teoria de dllo cognitivo fischer

8/12/2019 Teoria de Dllo Cognitivo Fischer

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Fischer, K. (1980). A theory of cognitive develoDment:The control

A newborn baby is mostly helpless ancunable to deal with much of the workaround him. Over t he years the baby grow:into a child, the child into an adult. Ex

plaining th e psycholo gical trans format iorthat the individual undergoes in these 20odd years is one of the most challenginltasks facing psychology.

The theory presented in this article, callecskill theory, attempts to explain a large parof this psychological transformation. Ifocuses primarily on cognition and intelligence, and it deals with aspects of learnin)and problem solving. Skill theory treat!cognitive development as the constructiorof hierarchically ordered collections ospecific skills, which are defined formallj

by mean s of a set -theory description.Of course, oth er psychologists have deal


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next higher level. The movement from onelevel fo tfie next occurs in many micro -developmental step s 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 same

level 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 t he 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 th e individual develops,this highest level increases, and so she can

be ind uced t o ext end th ese skill s to the new ,higher level.

Relat ion Bet wee n t he Theory and Its Da ta

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 my

jud gmen t, 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 seven

levels, has been at issue in the cognitive -developmental literature. A number of de -velopmental psychologists have argued thatdevelopmental sequences can be predictedon a purel y logical basis , where the termlogical seems to mean internally consistent(e.g., Brainerd, 1978; Kaplan, 1967; Kohl-

berg, 1969). According to t his way of thi nk -ing, if a coherent, logical argument can

be made fo r a predi cted devel opmen tal se -quence, that sequence must occur. Al -though the sequence of cognitive levels

predi cted by skill theor y is internally con -sistent, I do not believe that this consis -tency itself provides an adequate test of th e

sequence (Fischer & Bullock, in press). Also,research that has explicitly tested for develop -

mental sequenc es has frequently found thatcertain IogicaT sequences do not acfuaIIyoccur (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; Fur by, 1972; Hanson, 1961).The mostimportant test of the levels and of all other

predi ction s fro m skill the ory is empirical.The theory must also be internally consistent,

but i ntern al cons isten cy will be fo r naught ifthe theory cannot describe, predict, andexplain the develop ment 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. Concrete

example s of specific skills ar e used to illus -trate most concepts. To demonstrate howthe concepts relate more broadly to the re -search lite rature, 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 concept s or predictionsdo not yet have good research documenta -tion.

Ass ump tio ns and Defi nitio ns

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 t he characteristics of the levelsand transformation rules.

Concept of Cognitive Control

Cognition is a complicated concept. Inmuch of the developmental literature, theterm cogn ition is used to refer t o skills of a

pa rt ic ul ar ty pe of co nt en t - typicallyknowledge of the physical world (as op-

THEORY OF COGNITIVE DEVELOPMENT

posed to the social , emot iona l, or linguist icworlds) 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. Mo re 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, cognition

includes anything th at involves the personscontrolling 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.

Natu re of Skills

Skill theory assumes that cognitive skillscan be described effectively and precisely

in terms of elementary intuitive set theory(see Suppes, 1957). The general definition ofa se t is a collection of things. Why is itnecessary to talk about collections to ex -

plain co gnitive dev elo pmen t? When peop lecontrol 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 is

based in act ion.Cognition and action. All cognition

starts with action, in a very broad sense.Piaget (1936/1952;Piaget & Inhelder, 1966/1969) has pointed out that cogni:ion is es -sentially what the organism, from its own

point of v iew, can do, whether the doing is

commonly classified as motor, percept1or mentat. For example, an infant not ograsps a doll or shakes a rattle or kick

blan ket b ut als o wat ches the doll , listen!the rattle, and feels the blanket. Accordto skill theory, th e higher -level cognition:childhood and adulthood derive direc

from these sensory-

motor actions: Repsentations are literally built from sensolmotor actions.

The definition of action in skill theoryhowever, different from Piagets use ofterm. First of all, within Piagets frarwork, the sense in which cognitions beycinfancy are themselves actions (no t merderivative from actions) is not clear: w1-a child represents a leaf fluttering in

bree ze, fal ling to t he gro und , having a grtcolor, and turning red in the fall, in w.sense is the child acting? According to SItheory, the child is controlling representatiosets for leaves fluttering, falling to i

ground, being green, and turning red. Tcontrol of variations can be conceived asaction on the part of the child, in that ichild actively controls the variations CInitively. Also, all representational sets ;literally composed of sensory - motor Itions, as I will illustrate later.

Second, an action involves a set (rat1than merely a poin t) be cau se it mu st alwz

be appli ed to someth ing, and in being ; plied , it must always be adap ted to tlthing. Every time an infant grasps a rator every time an adult recognizes a familface, the action is adapted to the specithing acted upon. Thu s, every time an acti

is carried out, even on t he same thing, ifdone a little differently. Notice that easpecific realization of an action alwayscludes bot h a subject and an object -organism and an environment. An actiontherefore a set of similar behaviorsthings, but not just any such set: In an acticthe person can control the relevant vartions in the behaviors on things. An infiwho can consistently grasp a rattle has afor grasping that rattle. An adult who crepeatedly recognize a specific famil iar fahas a set for recognizing that face. The thiis always included with the behavior in tdefinition of a set. In many ways, this denition of action is closer to the behavioconcepts of operant and skill than to Piage


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

Set andaction are clearly synonyms within the

theory. How do they relate to skills? A skill 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 persons control ove r both eachindividual set and the relations between thesets. Fo r example, an infant who can shake arattle in order to listen to it has a skill com -

pos ed of tw o rela ted set s, sha king t he ra ttleand listening to the noise it makes.

The relation between the concept of skillin the theory and the concepts of scheme

and operant from Piaget and Skinner mayhelp to clarify the meaning of skill. Piagetsgeneral word for cognitive structure is

scheme - a structure for knowing, a pro -cedure that the child actively applies tothings in order to understand them. I n 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 -

por tan t diff erence s i nvol ves th e o rgani sm -environment problem: Piagets schemesallot much less importance to the environ -ment than the skills of the present theorydo. Schemes are assumed to have a high

degree of generality, encapsulated inPiagets concept of the struc ture d en sem ble(Piaget, 1957, 1968/1970: Inhelder & Piaget,1955/1958). This powerful generality ofschemes should produce a high degree ofsynchrony in development. Two tas ks 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 b een increasingastronomically in recent years; American

psych olog ists seem to tak e speci al delight

Skills, schemes, and o perants.

~ ~~~

in documenting new instances, especiallywhen the unevenness can be attributed toenvironmental causes. Unevenness has

bee n foun d so often and synchrony soseldom that many developmental psycholo -gists have begun to sug gest that unevennessmay well be the rule in development, and

synchrony the exception (e.g., Carey, 1973:Cole & Bruner, 1971; Feldman & Toulmin,1975). Unevenness has been demonstratedrepeatedly for every Piagetian period ofdevelopment.*

The concept of skill, in contrast toPiagets scheme, requires that unevenness

be pe rva siv e in deve lop ment , becau se 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 impor tant similarities with Skinnerianoperants (Skinner, 1938). The term operanrrefers to a behav ior th at is emitt ed by an

organism, not elicited by a stimulus. At thesame time, th e 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 environ mental stimuli. Hun t (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 have

pot ent effect s o n most kind s of be havio r in

Many of the Englis h translations of Piag ets worksuse the word schema instead of schem e to translatethe French sch?me. There is a problem with thisusage: In recent years Piaget has differentiated schimefrom schema (Furth, 1969; Piaget & Inhelder, 196611971). SchCma refers to an internal image of some -thing, which is very far from the meaning of schim e.

* Here are just a f ew of the relevant references: forthe sensory -motor period, Butterworth, 1976: Jack -son, Campos, & Fischer, 1978; Kopp, OConnor,& Finger, 1975; Uzgiris & Hunt, 1975; for the pre -operation al 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 animal s an d peop le. T he effect s are so power ful tha t a number of analyses ofhuman abilities have been developed thatdeal primarily with the influences of task on

perfo rmance (e.g., Fleishman, 1975; Horn ,1976). In addition, specific experience with atask has repeatedly been shown to be im -

port ant. The se two f acto rs, task d iffer encesand experience, likewise account for manyinstances of unevenness. Fo r 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., Barr att, 1975; Jackson e t al., 1978:Kopp, OConner, & Finger, 1975). Evensimple practice with a task affects stage of

perfo rmance (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 c an be useful

experimental 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 to

prov ide suc h a system.In general, then, scheme and operant are

synonyms 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 actually

composed of lower -level skills, schemes,or operants. The theory thu s 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 a s children develop, they masterspecific cognitive skills; they d o not developuniformly across the entire range of skills.

Similarly, since cognitive development proc eeds by the coord inat ion of specific

skills or schemes or operants, development

Horizontal

- VerticalSegment

Figure I . The spring -and -cord gadget.

through the seven levels must occur withirskill domain, not across skill domains.other words, the development of cognitiskills occurs in much the way that beh2iorally oriented psychologists have stgested (Baron, 1973; GagnC, 1968, 19;Schaeffer, 1975). The child mast ers speci

skills, builds oth er specific skills upon the]and transfers skills from one domain to aother. This mastery process involves quatative changes in skills, but the specichanges occur gradually, not abrupt ly.

An example ashow how development is induced jointly

both the perso ns skills and th e envi ramental circumstances in a particular situaticThe developmerit of conservation of lengin the gadget shown in Figure 1 (adaptfrom Piaget et al., 1968, chap. 4) provide:simple illustration of this joint inductionorganism and environment. In the gadgetcord is attached to a spring and drap

over a nail, so that the cord is divided intwo segments by the nail, a horizontal sement and a vertical segment. Differiweights attached to the cord will produchanges in the length of the horizontal sement of the cord and concomitant changin the length of the vertical segment.

Consider a 5- or 6 -year -old girl who :ready has two skills (or schemes or opeants) for the length of the cord: (a) SIunderstands approximately how th e lengof the vertical segment relates to the lengof the horizontal segment; that is, she c;roughly control the relation between tlvertical length and the horizontal lengtusing the vertical to predict th e horizonG

Inductio n of a new skill.


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(b) She also understands approximatelyhow the horizontaI Iength retates 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 (vertical

pre dic ts h orizo ntal, and hori zonta l pr edi ctsvertical). 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 no t beunderestimated. If the cord were not a cord

but 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 childs 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 ~ o o r d i n a t e . ~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 induced

by the mobile to coord inate th e shaki ngand the watching. It is a pro pert y of mobiles- and of many other things in the world -that shaking them produces interestingchanges in their appearance.

Deve lop ment al syn chro nies . This es -

sential contribution of the environment toskiII deveIopment 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 of

environmental factors such as practice andfamiliarity allow the prediction of specialinstances of near - perfec t syn chro ny, as wellas predictions of various degrees of syn -chrony un der differing circumstances. Such

predi ction s will be illu strate d late r.Because of the connotation of the word

skill, the phrase skill do main implies a fairly broad group ing of behav iors. However,methods for determining the developingchilds groupings of behaviors into skilldomains are cr ude 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 will

distinguish tas k dom ain from skill domain.A task domain is a set of behaviors thatinvolve only minor variations in the sametask, in contrast to the broad grouping of

behav iors acro ss task s in a skill domain.Within a task domain, there is virtually no

prob lem in determ ining which behaviors belong to tha t domai n. As will be shownlater, the theory can predict developmentalsequences within a task domain. It may also

pro ve useful in d etermi ning the natur e andscope of skill domains, but that usefulnessremains to be demonstrated.

Because task factors areso important in skill theory, task analysis

Task analysis.

This analysis differs from that of Piaget et ai.(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 coordination of skills relating vertical andhorizontal. instead, they describe three stages: relatingweight to spring, then understanding conservation,and finally understanding the proportional relation

between 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 theory

has been more fully elaborated.Closely related to the problem of specify -ing which sets and relations a perso n mus tcontrol in a task is the problem of definingthe boundaries of a set. Indeed, the mostuseful form of set theory may prove to bethe theory offuzzy sets (Negoita & Ralescu,1975),which does not requ ire precise defini -tions of set boundaries. The problem ofdefining the boundaries of a set is virtuallyidentical to the problem encountered by

behav iori sts in d efining the boun dary of a noperant (Schick, 1971). The problem may bemore serious theoretically than practically(Catania, 1978), but it is still a prob lem.

Skill theory a t least points in the directionof a solution by specifying a universe of possible skill stru ctu res and th us providing atool for partially defining behavioral units.Development is analyzed into a hierarchy ofoperants - skill levels of increasingly com -

plex cog nitiv e control - plus var ious trans i -tional forms specified by the transformationrules. A parti cular b ehavi or can be relat ed toone of the possible skill structures, and atthe minimum, the theory will then imply

parti cular ki nds o f cha nge s in the cores and boun darie s of set s acro ss trans format ionsand levels.

Conceptsfor

Defin ing L eve lsand

Transformations

Through the joint contributions of the person an d the enviro nment , 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 the

person can con tro l at th at level. Also, ateach level, the skills include all the lowerlevels. Fo r example, when a child is at Level5 for a specific skill. that skill subsumesskills at Leve ls 4 through 1. Not e, h owever ,that these lower -level skills become moredifferentiated at each higher level to which

the superordinate skill develops.

BefQre the l ev tl%ems&es an bescribed, a number of key con cepts mustintroduced.

Rela tion s bet ween skills an d levcContrary to the use of stage or per iod in mcognitive -developmental models, the levare used generally to characterize a chilskills, not the child in general. A child 1normally be at different levels for diffenskills. To characterize a specific child

cog niti ve profile is required, indicating leof performance on a wide range of sk(see, for example, Rest, 1976).

There is, however, one sense in which Ilevels are used to characterize the chiEach child has an opt imal leve l, indicatithe best per formance the child s hows , whiis presumably a reflection of both practand the upper limit of his or her process1ability. Just as in information - processitheories, this central processing limitcreases with development (Case, 1 9

Flavell & Wohlwill, 1969; Halford & $3son, 1980; Pascual -Leone, 1970; Scandu1973). But skill theory do es not require thomogeneity of performance demandedmany information - processing theo ries, sinthe optimal level is merely an upper limnot a characte ristic of all cognitive behaviat a given point in development. Also, tlimit is characterized by a skill structt.(one of the cognitive levels) rather thansimple whole number of items in workimemory.

The postulation of levels instead of cctinuous monotonic increases in complexihas implications for the form of the icrease in opt imal level with age: Associatwith the levels, there will be spurts in tspeed of developmental change. That is, a:child moves in to a new level, she will shcrapid change; but once the level has be,attained, she will show slower change.this way, th e speed of development will vacyclically with t he skill levels. Not e that tkhypothesis does not mean that develomental change is abrupt or discontinuouThe child moves into a new level gradualover a long period, but the speed of chan,during this period is relatively rapid.

Although I have defined the opti mal levas a single upper limit, there is a possibilisuggested by ability research that at tl


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Table 1The Cycle of Four Levels That Repe atsin Each Tier

Characteristic Set -theoryLevel structure description

I Single set Wl or [XI

I1 Mapping [W- I111 System W . 4 . B X m l1v

highest levels, a per son may h ave a few dif -ferent optimal levels in different broad do -mains. For example, an adults optimal levelin spatial skills may be different from his orher optimal level in verbal skills (seeHorn, 1976).

Map pin gs and sy ste ms . The concepts

of mapping and system define the possiblerelations between sets within a skill, and bot h of t hese con cep ts can be descri bed inset - theory terms. A mapp ing is a structurerelating two sets: a collection of ordered

pairs in which th e fir st membe r in ea ch pa iris from one set (W) and the second memberis from another set (X). The first set is saidto be mapped on to the second: [W - I.

A sys tem is composed of a relation be -tween two subdivided sets. Each set isdivided into two subsets, which are relatedto the two sub sets in the other set. The twosubdivided sets are said to form a system,with the subsets noted by subscripts:

[wA,B XA,B]. The double -headed arrowindicates that t he structure is a system evenwhen the subsets are not expressly listed inthe formula: [W ++ XI.

The psychological interpretation of map - pings and sys tem s is straig htfo rward. In amapping, a per son can rela te two set s in asingle skill - two sensory - motor actions,two representations, or two abstractions. I na system, a per son can rel ate t wo sub sets 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 the

per son can con tro l two sou rces of v ariati onin each set. As a result, a system can in -

FISCHER

clude much more complexity an d detail thana mapping4

A third type of structure, called a system of sy st em s, is a relation between two sys -tems, as shown for Level IV in Table 1. The

psych olog ical inter preta tion of a syste m ofsystems is that people can relate two sys -

tems in a single skill, which allows them toform a new kind of set: t he most elementaryset M at the next higher tier. In this newset, each system is one element, so that thesimplest set h as just two elements.

Not e tha t in all th ese st ruc tur es, 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 i ncreases markedly at thehigher levels. Consequently, I will at timesuse simplified descriptions of higher -level

The concepts of mapping and system are bothderived in part from Piagets and Wemers work.Piaget and his colleagues (Piaget et al., 1968; see alsoFlavell, 1977) have analyzed s everal behaviors of the

preschool child in te rms of what they call a function,which is similar to a mapping. But they se em 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 Piagetsconcept of function. The concept of system is notdirectly present in Piagets work, but it derives in partfrom Piagets concept of concrete operations (Inhelder& Piaget, 195911964; Piaget, 1942, 1949). One of themost central aspects of a concrete operation is that itis reversible, but research does not support Piagetsargument that reversibility is absent in the pre-opera-tional period and first emerges in the concrete opera -tional period (Moore & Hams, 1978; Schmidt &Paris, 1978; Fischer & Roberts, Note 3). The con -cept of system in skill theory is intended to explain the

behaviors that have been document ed by Piagetsresearch on concrete operations but without re-quiring that reversibility be absent from mappings.Both mapping and system also incorporate explicitlyWerners hypothesis that development proceeds bysimultaneous differentiation and hierarchical integra -tion (coordination). The meanings of mapping andsystem ar e sufficiently different fro m Piagets usagethat attempts to plug Piagets usage into skill theorywill lead to serious errors.


sets; phrases such as variations in lengthor the d x t o r r d e will be used as skort-hand in place of longer descriptions such as

the chi ld s r epres entat ion of varia tion s in the seen lengt hs of the cor d or the childs repre senta tion of va riati ons in what she canmahe a do cto r doll do in examinin g a pat ient

dol l.Transformation rules. The five major

transformation rules specify how a skill can be trans formed in devel opmen t. Seve ralrules deal with the ways that skills can becombined t o produce more complex skillsand how they change as a result of the com -

bina tions . The ot her rules indi cate alter a -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 occurgradually, 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 macrodevelopmental

predi ction s (acr oss level s), 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 th esimplest possible at each level. Adequateformal definitions of the transformationrules depend on the formal descriptions ofthe levels, and so the rules will be defined precisely later.

No ta tio nThe introduction of a notation system

will 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. Numb ers and plain capit al letter s J, K,and L designate skill levels. Lowercaseitalic letters indicate skills of unspecified

level. Uppercas e letters designate sets, wd iffe fe i t t tywaeesspecifying the tier o f tset, as shown in Table 2.

Superscripts and subscripts on a capiletter give additional information about a sfLines and arrows ind icate relations betwesets, and letters above or next to a line

arrow indicate a particular relation. Bracets designate a skill, and certain mathmatical symbols and abbreviations specithe application of transformation rules.

Recurring Cycl e o f Fo ur Leve ls

The progression of skills through thierarchical levels shows a repetitive cycdiagramed in Tables 1 and 3. This kindrepetition of structu re has been discussed

both Piaget (1937/1954, 1967/1971) aWerner (1948), although neither of them hdescribed the exact nature of the propos

paral lels. Th e str uc tur es of Level s 1 toare parallel to the structures of Levels 47 and 7 to 10, but at eac h cycle the strutures are composed of a different typeset, as illustrated in Table 3.

Each cycle of four levels is a tier andnamed for its type of set. For th e first tieLevels 1 to 4, the sets are sensory-motcthey are actions and perceptions of the chion things or events in the world. Within tftier, the combinations of sensory - motsets grow more and more complex as tlchild develops through the first four leveluntil at Level 4 the combinations create seof a new kind, represent atio nal sets.

These representational sets designaconcrete characteristics of specific objectevents, or peopl e (includin g the child heself). Note that the new sets subsume sesory- motor sets, as shown in Table 3; tlsets from the earlier tier do not disappeaFor Levels 4 to 7, the representationtier, the new sets are again combinedmore and more complex ways, producingcycle parallel to that for Levels 1 to 4.

At Level 7, the combinations of reprsentational sets create new s ets of anothjkind: ab str ac t sets, which are generaintangible attributes of broad categories (objects, events, or peopl e. The se n ew sesubsume the representational and sensorymotor sets from earlier tiers, as shown I


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496 KURT W. FISCHER

various of his own characteristics to variousa sp e c ts a f t h e career mat he is considefing-

At Lev el 8, 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 spouses careeridentity: Perhaps he sees his own careeridentity as requiring that his spouse be in aclosely related career or perhaps as re -quiring that his sp ouse be primarily a home -maker.

Lev el 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 spouses identity, such ascareer and parental identities, and thus con -sider in a more differentiated way what hisown identity requires of his spousesidentity and what his spouses identityrequires of his own identity.

Finally, at Leve l 10 , systems of abstractsystems. this person can coordinate two ormore abstract identity systems. He mightrelate his own and his spouses career and

parent al ide ntit ies now (o ne Level 9 sys tem)with their career and parental identities10 years ago when they were first married(a second Level 9 sqstem). The result is ahigher -level conception of what their jointcaree r and parental identities have been likeduring their marriage.

Although I know of no rigorous tests ofthis or any o ther developmental sequencesin abstract skills during adolescence andadulthood, several investigators have re -

port ed dat a t hat gener ally sup por t t he pre -dictions of development fro m 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 develop mentsof scientific theory that seemed to them toroughly follow Piagets description of cog -nitive developme nt from the pre -operational

perio d to the forma l opera tion al period.Miller illustrates this parallel for the de -velopment of quantum mechanics, andGruber for the development of Darwinstheory of evolution. If these scientifictheories were developing through Levels 7

to 10, their progression would resemble the

prog ressi on from pre -operational to formaloperatianal thugli t , accadhg t~ sk;iAtheory, because both the Piagetian periodsand the scientific progressions involvedevelopment within a tier from Levels Ito IV.8 Oddly, Piaget too (1970; Piaget inBeth & Piaget, 1961/1%6) has suggestedthat t here 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 such

parallels.Within Piagets framework, cognitive de -

velopment virtually e nds 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 conten t area s (Piaget,1972). Many people have been dissatisfiedwith this conception of formal operations(e.g. , Arlin, 1975; Gruber & Vo n k h e , 1976:Riegel, 1975; Wason, 1977), but there has

been no altern ative position for analyzingdevelopment beyond early adolescence.Consequently, major age differences in theacquisition of various of Piagets 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 require dif -ferent levels of abstraction.

Piagetian scientific tasks and t he 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 dir ector of a corpora -tion or a school system, the skills requiredto write an effective essay or novel, and theskills involved in programming and operat -

a Within the present theo ry, Piagets pre -operational,concrete operational, and formal operational periods

are explained by Levels 4 to 7.

THEORY OF COGNITIVE DEVELOPMENT L

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

Transformation Rules

Now th at th e str uct ures of th e levels ha ve been desc rib ed, the operat ion 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 can

be pr edict ed that have not yet b een inves ti -gated. In this section on the transformationrules, however, I will refrain from reviewin gempirical support for the rules, so that Ican present th e concepts briefly and directly.In a later section, several studies testing

predi ction s based on th e rules will be de -scribed.

The five transformation rules are inter -coordination, compounding, focusing, sub -stitution, an d differentiation. Intercoordina-tion and compounding specify how skillsare combined to produce new skills. Inter -coordination describes combinations that

prod uce dev elo pmen t from on e level to th enext (macrodevelopment) , and com -

pou ndi ng des cri be s com bi nat io ns th at pro duc e dev elo pmen t within a l evel (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 oth er four transforrtiofff wcws, b it can e be erately to predict microdevelopmental steThe microdevelopmental transformaticof differentiation, substitution, focusiand compounding eventually producemacrodevelopmental transformationintercoordination. These five transforntion rules are probably not exhaustifuture research will indicate whether Iditional transformation rules are require

All the transformations are defipstructurally. Two or more skills with gi\structures are transformed into one o r mcskills with a new type of structure. 1induction of a specific struct ural transforntion always involves both organismic aenvironmental factors. At least twoganismic factors are involved: Th e persmust initially have the skills requiredapplication of the transformation and mi

be capabl e of appl ying the trans format irules to those skills. For example, if a pson has the necessary initial skills but thare already at her optimal level, then she vnot be able to apply the transformation icombining those skills to reach the nthigher level.

Likewise, at least two environmen pro per ties are necessary. F irst, th e envircment must have properties such that if tinitial skills are transformed, the resultinew skill will work. S econ d, the specienvironmental situation must have prcerties such that it will induce the personuse the initially separate skills in juxtap otion, thus leading her to explo re the relatio

bet ween the initial skills and con str uct ttransformed skill (see also Schaeffer, 197The transformation therefore requires beorganism and environment; transformatiocannot be attributed to either organismenvironment alone.

Two of the transformation rules, intccoordination and compounding, involcombinations of tw o skills to produce a nemore complex skill. Many psychologirhave talked about combinations of skillsa mechanism to explain the developmentmore complex skills, especially in the litexture on skill acquisition (e.g., Bruner, 1971973; Fitts & Posner, 1967) and th e Piageti:

literature (e.g., Cunningham, 1972; Hur


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502 KURT W. FISCHER

The set 3P1, holding the cloth, is substitutedfur the originat set ?, hoTding the p i o w .The extension of the pretending skill to thecloth devel ops after the original skill (on theleft-hand side of Equation 15) and beforeany more comp lex skills (Watson & Fischer,1977).

Diffe renti ation

The final transformation rule for explain -ing development is diff erentiation, 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 arg ued, differentiation an dintegration always occur together. In skilltheory, differentiation and integration (com -

bination ) a re t hus comp leme nta ry, wh erea sin many other approaches they a re opposed(e.g. , Kaye, 1979; McGurk & MacDonald,1978).

Differentiation can theref ore be eithermicrodevelopmental or macrodevelop -mental, depending on which other trans -formation is involved. Fo r macrodevelop -ment, th e 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. (Th e 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 d = d (16)

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

Diff A = AH, A N . (17)

The development of conservation oflength in the gadget illustrates how dif -ferentiation occurs when a new skill i sformed. A child with Level 5 mappings forthe gadget understands generally how thelength of the vertical segment relates to the

length 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 th e 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 differen tiation in the gadget isresolved when t he 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, T, , and horizontallength, V H :

Diff ('CL, 'CH) b C b , 'CH, T , , H . (18)

In the set for total length, the child com- bines covar iatio ns in vert ical and horizontallengths into a concept of total length. Notealso that the sets for vertical and horizontallengths ca n 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 ar e 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.

THEORY OF COGNITIVE DEVELOPMENT 50

At the same time, with a gadget like the* 6fte, iR W k h he mrd is st8divided into vertical and horizontal seg -ments, he or she could tell that th e 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 par ado x in the devel opmen talliterature. 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 sam e child can show both kinds ofskills- ones demonstrating a global, syn -cretic whole that confounds several vari -ables and ones using virtually th e same vari -ables separately (Peters, 1977). In the taskswhere she uses the variables syncretically,the child must deal with a numb er of relatedvariables at t he 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 thre e types of lengthare not merely separated; they are alsointegrated.

The relation between differentiation andcognitive level has many other implicationsfor analyzing development, accordi ng toskill theory. For example, when a pers onhas at so me 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 child

has developed the Level 6 skill for conserva -

tion of the cerd , but beca use of fatigue Ee d r r y s e t is nowfunctioning at Levr5. She can use a skill that would not be poisible for someone who has never developethis skill to Level 6. She might use thcoordinated lengths of the two segments cthe cord to make coarse, qualitative Level

pred ictio ns abo ut the lengt h of t he spring:

W Y , H - LI (ISSo far, I have emphasized general issueabout differentiation because they are in-portant for understanding how differentiition and combination work together in skitheory. But differentiation can also be uselas a developmental transformation ruleThat is, it can be used to predi ct step s indevelopmental sequence. In the springand -cord gadget, a skill for coarsely predicting vertical length from horizontalength is less differentiated than a skill fo

predi cting t he sa me thing mo re exa ctly; anith e coarser skill will develop earlier than thimore differentiated one. In a sorting taskthe skill for putting different shades of reiinto a single category is more differentiate(than the skill for putting identical shades ored into a single category, an d the more differentiated skill will develop later (Fische& Roberts, Note 3).

Ordering the Results of Transformations

With five different transformation rulessome principles are needed for ordering thrresults of the different transformations intcdevelopmental sequences. First of all, for iclear -cut prediction of a sequence to obtainall skills must be in the same task domainGiven that they are in the same domainthe following principles allow ordering osteps:

1. If one of the transformations is appliecto a skill or skills, the skill resulting f r o nthe transformation will develop after thcinitial skills.

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

3. When Principles 1 and 2 do not provide


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504 KURT W. FISCHER

an ordering, then for skills at the same level,

4. If more than one skill is involved in a behav ior (e.g., beca use of the focus ingtransformation), that behavior will developlater than the behaviors specified by eachskill separately (by Principle 1). A skill thatcompounds th e several skills into on e willdevelop later than the same skills connected

by a change in focus. If the focusing skillsinvolve a greater number of distinct com -

pon ent s th an t he co mpo und ed skill, then asa rule of thumb the focusing skills willdevelop later.

Not ice tha t by the se prin ciple s, many pai rs of skills can not be order ed devel op -mentally. Of course, skills that have thesame type of structure but different com -

pon ent s can no t be orde red b ecause t hey 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 will

pres ent seve ral ex peri men ts th at hav e usedthe theory to predict specific developmentalsequences and synchronies and will thenexplain a few of the many possible generaldeductions from the theory.

Htefe wirk H t e f e fe+s *tleAq? &*.

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 amon g 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 theor y to explain developmentrequires a behavioral analysis of perform -ance on the specific task or tasks in ques -tion: What exactly must a per son 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 behav ioris t t rying 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 analyzing

behav ior into it s natural uni ts (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 situati ons demon -strated the formation of new, higher -level

behav ioral units .The skill structures specified in the theory

are intended to reflect the natural units of behav ior (bo th thou ght and actio n), 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 structu res necessi tates, first of all,a thorough knowledge of the available uni-verse of skill struct ures defined by t he levelsand transformation rules. Given that onehas this knowledge, then task analysis can

be facilitated by usin g 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 at

least two social categ ories in relation t o each


other (Brown, 1965; Mead, 1934). For

the 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 fo r task analysis fall withintwo general categories: guidelines for deter -mining what the person must control andguidelines for designing and interpreting

parti cular task s.

ff ls iSKx3 , Hte seistf f efe &Ie requires

Control

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

1 . Does the skill require sensory - motor,representational, or abstract sets? Fo runderstanding 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 a s involving o ne 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 th edoctor role, the child would have to controltwo representational sets, not only the setfor a pers on actin g as do cto r, RD, but alsothe set for a perso n filling th e complement aryrole 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 -

binat ions of sens ory - motor systems. Forthe roles of doctor and patient, the action

systems are essentially role -specific bh V i c m or . Fur exampte,doctor gives a patient inoculations 01sensory - motor system) and examines hears (a second system), and a patie nt tak,the inoculation and poses for the ear eamination.

3. What are the relations between sethat the child must control (among tlvarious possible relations shown in Table 3Once the first two questions have betanswered, determination of the relatioi

betwee n sets is often simple. Fo r the doctcrole, the set for doctor must have at leaa mapping relation with the set for patient

(2With a mapping, the child can relate tfdoctor role to the patient role, which is ithat is necessary to meet the minimal CIterion of relating a social role to its compl,ment.

TasksThus far, the skill analysis for the role I

doctor has proceeded as if the skill could 1considered independently of a particul;task. But in fact, the analysis must take tl-

parti cular task into acco unt . At leas t thrcmajor issues are involved in designing aninterpreting specific tasks.

4. What is the particular task, and whimust the person control to perform it? Fcthe role example, Watson and I devisedtask for assessing the child's un derstandinof the role of doctor (Watson & Fische1980). Seated at a table, a child was showtwo rigid -cardboard, stand - up dolls (doctor and a child patient) and a few doctor'instruments. The experimenter acted OLthe doctor's examination of the patient anthen asked the child to act out a similastory. The child was not asked to copy thstory precisely, so that no requirement cexact imitation would interfere with thchild's demonstrating her knowledge. Tshow the role of doctor, the child had thave the doctor doll carry out at least tw,appropriate actions in relation to th e patiendoll. The doctor might, for example, givthe patient a shot and look in her ears otake the patient's temperature and examin

her throat.

. .

[iR -D 'SF'].


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506 KURT W. FISCHER

In analysis of a parti cular task , sou rcesu f v a r k t i m W i f t O f t e n i J f x ~that are not evident if one erroneouslyattempts t o consider the skill independentlyof a task. In the present case, the task

brin gs n o ch ange in t he bas ic mapping skillas diagramed in Formula 20. But the com -

po ne nts of th e repre sentat ional set s ar e 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. Fo r 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 e ar examination.

One problem that can arise in interpreting par ticu lar t ask s is that incor rect task analy -ses in the developmental literature mayinterfere with determination of what a per -son actually must do to perform a task. Forinstance, for Piagets 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 -

pla ceme nts by t he child (Piag et, 1937/1954;Uzgiris & Hunt, 1975). Recently, this inter -

pre tat ion has been quest ione d (Jenn ings ,1975; Harris, Note 6), and several investi -gators have shown that the task does not

pro duc e cogn itiv e manip ulat ion 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 meant

by the con cept and then det ermi ne th eeasiest task that would demonstrate it.Without specification of a minimal task,erroneous inferences may be made aboutthe childs ability (Shatz, 1977). Task com -

plexi ties th at are basically irrel evant to theability in question will overload the childcognitively and prevent him from showinghis ability. Th e skill level at which a perso ncan control an ability or concept is a func -tion of the complexity of the task used to

assess that ability or concept (Bertenthal

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 fo r this concept is the doll - playtask, with just two dolls, the do ctor and the

patie nt. Many child ren who can demon -strate the doctor role in this task will notshow it in a more complex task: If theexperimenters story involves, for instance,a mother bringing her child patient to thedoctors 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 thesequenc e within the same task domain. Withthe docto r role, for example, th e levels andtransformation rule s can be used to producean ordering of developmental complexity.with tasks more ( or less) complex than the

basic do ctor -role task. Bu t if those task s usedifferent procedure s or varying roles (such asmother - child), the theory can not predict a

preci se de velop mental sequ ence . Th e manyenvironmental and organismic factors that

prod uce uneve nness mean th at develop -mental sequences can only be predictedunambiguously when as many sets a s pos -sible are kept the same from on e develop -mental step to the next. To make clear pre -dictions from the task analysis of the doctor

role, the same demonstration procedureshould be used at every step, the same dollsshould be included, and the doctor - pati entrelation should remain the basis of everystep. The more microdevelopmental the

predi cted sequ ence , the mor e 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. predi ctions based u pon it follow fairlyeasily from the levels and transformationrules.

8z Fisc m, WW; w=il, m .


Predi cting Dev elo pme nta l S equences

Beginning from a task analysis, one canuse the transformation rules to predict adevelopmental sequence. The sequence can

be eit her macrod evelo pment al or micro -developmental or both, and it can havevirtually any number of steps, depending on

the 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 the

parti cular tas ks that he or she experiences.Previous studies attempting to test detaileddevelopmental sequences (mostly predictedfrom Piagets 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,

Not e 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, jTN, 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 th e doctorrole to the complementary patient role andthe other relating the doctor role to the

complementary nurse role. When thosetwo skills are combined by compounding,*they produce the skill on the right of theequation: The child can make the doctordeal with both th e nurse and the patient insuch a way that the doctor takes into ac -count the nurses role relation to t he patient(symbolized by the mapping of TN and?SP in the compounded skill).

Besides the steps shown in Table 4, manyother microdevelopmental steps can be pre -dicted. With application of th e focusing rule,for instance, an intermediate step can be

predi cted th at is less devel opmen tally ad -vanced than t he compounded skill relating

doctor, nurse, and patient (Step 3) but mczn+v-*--mfewm:

FOC [Rn - Sp] VRD- T N ] ) =i ( % D - s p ) > ( % D - ~ T ~ ) ] . 2

The child can make th e doctor deal with t pati ent and then make th e do cto r deal withe nurse, but does not integrate doctcnurse, an d patient all together in the appr

priat e role relati ons. This behav ior is moadvanced developmentally than the doctrole at Step 2 bec ause th e child must possetwo complete Level 5 skills. The behaviis less advanced than th e compounded skat Step 3 bec ause alth ough it conta ins tlsame components, they are not unified ina single skill.

Another microdevelopmental step can I pred icte d by use of t he subs titut ion rule:

Sub P R O- Th - =[ R D - TN,x - Sp]. (2

The child shows the same behaviors as fiStep 3 but replac es the nur se doll withsubstitute object that does not normallythe nurse role, such as a plain adult madoll. This skill is more advanced develomentally than the skill on the left of Eqution 22.

Thus, Equations 20, 21, and 22 lead predi ction of a four -step developmentsequence. First, the child develops the basdoctor - role skill in Equation 20 (shown iStep 2 in Table 4), then the skills resultirfrom the indicated transformations in tkfollowing order: Equation 21, Step 3 ITable 4, and Equation 22.

Besides these and many other micridevelopmental predictions, macrodevelojmental predictions ca n be made, of courstThe intercoordination rule specifies tranformations from level to level. Reversof the intercoordination rule decompostthe doctor -role skill (Step 2 in Table 4) In1its two component Level 4 skills: the si mprepresentational sets for doctor, R D ,an

Several alternative pairs of simple Level 5 ski1could be combined to produce the same compoundcLevel 5 skill relating doctor. nurse, and patient roleFor example, [>RD-- ] could be compoundcwith [I

-S,]


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Table 4 A D evc lop mc~ n to lSe q u e n c e of Socicil Role Playing

Cognitive Role - playingStep level skill Example of behavior Skill stru ctur e Transformation rule

I 4: Representa - Behavioral role The child pretends that a doctor [ 'RD]tional sets doll uses a thermometer and

a syringe.

2 5 : Representa - Social role The child pretends that a doctortianalmappings

doll examines a patient doll,and the patient doll makesappropriate responses duringthe examination.

3

4

Intercoordination:

[ 'RDj.[ 'Si,]= Step 2

Compounding:['R - sD 11+ ['Ru - TNI = Step 3

Social role withtwo compli-mentary roles

The child pretends that a doctordoll examines a patient dolland is aided by a nurse doll.

[SR 5 T N-

SS,] Focusing:

Foc([ R,:-

S r l ,

Both patient and nurserespond appropriately.

Shifting betweenfamily role anddoctor role

The child pretends that a doctordoll is the father of the patientdoll, and then he or she

[t5RR,-

) > ( W, - N- P ) ] Intercoordination:~ R D - - S i , j . ~ R ' R , - - S , j = S t e ~

switches to having the doc tordoll f i l l only the doctor role -examining the patient dollwith the help of the nursedoll, as in Step 3.

5 6: Representa - Intersection of The child pretends that a doctor t B R w ++ SI.,( 1 Compounding: "two roles and

ments

doll examines a patient dollionalsystems their comple - and also acts as a father to

the patient, who is his son ordaughter. The patient dollacts dppropriately as bothpdtient and offspring

L Rii,,* SP,~ + [ 'RDJI* VM,W]+ L'Vv,.,, * Si, 1= Step 6

Tuble c o n l i t i r i c > )

-*

Role - playingSte p skill Example of behavior Skill structure

6 Intersection of The child pretends that the [%F. ++ 'VM,W ++ SP,,Ihthree roles andtheir comple -ments

doctor doll is doctor, father,and husband, relating to the

patient doll, who is a patientand the man's offspring, andto the woman doll who is the


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522 KURT W. FISCHER

Table 7Age Periods ctf Which ed s First O~velop~

Cognitive level Age period a

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

representational sets5: Representational mappings6: Representational syst ems7: Systems of representational systems, which are single

abstract sets8: Abstract mappings

9 Abstract syst ems1 0 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

~~

=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 therefore be an analy sis of some of the specif icskills that develop in language and in socialrelationships (see, e.g., Harter, 1977).Starting with th ese 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).

Noti ce tha t langu age skills, social skills ,and skills in Piagetian tasks are all equalin skill theory (as they are in the approachof Vygotsky, 1962). Many recent ap-

pro ache s to lang uage deve lopm ent andsocial development have postulated that cog-nitive skills are somehow more fundamentalthan language skills or social skills. Forexample, th e 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 ofimportant social skills, such as

per spe ct ive -ta kin g and mor ali ty. Th ePiagetian skill is again elevated to a specialstatus, as if it were more fundamentalthan the social skills.

According to skill theory, there is nothing par tic ul arl y fu nd ame nt al abo ut ob jec t perma nence , con serv ati on, or any oth erPiagetian measure of development. The

only thing special about these Piagetiancognitive skills is that their developmentwas investigated first - befor e 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 hig hly spec ific inter action s,not general relationships in which one typeof skill will be a general prerequisite forthe other. And interactions will occur in

both direct ions, not ju st 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 childrens optimal level, and(c) specific interactions only when a par -ticular skill in one domain becomes a com-

pon ent of a parti cular skill in th e otherdomain. Note that the kind of specificinteraction to be expected is what be -havioral analyses of transfer have always

predi cted: Specif ic compo nent s of one skill beco me comp onen ts of a seco nd skill(e.g. , Baron, 1973; Mandler, 1962; Reed,E m s t , & Banerji, 1974).

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

THEORY OF COGNITIVE DEVELOPMENT 5:

lem solving. These chzinxes should be pre-ctictabfe by th e micrmk&pmenta tfm-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, then

pret end t o pu t a b lock t o slee p, an d 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 complex prob lem or r ats le arnin g to run a maze sh owsystematic changes in the organization oftheir behavior (Duncker, 1935/1945;Fischer, 1975; Siege1& 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.

Behav ior 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-

pose d of repre sentat ional skills and there-fore sensory - motor skills. Consequently,there is no separation between thought and

action, since thought is literally built fro

motor development does not cease at tlend of the sensory - motor tier but cotinues at higher levels.16

Representational and abstract skills prduce and direct sensory - motor actionThis relation between representation aiaction is illustrated by the example of tlchilds understanding of the spring-and-cogadget at Level 5. When the child undtstands the mapping of weight (represenltional set W onto the length of the spri(representational set %), her controleach representational set is based on sesory - motor sets. With her Level 5 sklshe can therefore directly control tvarious weights to manipulate the lengththe spring. She is not left sitting in a cornmerely thinking about how weight relatto length. Behaviors studied in our lab01tory also illustrate this relationship betwerepresentational and sensory - motor st(Bertenthal & Fischer, 1978; WatsonFischer, 1977, 1980; Fischer & Rober

Not e 3).The inclusion of sensory - motor ski

in representational skills is especially edent in language. Speech and gesture, whiare both sensory - motor skills, are essentcomponents of the representational skillslanguage (e.g., Fischer & Corrigan,

pre ss; MacWh inn ey, 1977).In addition, the control of sensory - mo

skills by representational skills extends 1yond the direction of sensory - motor skthat are already present. Higher-level skalso direct the acquisition of new lowlevel skills. Jacquelines bimbam skdescribed earlier, provides an exam](Piaget, 1946/1951,Observation 64). Whshe first combined two Level 3 sensormotor systems into the Level 4 bimb.representation for fluttering, her skill cctrolled just two things that fluttered: herscwhen she rocked back and forth on a pitof wood, and leaves, when she made th

settsory-f&&F &kills. A b , e n s a 3

l6 In Piagets theory, the nature of the relationtween sensory -motor action and representation isclear, but it seems that sensory -motor developnstops at the end of the sensory -motor period fcPiaget, 1946/1951, p. 75).


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524 KURT W

flutter. Then, through compounding ands k km, she e x t a n l e d the skiH to n e wobjects, such as curtains, that she couldmake flutter or th at 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 this

skill thus became a new sensory - motorZomponent of the Level 4 bimbam skill.In the same way, representational skills

at higher levels are constantly used to con -struct new sensory - motor skills. Develop -ment from Levels 4 to 7 pro duc es skillsthat subsume more and more sensory -motor actions and at t he same time controlfiner and finer differentiations of sensory -motor actions. Consequently, skill theoryshould be able to predict the developmentof complex sensory - motor skills likejriving a car, using a lathe, or operatinga balance scale - skills that develop afterthe first 2 years of life. Research does sup -

port the argum ent th at orde rly deve lop -mental changes occur in sensory - motorskills during both childhood (e.g., Green -field & Schneider, 1977; Nini o & 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 theoreticalmalyses of skill development and learningin spheres that have been traditionallytreated as distin ct, and the relation between

behavior and thou ght. But skill t heo ry 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 the

pro cesses b y which skills are accessed.

Defining Skill Domains

Skill theory provides a mechanism for predicti ng and expla inin g t he dev elo pme nt3f skills in specific task domains, and italso gives a general portrait of how popula -tions of skills chang e with development. But

I FISCHER

at this time it does not deal adequag lywith skill bo&.

A task domain involves a series of tasksthat are all very similar to each other,typically sharing a basic grou p of com -

pone nts but differin g in t he a ddit iona l com - pon ent s tha t ar e requ ired to perfo rm 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 prima rily empi rical 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. T o deal with skill domains in a moresatisfactory way, skill theory will ultimatelyrequire concepts for specifying the gluesthat tie task domains together. T hese con -cepts will presumably lead to a graduatednotion of skill domain rather than an all-or -none notion: Task domain s will vary interms of the proportions of skills that theyshare.

Accessi ng Skills

The second limitation involves a matterthat skill theory says little about. No pro -cesses are desi gnated t o deal explicitly withthe way in which skills are accessed. A

perso n m ay hav e ava ilable the skill neededto perform a parti cular 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 per son do on e th ing 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 -

proc essin g fram ewor k (see Est es, 1976).Skill theory should be able to predict thedevelopment of memory skills, and it hasalready been used as a tool f or uncoveringsome new memory phenomena, such as a

TH E ORY OF COGNITIVE DEVELOPMENT 52:

r e h t k n betwe en recall success and skillkvef ( see Watson & Fisctrer, W77 . t 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 - proc essin gframework. 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 cognitive

psyc holo gy with t he info rmati on - proce ssingapproach. This equation ignores the factthat a long and venerable tradition of cog -nitive psychology existed decades beforethe information - proce ssing app roa ch 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 - proc essin g te rms. Suc h a for -mulation might provide more precision insome parts of the theory and thereby helpto overcome some of the theorys limita -tions, including the treatment of accessingskills.

Any attempt to provide an information - proce ssin g formu latio n, how ever , shou ldavoid a major pitfall that has plagued manyinformation - proce ssing anal yses 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 - proce ssin g formu lati on of th etheory 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 persons adaptation toit are effectively left out. The issue of the

pro cess es by which skills are accessedshould not be confused with this issue of

competence v e r sm performance, AlthOUBlthere is s m e overtap between the twrissues, they are not the same. The extremiformulation of the competence - perfo rmance model assumes that a structure i:

prese nt but tha t t her e i s so me perfoi-manctlimitation that prevents it from being full!realize

teoria de dllo cognitivo fischer

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