged so that she can see only the verticalsegment and the spring, which requires theskill

[5Cy_5L] (9)

By shifting what is covered, the experi-menter can thus control the child's changein focus:

[5 W — 5C v] > [5C v — (10)

For the child to do this task as describedin Formula 10, she must have both Level 5skills. The focusing rule therefore predictsthat the skills in Formulas 8 and 9 willdevelop before the change in focus inFormula 10. A developmental sequence ofthis type has been demonstrated by Gottlieb,Taylor, and Ruderman (1977).

With the covering procedure, the experi-menter can teach the child to change focusconsistently. The child will thus learn a newskill involving a change of focus:

Foc([5W 5CV],[5CV — 5L])5Cv)>(sCv— (11)

which will allow her to do the task evenwhen all three variables are uncovered.This controlled-focusing skill is slightlymore advanced developmentally than thesimple change in focus in Formula 10. It isalso transitional to the compounded Level5 skill

which involves control of all three variablesat once instead of only two.

According to this analysis, then, the childwill show the following microdevelopmentalsequence of skills: first Formula 8 or 9, thenFormula 10, then Formula 11, and finallyFormula 12. Similarly, the focusing rulepredicts many microdevelopmental se-quences, such as transitional steps betweenacquisition of the simple Level 3 skills onthe left-hand side of Equation 4 and acquisi-tion of the compounded Level 3 skill on theright-hand side of Equation 4. See Hand(1980) and Watson (1978) for tests of ad-ditional sequences involving focusing.

Substitution

The transformation rule of substitutiondeals with one type of generalization: Askill at Level L is mastered with one task,and then the person attempts to transfer itto a second, similar task. The rule applieswhen all components but one in the first taskare identical with those in the second taskand when that one different component canbe generalized to the second task. AtLevels II and III, the component must be aset; at Level IV (which is Level I of the nexttier), it can be a set or a system. The skillwith the substitute component will bemastered after the original skill and beforeany skills of greater complexity in the sametask domain. Substitution is diagramed asfollows:

Sub d = dlt

or for a specific level,

Sub [5A — 5fi] = [5A

(13)

(14)

The set 5Bt is the substitute set.The skill for pretending to go to sleep

provides an example of the application ofthis rule. After the child develops the skillin Equation 4, she extends that skill to asubstitute object. Instead of holding herpillow and pretending to go to sleep, shesubstitutes a piece of cloth for the pillow:

Sub [3P <-» 3H <-» 3S]

= [3Pt <-> 3H «-» 3S]. (15)

502 KURT W. FISCHER

The set 3Pj, holding the cloth, is substitutedfor the original set 3P, holding the pillow.The extension of the pretending skill to thecloth develops after the original skill (on theleft-hand side of Equation 15) and beforeany more complex skills (Watson & Fischer,1977).

Differentiation

The final transformation rule for explain-ing development is differentiation, in whichwhat was initially a single set becomesseparated into distinct subsets. Differentia-tion is probably always a product of one ofthe other transformations, especially inter-coordination or compounding. As Werner(1948, 1957) has argued, differentiation andintegration always occur together. In skilltheory, differentiation and integration (com-bination) are thus complementary, whereasin many other approaches they are opposed(e.g., Kaye, 1979; McGurk & MacDonald,1978).

Differentiation can therefore be eithermicrodevelopmental or macrodevelop-mental, depending on which other trans-formation is involved. For macrodevelop-ment, the degree of differentiation is so greatthat a set at Level L should be considereda different set when it reaches Level L + 1.At higher levels, earlier global sets aredivided into distinct new sets that servein place of the earlier sets. (The superscriptsto the left of the capital letters designatingsets—see Tables 2 and 3—indicate thelevel of the set and thereby serve as areminder that a set differentiates as it de-velops to higher levels). Because of theformation of these new sets, the personcontrols an ever larger repertoire of sets asdevelopment proceeds. The expansion ofthe number of sets leads to a correspondingincrease in the number of skills, since thenewly differentiated sets can becomeseparate components in new skills.

The process of differentiation is dia-gramed as follows:

Diff A = AM, AN. (17)

Diff d=d* (16)

where the subscripts indicate subsets in theskill d. Differentiation of a specific set A isdesignated:

The development of conservation oflength in the gadget illustrates how dif-ferentiation occurs when a new skill isformed. A child with Level 5 mappings forthe gadget understands generally how thelength of the vertical segment relates to thelength of the horizontal segment and viceversa but does not yet understand conserva-tion of the total length of the cord. Anotherway of stating this confusion is that in thistask, the child has not adequately differ-entiated the total length of the cord from thelengths of the horizontal and vertical seg-ments. When asked about the total lengthof the cord, the child confuses it with thelength of the horizontal or vertical segment.Although this kind-of lack of differentiationmay seem odd to an adult, it occurs com-monly in children and indeed is charac-teristic of earlier cognitive levels (Smith &Kemler, 1977; Werner, 1948).

The lack of differentiation in the gadget isresolved when the child intercoordinates thetwo Level 5 mappings to form the Level 6system for conservation of the total lengthof the cord, as shown in Equation 2. Theintercoordination produces differentiationof the set for total length, 6CV,H, from thesets for vertical length, 6CV, and horizontallength, 6CH:

Diff (5CV, 5CH) = 6CV, 6CH, 6CV,H. (18)

In the set for total length, the child com-bines covariations in vertical and horizontallengths into a concept of total length. Notealso that the sets for vertical and horizontallengths can be differentiated more finely atLevel 6 than at Level 5: The child can dealwith smaller variations in length in each ofthe sets.

The specific variables that are separatedin a child's behavior are a function not onlyof the level but also of the particular task.For a child with skills at a given level,changes in the task alone can produceseparation. For example, if the cord in thegadget (Figure 1) were straightened out, achild with the Level 5 skills in Equations 2and 18 could easily control the set for thetotal length of the cord in the modifiedgadget, since it would be only a single set.


At the same time, with a gadget like theoriginal one, in which the cord is stilldivided into vertical and .horizontal seg-ments, he or she could tell that the verticaland horizontal segments were each differentfrom the total cord in the modified gadget.Likewise, certain experimental training pro-cedures can produce such separation or dis-crimination (Denney, Zeytinoglu, & Selzer,1977).

The interaction of task and level helps toresolve a paradox in the developmentalliterature. In some experiments, young chil-dren confuse variables like the several typesof cord length in the gadget, but in otherexperiments children of the same age easilyseparate variables that seem at first to be thesame as the ones they confused (Kemler &Smith, 1978; Smith & Kemler, 1978). In-deed, the same child can show both kinds ofskills—ones demonstrating a global, syn-cretic whole that confounds several vari-ables and ones using virtually the same vari-ables separately (Peters, 1977). In the taskswhere she uses the variables syncretically,the child must deal with a number of relatedvariables at the same time, and her skill levelis not sufficiently advanced for her to sepa-rate the variables. But in the tasks whereshe separates them, she does not need todeal with all of them simultaneously; able towork with first one variable and then an-other, she can easily separate them.

This separation is, of course, not the sameas the differentiation that is required to co-ordinate all the variables in a single skill.For instance, with the Level 6 conservationskill in the gadget, the child must differ-entiate covariations in vertical and hori-zontal lengths and combine them into a con-cept of total length. The three types of lengthare not merely separated; they are alsointegrated.

The relation between differentiation andcognitive level has many other implicationsfor analyzing development, according toskill theory. For example, when a personhas at some point developed a skill to LevelL but is now using the skill or some of itscomponents at a lower level, the sets willstill show the effects of the earlier differ-entiation at Level L. Suppose that a childhas developed the Level 6 skill for conserva-

tion of the cord, but because of fatigue oremotional upset is now functioning at Level5. She can use a skill that would not be pos-sible for someone who has never developedthis skill to Level 6. She might use thecoordinated lengths of the two segments ofthe cord to make coarse, qualitative Level 5predictions about the length of the spring:

[6CV,H — (19)

So far, I have emphasized general issuesabout differentiation because they are im-portant for understanding how differentia-tion and combination work together in skilltheory. But differentiation can also be usedas a developmental transformation rule.That is, it can be used to predict steps in adevelopmental sequence. In the spring-and-cord gadget, a skill for coarsely pre-dicting vertical length from horizontallength is less differentiated than a skill forpredicting the same thing more exactly; andthe coarser skill will develop earlier than themore differentiated one. In a sorting task,the skill for putting different shades of redinto a single category is more differentiatedthan the skill for putting identical shades ofred into a single category, and the more dif-ferentiated skill will develop later (Fischer& Roberts, Note 3).

Ordering the Results of Transformations

With five different transformation rules,some principles are needed for ordering theresults of the different transformations intodevelopmental sequences. First of all, for aclear-cut prediction of a sequence to obtain,all skills must be in the same task domain.Given that they are in the same domain,the following principles allow ordering ofsteps:

1. If one of the transformations is appliedto a skill or skills, the skill resulting fromthe transformation will develop after theinitial skills.

2. Starting with specific skills at Level L,a skill resulting from an intercoordinationtransformation will develop after a skillresulting from microdevelopmental trans-formations, because the skill resulting fromintercoordination will be at Level L + 1.

3. When Principles 1 and 2 do not provide

504 KURT W. FISCHER

an ordering, then for skills at the same level,those with more sets will develop later.

4. If more than one skill is involved in abehavior (e.g., because of the focusingtransformation), that behavior will developlater than the behaviors specified by eachskill separately (by Principle 1). A skill thatcompounds the several skills into one willdevelop later than the same skills connectedby a change in focus. If the focusing skillsinvolve a greater number of distinct com-ponents than the compounded skill, then asa rule of thumb the focusing skills willdevelop later.

Notice that by these principles, manypairs of skills cannot be ordered develop-mentally. Of course, skills that have thesame type of structure but different com-ponents cannot be ordered because they arein different task domains. But in addition,many skills within the same domain can-not be ordered—for example, two skillsthat are the same except that one has asubstituted set and one has a differentiatedset.

With the descriptions of the transforma-tion rules, all the major concepts of thetheory have been presented. The next stepis to demonstrate how the theory functionsas a tool for explaining and predict-ing development. After describing a setof guidelines for analyzing tasks and relatingthem to the constructs of the theory, I willpresent several experiments that have usedthe theory to predict specific developmentalsequences and synchronies and will thenexplain a few of the many possible generaldeductions from the theory.

Using the Theory to Predict Development

The theory can be used to predict andexplain various developmental phenomena,including developmental sequences andsynchronies, certain effects of the environ-ment on developing skills, individual dif-ferences in development, the nature ofdevelopmental unevenness, and structuralrelations among developing skills. But all ofthese predictions and explanations dependon a prior step—task analysis (Brown &French, 1979; Gollin & Saravo, 1970; Klahr& Wallace, 1976).

Guidelines for Task Analysis

Use of the theory to explain developmentrequires a behavioral analysis of perform-ance on the specific task or tasks in ques-tion: What exactly must a person do to per-form each task?

This kind of behavioral analysis is not assimple as it may seem. The situation isanalogous to that of a behaviorist trying todetermine which specific operants or re-sponses comprise performance on a giventask. Finding the operants is no easymatter (Breland & Breland, 1961; Schick,1971).

On the other hand, many investigatorshave been highly successful in analyzingbehavior into its natural units (see de Villiers& Herrnstein, 1976; Marler & Hamilton,1966). Premack (1965), for instance, foundthat simple observation of the actions thattend to recur regularly in an animal's be-havior allowed him to infer a long list ofnatural operants that formed a hierarchy ofreinforcers. And Fischer (1970, 1980) foundthat changes in patterns of responding overtrials in common learning situations demon-strated the formation of new, higher-levelbehavioral units.

The skill structures specified in the theoryare intended to reflect the natural units ofbehavior (both thought and action), in-cluding its hierarchical character, withhigher-level units subsuming lower-levelones. Determination of the validity of thesestructures will, of course, require extensiveresearch.

Use of the theory to analyze behaviorinto skill structures necessitates, first of all,a thorough knowledge of the available uni-verse of skill structures defined by the levelsand transformation rules. Given that onehas this knowledge, then task analysis canbe facilitated by using a set of guidelinesthat have been helpful for me and my col-leagues. To illustrate the use of these guide-lines, I will show how each one applies toan analysis of the development of an under-standing of a social role during childhood(Watson, 1978; Watson & Fischer, 1980).

For a social category to be a social role,according to role theory, it must involve atleast two social categories in relation to each


other (Brown, 1965; Mead, 1934). Forinstance, the social role of mother requiresthe complementary role of child, and thesocial role of doctor requires the comple-mentary role of patient. Which skill struc-ture is required, then, for a child to under-stand a social role, such as a doctor ex-amining a patient?

The guidelines for task analysis fall withintwo general categories: guidelines for deter-mining what the person must control andguidelines for designing and interpretingparticular tasks.

Control

At least three major questions are in-volved in analyzing what the person mustcontrol.

1. Does the skill require sensory-motor,representational, or abstract sets? Forunderstanding a social role, sensory-motorsets are clearly not sufficient, since the roleinvolves more than the child's own actions.Representational sets are necessary, be-cause the role involves the characteristicsand actions of people independent of thechild. Abstract sets are not needed, sincesocial roles as defined here require onlyconcrete characteristics and actions ofspecific people (a doctor relating to a pa-tient) rather than intangible attributes.Understanding the general definition of asocial role as involving one social categoryand its complement would necessitate thecontrol of intangible attributes, that is,abstract sets.

2. What are the sources of variation thatthe person must control in the skill? For thedoctor role, the child would have to controltwo representational sets, not only the setfor a person acting as doctor, ^?D, but alsothe set for a person filling the complementaryrole of patient, SP. Both of these sets arerequired because according to the definitionof social role, a role must be related to itscomplement.

Also, note that, by definition, at leasttwo sensory-motor action systems mustcomprise each representational set, becauserepresentational sets are formed from com-binations of sensory-motor systems. Forthe roles of doctor and patient, the action

systems are essentially role-specific be-haviors or characteristics. For example, adoctor gives a patient inoculations (onesensory-motor system) and examines herears (a second system), and a patient takesthe inoculation and poses for the ear ex-amination.

3. What are the relations between setsthat the child must control (among thevarious possible relations shown in Table 3)?Once the first two questions have beenanswered, determination of the relationsbetween sets is often simple. For the doctorrole, the set for doctor must have at leasta mapping relation with the set for patient:

[5/?D—55P]. (20)

With a mapping, the child can relate thedoctor role to the patient role, which is allthat is necessary to meet the minimal cri-terion of relating a social role to its comple-ment.

Tasks

Thus far, the skill analysis for the role ofdoctor has proceeded as if the skill could beconsidered independently of a particulartask. But in fact, the analysis must take theparticular task into account. At least threemajor issues are involved in designing andinterpreting specific tasks.

4. What is the particular task, and whatmust the person control to perform it? Forthe role example, Watson and I devised atask for assessing the child's understandingof the role of doctor (Watson & Fischer,1980). Seated at a table, a child was showntwo rigid-cardboard, stand-up dolls (adoctor and a child patient) and a few doctor'sinstruments. The experimenter acted outthe doctor's examination of the patient andthen asked the child to act out a similarstory. The child was not asked to copy thestory precisely, so that no requirement ofexact imitation would interfere with thechild's demonstrating her knowledge. Toshow the role of doctor, the child had tohave the doctor doll carry out at least twoappropriate actions in relation to the patientdoll. The doctor might, for example, givethe patient a shot and look in her ears ortake the patient's temperature and examineher throat.

506 KURT W. FISCHER

In analysis of a particular task, sourcesof variation will often become apparentthat are not evident if one erroneouslyattempts to consider the skill independentlyof a task. In the present case, the taskbrings no change in the basic mapping skillas diagramed in Formula 20. But the com-ponents of the representational sets are alittle more complicated than they appearedin the analysis of Question 2. Because thechild must manipulate the dolls, each repre-sentational set must include a minimum ofnot just two but three sensory-motorsystems. For each representational set, thechild must manipulate the appropriate dollin addition to performing at least two role-specific actions, such as giving an inocula-tion and an ear examination.

One problem that can arise in interpretingparticular tasks is that incorrect task analy-ses in the developmental literature mayinterfere with determination of what a per-son actually must do to perform a task. Forinstance, for Piaget's final object-perman-ence task, where the child must find anobject that has been put through a series ofinvisible displacements, most investigatorshave assumed that the task requires thecognitive recreation of the invisible dis-placements by the child (Piaget, 1937/1954;Uzgiris & Hunt, 1975). Recently, this inter-pretation has been questioned (Jennings,1975; Harris, Note 6), and several investi-gators have shown that the task does notproduce cognitive manipulation of rep-resentations of invisible displacements(Bertenthal & Fischer, in press; Corrigan,in press).

5. What is the minimal task that woulddemonstrate the skill in question? If theskill is a specific concept, for example,one must first specify exactly what is meantby the concept and then determine theeasiest task that would demonstrate it.Without specification of a minimal task,erroneous inferences may be made aboutthe child's ability (Shatz, 1977). Task com-plexities that are basically irrelevant to theability in question will overload the childcognitively and prevent him from showinghis ability. The skill level at which a personcan control an ability or concept is a func-tion of the complexity of the task used to

assess that ability or concept (Bertenthal& Fischer, 1978; Opaluch, 1979).

For the doctor role, the definition is thatone agent must show doctorlike behaviorsin relation to a second agent, which mustshow reciprocal patientlike behaviors. Aminimal task for this concept is the doll-playtask, with just two dolls, the doctor and thepatient. Many children who can demon-strate the doctor role in this task will notshow it in a more complex task: If theexperimenter's story involves, for instance,a mother bringing her child patient to thedoctor's office and consulting with thedoctor and nurse while the patient is beingexamined, many of the children will demon-strate an apparent inability to understandthe role of doctor (Watson & Fischer, 1980).

6. To go beyond an analysis of an in-dividual task and predict a developmentalsequence, one must keep all tasks in thesequence within the same task domain. Withthe doctor role, for example, the levels andtransformation rules can be used to producean ordering of developmental complexity,with tasks more (or less) complex than thebasic doctor-role task. But if those tasks usedifferent procedures or varying roles (such asmother-child), the theory cannot predict aprecise developmental sequence. The manyenvironmental and organismic factors thatproduce unevenness mean that develop-mental sequences can only be predictedunambiguously when as many sets as pos-sible are kept the same from one develop-mental step to the next. To make clear pre-dictions from the task analysis of the doctorrole, the same demonstration procedureshould be used at every step, the same dollsshould be included, and the doctor-patientrelation should remain the basis of everystep. The more microdevelopmental thepredicted sequence, the more essentialit is that the content and procedure remainthe same from one step to the next.

Even with these six guidelines, doing atask analysis is no trivial matter. Unfortu-nately, it still involves a degree more art thanI would like. Yet once a task analysis is inhand, predictions based upon it follow fairlyeasily from the levels and transformationrules.


Predicting Developmental Sequences

Beginning from a task analysis, one canuse the transformation rules to predict adevelopmental sequence. The sequence canbe either macrodevelopmental or micro-developmental or both, and it can havevirtually any number of steps, depending onthe number of transformations that are used.There is no one true sequence that allchildren will always show, because theexact sequence that a child demonstrateswill be determined to a great extent by theparticular tasks that he or she experiences.Previous studies attempting to test detaileddevelopmental sequences (mostly predictedfrom Piaget's work) have shown a singularlack of success (e.g., Hooper, et al., 1979;Kofsky, 1966). Tests of sequences predictedfrom skill theory, however, have beenhighly successful (Bertenthal & Fischer,1978; Hand, 1980; Tucker, 1979; Watson &Fischer, 1977, 1980; Fischer & Roberts,Note 3).

Starting from the task analysis for thedoctor-role skill, one can predict manydevelopmental steps (Watson & Fischer,1980). Table 4 shows just a few of them.Application of the compounding rule to thedoctor-role skill (Step 2) expands the doctorrole to include a second complementaryrole, that of nurse, 5JN, thus producing amore complex Level 5 skill (Step 3). Thechild starts out with the two simple Level 5skills on the left of the transformationequation in Table 4: one relating the doctorrole to the complementary patient role andthe other relating the doctor role to thecomplementary nurse role. When thosetwo skills are combined by compounding,12

they produce the skill on the right of theequation: The child can make the doctordeal with both the nurse and the patient insuch a way that the doctor takes into ac-count the nurse's role relation to the patient(symbolized by the mapping of 57N and55P in the compounded skill).

Besides the steps shown in Table 4, manyother microdevelopmental steps can be pre-dicted. With application of the focusing rule,for instance, an intermediate step can bepredicted that is less developmentally ad-vanced than the compounded skill relating

doctor, nurse, and patient (Step 3) but moreadvanced than the doctorrole skill (Step 2):

D — SSP], [5/?D — STN]) =

— »sp) >(*/?„ — 5rN)j.Foe

The child can make the doctor deal with thepatient and then make the doctor deal withthe nurse, but does not integrate doctor,nurse, and patient all together in the appro-priate role relations. This behavior is moreadvanced developmentally than the doctorrole at Step 2 because the child must possesstwo complete Level 5 skills. The behavioris less advanced than the compounded skillat Step 3 because although it contains thesame components, they are not unified intoa single skill.

Another microdevelopmental step can bepredicted by use of the substitution rule:

Sub[5/?D— 57N — 55P] =

[5/?D — (22)

The child shows the same behaviors as forStep 3 but replaces the nurse doll with asubstitute object that does not normally fitthe nurse role, such as a plain adult maledoll. This skill is more advanced develop-mentally than the skill on the left of Equa-tion 22.

Thus, Equations 20, 21, and 22 lead toprediction of a four-step developmentalsequence. First, the child develops the basicdoctor-role skill in Equation 20 (shown asStep 2 in Table 4), then the skills resultingfrom the indicated transformations in thefollowing order: Equation 21, Step 3 inTable 4, and Equation 22.

Besides these and many other micro-developmental predictions, macrodevelop-mental predictions can be made, of course.The intercoordination rule specifies trans-formations from level to level. Reversalof the intercoordination rule decomposesthe doctor-role skill (Step 2 in Table 4) intoits two component Level 4 skills: the simplerepresentational sets for doctor, 4/?D, and

12 Several alternative pairs of simple Level 5 skillscould be combined to produce the same compoundedLevel 5 skill relating doctor, nurse, and patient roles.For example, [sRn

5TN] could be compoundedwithprN — *$,,].

Table 4A Developmental Sequence of Social Role Playing o

00

StepCognitive

levelRole-playing

skill Example of behavior Skill structure Transformation rule

1 4: Representa-tional sets

Behavioral role The child pretends that a doctordoll uses a thermometer anda syringe.

[4«D] Intercoordination:

[4KDH4SP] = Step!

5: Representa-tionalmappings

Social role The child pretends that a doctordoll examines a patient doll,and the patient doll makesappropriate responses duringthe examination.

[5RD - 55P] Compounding:

p«D 55P] + pRD

5TN] = Step 3

Social role withtwo compli-mentary roles

Shifting betweenfamily role anddoctor role

The child pretends that a doctordoll examines a patient dolland is aided by a nurse doll.Both patient and nurserespond appropriately.

The child pretends that a doctordoll is the father of the patientdoll, and then he or sheswitches to having the doctordoll fill only the doctor role —examining the patient dollwith the help of the nursedoll, as in Step 3.

5SC) > (5«D

5SP] Focusing:

Foc(pRF 55C],

P«D 3r;V

55P]) = Step 4

5rN — 5Sp)] Intercoordination:

[5RD — 55P] • [5tf F — 55C] = Step 5

I

«53oKw

6: Representa-tionalsystems

Intersection oftwo roles andtheir comple-ments

The child pretends that a doctordoll examines a patient dolland also acts as a father tothe patient, who is his son ordaughter. The patient dollacts appropriately as bothpatient and offspring.

Compounding:3

[6RD,r <-» «5P,C] + ["«„,„ ** «VM,W]

+ PVM,W ̂ 65P,C] = Step 6

(Table continues)

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patient, 45P. Thus, the theory predicts thatat Level 4 the child will be able to handlebehavioral roles—behaviors relating to thedoctor role alone or the patient role alone.He or she will know, for example, that adoctor uses a thermometer or a syringe,but will not include the patient as a partici-pant in these actions by the doctor.

Going in the other direction—up the de-velopmental scale—the skill for the doctorrole can be intercoordinated with the relatedskill for the father role, in which the adultmale plays the role of father, 5/?F, in relationto the role of child (son or daughter), 55C.Since an adult male can be both a doctorand a father, and a young person can be botha patient and a son or daughter, the childcan intercoordinate the two skills as shownfor Step 5. The symbol 6/?D,F stands for therepresentation for the behavior of a manwho is both doctor and father to his child,and the symbol 85P)C stands for the repre-sentation for the behavior of a young personwho is both a patient and a son or daughterto the father. Each new Level 6 representa-tion is thus a combination of two of theLevel 5 representations on the left of thetransformation equation in Table 4. With thenew Level 6 skill, the subject takes the per-spective of a man who is a doctor and istreating his son or daughter and simul-taneously takes the perspective of the son ordaughter who is a patient of the doctorfather. That is, at Level 6, the subject canact out this kind of social-role intersectionwith the doctor and patient dolls. This typeof social-role intersection is what the childneeds to understand how one of his parentscan fill two roles, such as parent and jobholder or parent and spouse (Fischer &Watson, in press).

Given any careful task analysis, the levelsand transformation rules thus make directpredictions about developmental se-quences. Application of the microdevelop-mental rules to the analysis for the gadgettask, for example, produces predictions of alarge number of developmental steps be-tween the levels. And application of thetransformation rules to any other taskanalysis presented in this article will like-wise predict developmental sequences.

510 KURT W. FISCHER

Predicting Developmental SynchroniesAcross Task Domains

Because of the importance of environ-mental factors, precise predictions of micro-developmental sequences can be made onlywithin a task domain, where most of thecomponents are the same or very similarfor adjacent steps in a sequence. The pre-diction of synchronies across task domainsis much more complicated, because few orno components are shared across domains.Yet predictions about synchrony are clear.First, because unevenness is the rule indevelopment, the degree of developmentalsynchrony between two task domains willseldom be high. It will usually be moderatefor familiar domains, because each inde-pendent skill develops with age and thisrelation with age produces some correlationbetween the two skills.

Second, manipulation of environmentalfactors such as degree of practice willdrastically alter the degree of synchrony.For instance, sequences in two highlypracticed domains should show nearly per-fect synchrony, as will be explained later.

Third, whenever developmental se-quences in two different domains intersectso that a skill in one domain becomes partof a skill in the other, the development ofthe skill in the first domain will predictthe development of the skill in the second.This correspondence will be precise, withvirtually every child that develops throughthe two intersecting sequences snowing thepredicted correspondence.

Corrigan (1977, 1978, 1979, 1980) hasfound support for these predictions aboutsynchrony between task domains for therelationship between the development ofobject permanence (finding hidden objects)and the development of language. First, thegeneral correlation between object perma-nence and language development in a groupof infants between 10 and 26 months of agewas only moderate, r (29) = .36, p < .01.Further analyses indicated that this correla-tion was produced entirely by the relationof performance in each task domain to age.

Second, one point of precise correspond-ence between the two skills could be pre-dicted. When the child reached Level 4 for

the object-permanence tasks, it was pre-dicted that he would also begin to use wordsto ask about or refer to objects that werenot present, especially in the object-per-manence tasks.13 For example, he wouldstart using "all gone" and "more" appropri-ately for the absent objects. This corres-pondence was predicted from skill theorybecause with Level 4 skills, the child con-trols representational sets and therefore canunderstand that objects are agents of actionindependent of him: He can control therepresentational set or sets for objects inthose tasks even when he cannot perceivethe objects. He should, therefore, be ableto speak spontaneously about objects thatdisappear in those tasks or in similar situa-tions. Corrigan's findings supported thisprediction of precise correspondencebetween object permanence and use of "allgone" and "more."

Testing for developmental synchroniesbetween task domains is unfortunately morecomplex methodologically than it at firstappears. The correlation produced by agealone is a difficulty that is too often ignored.If the age range tested is wide, the cor-relations can be substantial. The develop-ment of classification skills between 1 and7 years, for example, correlates highly withshoe size, r(68) = .85, p < .001 (Fischer &Roberts, Note 3).

Skill theory suggests several ways ofovercoming this problem in testing for de-velopmental synchronies. First, whenprecise predictions can be made aboutexactly which developmental steps in thedifferent domains should coincide, thencorrespondence between domains can betested directly rather than indirectly throughcorrelations.

Second, predictions about relative de-

13 This hypothesis may seem at first to contradictthe earlier discussion of the problems with the Piagetiantask analysis of the invisible-displacements tasks.There is no contradiction for two reasons: First,Corrigan used a more complex testing procedure thatseemed to provide a better assessment of the use ofrepresentation in object-permanence tasks than thePiagetian procedure. Second, an object-permanencetask can require representation for reasons otherthan those embodied in the Piagetian task analysis(Fischer & Jennings, in press).


grees of synchrony can be tested. Considerdevelopmental sequences x, y, and z, wherex and y are hypothesized to involve virtuallythe same skills, and z is hypothesized toinvolve different skills. Within a given agerange, sequences x and y should correlatetogether more highly than either of themcorrelates with sequence z. Similarly, if aparticular environmental condition such aspractice is hypothesized to increase thesynchrony between two developmental se-quences, then the correlation between thesequences under that condition should behigher than the correlation under other en-vironmental conditions. Indeed, accordingto skill theory, an experimenter should beable to control the degree of synchronythat he or she will obtain by simple en-vironmental manipulations.

Role of the Environment

According to skill theory, environmentalfactors play a central role in determiningthe relative degree of synchrony betweendevelopmental sequences, and they alsoaffect the specific developmental sequencesthat people show. Some of these predictionsare presented below, primarily for theeffects of specific testing procedures, in-cluding the differences between longitudinaland cross-sectional procedures and theeffects of the specific tasks used to testdeveloping skills.

Effects of Testing

Longitudinal and cross-sectional pro-cedures should produce very differentpatterns of synchrony across task domains,as a function of the effects of practice.Because skills must be practiced to bemastered, a skill that is practiced regularlyshould develop faster than a skill that ispracticed less often. In most longitudinalstudies, children are effectively given re-peated practice with the skills being in-vestigated, because they perform the sameor similar tasks session after session. Inmost cross-sectional studies, on the otherhand, children are not given regular practicewith the skills being investigated, becausethey are tested on each task only once.

Longitudinal testing should thereforeproduce faster movement through a de-velopmental sequence than cross-sectionaltesting. Jackson, Campos, and Fischer(1978) tested this prediction by comparingthe effects of longitudinal and cross-sec-tional procedures on development throughan eight-step sequence of object perma-nence. Longitudinal testing produced a largepractice effect, as predicted: two to threesteps in the eight-step sequence.

Because of this practice effect, longi-tudinal testing should produce an inflatedestimate of the synchrony between develop-ment in two different task domains. Usually,in a group of children who have not experi-enced longitudinal testing, most of thechildren will have differential experiencewith the skills in any two domains. Conse-quently, in cross-sectional testing, thesynchrony between the two developmentalsequences will not be high, except in thecase where the sequences actually belongto the same skill domain. (Recall that a skilldomain is composed of a group of taskdomains that develop in close synchrony.)On the other hand, the extensive practicethat occurs in much longitudinal testingvirtually eliminates this differential experi-ence and elevates the skills in both taskdomains to the person's optimal level. Con-sequently, even when the skills are in factfrom independent skill domains, longi-tudinal testing will usually produce a highsynchrony between them—and a highcorrelation.

Corrigan's study of language develop-ment and object-permanence developmenttested this prediction (Corrigan, 1977, 1978).As I reported above, she found that for agroup of infants tested cross-sectionally,the correlation between the developmentalsequences was only .36. But for threeinfants who were tested longitudinally overthe same age range, the correlations weremuch higher: .75, .78, and .89 for the in-dividual infants. Liben's (1977) study of theeffects of training and practice on memoryimprovement and Jackson et al.'s (1978)comparison of cross-sectional and longi-tudinal procedures also corroborate theprediction.

These findings thus support the argument

512 KURT W. FISCHER

that cross-sectional testing in general pro-vides a better test of the naturally occurringsynchrony between task domains thanlongitudinal testing. Developmental psy-chologists commonly disparage the useful-ness of cross-sectional methodology indevelopmental research, but the ability topredict developmental sequences makescross-sectional testing a powerful develop-mental tool (Fischer, Note 7): Specificparallel sequences can be predicted in differ-ent task domains, and a separate task can bedevised for each step in each sequence.Then, with cross-sectional testing of everyperson on every task, scalogram analysiscan be used to test the validity of the se-quences, and the synchrony between se-quences can be compared step by step(Bertenthal & Fischer, 1978; Watson, 1978;Watson & Fischer, 1977).

Variations in testing procedure will affectnot only the degree of synchrony but alsothe particular developmental sequencesthat people show. Many developmentalpsychologists assume that every skilldomain shows only one true developmentalsequence, one set of stages of a fixed num-ber (e.g., Kohlberg, 1969). Skill theorypredicts, to the contrary, that the develop-mental sequence that a person progressesthrough will vary depending upon the as-sessment tasks and procedures used, as wellas analogous environmental factors thatoccur naturally, outside the experimentalcontext (Fischer & Corrigan, in press).

The variation in sequences as a functionof testing is especially obvious for micro-developmental sequences. The develop-mental transformation rules can be used topredict a large number of microdevelop-mental steps. For example, use of the sub-stitution rule on Steps 2,3, and 4 in Table 4would have produced six microdevelop-mental steps instead of three. Yet if chil-dren are not exposed to the specific taskscorresponding to each predicted step, manyof the steps will not appear in their behavior.If their environment never induces the useof a substitute object, for example, theywill never show these three new substitutionsteps for Table 4, nor any of the other pos-sible substitution steps in the developmentof social role playing. Likewise, steps in-

volving focusing, compounding, or differ-entiation will not appear in their behaviorif they are not exposed to the specific tasksor situations that will induce those par-ticular skills.

Even macrodevelopmental steps in-volving intercoordination may be skippedfor particular sequences. Recall, for in-stance, the Level 7 skill for the abstractconcept of conservation, that is, the conceptof quantities that do not change becausethey are composed of two constituentquantities that compensate for each other.Suppose that a person develops this con-cept of conservation without ever havingdeveloped the Level 6 skill for conservationof length. Perhaps he coordinates a Level 6skill for conservation of amount of clay withanother Level 6 skill for conservation ofnumber and so generates the abstract con-cept of conservation without ever dealingwith conservation of length. When he isthen tested for conservation of length inthe spring-and-cord gadget, he can gen-eralize the Level 7 skill for abstract con-servation to conservation of length in thegadget, and thus he will have developed theskill for conservation of length withoutever having gone through Level 6 for thatparticular skill. He will have effectivelyskipped Level 6 in the developmental se-quence for conservation of length.

Many of these irregularities and varia-tions in developmental sequences will be re-duced or eliminated by repeated testing withsimilar tasks. Suppose, for example, that an8-year-old child has many other Level 6skills but has not been induced to developconservation of length. Exposure to the taskfor conservation of length with the gadgetwill normally induce him to develop con-servation of length (Hooper, Goldman,Storck, & Burke, 1971). Because of effectslike this, performance in later testing ses-sions will commonly fit a sequence betterthan performance in the initial session(Tucker, 1979).

The effects of specific tasks and testingprocedures may explain many of the dis-agreements in the developmental literatureabout sequences in a given skill domain.For example, different investigators, usingdifferent procedures, have found different


microdevelopmental sequences for objectpermanence (compare for example, Cor-rigan, 1977, 1978; Opaluch, 1979; Uzgiris& Hunt, 1975; Wise, Wise, & Zimmerman,1974).

These effects of testing procedures onvariations in sequences and on synchroniesacross sequences are more than a meremethodological nuisance. They are a reflec-tion of the general importance of environ-mental factors as determinants of cognitivedevelopment.

Why Unevenness Must be The Rule

If environmental factors are as importantas I have argued in determining sequenceand synchrony, then indeed unevennessmust be the rule in development. The level,or step within a level, that an individualattains on a task is affected by so manyenvironmental factors that he or she couldnot possibly perform at the same level orstep on all tasks. Jackson et al. (1978), intheir study of object permanence, examinedthree different potential sources of uneven-ness: practice, task, and content. All threesources produced unevenness. As de-scribed earlier, the difference between thelongitudinal and cross-sectional groupsshewed strong unevenness due to practice:two to three steps in an eight-step sequence.Similarly, the specific task used to assessobject permanence created substantial un-evenness: two steps in the eight-step se-quence. Finally, the content (the type ofstimulus searched for) often produced smallbut reliable unevenness, especially with thecross-sectional procedure: Both the type ofobject and the familiarity of the object pro-duced unevenness ranging up to one step inthe eight-step sequence.

Individual Differences

Just as environmental factors make un-evenness the rule within an individual, sothey ensure that different individuals willshow different patterns of cognitive de-velopment. Of course, hereditary factorsalso contribute to individual differences indevelopment (as well as to unevenness);but even without those hereditary differ-

ences, the environment would induce largeindividual differences in development.

Individual differences can take severalforms. People differ in rate of development:Some move through the hierarchy of levelsmuch faster than others. People differ intheir profiles of cognitive skills—cataloguesof which skills have attained which levels.And most interestingly, people differ in thepaths through which they develop.

Many cognitive-developmental psychol-ogists have assumed that all people nor-mally develop through the same develop-mental path in any single domain, but re-cently a large number of researchers havebegun to argue that individual differences insome or all developmental paths are thenorm (e.g., Braine, 1976; Nelson, 1973;Rest, 1976).

Skill theory predicts that individuals willfrequently follow different paths of develop-ment and that these differences will take atleast two forms. First, different individualswill develop in different skill domains. Oneperson will develop basket-making skills butnot reading skills; another will develop bothbasket-making skills and reading skills, butnot skills for drawing maps.

Second, different individuals will followdifferent developmental paths in the sameskill domain (Fischer & Corrigan, in press).The developmental transformation rulespredict a large number of different possiblepaths in any single domain. The spring-and-cord gadget illustrates how individualscan take different paths within the samedomain. The way that an individual movesfrom Level 6 skills for the gadget to a Level 7skill integrating all four variables of thegadget (weight, length of spring, verticallength of cord, and horizontal length) willvary depending upon the particular Level 6skills that he combines. The results of twopossible alternative paths are shown inTable 5. In the first path, an individualbegins with two Level 6 skills: the systemrelating weight, 6W, to the length of thespring, 6L, and the system for conservation,relating total length of the cord at two dif-ferent times, iCv,H and iCV,H- As shown inTable 5, the individual forms a Level 7 skillfor the entire gadget by intercoordinatingthese two Level 6 skills.

514 KURT W. FISCHER

In the second path, a different individualbegins with a different group of Level 6systems, each involving weight 6W; weightand length of the spring, 8L; weight andvertical length of the cord, 6CV; and weightand horizontal length of the cord, 8CH. Hetoo combines these skills to form a Level 7skill for the entire gadget; but to do so, hemust go through more developmental trans-formations, as shown in Table 5, and heends up with a different skill from the in-dividual who followed the first path.

The first path is more efficient than thesecond one: It requires fewer transforma-tions, and the final skill (Step 2 of Path 1in Table 5) relates the four variables to-gether without redundancy. The secondpath not only goes through more trans-formations but also produces a skill (Step 3of Path 2 in Table 5) that is full of redun-dancy, with the weight variable reappearingin every representational system. The skillsalso differ somewhat in the behaviors thatthey control. For example, the first skill

allows direct access to the concept of con-servation of the total length of the cord,whereas the second skill requires that theconservation be inferred from the coordina-tion of two representational systems.

On the other hand, the two final Level 7skills are equivalent for most purposes.Both of them interrelate the same four vari-ables, and both of them reflect accuratelythe relations among the variables in the realgadget. Individuals using the two skills willcome to mostly the same conclusions aboutthe variables in the gadget.

Similarly, for virtually every skill at everyone of the levels, different individuals cantake different developmental paths within askill domain, and usually the end productsof the different paths will be skills that areequivalent for most purposes. That is not tosay, however, that individual differencesare minimal. The different paths within adomain are often significant; and more im-portant, individuals normally develop indifferent skill domains and to different skill

Table 5Alternative Developmental Paths to a Level 7 Skill for All Four Variables in the Gadget

Cognitive level Path Path 2"

6: Representational Step 1: [eW <-> "L] andsystems fiCv,n <-* |CVlH]

7: Systems of repre- Transformation:

Step 1: [6W <-> 6L], [8W <-> 8CV], and['W <-» 6CH]

Transformation:sentational systems [6W «•» 6L] • [?CV,H ** |Cv.H] = Step 2 \?W <-» SL] • \6W «-»• 6CV] = Step 2a

Step 2: Step 2a: ['7cv

Transformation:[«VV <-» "Cvl • ['W <-> 6CH] = Step 2b

Step 2b: f 7 7CV

7C,,

Transformation:

<-* 7L

t<-» 7CV 'W

7CV

7CH

= Step 3

Step 3:I

7W <-> 7CV

\!/7Ci. .

a Steps 2a and 2b form separate skills, but they do not develop in sequence withaccording to this skill analysis.

respect to each other,


levels in the same domains. The environ-mental diversity of human experience, aswell as the genetic diversity of the humanspecies, ensures the occurrence of majorindividual differences in development.

Skill theory thus makes several generalpredictions about the effects of environ-mental factors on sequence and synchronyin development and provides tools for ana-lyzing some of these effects. In addition,the structures defined by the theory suggesta number of general corollaries about struc-tural relations and how they determine se-quence and synchrony.

Structural Corollaries

I shall not attempt to provide an ex-haustive list of structural corollaries but in-stead will present a few illustrations ofpotentially useful ones.

Consistent Decalage Within a Task Domain

Unevenness in skills across domainsseems to be a fact of development. Butaccording to the theory, many phenomenathat are commonly classified as instances ofunevenness are in fact microdevelopmentalsequences: The unevenness follows thesame pattern in virtually all children in agiven social group, and it seems actually toarise from differences in the complexity ofthe skills. Most of the instances of horizon-tal decalage (unevenness within a stage orperiod) studied by Piaget and his colleaguesshow such microdevelopmental sequences.The skill theory explanation is simplest incases where the skills belong to the sametask domain. The skill that develops latercan be derived by the transformation rulesfrom the skill that develops earlier.

Among the best documented cases ofconsistent decalage within a task domain isthe development of conservation of sub-stance and conservation of weight. Re-search has repeatedly shown that schoolchildren develop conservation of substance1 to 3 years before conservation of weight(e.g., Hooper et al., 1971; Piaget & Inhelder,1941/1974, especially in the introduction tothe 2nd edition; Uzgiris, 1964). In conserva-tion of substance,14 children understand,

usually by 7 or 8 years of age, that theamount of clay does not change when a ballof clay is elongated into a sausage, flattenedinto a pancake, or changed into some othershape. At the same age, however, they stillbelieve that the weight of the clay ball doeschange when the shape changes. Typically,they will not develop the skill for conserva-tion of weight until 9 or 10 years of age.Within Piaget's framework, this consistentsequence is puzzling because both types ofconservation are said to require exactly thesame kind of concrete operational scheme:Two factors (height and length) covary insuch a way that changes in one compensatefor changes in the other.

According to skill theory, conservation ofweight develops after conservation of sub-stance because it requires a compoundedLevel 6 skill that subsumes the skill for con-servation of substance. In conservation ofsubstance, the child must coordinate thelength and width of the original piece ofclay, ?BL,W» with the length and width of thetransformed piece, i#Lw (Halford, 1970;Peill, 1975; Verge & Bogartz, 1978).15 Inconservation of weight, on the other hand,the child must go beyond mere amount ofclay and think about weight of clay. That is,he must relate the changes in the length andwidth of the clay to a third factor, such asthe weight readings on a scale or the amountofferee that he feels when he holds the clayin his hand, 6F. To coordinate all three setstogether in a single skill, he must compoundthe skill for conservation of the substanceclay with a skill involving the weight of theclay, such as the skill in which the childrelates the length of pieces of clay (forinstance, sausage-shaped pieces) to their

14 Note that this type of conservation is properlycalled conservation of substance. It has often beenerroneously translated as conservation of matter orconservation of volume. Both matter and volume aremuch more abstract and difficult concepts than amountof a substance such as clay, and they develop atlater ages.

15 A precise measure of the amount of clay, ofcourse, requires three dimensions (height, length, andthickness), not just two; but with early Level 6 skills thechild does not yet understand true volume—that is,three-dimensional volume. His understanding ofamount of clay is based on a relatively crude coordina-tion of just two dimensions.

516 KURT W. FISCHER

Table 6A Few Examples of Mimicking

Actualcognitive levels

Levels 2 and 3

Levels 2 and 3

Levels 6 and 7

Mimicking skill at Level L

[% — 2M2 — 2G2 —

2M, — 2S,]

[% — 2M2 — 2G2] > PG, — 2M, — %]

PM <H» W <H» «p <H» «Q]

Mimicked skill at Level L + 1

PS <-»• 3M <-»

PS <-» 3M <-»

r*TwL 7P <-> 7Q

3G]

• 3G]

IJ

weight:8F] =

[l^L.W *~* l^L.W **'/*']• (23)

Consequently, the child will develop con-servation of the weight of clay after con-servation of the substance of clay.

This same kind of analysis should be ableto explain most cases of consistent decalagewithin a skill domain, including cases wherethe differences in complexity are not ob-vious, as when differences in stimulus sali-ence produce decalage (Odom, 1978;Fischer & Roberts, Note 3). The skills ineach case actually differ in complexity, butpsychologists have previously categorizedthem as showing unevenness simply be-cause there has been no tool for analyzingthe skills and thus recognizing the dif-ferences in complexity.

Mimicking

Besides explaining phenomena like thelag between the development of conserva-tion of substance and conservation ofweight, microdevelopmental transforma-tions also predict another phenomenon:mimicking, in which a complex skill orseries of skills at Level L produces behaviorthat seems at first to require a skill at LevelL+ 1.

A person can mimic a skill at Level L + 1by acquiring a complex skill or series ofskills at Level L that includes all the setsthat comprise the higher-level skill. Themimicking skill will usually result from thetransformations of compounding or focus-ing (or both), as illustrated in Table 6.1 usethe word mimic intentionally because the

mimicking skill at Level L is by no meansidentical with the mimicked skill at LevelL + 1. In general, the skill at Level L + 1will be much more flexible and differentiatedthan the skill at Level L, and the child willhave much better control over the relationsamong sets. But there will still be manysimilarities between the mimicking skill andthe higher-level skill.

An example from the sensory-motortier will illustrate how mimicking occurs.By compounding Level 2 mappings, thechild can mimic the flexibility and com-plexity of a Level 3 system, as shown inTable 6. Consider the actions of grasping adoll, G, looking at the doll, S, and movingthe arm, M. When a child has a Level 3system controlling all three of these actions,he can combine several aspects of each ofthe three actions in a great variety of ways.For example, he can look at the doll anduse what he sees to guide the movement ofhis arms to grasp the doll, and then once hehas grasped it, he can move it in front of hisface and visually examine it. More generally,he can carry out plans that require him toconsider the relations among several as-pects of all three actions simultaneously.He can use his looking to guide his movingall along the path of movement; he can placethe doll at any point in space within hisreach; he can remember where he saw thedoll a few seconds before and reach thereto grasp it. And he can do all these complexthings smoothly and planfully, without trialand error.

At Level 2, the infant can mimic thisLevel 3 system by compounding the threeactions (Table 6). First suppose that he hasa sensory-motor mapping relating grasping


the doll, 2G, moving it, 2M, and looking atit, 2S: When he happens to grasp the doll,he can move it in front of his eyes and lookat it. He also has the related mapping oflooking, moving, and grasping: When hehappens to look at the doll, he can move hishand to where he sees it and then grasp it.By compounding these two skills, he canconstruct a complex Level 2 skill that mimicsthe Level 3 skill, as follows:

2M2 — 2G2] + pG,

— 2M2 — 2G2 — ! — 2S,]. (24)

With this mimicking skill, the child candemonstrate a complexity and recombina-tion in his actions that mimics the com-plexity and recombination of Level 3. Whenhe happens to look at the doll, he can movehis hand to it, grasp it, move his hand infront of his body, and look at the doll there.The sequence of actions is thus physicallyreversed and looks superficially like the re-combination of looking, moving, and grasp-ing that occurs so fluidly in the Level 3 skill.But in fact it is still only a chaining of actions.The infant can carry out the sequence, buthe cannot reorder it into the many flexiblecombinations that typify Level 3.

A more primitive form of mimicking canalso occur in this situation, as shown inTable 6. When the child has only the twosimpler Level 2 skills shown in Equation 24,the stimulus context can lead him to changefocus from the first skill to the second: Hehappens to look at the doll, moves his handto where he sees it, and grasps it. As heholds it in his hand, he then loses sight ofit and so changes focus to the second skill:He maintains his grasp on the doll, moveshis hand in front of his face, and looks.Thus, the context produces behavior thatsuperficially appears to show the mimickingLevel 2 skill or the mimicked Level 3 skill,but the child cannot actually control either ofthese complex skills.

Mimicking has been produced in thelaboratory by a number of ingenious experi-mental psychologists (e.g., Case, 1974;Harris & Bassett, 1975; Siegler, 1976),and some of these studies nicely supportthe skill-theory argument that the mimickingskill is different from the higher-level skill

that it mimics. For example, Bryant andTrabasso (1971) carefully trained preschoolchildren to correctly judge the larger ofevery pair of sticks in a five-stick series.When the children were asked about non-adjacent parts from the series without beingshown the specific lengths again, many ofthem correctly inferred the longer stick—thus apparently demonstrating transitive in-ference, which for their series of stickswould seem to be a Level 6 skill. How-ever, the training procedure was perfectlydesigned to teach a compounded Level 5skill that would mimick the Level 6 skillfor transitive inference.

If the children had only been taught amimicking skill, their correct performanceshould have been limited. For example,they should not have been able to solve atransitivity problem that required them toorganize the needed information about non-adjacent sticks on their own. In a follow-upstudy, Bryant (1974, pp. 54-56; 1977) foundexactly that: Children who after trainingcould consistently solve the original transi-tivity problems could not solve similar newtransitivity problems that required them toseek out the needed information on theirown. According to the mimicking corollary,all instances of mimicking should showsimilar kinds of limitations.

When one uses skill theory to analyzebehaviors that Piaget has studied, it isimportant to be aware of mimicking, es-pecially for many of his infant observations.Most cases of primary, secondary, andtertiary circular reactions, for instance,seem at first to require sensory-motorskills at Levels 1, 2, and 3, respectively.But closer examination shows that manyof these reactions are probably complexskills at the previous levels.

Mimicking is not just a laboratory curios-ity or a measurement problem, however.It occurs normally when the child con-structs transitional steps in the spontane-ous development of a skill. Indeed, mimick-ing skills probably lay the foundation forthe child's development to the next level.

Parallels Between TiersA third corollary involves the relations

between tiers. Because the general Levels I

518 KURT W. FISCHER

to IV (Table 1) repeat at every tier, behaviorshould show structural parallels betweentiers. If a specific developmental sequenceoccurs at the sensory-motor tier, forexample, then in the proper environment asimilar sequence should appear at the repre-sentational tier, but it should of course in-volve changes in the structure of representa-tions rather than changes in the structure ofsensory-motor actions.

I know of only two sets of studies thatprovide data relating to precise parallelsbetween tiers. One shows a parallel in therepresentational tier to a sensory-motorsequence; conversely, the other shows aparallel in the sensory-motor tier to arepresentational sequence.

In the sensory-motor tier, the infantdevelops skills for finding hidden objects.By Level III of the sensory-motor tier,he can follow the visible displacements ofan object and look for it where it last disap-peared (see Piaget, 1937/1954, Stage 5 inchapter 1). Because of the parallel betweentiers, a similar skill for search should de-velop at Level III of the representationaltier. Drozdal and Flavell (1975) have de-scribed exactly such a behavior, which theycall "logical search behavior." By 7 or 8years of age, most children could representthe probable displacements of a lost objectand so look for it where it had probablybeen lost. (See also Wellman, Somerville,& Haake, 1979.)

Mounoud and Bower (1974/1975) report aparallel in the opposite direction: from therepresentational tier to the sensory-motortier. At Level III of the sensory-motortier, infants developed a skill that was ap-parently parallel to the skill for conservationof weight at Level III of the representationaltier: When a familiar object made of amalleable substance like clay was alteredfrom its usual shape, the infants grasped it asif its weight remained the same, even thoughin other situations they routinely adjustedtheir grasp to fit the differing weights ofvarious objects. That is, they seemed toassume that the familiar object's weight re-mained the same even though its shape hadchanged. This sensory-motor conserva-tion was not present in young infants andemerged by about 18 months of age.

More tests of the predicted parallel be-tween Levels 1 to 4 and Levels 4 to 7 areclearly necessary, but besides generatingtests of skill theory, the parallel servesanother important function in research. Itoffers a source for new hypotheses. Forevery phenomenon that is discovered insensory-motor development, a similarphenomenon can be searched for in repre-sentational development, and vice versa.Likewise, developments at the sensory-motor and representational tiers suggestsimilar developments at the abstract tier.

Other investigators have proposed ageneral parallel between sensory-motordevelopment and later development (Piaget,1937/1954, 1967/1971; Mounoud, 1976;Siegel & White, 1975; Werner, 1948). Piaget(1'941) even gave a special name to parallelsacross his developmental periods: verticaldecalages (distinguished from horizontaldecalages, which are "parallel" develop-ments within the same period). Greenfieldand her colleagues have searched for struc-tural parallels between language and manip-ulative play (Goodson & Greenfield, 1975;Greenfield, Saltzman, & Nelson, 1972;Greenfield & Schneider, 1977). None ofthese investigators, however, has provideda system for analyzing and predicting theparallel structures, and consequently it hasbeen impossible to test the validity of sug-gested parallels. Skill theory, with its sys-tem for analyzing the structure of skills,may allow more precise tests of proposedstructural parallels.

Besides specific structural parallels be-tween tiers, skill theory also predicts newtiers, because Level IV of each tier pro-duces a new kind of set. Both before andafter the three specified tiers, the cycle offour levels can occur again with differenttypes of sets. There must, of course, besome limit on the recurrence of the cycle,since it cannot go on infinitely; but thatlimit will have to be determined by futureresearch.

Reflex Tier

The tier before the sensory-motor tiercould be called the reflex tier and might wellprovide the starting point for skill develop-


ment: The infantile reflexes seem to bereasonable candidates for the initial unitsfrom which skills are constructed. Un-fortunately, almost no research has beendone that can be used to test the existenceof these levels, and consequently I havetreated this tier as a corollary rather thanas a more firmly established part of thetheory.

The infant or fetus begins with singlereflexes, combines the single reflexes intoreflex mappings, then combines the map-pings into reflex systems, and finally com-bines the reflex systems to form systems ofreflex systems, which are single sensory-motor sets (Level 1 in Table 3).

The term reflex is used in a number ofdifferent ways in the psychological litera-ture. Some psychologists reserve the termfor behaviors that are not subject to operantcontrol and that are often assumed to becontrolled by the peripheral nervous sys-tem, like the knee-jerk reflex. I use the terminstead in the sense that it is used by ethol-ogists (e.g., Hinde, 1970) and many psychol-ogists (e.g., Piaget, 1936/1952): It refers towhat might be called preprogramed be-havior— species-specific activities thatseem to be biologically programed into thenervous system (Teitelbaum, 1977). Forexample, Zelazo, Zelazo, and Kolb (1972)have worked with the stepping reflex, acomplex response that can be elicited in thenewborn infant and that seems to be or-ganically related to the voluntarily con-trolled walking that develops toward theend of the first year after birth. Other ex-amples would be the sucking reflex, which iselicited by stimulation of the lips, and thetonic neck reflex, in which the infant turnshis head to one side and raises his arm onthe opposite side. Even complex behaviorslike looking are reflexes within this meaning:The sophisticated rules for visual scanningdescribed by Haith (1978) seem to be pre-programed properties of the looking reflexor reflexes. To distinguish these reflex be-haviors from peripherally controlled re-flexes like the knee jerk, I will call themreflex skills or sets, because skill theorypredicts that they normally develop intosensory-motor skills.

I know of only one study that relates

directly to the prediction of a reflex tier—a study by Bullinger (1977, Note 8). Much ofthe large quantity of other research on thenewborn (Haith & Campos, 1977) could beinterpreted in terms of such a tier, but noneof it seems to provide a direct test of thepredicted four levels of reflex development.Bullinger describes how the tonic neck re-flex becomes gradually coordinated with thelooking reflex and eventually develops into alooking skill that is independent of the tonicneck reflex.

In a sense, there are really two tonicneck reflexes. In one, the infant turns hishead to the right and raises his left hand,and in the other, he turns his head to theleft and raises his right hand. The tonicneck reflexes and various looking reflexesshow a significant physical dependency:When the young infant is producing a giventonic neck reflex, he can look only to theside of his midline where his head is turned.For example, when his head is turned to theright, he can look at stimuli within hisvisual field to the right of his midline, but hecannot look at stimuli to the left of midline.To look at stimuli to the left, he must pro-duce the other tonic neck reflex, in whichhis head is turned to the left. Bullingerdescribes how the infant gains control ofthis relation. My description of Bullinger'sresults includes an interpretation in terms ofthe four reflex levels.

At Level I, single reflex sets, the infantproduces single reflexes, like each of thetonic neck reflexes and each of the variouslooking reflexes; but he cannot controlany relations between reflexes. Bullingerfound that infants from 15 to 45 days of ageproduced the tonic neck reflexes and variouslooking reflexes, but usually could not con-trol any relation between tonic neck reflexand looking.

At Level II, reflex mappings, the infantmaps one reflex onto another and thusbegins to control relations between reflexes.For example, he should be able to producethe head-right tonic neck reflex in order tolook at a stimulus to his right. At Level III,reflex systems, the infant relates two map-pings to each other, integrating the twotonic neck reflexes with the two lookingreflexes (left and right) in a reflex system.

520 KURT W. FISCHER

He should therefore be able to shift fromone tonic neck reflex to the other as neces-sary to look anywhere within his left andright visual fields. Bullinger describes thedevelopment of control by the infant overthe relation between the tonic neck reflexesand the looking reflexes, but he does notdiscriminate between the predicted Level IIand Level III skills. Infants usually showedsome control of relations between the twotypes of reflexes at 45 to 80 days of age.

At Level IV, systems of reflex systems,the infant coordinates two Level III sys-tems into a higher-order system and thusgenerates a single sensory-motor set(sensory-motor Level 1). He should beable, for example, to relate the tonic-neck-reflex-and-looking system with anotherreflex system involving posture and looking,thus showing highly flexible looking be-havior that is relatively independent ofspecific postures: He has generated a newkind of set, the single sensory-motoraction of looking. Bullinger found suchflexible looking behavior commonly ininfants 80 to 120 days old.

In this way, development through thereflex tier produces a single sensory-motorset. Note, however, that such a set involvesnot only one reflex system but two or more,because a Level IV skill involves the co-ordination of at least two Level III systems.In the Bullinger example, the child co-ordinates the tonic-neck-reflex system withanother postural system in such a way thatthe postural adjustments go almost un-noticed, but in other cases the two systemsare more obvious. For example, an infantcan coordinate a reflex system for suckingwith a reflex system for looking, and therebyhe can look while he is sucking. This kindof analysis can provide a mechanism forpredicting and explaining the compositionof sensory-motor sets, especially the typesof co-occurring behaviors that can beglobally combined in the single, poorly dif-ferentiated sensory-motor sets describedearlier.

Skill theory produces, then, at least thesefour structural corollaries: the reflex tier,parallels between tiers, mimicking, and con-sistent decalage within a task domain. Thetheory should also be able to predict other

structural corollaries, as well as othergeneral effects of the environment on skilldevelopment and, of course, many otherspecific developmental sequences and syn-chronies. Rather than enumerating moresuch predictions, however, I would like toturn to some general implications of skilltheory for conceptions of cognition, learn-ing, and development.

A Few Implications of the Theory

Any theory worth its salt should do morethan answer the original questions it wasdevised to answer. It should have implica-tions for other important questions. Severalof the most interesting implications of skilltheory involve central topics in cognitivepsychology: the nature of the big picture ofcognitive development, the analysis ofcognitive development and learning acrossskills, and the relation between behaviorand thought.

The Big Picture of Development

Skill theory emphasizes careful analysesof specific tasks and predictions of specificsequences and synchronies in circum-scribed task domains. But it also goes be-yond these specifics to predict the generalnature of major shifts in cognitive develop-ment—how skills are changing across theboard as the person develops.

Although particular skills do not showabrupt or discontinuous change, majorstatistical shifts in populations of skills dooccur (Feldman & Toulmin, 1975). In skilltheory, the child's optimal level increaseswith age, and the speed of the increase isfaster when the child is moving into a newlevel (Fischer & Bullock, in press; Fischer,Note 7). Together with environmental in-duction, these spurts at each level willproduce major changes in the profile of skilllevels. Transition periods between "stages"can therefore be defined as times when anincrease in optimal level is producing amajor shift in the population of skills, withmany skills gradually moving to the newoptimal level. To the extent that the newoptimal level applies broadly across a widerange of skills, the shift in the skill profileshould be dramatic and easy to detect.


The study by McCall et al. (1977) onshifts in the profiles of infant skills showsone method for inferring such transitionpoints. These researchers found instabilitiesin the correlation patterns of infant teststhat correspond generally to what is pre-dicted by skill theory. When a shift to a newoptimal level occurs, an increased uneven-ness in the levels of performance willappear in the individual child. The reasonfor this greater unevenness is that the speedof increase in optimal level becomes largerat these times and the child can initiallyapply this new capacity to only a few skilldomains. Consequently, many correlationsacross domains decrease. The periods ofcorrelational instability thus reflect times ofmaximal change. McCall et al. found foursuch periods of instability during the first2 years of life, exactly as is predicted fromthe four sensory-motor levels. (Theyfound these periods of instability beforethey knew about skill theory.)

Presumably, similar instabilities couldbe found for all the higher levels as well.For example, Kuhn (1976) finds instabilitiesin ability-test correlations in early adoles-cence, when people are presumably movingto optimal Level 7, single abstractions.Epstein (1974a, 1974b, 1978) reports spurtsin mental age and brain growth that seem tocorrespond with the emergence of Levels 5,6, 7, and 8.

There is a difficulty, however, with usingage as the dimension along which one looksfor instability. After infancy, developmentalcanalization decreases (McCall, 1979;Scarr-Salapatek, 1976), and consequentlypeople probably no longer change to a newoptimal level at the same approximate age.This variability in the age of shifting shouldincrease dramatically at higher levels. Also,at higher levels, the prevalence of uneven-ness within an individual should becomemuch greater. This problem with age canbe eliminated if good measures of skilllevels are used. Then people can be groupednot by age but by their optimal level, andthe distribution of optimal levels within asample will demonstrate whether spurts andinstabilities exist (Fischer & Bullock, inpress; Fischer, Note 7).

Skill theory thus predicts general types of

shifts in patterns of skills with development.These general shifts allow one to predictnot only broad statistical changes but alsomany other general skill patterns, such asthe probability of possession of a specificskill in all people in a large, culturallyhomogeneous population. One can predict,for example, the average age at whichvirtually all children of a given culture willhave attained a specific level of a skill thatis important for that culture: Virtually allAmerican middle-class children will haveattained an understanding of the social roleof doctor (Level 5: Step 2 in Table 4) by5 years of age. One can specify the normalrange in which American middle-classchildren will normally be moving onto a newcognitive level for skills that are importantto them, as shown in Table 7. Also, testscan be made of the levels predicted by skilltheory versus those predicted by othertheories (e.g., Bickhard, 1978; Case, 1978;Halford & Wilson, 1980; Isaac & O'Connor,1975; Mounoud, 1980; Mounoud & Hauert,Note 9).

Application to Other Skill Domains

As the social-role example implies, the"big picture" to which skill theory appliesis not limited to the standard cognitive-developmental tasks (mostly Piagetian tasksand IQ-type tasks). It has the promise ofapplicability across many different skilldomains and consequently the potential forintegrating theoretical analyses in areas thathave usually been treated as theoreticallydistinct. Skill theory may be applicable toareas as diverse as language development,social development, and learning.

The skill levels should apply to any skillsthat develop, since they characterize thegeneral information-processing system ofhuman beings. Applying the theory to a newskill domain will not be an easy matter, ofcourse, because it will require careful de-scriptive analysis of the specific skills thatdevelop in that domain. This kind of carefulanalytic research has only recently becomecommon in cognitive-developmentalpsychology.

The first step in applying skill theory tonew spheres such as language develop-

522 KURT W. FISCHER

Table 7Age Periods at Which Levels First Develop

Cognitive level Age period"

1: Single sensory-motor sets2: Sensory-motor mappings3: Sensory-motor systems4: Systems of sensory-motor systems, which are single

representational sets5: Representational mappings6: Representational systems7: Systems of representational systems, which are single

abstract sets8: Abstract mappings9: Abstract systems

10: Systems of abstract systems

Several months after birthMiddle of first yearEnd of first year and start of second year

Early preschool yearsLate preschool yearsGrade school years

Early high school yearsLate high school yearsEarly adulthoodEarly adulthood

a These periods are merely estimates for middle-class Americans. For Levels 9 and 10, existing data donot allow accurate estimation.

ment or social development must thereforebe an analysis of some of the specificskills that develop in language and in socialrelationships (see, e.g., Harter, 1977).Starting with these specific skills, the theorycan be used to predict how they will de-velop through the skill levels, as was demon-strated earlier by the prediction of a de-velopmental sequence for social-role skills(Table 4).

Notice that language skills, social skills,and skills in Piagetian tasks are all "equal"in skill theory (as they are in the approachof Vygotsky, 1962). Many recent ap-proaches to language development andsocial development have postulated that cog-nitive skills are somehow more fundamentalthan language skills or social skills. Forexample, the development of some Piagetianmeasure of cognitive development, such asobject permanence, is hypothesized to bethe one prerequisite for the appearance oflanguage (see Corrigan, 1979; Fischer &Corrigan, in press). Similarly, researchersin social development use conservation orsome other Piagetian measure to explain theemergence of important social skills, such asperspective-taking and morality. ThePiagetian skill is again elevated to a specialstatus, as if it were more fundamentalthan the social skills.

According to skill theory, there is nothingparticularly fundamental about objectpermanence, conservation, or any otherPiagetian measure of development. The

only thing special about these Piagetiancognitive skills is that their developmentwas investigated first—before the develop-ment of the language skills or social skillsthat they are supposed to explain. Interac-tions between some Piagetian skills andsome language skills or some social skillswill undoubtedly occur in development,but they will be highly specific interactions,not general relationships in which one typeof skill will be a general prerequisite forthe other. And interactions will occur inboth directions, not just from Piagetianskills to language or social skills, but alsovice versa. The earlier discussion of syn-chrony explained the kinds of relationshipsthat should be expected: (a) a low generalsynchrony across domains, (b) high generalsynchrony only when the skills in thespecific domains being tested are all main-tained at the children's optimal level, and(c) specific interactions only when a par-ticular skill in one domain becomes a com-ponent of a particular skill in the otherdomain. Note that the kind of specificinteraction to be expected is what be-havioral analyses of transfer have alwayspredicted: Specific components of one skillbecome components of a second skill(e.g., Baron, 1973; Mandler, 1962; Reed,Ernst, & Banerji, 1974).

In addition to large-scale developmentalchanges, skill theory is also applicable tochanges in behavioral organization that areusually categorized under learning or prob-


lem solving. These changes should be pre-dictable by the microdevelopmental trans-formation rules of the theory. For example,in the microdevelopmental sequence inwhich children pretend about going to sleep,the successive steps in the sequence areessentially steps in the generalization ofan action: Children pretend to go to sleep,then pretend to put a doll to sleep, thenpretend to put a block to sleep, and so forth(Watson & Fischer, 1977). Similarly, manymicrodevelopmental sequences typicallycategorized under cognitive developmentcould equally well be categorized underlearning or problem solving (e.g., Fischer& Roberts, Note 3).

Likewise, adults solving a complexproblem or rats learning to run a maze showsystematic changes in the organization oftheir behavior (Duncker, 1935/1945;Fischer, 1975; Siegel & White, 1975). Thesechanges can be treated as microdevelop-mental sequences, and therefore skill theoryshould be able to predict and explain them(Fischer, 1974, 1980).

Skill theory, then, may help to integratesuch apparently diverse research areas aslearning, problem solving, social develop-ment, language development, and cognitivedevelopment. It also has important implica-tions for another major research problem—the relation between behavior and thought.

Behavior and Thought

A classic problem for most cognitiveapproaches has been that their constructstypically do not explain how thought isturned into action (see Hebb, 1974). Assome wit said, they leave the organismsitting in a corner thinking.

Skill theory provides a possible way outof this dilemma. Thought (representationand abstraction) develops out of behavior(sensory-motor action), and the skills ofthought hierarchically incorporate the skillsof action that they have developed from.That is, representational skills are actuallycomposed of sensory-motor skills; andlikewise, abstract skills are actually com-posed of representational skills and there-fore sensory-motor skills. Consequently,there is no separation between thought and

action, since thought is literally built fromsensory-motor skills. Also, sensory-motor development does not cease at theend of the sensory-motor tier but con-tinues at higher levels.16

Representational and abstract skills pro-duce and direct sensory-motor actions.This relation between representation andaction is illustrated by the example of thechild's understanding of the spring-and-cordgadget at Level 5. When the child under-stands the mapping of weight (representa-tional set 5W) onto the length of the spring(representational set 5L), her control ofeach representational set is based on sen-sory-motor sets. With her Level 5 skill,she can therefore directly control thevarious weights to manipulate the length ofthe spring. She is not left sitting in a cornermerely thinking about how weight relatesto length. Behaviors studied in our labora-tory also illustrate this relationship betweenrepresentational and sensory-motor sets(Bertenthal & Fischer, 1978; Watson &Fischer, 1977, 1980; Fischer & Roberts,Note 3).

The inclusion of sensory-motor skillsin representational skills is especially evi-dent in language. Speech and gesture, whichare both sensory-motor skills, are essentialcomponents of the representational skills oflanguage (e.g., Fischer & Corrigan, inpress; MacWhinney, 1977).

In addition, the control of sensory-motorskills by representational skills extends be-yond the direction of sensory-motor skillsthat are already present. Higher-level skillsalso direct the acquisition of new lower-level skills. Jacqueline's "bimbam" skill,described earlier, provides an example(Piaget, 1946/1951, Observation 64). Whenshe first combined two Level 3 sensory-motor systems into the Level 4 bimbamrepresentation for fluttering, her skill con-trolled just two things that fluttered: herself,when she rocked back and forth on a pieceof wood, and leaves, when she made them

16 In Piaget's theory, the nature of the relation be-tween sensory-motor action and representation is lessclear, but it seems that sensory-motor developmentstops at the end of the sensory-motor period (e.g.,Piaget, 1946/1951, p. 75).

524 KURT W. FISCHER

flutter. Then, through compounding andsubstitution, she extended the skill to newobjects, such as curtains, that she couldmake flutter or that fluttered in the breeze.For each object to which she extended theskill, she constructed or included a newLevel 3 sensory-motor system involvingthe fluttering of the new object, and thisskill thus became a new sensory-motorcomponent of the Level 4 "bimbam" skill.

In the same way, representational skillsat higher levels are constantly used to con-struct new sensory-motor skills. Develop-ment from Levels 4 to 7 produces skillsthat subsume more and more sensory-motor actions and at the same time controlfiner and finer differentiations of sensory-motor actions. Consequently, skill theoryshould be able to predict the developmentof complex sensory-motor skills likedriving a car, using a lathe, or operatinga balance scale—skills that develop afterthe first 2 years of life. Research does sup-port the argument that orderly develop-mental changes occur in sensory-motorskills during both childhood (e.g., Green-field & Schneider, 1977; Ninio & Lieblich,1976) and adulthood (e.g., Hatano, Miyake,& Binks, 1977).

In addition to making numerous specificdevelopmental predictions, then, skilltheory has significant implications for thenature of changes in populations of skills indevelopment, the integration of theoreticalanalyses of skill development and learningin spheres that have been traditionallytreated as distinct, and the relation betweenbehavior and thought. But skill theory alsohas several limitations.

Limitations of Skill Theory

Two limitations of skill theory are theneed for a more powerful definition of skilldomains and the need to deal with theprocesses by which skills are accessed.

Defining Skill Domains

Skill theory provides a mechanism forpredicting and explaining the developmentof skills in specific task domains, and italso gives a general portrait of how popula-tions of skills change with development. But

at this time it does not deal adequatelywith skill domains.

A task domain involves a series of tasksthat are all very similar to each other,typically sharing a basic group of com-ponents but differing in the additional com-ponents that are required to perform thetasks. A skill domain, on the other hand,involves a number of task domains thatshare similar skills and therefore developin approximate synchrony.

At present, skill theory determines skilldomains in a primarily empirical way. Whendevelopments in two task domains show adegree of synchrony that cannot be ac-counted for by environmental factors suchas practice effects, then the two task do-mains are said to belong to the same skilldomain. To deal with skill domains in a moresatisfactory way, skill theory will ultimatelyrequire concepts for specifying the gluesthat tie task domains together. These con-cepts will presumably lead to a graduatednotion of skill domain rather than an all-or-none notion: Task domains will vary interms of the proportions of skills that theyshare.

Accessing Skills

The second limitation involves a matterthat skill theory says little about. No pro-cesses are designated to deal explicitly withthe way in which skills are accessed. Aperson may have available the skill neededto perform a particular task or to show aspecific behavior and yet in the appropriatecontext may fail to use that skill. Skilltheory does not deal directly with phe-nomena of this type, which are commonlyclassed under the rubric of motivation.What makes a person do one thing insteadof another when she is capable of doingeither?

The omission of accessing also means thatskill theory neglects many of the phenomenaof memory and attention that are suchcentral concerns within the information-processing framework (see Estes, 1976).Skill theory should be able to predict thedevelopment of memory skills, and it hasalready been used as a tool for uncoveringsome new memory phenomena, such as a


relation between recall success and skilllevel (see Watson & Fischer, 1977). It doesnot specify, however, how the process ofaccessing skills relates to individual differ-ences and task differences in memory per-formance.

Skill theory in its present formulationdoes not use the information-processingframework. It is a structural theory thathas its roots in the classical tradition ofcognitive psychology (see Catania, 1973;Fischer, 1975). In recent years many psy-chologists have come to equate cognitivepsychology with the information-processingapproach. This equation ignores the factthat a long and venerable tradition of cog-nitive psychology existed decades beforethe information-processing approach wasinvented.

On the other hand, skill theory is notinconsistent with the information-pro-cessing approach. Indeed, I would hope thatsome parts of it could be reformulated ininformation-processing terms. Such a for-mulation might provide more precision insome parts of the theory and thereby helpto overcome some of the theory's limita-tions, including the treatment of accessingskills.

Any attempt to provide an information-processing formulation, however, shouldavoid a major pitfall that has plagued manyinformation-processing analyses of cog-nitive development: They neglect the adap-tive process that is the very basis of cog-nition according to skill theory. The cog-nitive organism is constantly adapting skillsto the world, and this adaptation providesthe foundation for cognitive developmentand learning (see MacWhinney, 1978). Anyinformation-processing formulation of thetheory must include this adaptive processif it is to provide a fair representation ofthe entire theory.

A person should not be treated as adisembodied brain developing in a virtualenvironmental vacuum. In some cognitivetheories that make sharp distinctions be-tween competence and performance, theenvironment and the person's adaptation toit are effectively left out. The issue of theprocesses by which skills are accessedshould not be confused with this issue of

competence versus performance. Althoughthere is some overlap between the twoissues, they are not the same. The extremeformulation of the competence-perform-ance model assumes that a structure ispresent but that there is some performancelimitation that prevents it from being fullyrealized in behavior (Chomsky, 1965). Theaccess question, on the other hand, entailsno such assumption, because skill theorydoes not posit powerful structures that havedifficulty eventuating in behavior. Theaccess question is simply: What are theprocesses that determine which skill anindividual will use in a particular task at agiven moment?

Concluding Comment

Whatever their form, theories are toolsfor thought (Hanson, 1961). The essentialtest of a theory is whether it is a good tool.This theory is intended to be a useful toolfor understanding cognitive developmentand facilitating the process of theoreticalintegration that is essential to progress inpsychology (Elkind & Sameroff, 1970;Haith & Campos, 1977). The theory prom-ises to provide a system for predicting andexplaining developmental sequences andsynchronies in any skill domain throughoutthe life span, and it also promises to inte-grate analyses of development with treat-ments of learning and problem solving.Time and research will tell whether thispromise becomes fact.

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3. Fischer, K. W., & Roberts, R. J., Jr. A develop-mental sequence of classification skills in preschoolchildren. Manuscript submitted for publication,1979.

4. Fischer, K. W. The hierarchy of intellectual de-velopment: Piaget systematized. Paper presentedat the meeting of the American PsychologicalAssociation, New Orleans, September 1974.

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5. Miller, A. I. Piaget's genetic epistemology andthe development of quantum mechanics from 1913to 1927: A study of structuralism. Unpublishedmanuscript, Lowell Institute of Technology, 1972.

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Received February 22, 1980 •

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