Constructing Cognitive Operations Linguistically

CONSTRUCTING COGNITIVE OPERATIONS LINGUISTICALLY

1lurr.v Beilin CITY UNIVERSITY O F NEW Y O R K

I . LANGUAGE AS REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . I1 . T H E MECHANISMS OF CONSERVATION . . . . . . . . . . . . . . . . . .

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Ill . METHODOLOGICAL ISSUES IN PIAGETIAN TRAINING RESEARCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . EARLY HISTORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. METHODOLOGICAL ISSUES . . . . . . . . . . . . . . . . . . . . . . . . .

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IV . THE GENERAL TRAINING MODEL: METHODOLOGICAL ISSUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . PRETEST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B . TRAINING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C . POSTTEST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D . TRANSFER AND DECALAGE . . . . . . . . . . . . . . . . . . . . . . . . . E . STRONG VERSUS WEAK CRITERIA . . . . . . . . . . . . . . . . . . .

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V . LINGUISTIC TRAlNlNG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . VERBAL RULE INSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . B . LEXICAL TRAINING AND LEXICAL KNOWLEDGE . . . . . . . C . SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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VI . SUMMARY OF RESULTS AND THEORETICAL CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . SOCIAL LEARNING THEORY . . . . . . . . . . . . . . . . . . . . . . . . B . REPRESENTATIVE FUNCTIONALISM . . . . . . . . . . . . . . . . .

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C. LINGUISTIC S T R U C T U R A L I S M . . . . . . . . . . . . . . . . . . . . . . . D. V E R B A L R U L E INSTRUCTION: T H E O R Y . . . . . . . . . . . . . . .

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REFERENCFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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I. Language as Representation Cognitive structure in Piaget’s theory derives from the child’s action on objects and from internalized activity that is the analog of overt action. Language is also said to have its origin in action. The child’s first words-verbal signs such as “mommy” and “daddy,” and “semiverbal signs” such as “tch-tch”-are said t o “really represent complex schemes of actions, either related t o the subject or partly objective” (Piaget, 1962, p. 219). The process of naming an object is interpreted too as a statement of possible action (p. 222). The advance of true language over intuitive action, which is represented in images, and over the very earliest language, which is characterized as preconceptual, is that it constitutes a form of representation of concepts (pp. 279-280). This representational function of language remains for Piaget its most important characteristic. Language thus becomes the principal vehicle for representing concepts and operations, although it is not itself the source of the concepts and operations basic to the conception of space, time, causality, and other aspects of the real world. The by now well-known conservation phenomenon, for example, has its origin in the elaboration of elementary sensorimotor schemes. The rudimentary conservations are first realized (at 12 t o 18 months) in the concept of a permanent object and are fully attained (at about 7 years) in the construction of concrete operational schemes. Language enters into this process only for representing structures and functional relations already developed. Although the child does not attain the object concept until it is capable of representative activity (i.e., can symbolically represent the object that is not present), the form of representation which is needed for its realization is not linguistic but the image (Piaget, 1954a). This is evident in the child’s ability t o conceive of the object’s displacement through a series of detours behind or under screens. When knowledge of conservation is acquired later, it is again not language which ensures its construction but the composition of operations that entails internal symbolic action whose properties (such as reversibility) are basic to all logical structures and systems (Piaget & Inhelder, 1974). Much effort has been directed to testing and exploring the implications of Piaget’s theory, but no aspect of the theory has received more attention than Piaget’s characterization of conservation. And one of the principal vehicles for

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exploring the mechanisms of conservation has been the training study. The first efforts t o train conservation interestingly enough were initiated by the Genevans themselves, in an effort t o show that Piaget’s equilibration theory better accounts for cognitive change than other explanations, particularly enipiricistbehaviorist theories. Non-Genevan attempts t o account for conservation acquisition are not confined t o behaviorist or neobehaviorist theories, however. Among the alternatives [which are dctailcd by Beilin (1971a, in press)] are explanations based on a significant place given to the role of language. The purpose of this review is t o describe research, including that of the present author, designed t o show how conservation can be acquired by linguistic means, despite assertions of Piaget and H. Sinclair (the principal Genevan investigator of language development) that conservation is not acquired in this fashion. This paper goes one step further, however, in showing that in addition to its empirical demonstration, there is a theoretical basis for expecting such achievements t o occur, based in fact on Piaget’s more recent views on the relation between language and thought. Before describing the language-oriented training studies, we will set forth Piaget’s evolving views on conservation as background for the later discussion. We will also consider some of the more significant methodological issues that have arisen in Piagetian training research.

11. The Mechanisms of Conservation One of the marked characteristics of Piaget’s developmental theory is its emphasis on the construction of logical, semilogical and infralogical structures. These constructions extend over many years, with their most advanced level ordinarily achieved in technologically advanced societies in late adolescence or early adulthood, although the end point in the process is not really known. The natural process of construction, accoiding t o the theory, results from a selfregulating (i.e., equilibrating) niechanism that integrates the products of the subject’s own actions (experience) with internal change that occurs through another kind of biological regulation (maturation). The structural product of this interaction, according t o Piaget, is defined exclusively by neither nativist nor empiricist formulations. Piaget’s theory details the nature of the cognitive structures and the functional principles by which they are constructed. But it provides only a nonspecific characteriLation of the nature of experience and, similarly, a nonspecific characterization of natively given mechanisms, except for the reflexes observed at birth (Beilin, 1971b). Conservation is both the process and product of one such construction. As originally described by Binet (1890), it pointed t o the child’s difficulty in differentiating the number of elements in an array of objects from the length of the array. As Piaget’s studies disclose, this phenomenon is not confined t o the

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conservation of number but applies to all concepts that embody quantitative invariants (Piaget & Inhelder, 1974). In his account of conservation that refined and expanded upon the original formulation, Piaget (1 968) asserted that conservation was possible only when a composition of quantitative variations occurred. These compositions are of two kinds. One takes the form of a composition of transformations (higher X thinner = the same amount) and is manifest in the conservation of liquid (or continuous) quantity. The other takes the form of additive composition (nothing added, nothing taken away = the same amount). This form is evident when a wire in the form of an arc is extended to a straight line (or the reverse). The composition here is based on the intervals between the end points which form a system of additive inclusions (Piaget, 1968, p. 27). The additive and compensatory compositions plus the notion of operational identity, which is a necessary component of the compositions, are evident too in the child’s verbal justifications of his conservation judgments. These justifications involve two reversibility notions plus the identity argument. One is reversibility by inversion (a return to the original state, as when the child suggests that a row of counters, after being expanded to a wider length, can be contracted to return them to their original state); the other, reversibility by compensation, in which a change in one dimension is compensated for by a change in the other dimension (as in the pouring of a liquid from one jar to another of different dimensions with concomitant change in water level). Both reversibilities embody the logical negation of an operation carried forward in one “direction.” Conservation in essence requires the ability to concurrently or successively carry out an operation and then undo (reverse) it. Operational identity is inherent in the total scheme of conservation. In contrast to preoperational identity, which is concerned with maintaining the identity of the object (e.g., it is the same water), it is concerned with the identity of quantities. Entailed is an “identity operation” of an operational grouping ( t o - O = O ) that is only associated with other operations as part of a total system (the additive composition, etc.). Conservation thus requires a conjunction of operations with reversibility and (operational) identity coordinated in a system of additive and compensatory structures. The 1968 formulation emphasized the significant role of transformations in conservation, as did the theory prior to that. In fact, Piaget (1968) asserted, “where there is no transformation we cannot speak of conservation” (p. 18). Piaget has now altered his view of the necessity of transformation in conservation and other cognitive processes (in an address to the Jean Piaget Society, Phdadelphia, June 1975). He now proposes a significant role for correspondences that are sought by the subject in the matching and comparing of states before being able to respond adequately to transformations themselves. Transformations thus emerge as no longer sufficient for an understanding of cognition. Piaget presents three hypothesized relations between correspondences and trans-

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formations: (1) Correspondences pave the way for transformations (i.e., fixed states precede transformation). (2) There is an interaction between correspondences and transformations. (3) In operational structures there is an entirely new kind of necessary correspondence between a transformation and its inverse. In correspondences the relation between states is that of reciprocity. Conservation is offered as an example in which correspondences play a role. A comparison between states, e.g., a piece of clay observed in one shape compared with another in which a part has been transposed to the other end, while the body of the clay remains untransformed, leads to conservation judgments. In contrast to transformations, correspondences entail no inverse operation (and thus reversibility) but are related to one another when two states are compared in a relation of reciprocity. Beilin (1969) previously distinguished between two types of conservation-transformational invariance and fixed-state (or static) invariance, depending upon whether invariance in a quantitative concept is maintained in spite of a transformation or whether invariance is achieved by an implicit process of object transposition. Fixed-state invariance was demonstrated in a series of studies on area conservation, in which segmented squares of different configuration were compared, with the subject required to judge the equality of identical areas when they “appeared” to be different. This type of conservation ostensibly achieved by correspondence was referred to as quasiconservation, although it would appear now that Piaget accords this the status of conservation. Piaget reports that these correspondence processes lead to “precocious” conservation, although in Beilin’s experiments subjects experienced considerable difficulty in the task and were not successful in it until long after transformational conservation. This may have been due in part, however, to the dkcalage imposed by the task’s concern with area in contrast with the conservation of mass (solid quantity) o r number, or to the nature of the subjects, who were predominantly lower class. In sum, Piaget’s developmental theory, as well as the specific theory of conservation, has undergone a further significant development. This newer recognition of the significance of correspondences embodies the basis of a possible rapprochement with information-processing theories based on matching and comparison processes.

111. Methodological Issues in Piagetian Training Research A . EARLY HISTORY

Piaget’s theory of a cognitive system constructed by virtue of equilibrating mechanisms is not easy to test. Some of its assertions, such as those dealing with

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assimilation and accommodation, are quite abstract and general. These difficulties with the general theory probably account for conservation’s having been so popular with researchers. It is an easily observablc, intuitively interesting phenomenon about which Piaget makes very specific claims. At the same time it is informed by the most abstract elements of Piaget’s theory. The principal means of testing Piaget’s ideas of conservation has been through attempts to train conservation. As already indicated, the Genevans themselves embarked on such studies in the mid-1950s to show the superiority of the equilibration model over alternative empiricist explanations. These studies did not become widely known to American audiences until the appearance of Flavell’s (1963) book on Piaget’s theory, the reports of Smedslund’s (1961a, 1961b, 1961c, 1961d, 1961e, 1 9 6 1 0 studies in the Scandinavian Journal of Psychology, and Wohlwill’s (Wohlwill & Lowe, 1962) studies in American journals. Many other studies carried out in the United States and in the Soviet Union seemed to the Genevans to be focused merely on accelerating the acquisition of conservation and other cognitive functions, which Piaget derided. Though some of these studies did in fact have that emphasis from the start, others were addressed to the nature of conservation mechanisms (Beilin, I97 la. in press). Many of the training studies reflect dissatisfaction with Genevan methods of inquiry. What used to be called the “clinical method” and is now more aptly characterized as the “method of critical exploration” (Inhelder, Sinclair, & Bovet, 1974)-which we shall call here the “critical method”-has often been criticized as unstandardized and overly verbal. Consequently, much non-Genevan training research attempts t o provide a standardized means of eliciting and gauging the child’s cognitive performance. These more standardized procedures have their origin, however, in the earlier Genevan experiments. The earliest training studies (Apostel, 1959: Morf, 1959; Piaget, 1958, 1959a, 1959b, 1959c; Smedslund, 1959, 1961b; Wohlwill, 1959), which were begun in Geneva, and in some cases carried out elsewhere, started simply. In Smedslund’s (1959) case, it was with a procedure that employed a scale to verify that the weight of a plasticine ball was conserved as it was transformed through various deformations of the material. Feedback provided by weighing on the scale was said to be comparable to a “reinforcement,” in that it was external information that was used to establish proof of a conservation judgment. The weighing procedure over deformation trials was followed by addition/subtraction trials in which pieces of plasticine were added and subtracted from the original mass. Smedslund observed that learning in this circumstance was very rapid and inferred from this that nonconserving subjects were actually close to spontaneous acquisition (that is, they were transitional conservers). This latter fact was used to denigrate the effects of training (Oleron & Thong, 1968). In Smedslund’s later experiments, through various refinements, the effects of “external rein-

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forcement” were contrasted with a method of conflict-equilibration training based on Piagetian theory. The results of these experiments (Smedslund, 196 l c , 1961d, 1961e, 1961f) suggested that while “reinforcement” could be effective for learning it did not compare with the effectiveness of the conflict-equilibration procedure. Again Smedslund emphasized that when learning did occur it was with subjects who had the rudiments of operational structures already instated. Piaget (19641, taking note ot’ Sinedslund’s studies, observed that while Smedslund was successful in inducing weight conservation he was unsuccessful with the same method in inducing transitivity. Piaget proposed that training is more likely to be successful when physical relations are critical t o the task, as it is in the conservation of weight where weighing itself is required. When logicomathematical relations are involved, however, as in transitivity, and physical experience is not critical to the operation, training should be ineffective. Piaget proposed, additionally, on the basis o f Wohlwill’s (1959) success in inducing number conservation through addition operations, that learning is most likely to occur if more complex structures are approached by way of simpler structures logically related to them. These early training studies led t o the following general conclusions, which set the stage for much subsequent debate: (1) Successful training of relations embodying logicomathematical operations in children who had not acquired them naturally was not likely to occui. (2) If it did occur it was most likely to occur with children who showed some evidence of acquired structure. (3) When training was successful in inducing conservation it would be by methods that were consistent with Piagetian theory of how mathematical cognitive structures are naturally acquired, namely, by a conflict-equilibrium method. Alternative methods associated with behavioristic or neobehavioristic theories of learning would not be effective in creating cognitive structures in children who did not have them. Training of conservation and other cognitive functions by non-Genevans was already underway (e.g., Beilin & Franklin, 19621,’ and alternative interpretations were quickly proposed for the conservation phenomenon (e.g., Zimiles, 1963). The large number- of studies t h a t were t o follow reflect various kinds of dissatisfaction with Piagetian theoi-y. First is the conviction that Piagetian stage theory imposes t o o restrictive a limitation on cognitive learning. The view that each logical structure requires the acquisition of prior structures in strict developmental order impresses some as overemphasizing developmental control and underemphasizing learning.

’This study was motivated by the desire t o test the control of the child’s cognitive level on his ability to profit from training in measurement tasks.

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Secondly, it is argued that training and learning paradigms that are successful in other concept formation and attainment studies should be equally successful with the concepts described by Piaget. The implication is that Piaget’s characterization of learning, principally as “external reinforcement,” is methodologically if not conceptually out of date. Consequently, a number of other experimental approaches have been tested and have turned out to be successful in inducing cognitive change (Beilin, 197 la). A third dissatisfaction is with Piaget’s description of the mechanisms necessary for the development of logical thought, particularly for conservation. Alternatives to the necessary role of reversibility, compensation, and identity operations have been proposed and tested. These reductionist alternatives emphasize one type of Piagetian operation (such as identity or reversibility), instead of the complex of operations proposed by Piaget, or they provide alternative system explanations based on attention, memory, language, etc. These challenges to Piaget’s theory have resulted in periodic clarifications, additions, and changes in the theory, although at the same time the essential validity of the theory is reasserted. The most recent relevant work of the Genevans (Inhelder el al., 1974) manifests a modification of the Piagetian attitude towards training, although their fundamental posture on the relation of learning to development is not altered. B. METHODOLOGICAL ISSUES

Many methodological problems have arisen to complicate the task of the training study in providing insight into cognitive structures and the processes by which they develop. In the prototypic study of the conservation of number, for example, the subject is provided with two rows of objects (abstract objects such as circles, or concrete objects such as dolls). The experiment essentially starts with two rows of objects laid out in one-to-one correspondence, i.e., for each object in one row there is a corresponding object in a corresponding position in the other row, usually below it. The experimenter then determines whether the subject understands that the two rows are the “same” or “different” in number or amount, or whatever. Controls may include unequal numbers of objects so that a response set to “same” is minimized. One of the rows is then either contracted or expanded so it “appears” to be less or more than the intact row. The subject is again asked whether they are the “same” or “different” in number or amount, and once the judgment is made, is asked why. In studies of the conservation of liquid (also referred to in the literature as continuous quantity) two prototypic forms are used. In one, a jar of particular proportions (width X height) is filled with water. A second jar of different proportions is shown to the subject, water is poured from the first jar to the

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second, and the subject is asked whether the amount of liquid is the “same” now as before. Elkind (1967) refers t o this as the “identity” case and implies that up to the time of his paper it was not used as a standard method of testing conservation. He cites another procedure, the “equivalence” case, which starts with two jars of equal dimensions as the more typical form of testing. With equal amounts of water poured into the two jars, the child is expected t o assert that the amount of liquid is the same in both. The water in one of the jars is then poured into a third jar of different dimensions while the first jar is kept within the child’s sight, and the standard question is asked. Elkind holds that the latter equivalence procedure is more difficult to conserve than the identity procedure and involves in fact a different form of conservation. Some controversy has arisen over whether different types of conservation are involved in the two procedures (e.g., Brainerd & Hooper, 1975; Moynahan & Click, 1972), but this issue will not be pursued here except to note later Piaget’s criticism of Jerome Bruner’s approach to the problem (Section IV, E).

IV. The General Training Model: Methodological Issues The procedure for each test o f conservation (i.e., length, area, volume. etc.) differs depending upon the attributes involved, but they generally follow the prototype procedures just outlined. The procedures for training conservation are much more varied, however. These depend mainly on the theoretical conception of the mechanisms involved in conservation and the conservation type. A . PRETEST

Training studies for the most part now converge on a common design. They usually start with a pretest to establish the child’s pretraining cognitive level. This is not always so, however, for pretesting is said to entail procedures that provide training prior to the testing itself (e.g., Beilin, 1965), or it is argued on the contrary that the pretest has negative transfer value in that it may increase the salience of “misleading” cues, particularly to transformation itself (Greitzer &Jeffrey, 1973). To assess for potential pretesting effects some studies include a no-pretest control group. The more usual practice, however, is to include a pretest to provide an assessment of the subjects’ pretraining cognitive status. This pretest is used as a device for selecting nonconservers and/or partial or transitional conservers for training. In some cases, however, subject selection is made o n the basis of the subject’s age. This procedure may be justified when gross difference in age (e.g., 5-year-old versus 8-year-old subjects) is taken as a gross indication of cognitive level difference. Brainerd (1972) makes the point

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that age and pretraining cognitive level are often confounded in training research. Unfortunately, in the two cases he cites t o support this point, the authors in question have made an issue of showing that performance is more critically related t o pretest cognitive level than t o age. Age status is introduced as a rule only when it correlates highly with cognitive status (e.g., 4-year-old subjects are rarely anything but nonconservers on pretest). Much has been made by experimentalists of the essentially verbal nature of Piaget’s assessment methods. Nonetheless, even when experimental training is ostensibly nonverbal or minimally verbal, it usually involves response to questions with comparative and related lexical constituents such as “same,” “more,” “less,” “amount ,” and “number.” This quantitative and comparative vocabulary may not in fact be known t o the subjects of these experiments (Beilin, 1964, 1965, 1975; Griffiths, Shantz, & Sigel, 1967). In this case, lack of conservation may be falsely attributed t o a child when the deficiency may be linguistic. This can occur in spite of the fact that progression in knowledge of the lexicon (such as the number lexicon) dcvelops in parallel with cognitive development (Beilin, 1975). (This issue will be treated more extensively in Section V.) It is evident too from recent studies that nonquantitative meanings of comparative terms such as “more” and “less” are known before quantitative meanings (Beilin, 1968; Bloom, 1970). Consequently, training studies increasingly utilize pretest procedures for assessing the child’s linguistic knowledge of relevant terms; nonknowledgeable subjects are dropped from the study or else trained in the use of the appropriate terms. B. TRAINING

Training may be given to one experimental group or it may be contrasted with other types of training, in which case there would be as many experimental groups as there are pure or mixed training procedures. Training procedures ordinarily utilize materials somewhat different from the pretests, though the same pretest materials are often used in training with a change made in the posttest or transfer tests. The more desirable procedure is one with different materials t o ensure that posttest change is a consequence of the concepts trained and not of familiarity with the materials used or of response learning attuned t o the specific set of objects. Pretests, including both assessment of cognitive status (or knowledge of the task) plus linguistic knowledge, are followed by training with as many experimental groups as is appropriate t o the nature of the study and at least one no-training control group. A number of studies fail to include controls, sometimes for legitimate reasons, sometimes not. The function of control groups, as traditionally interpreted, is t o ensure that whatever change occurs in posttest is a function of the experimental procedures and not a function of pretest experi-

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ence or learning that occurs from sources other than the manipulation of the independent variable. A separate control group may be necessary t o partial out the effect of pretesting from other effects, however. C. POSTTESTS

Training is usually followed by at least one posttest given immediately after training or following a short interval. Posttests may also follow after a longer delay, usually from 1 week to several months. Two types of task appear in posttests as a rule: (1) those testing specific (or “near”) transfer, which repeat the pretest if training is with different materials or entail a test of the same concept with different materials from those used in pretest and training; and (2) those testing nonspecific (“far”) transfer, tasks different in kind from the conservation training task, such as area, weight, or length tasks when training is with number conservation. D. TKANSI’EK A N D DkCALAGE

Posttest transfer tasks are used to provide a “strong” test of the effectiveness of training. If cognitive change were said to occur by virtue of learning, the change would have t o b e demonstrated to be nontrivial and stable. Transfer tests are considered t o provide a measure of such stability. Some special problems have arisen with transfer in Piagetian experiments, however. Nonspecific transfer is predicated by Piagetian theory on the basis of common structure. Inasmuch as conservations share a common structure or common mechanism (those of additive and compensatory composition, reversibility, and operational identity and possibly reciprocity in correspondences), conservations should be achieved normally in the same stage period. Thus when one conservation is learned, transfer should readily occur t o the others. This expectation has created much debate because the so-called horizontal ddcalage phenomenon, also posited by Piaget, appears to contradict this expected transfer by virtue of common structure. Empirically, dCcalage is manifest in the regularly ordered acquisition of different types of conservation, starting with conservation of number and ending with conservation of volume as much as 4 or 5 years later. The de‘calage is accounted for theoretically by the presumed common logical structure in each case of Conservation conjoined with a secondary or specific logical or physical knowledge structure particular to the quantitative concept involved. The structures involved in the conservation of length, for example, are more complex and more difficult to attain than those of number (as is spelled out in detail in Inhelder, et al., 1974). Each conservation, then, has two components-a common structure coniponent shared with other conservations, and a specific component that is not shared with other conservations but is

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shared instead with other cognitive structures (number, for example, has component properties that are shared with number classifications and number relations, etc.). This distinction is reminiscent of g and s factors in factorial theories of intelligence. One difficulty which the common factor versus de‘calage conflict engenders is that it complicates the definition of “stage,” in that stage in Piagetian theory is defined by both common structure and vertical ddcalage (i.e., the difference in age of attainment between common structures, for example, concrete operations vs. formal operations). Difficulty arises empirically when horizontal and the so-called oblique dCcalages2 merge into the vertical de‘calages, making clear-cut patterns of achievement difficult t o discern. In training studies, horizontal and oblique decalage becomes an issue in the seeming paradox that if the basic conservation structures are attained they should transfer-yet at the same time should not, because of the complications of horizontal and oblique ddcalage. If nonspecific transfer to another type of conservation does not occur, Piagetians are inclined to attribute it t o the de‘calage, although it might be argued contrariwise that training in respect to the common structure plus specific context knowledge should generalize to all appropriate contexts with sufficient training. The results of such attempts have not been consistent, although, in the main, training does lead to both specific and nonspecific transfer, for most types of training (see Beilin, 1971a, in press). E. STRONG VERSUS WEAK CRITERIA

Delayed posttests also provide a strong test of training. The need for such strong tests arises in part from Piaget’s criticism of training studies that are claimed to have induced cognitive attainments from relatively weak experimental evidence. Piaget puts it this way: “But, when I am faced with these facts, I always have three questions which I want to have answered before I am convinced. The first question is, ‘Is this learning lasting?’ What remains two weeks or a month later? . . . The second question is, ‘How much generalization is possible?’ . . . Then there is the third question, ‘. . . what was the operational level of the subject before the experience and what more complex structures has this learning succeeded in advancing?’ ” (Piaget, 1964). The experimental methods already discussed deal with three of these four questions: the pretest establishes the subjects’ operational level; specific and nonspecific transfer posttests establish whether there is generalization; and the delayed posttest establishes whether it is lasting. Another posttest procedure is often used t o answer the question as to whether what is learned is lasting and also t o explore

* Oblique ditcalage is indicated in differential achievement between conservation, for example, and classification and ordering tasks, which are informed by common concrete operational structures but different component structures.

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what structures have been learned. Smedslund ( 1 9 6 1 ~ )used a method designed to challenge the security of the child’s judgment by presenting him with a situation that is in conflict with his conservation judgment. The impetus for this was Piaget’s claim that when conservation becomes operational the child feels that conservation is necessary (i.e., “logically” necessary) and in fact will often ridicule the experimenter for presenting him with questions relating to the “obvious” equality of the presented quantities. Thus, if conservation were truly attained in a training experiment, the argument goes, trained conservers would resist extinction as d o natural conservers. After establishing that two clay balls weighed the same before and after deformation, Smedslund ( 1 9 6 1 ~ )surreptitiously removed some clay from one of the balls. The child was again tested t o see if he maintained conservation after weighing the clay or reverted to a nonconservation judgment and explanation. Extinction tests or trials have become part of many studies, even though Smedslund found that all l l subjects trained in his study extinguished in the countersuggestion test, and 6 of the 13 natural conservers resisted extinction. [See Miller (197 1) and Miller and Lipps (1 973) on this issue.] Possibly the most controversial issue in conservation training research concerns the knowledge acquired in a training experiment and the criteria by which one judges the attainment of such knowledge. Ostensibly, if training is successful, the general conservation structures or mechanisms already referred t o are acquired as well as the particular context knowledge associated with the particular type of conservation trained. Two behavioral criteria are employed by the Genevans in assessing such knowledge. One is a correct judgment or series of judgments for the particular quantitative concept trained, with the critical response usually that the “amount” of material is the “same” in respect to number, area, substance, etc. The other is the subject’s justification or explanation of his judgment. Both judgtnent and appropriate justification are required to establish the subject’s cognitive level. Controversy arises as t o whether both criteria are needed for minimal evidence of conservation. Because of the potential inhibition and/or confounding of performance when verbal means of testing are used, the effort is sometimes made to judge the presence of operations by nonverbal means (e.g., Beilin, 1965; Braine, 1959). kxplanations or justifications can only be verbal but “judgments” may be verbal or nonverbal (i.e., the subject can make a motor response that would be equivalent t o “same” and another that would signal “different” or “more.” As already indicated, however, some verbal instructions are necessary to establish the experimental conditions for the subject. Since a child could be a conserver and at the same time lack insight into why he is performing as he does, or because of limited language facility is incapable of expressing what he understands, an argument is made for using the judgmental criterion alone. This, however, is not the sole source of difficulty concerning the criterion problem. There is a more general question regarding the

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use of strong versus weak criteria in accepting evidence of conservation. Weak as against strong can be defined by the criteria suggested by Piaget: the strong are those satisfying all four of Piaget’s criteria; the weak are those satisfying fewer than four. Weak and strong criteria can be defined as well, however, by the nature of the unit of description and analysis. An individual subject’s responses can be considered in two ways. One is to take the subject’s response(s) as a unit (a within-subject measure). When this is done a categorical decision is taken (conserver versus transitional versus nonconserver) as the basic datum, and the number of subjects in the conservation (or transitional) category before and after training is used as the index of training success. A second criterion is needed, however, for determining when a response is a conserving, transitional, or nonconserving response. This may be a qualitative judgment based on justifications, o r it may be quantitative (based, say, on five of six trials with correct responses), or it may be a combination of these. The other way that subjects’ responses are treated statistically is to add or pool them for the number of subjects in a group (between-subject measure). In this case the number of correct responses in a series of trials is summed and the criterion of successful training is the mean of correct responses in posttest compared with the pretest mean. The number of correct responses both on posttest and pretest could be a small percentage of responses (say, 10% and 20%), however, and still show a significant difference with a large enough sample. In consideration of the fact that a statistically significant change could in this way be recorded, even though not a single subject could be identified as a consemer using a within-subject categorial criterion, one can only identify the between-subject nieasure as providing a weak criterion of conservation training. Nevertheless, many experimenters utilize just such group change data based on conservation responses, without at the same time indicating the number of conservers involved. The fact that the choice of criterion can affect the decision as t o whether conservation is present, o r learning has taken place, is demonstrated by Gruen (1966), among others. There are two aspects to the issuc, one conceptual and the other methodological. If one chooses a conceptual definition for conservation that is different from Piaget’s, can it be legitimately claimed that eonservation is being investigated? And if one uses procedures that d o not expose the ostensible Conservation operations a la Piaget, can one legitimately claim one is studying conservation? An exaniple of the conceptual difficulty is the argument between Piaget and Bruner (and Elkind) over the role of identity in conservation. Bruner (see Bruner, Olver, Greenfield, et al., 1966) holds that knowledge of identity is sufficient for conscrving quantity (as does Elkind, 1967). Piaget (1968) argues, however, that only operational identity (same amount) and not object identity (same water) qualifies as a necessary ingredient of operational conservation. In other words, the way conservation is defined b y Piaget requires operational identity for its comprehension. [Piaget also addresses a methodological limitation in Bruner’s studies that yield false positives by using

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a weak procedure (criterion) l.or judging conservation.] The studies of Mehler and Bever (1967) and those of Bryant (1974) appear to share the same conceptual difficulty. What these studies collectively imply is that a “truer” notion of conservation is embodied in a dirfet-ent definition of conservation. Thus, if conservation were identified simply as an invariance problem without the properties identified by Piaget (e.g., reversibility plus operational identity), one might find evidence for it at very young ages. With a conceptual definition different from Piaget’s, different methods 01- standards of measurement become acceptable. Thus, although one could identify a phenomenon as identity conservation, it is not the conservation uf a quantitative concept which Piaget identifies as conservation and justifies in various ways. A number of arguments directed against Piaget’s theory may similarly he reduced to differences in conceptual definition. Another aspect of the issue concerns whether it makes any difference if strong or weak criteria are used to assess the presence of conservation. Brainerd (1973; see also Brainerd & Allen, 1971) argues first that the criterion problem is not significant because strong criteria have been used in both successful and unsuccessful training studies. He argues fiirtlier, however, that only judgments are necessary for assessing subject competence. If the only question addressed in these studies was whether conservation training was successful, then the use of such a criterion might be justified. Furthermore, if one assumed that judgments and explanations probe the s u m structures, then judgments alone would be sufficient t o assess the robustness of such structures, as Brainerd claims (assuming, of course, that other sufficiently strong methodological criteria were adopted). What a judgmental criterion fails to do, however, is fully t o expose the nature of the underlying structure. Brainerd’s and similar proposals neglect to take cognizance of the fact that for Piaget concrete operational thought is more than rule-regulated behavior. Though the judgmental response and equivalent nonverbal response patterns may provide adequate knowledge of the underlying structures that govern choice, since such structures by their nature are nonverbal, it does not reflect the child’s consciousness of the events with which he deals. The verbal justification does this best in demonstrating that a symbolic (and operational) level of underlying structure has been reached that can be represented in a verbal justification. Consciousness of the relations that underlie behavior reflects capacities that go beyond those of rule-governed or structuregoverned behavior alone. I t is n u t an accident that Piaget so often titles his A judgmental criterion thus ignores an books “The child’s conception o f -.” essential ingredient in an adequate assessment of the child’s knowledge (Piaget, 1971, pp. 47-49). Brainerd makes the additional claim that judgments are devoid of built-in errors which are characteristic of explanations and incapable of being eliminated by methodological refinement. [See Recse and Schack (1974) for further comments o n Brainerd’s argument.] The “judgments” Brainerd refers t o do as a rule

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(e.g., in his own studies) embody verbal responses, if not verbal explanations. If one considers the difficulty, as evidenced by a great deal of conflicting research, in determining what lexical terms such as “more” mean to 2- to 5-year-old children (see, e.g., Beilin, 1975, Chapter 5), one would surely hesitate t o say that a judgmental criterion that embodies the use of such terms is readily amenable to methodological refinement, whereas verbal explanations are not (and therefore should be avoided). There are in fact difficulties with both sets of criteria that methodological refinements can improve upon but cannot fully eliminate. Brainerd (1974) again argues that whatever errors (“false positives” and “false negatives”) may appear with either response criterion chosen (judgments or explanations), they are both spuriously supportive of theoretical predictions, and so it does not matter which criterion is chosen. On this basis he holds that the judgmental criterion should be used because it is simpler. Since critical information is missed by omitting justifications, simpler is not necessarily better. Brainerd also argues that the nature of a Piagetian assessment is solely t o determine underlying structure of different concepts, apparently without recognizing that some phenomena such as transitivity and conservation have both common and unconimon structures. He argues further that Piaget theorizes only general synchrony in the achievement of a stage, when in fact the Genevans (see Inhelder et aL, 1974) posit, by virtue of dicalage, asynchronies in development of the very types Brainerd himself proposes. In sum, appropriate research design depends on a number of factors related t o the conceptual criteria by which conservations are defined. These criteria require the following: an assessment of the child’s pretraining operational level; an assessment of pretraining linguistic knowledge; control groups; posttesting for specific and nonspecific transfer; adequate assessment of the child’s posttraining operational level, both behaviorally and verbally; tests delayed a week or 2 months after training; and extinction trials. Not all studies require so strict or so extensive a set of design features. Studies of limited scope that deal with specific issues may require only some of these features. None of the studies that will be reviewed here includes all of the methodological constraints. For the most part they do follow a pretest, training, posttest design and vary in the extent to which they employ strong criteria. Where methodological problems require qualification of the findings, these will be discussed.

V. Linguistic Training A. VERBAL RULE INSTRUCTION

Piaget and his colleagues have made a particular effort to show that language at and before the stage of concrete operations is not critical to the development of

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cognitive structure; instead, cognition is critical to language development (cf. Beilin, 1975). Thus, for the development of conservation and related concepts, it is argued that language instruction and linguistic experience are unrelated to their construction. Sinclair [as will be discussed more fully in Section V, B,] attempted to verify the Piagetian claim by showing that training nonconservers with linguistic structures typically used by conservers resulted in n o improvement in conservation [see also Sinclair-de Zwart (1967)j. A quite different language training method was used by the present author (Beilin, 1965). Instead of stress on the lexicon, this method was based on the embodiment of conservation operations in rule statements that were coordinated in training with relevant expcrimcntal manipulations. The rules represent reversibility by inversion, reversibility by compensation, and the identity operation, and reflect the typical verbal justifications given by conserving subjects (Piaget, 1968). The verbal-rule instruction procedure was compared in effectiveness with a deformation-eqiiilibration procedure, an attention-orientation method, a method based on creating a nonverbal “learning set,” and a control procedure. Pretests and training werc with length and number conservation, and the posttests included specific and nonspecific transfer (area). Verbal-rule instruction was the most effective procedure in inducing conservation in the specific transfer posttests. There was little transfer, however, to the nonspecific transfer task (static area conservation). (Natural conservers by contrast did transfer t o the static area conservation task.) The lack of nonspecific transfer was attributed to area conservation being (1) a more advanced task in the normal de‘calage; and ( 2 ) , as a static invariance task devoid of transformations, more difficult than the usual transformation task (Beilin, 1969). It was proposed (Beilin, 1965, 197 1a) that learning occurred because verbal-rule instruction provided an instructional algorithm for processing perceptual input. Such an algorithm may or may not lead to true operatory structure, depending on the cognitive level of the child. I f the child had n o available relevant operatory structure t o which the algorithm could be assimilated, it could act as a placeholder until the relevant structures developed naturally. Nevertheless, without cognitive conflict, functional conservation was induced as a consequence of verbal-rule instruction. Operatory conservation was not ruled out, however, as we will consider later. The two linguistic approaches, lexical training in relational terms and verbalrule instruction, were combined in a study (Carlson, 1967a) that found this combination was more effective than “minimal verbal instruction.” Carlson holds (with Sinclair) that verbal instruction acts to orient the child’s attention to relevant features of the stimulus, and also suggests (with Beilin) that verbal training provides the subject an opportunity to use a model rule for processing relevant input. In another study, Carlson (1967b) employed a more stringent delayed posttest in which the combined rules-and-lexical training was contrasted

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with training without (or with a minimum of) these types of training. The provision of both lexical and rule instruction was as effective in this as in the prior study. The verbal-rule procedure was used by Smith (1968) in a conservation of weight study, and the effectiveness of the method was again shown. It was compared with a “reinforced practice” method and an addition/subtraction conflict procedure. Only the verbal-rule group showed significantly better performance than a control. Where the verbal-rule procedure was combined with extension and contraction manipulation of length in a number conservation task (Blum & Adcock, 1969), it resulted in nine of ten nonconserving trained subjects conserving on posttest, with one becoming transitional. In a delayed posttest, six of eight older subjects in the sample maintained their conservation performance, while two regressed. It is not uncommon for verbal-rule instruction to be introduced as a subsidiary part of an experiment where the focus is ostensibly on other procedures. In such cases, as in the Overbeck and Schwartz (1970) study, rule instruction was confounded with the other procedures to such an extent that it is difficult t o isolate its effect even when training was successful. The effectiveness of verbal-rule instruction was further confirmed by Peters (1 970), although a “perceptually-guided cue discrimination” procedure, in which configurations of dots aided the differentiation of number, was also effective. Verbal rules in conservation training usually comprise a number of components, as does conservation itself. Sjoberg, Hoijer, and Olsson (1970) attempt to isolate which of three components would be effective in inducing conservation of weight: “decentering” (change in form, not in weight); reversibility (transformed object returned to original shape and retaining weight); and addition/ subtraction (with nothing added or subtracted, weight must be unchanged). In addition to verbal-rule groups, there was a “reinforcement” control group which saw a demonstration without any experimenter explanation. The posttest included a transfer task (volume) and some extinction items. In training, the subject made a prediction of weight and, irrespective of whether he was correct or incorrect, obtained feedback together with a statement of the specific conservation principle. In training, 90% of each nonconserver training group of 15 was successful. In posttest, the three verbal-rule groups had high rates of success and were significantly better than the control (e.g., reversibility: 13). The demonstration control group had one conserver. Only the addition/subtraction group, however, showed a high degree of transfer ( l l ) , although the demonstration control group improved too (6). Posttested natural conservers dropped from 23 to 11 in extinction trials with a similar drop in the addition/ subtraction group. The other groups regressed much more. Verbal justifications yielded the same principles enunciated in the verbal-rule instructions, even in

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transfer, although with reduced frequency. Overall, rule instruction proved to be effective, with the addition/suhtraction type of verbal rule, and weight precliction most effective among those used. The authors held that the transfer and extinction test results demonstrated that verbal-rule training led t o true operational change. As with many verbal-rule instruction studies, no suggestion was offered as t o why verbal-rule instruction was effective. Verbal-rule instruction was also tested in a study b y Hamel and De Witt (1971), the results of which were related t o the pretest language level of the subjects, as determined b y three language tests. Subjects predicted water levels in a conservation of liquid experiment. Liquid was poured by either the ?xperimenter or subject, followed by visual verification of the subject’s prediction. Incorrect response was followed by verbal-rule instruction (as in Beilin, 1965). Posttests showed considerable improvement, from 4 subjects correct on the first trial t o 25 on the fourth trial, with about 30% overall conserving. Pretest language level was significantly related t o conservation performance. The inore verbal subjects started at higher conservation levels and acquired more conservation as a consequence of rule instruction (53% versus 38% of the less verbal group). In a later study (Hamel & Riksen, 1973), two groups of nonconservers were each given a different kind of verbal-rule instruction. One focused on identity, the other on reversibility for discontinuous and continuous quantity conservation. A common base of rule instruction was given to both groups (“same amount of water”), with identity instruction (“it’s the same ~vatcr”) given t o one group and reversibility (“when you pour it back it reaches the same level”) given t o the other. Both training groups did better than a control group, but there was n o difference between the trained groups on posttest. The identity instruction group showed greater gains in nonspecific transfer (to space, number, substance, and weight), whereas the reversibility group showed greater gains from pretest t o a delayed posttest. Equality and inequality conditions were included in the posttests to negate the possibility that the results were due to simple response sets, a type of control not always included in conservation experiments. In this study, then, rule instruction led to effective learning with nonspecific transfer that carried over to delayed posttests. Hainel is iriclined to an interpretation of his results that supports Bruner’s identity reduction thesis, but since training included rule instruction for invariance of quantity (“same amount of water”) in addition to object identity, it is difficult t o accept the reductionist thesis. (Bruner, it should be noted, used the same instructions.) Inasmuch as invariance of quantity is the critical aspect of the Piagetian thesis, its very addition t o the object identity rule precludes rejecting the Piagetian thesis even if the effect of the object identity rule exceeds the effects of the reversibility rule. A study that included a verbal-rule procedure (Figurelli & Keller. 1972) was designed primarily t o determine whether training differentially affected middle-

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versus lower-class children. Posttest effects of training in number, continuous and discontinuous quantity, size, and substance were significant, independent of socioeconomic status, although on transfer middle-class subjects were better than lower-class subjects, as they were on pretest. On the whole, nonspecific transfer to area and length was not effective. In addition, training was effective with pretest partial conservers, but not with nonconservers, as is often claimed by the Genevans (e.g., Inhelder e f al., 1974). A study of English mentally retarded children who ranged in age from 9 to 16 years (IQs 47 t o 81) was concerned principally with the dCcalage among conservation tasks (Lister, 1972). Additionally, however, two groups of subjects were trained by verbal-rule instruction-one group in understanding quantity in several attribute contexts; the second, in area conservation. A third group was a control. The experimental groups were given four types of rule statement: (1) quantitative identify, “nothing added or taken away”; (2) appearance-reality, “looks different but is really the same”; (3) compensation, “one is more this way, the other is more that way”; and (4) reversibizity, “you can get it back as it was before.” Rule giving was in conjunction with observation of transformations, manipulation of reversible transformations, and verification. In the quantity training group and in the area training group 15 of 17 subjects conserved on every posttest item. The two subjects in each group who did not profit from training did not conserve at all. This was even true for number, although 11 other subjects who had n o conservation on pretest did profit from training. The four nonlearners were given additional training in various conservation problems and then caught up with the others. All trained conservers gave “clear” justifications. The most frequent explanation was “nothing added or taken away”; compensation and material identity were rarely given as justifications. None of the 17 control children showed conservation on any test. Thus, educable mentally retarded children as well as normal children were capable of learning to conserve by means of verbal-rule instruction. It is possible t o make rule instruction contingent solely on incorrect response, or it can be given after both incorrect and correct response. Independently, informational feedback as t o the correctness of the response can be offered or omitted in an experiment. Beilin (1965) provided rule instruction only after incorrect responses, and corrective feedback after all responses. In other studies rule instruction and feedback have been given after both correct and incorrect responses. Two studies were specifically directed to the relation of verbal-rule instruction to feedback. In one, Siegler and Leibert (1972) followed the Beilin rule procedure with four training groups (feedback versus no feedback; rules versus n o rules) in training conservation of liquid quantity. Pretests and posttests additionally tested for solid quantity (clay) and length. Nonconservers ( N = 40) were selected for training from those who failed in liquid Conservation. Verbal rules given depended on the nature of the trials: “same amount”; quantitative

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identity (nothing added or taken away); compensation (thinner and u.idci-); object identity; reversibility-inverse. Feedback was either positive o r neutral (ix.. the child was not told he was “wrong”). The results showed that the rule plus feedback treatment was best in all test trials: 70% of the subjects consei-vctl 111 conservation trials; 50% were correct in nonconservation, perceptually discrepant trials; and 50% of nonconservation, perceptually consistent tlials wci-e responded t o correctly. Of rule-trained subjects, 35% gave both correct judgments and correct explanations in liquid and solid quantity conservation (Xi7 for clay). Only 10% of the feedback-only group did as well. At the saiiit t i i i w . only one subject generalized t o length conservation. Thus, while feedback ~ i i d rule instruction were each effective in improving performance, the conjuiictioii of the t w o was even more effective on b o t h judgments and explanations. l l i e results, the authors point out, could not be attributed t o “mere niimiciv” 0 1 response bias t o the word “same,” as performance improved in rclevaiit I I O I I C I servation trials where a “same” response was not called for. In addition. 6 t i t :‘O subjects generalized in specific transfer trials (solid quantity) although i i o t i i ! ‘I nonspecific transfer (length) task. In a second study, Siegler (1973) used simple one-sentence rules rathci tlian rules that include “descriptions and justification.” Subjects were pretestcd on solid and liquid quantity and trained on liquid quantity. There was a rulc plus feedback group and a control group. The rule used stated that “when w c p o i i t all the water from one glass t o an empty glass there is the same amount ofwaier to drink as before,” with variations for the amount of liquid poured. On s o - d l e t l “all plus some” trials, the rule was that “when we pour all the watcr fro111 oiic glass plus some water from another glass into an empty jar we havc moIc w a i ~ ‘ t in the new glass than there is in any of the other glasses.” Similarly, i n the “ o i r l ! some” trials (i.e., with the rule “. . . pour only some water . . . there is less. . .”) subjects received feedback whether they were right or wrong. Negative fecdl)acl\ was employed in this study: “That is not the right answer.” Again v e r M riiic plus feedback training resulted in significant learning. Of nine trained S L t h j ~ C i S . eight succeeded on all posttest problems or on none at all. I n noiisp~,cil’i~: transfer (to clay), however, there was a drop in conservation. Since there wiis I I O direct reference in the rules t o reversibility in this experiment, Siegler believes it is not a necessary component in conservation and thus the experiment is s:ii(l i o disconfirm Piaget’s view of conservation. Training is said instead to providi’ :\ strategy of attending to manipulations and connecting them with thcir c o i ~ v quences, which is close to Sinclair’s notion (see Inhelder ef al., 1074) 1ll:iI linguistic training merely leads t o chsnges in attention, although Siegler tags on ;I more traditional learning explanation. The rejection of reversibility as s co1llp(jnent in conservation is questionable, however, since in the experiment there IS x i i implied reference t o reversibility in that part of the rule statement refcrriiig to “the same amount of water to drink as before.” In addition, since Pi:iyt jii

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presently holds that conservation can be attained in situations where correspondences are noted between initial and end states with no focus on the transformation itself, it may be that Siegler’s rule statement embodies a comparison that establishes such a correspondence. Siegler’s interpretation also differs from the I’iagetian opinion in holding to the more traditional view that generalization is due t o similar perceptual transformations rather than t o generalization by coninion structure. Sullivan (1969) has been interested not only in rule instruction but also in the effectiveness of models in filmed presentations of conservation experiments. In one study, a filmed model demonstrated conservation together with verbal statement of the conservation principle (rule), and in another case simple conservation judgments were stated without rule specification. The verbal rule spelled out compensation, identity, and the appearance-reality distinction. In the no-principle condition the filmed model would merely respond “same” (correctly) after a transformation but give no rule information in response t o a question put by the film’s interrogator. The posttests, which included repetition of the pretest (substance: water or orange juice; wire), a nonspecific transfer test (clay), and an extinction test (the Smedslund method) showed rule instruction t o be better in all posttests than no-principle modeling (7 versus 3 subjects conserving; 7 versus 2; 7 versus 2-011 the respective tests). The results of this study differed f r o m a prior study in which the no-principle group also learned. In another experiment, rule instruction had no differential effect, but t h s result was discounted by Sullivan as due t o artifacts in the experiment. The inconsistent nature of these “modeling” plus rule training results is evident in a later study on training conservation of substance (Waghorn & Sullivan, 1970). Again the materials were wire, water, and clay in a pretest-posttest generalization design. The critical groups were shown conservation modeling films that had two actors, an interrogator and an adult model. In the verbal-principle group the model conserved liquid quantity and gave reversibility, identity, and compensation arguments in his justifications. The no-principle model conserved without explanation. There was substantial improvement in both principle and no-principle groups, not differing from each other, but differing from the control. In contrast t o Sullivan’s earlier study, rule instruction was interpreted as of little consequence relative t o the effect of simply modeling correct answers. Another series of studies on the effects of modeling with verbal-rule procedures has been interpreted within the context of social learning theory. In one experiment, Rosenthal and Zimmerman (1972), like Siegler, varied both feedback and rule instruction to yield four experimental groups plus a control. The subjects were divided on the basis of pretests into a nonconserver group (providing four or fewer conservation responses) and a conserver group (with five o r six conservatiun responses). The latter group was reserved for extinction training. The verbal rule used was, “They were the same in the first place,” which the

model said in response t o the cxpcriinenter’s request for an expianation of‘ a conservation manipulation. All ti-ealincnts led t o equal gains in posrtests arid also in transfer, using a judgments-only criterion. With an explanation criteiion the verbal-rule group showed a signiiicant training effect, whether o r not feedback was given during training. (Feedback was detined as verbal praise from the model, not as corrective feedback.) The fact that the feedback n o d e suhlccts were better than the controls was attributed t o the effect of simply observing the model. In a second part of tlic study, partially conserving pretest su1)jccts who observed tlie model fail t o give conscrvation judgments were tested t o see whether they extinguished their conservation responses. For both judgments and judgments plus explanation criteria there was a drop in conservation pcrtorniance and a drop in the level of conservation explanations, indicating partial extinction. In a third experiincnt with economically disadvantaged Mexican-American children there was a noiiniodeling verbal instruction variation i n which the experimenter rather than the model stated the rule plus the correct judgment. The modeling group was supcrior t o the verbal instruction group in both posttest and transfer. In a fourth expeiiinent cariied out with very young children (age: 4 years, 2 months to 4 years, 9 months; median: 4 years, 6 months), verbal-rule instruction and modeling led to significant increases in correct responding but no increase in verhal justifications. In Rosenthal and Zimmerman’s (1972) experiments the m success was the mean of correct 1-esponses and not a subject criterion. One does not know then how many subjects responded with sufficient consistency to be considered conservers. Nevertheless, the authors conclude that observing the model conserve without giving explmations was “indicative of inferential thinking elicited by modeling” in accoi-d with the assumptions of social lear-ning theory. In a further study, Zimniernian and Rosenthal (1974a) again assessed the effects of modeling, this time with corrective feedback, in length, number, and “2-dimensional space.” The subjects were those who failed on pretest (mean age: 5 years, 7 months). Both equality and inequality conservation were tested. Inequality items were transformed so that they still appeared unequal? but in reverse of the starting configuration. Inequality and equality trials were pooled in the analyses. Training entailed the use of a model plus rule instruction. The rule statement was the same as in the prior experiment, except for the substitution in the inequality condition o f “had more or larger.” The training gi-oups were as follows: (1) positive feedback with rule; (2) model plus correction and verbal rule; (3) model, no correction; and (4) control. All training gi-oups improved with both judgments ;ind judgments plus explanation criteria. The most effective procedure was tlie model plus correction (and verbal ride), followed by correctioiz-no modcl, next model-no correction, and last the control. The subjects were also tested on the frequency with which they correctly returned transformed materials t o their initial conditions. Again the

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phis correction (and verbal rule) group was best, and the poorest was

r u ~ ~ ~ d -corrcctiorz. no The study thus shows that verbal rule instruction was the

inost effective method, with corrective feedback more effective than modeling :ilone. Thus, contrary t o their earlier study with Chicano youngsters, the additJon of the model was not the critical element in training. A later study (Zimmernian & Lanaro, 1974) was concerned with relating verhnl rule instruction to the (nonverbal) demonstration of a reversibility response. with 4-year-old subjects, in response t o Beilin’s (1971 a ) observation that no i:hiltlren in that age range or younger had been shown t o that time t o profit i r o i n training to conserve. There were three experimental groups: modeling ~ I ~ i n modeling e; plus reversibility; and a control. All modeling included rule instruction. The same materials were used as in the prior experiments. In the ii,vt.tsihility condition, the subject observed the transformation in materials; in ttic others, not. Treatment and control conditions were repeated t o enhance “t-c.c.all” with a different set of materials 2 days after the first training session. Tlic p a t e s t gains from pretest t o posttest, in judgment alone, was for the model plits reversibility group relative to the modeling alone and control groups. In the i!cl;iyetl posttest the modeling alone group was superior. With the judgments plus cxpl:ination criterion, the training effect was significant, with slightly greater s c ‘ o i - c ~on the delayed posttest. There was, however, no difference between the ttioJclin~yplus reversibility and modeling alone groups. Transfer occurred and w s best in the modeling alone group. The authors concluded that 4-year-old :,uh,jects can be trained with rule instruction plus models and that the acquisition is stable. The authors also concluded that learning was not dependent upon the children’s cognitive level. One difficulty with the Zimmerman and Lanaro experiment is that no evidence is provided that the 4-year-old subjects had the requisite knowledge of such terms as “same length” and “as before,” although they were more likely t o understand “longer,” which the data d o show. With verbal instruction the child riiay simply have learned an algorithm-answer t o “before” and then applied it to tlic perceived transformations, for there is evidence that children at this age have olily ;I very limited conception of “before-after’’ time relations (Beilin, 1975). Another, and more serious, difficulty with the experiment is that although the chxnge data reported are statistically significant in respect t o responses, they are ver.y ineager and not enough t o suggest that individual children were conserving. None, in fact, appeared to have reached an above-chance performance level. With ;in expected chance level of 3.5 responses correct, and obtained mean response It.vels u t 2.5 correct, subjects on the whole were not responding even at chance level. Training was clearly “effective,” t o some extent, but whether it made conservers out of nonconservers is questionable. ‘I’he conclusions to be drawn from studies utilizing verbal-rule instruction will be presented later. First we wish t o consider those studies concerned with lexical kiiowledge and conservation.

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B. LEXICAL TRAINING AND LEXICAL KNOWLEDGE

Piaget’s position on the development of language vis-A-vis cognition i s that knowledge of the lexicon appropriate to an experimental task such as conservation is not expected t o be attained and understood prior t o the development of related cognitive operations. In other words, linguistic competence cannot be in advance of cognitive operations; in fact it should be a reflection of them (e.g., Piaget, 1954b). The role that the lexicon plays in knowledge of conservation is deeply rooted, then, in the general relation between language and cognition. Nevertheless, the argument is made by some authors (e.g., Griffiths et al., 1967) that success in conservation tasks may not become evident or can be inhibited because the subject lacks knowledge of the testing vocalary that includes such terms as “same amount,” “more,” and “less.” Sinclair (see Sinclair-de Zwart, 1967; Inhelder et al., 1974), in an attempt t o confirm the Piagetian claim, examined the words typically used b y subjects in conservation experiments. These fell into two classes, descriptive (“one,” “quantity,” etc.) and comparative (‘‘rnoi-e,” “less,” etc.). They were also characterized by Sinclair as “scalar” and “vector” terms, respectively. A study was then made of how these terms were understood and used in a conservation of quantities experiment (with clay). Though most terms used by the experimenter were understood by even the youngest subjects (age: 4 years, 6 months) in the experiment, their use differed depending upon whether the subject was a conserver or a nonconserver. Most nonconservers’ statements employed two-part (coordinated) structures embodying the use of scalars (e.g., “a lot,” “not a lot”) and much less use of vectors (“more,” “less”). The nonconservers also typically used undifferentiated terms (length terms in one instance; thickness terms in the other), whereas conservers used pairs of opposites (long/short ; thick/thin). In a conservation of length task (with pencils) conservers used four-part constructions: “This is long but thin, the other short but fat”; whereas nonconservers said, characteristically, “This pencil is long, that one is short, this one i s thin, that one is fat.” In a second experiment, subjects were trained in the use of the terms and constructions Sinclair found in the speech of conservers. Children were “encouraged” t o use examples proposed by the experimenter, e.g., “Give more t o one and less to the other,” in respect to dolls possessing different amounts of clay and marbles. Of 31 pretest subjects, 28 were nonconservers on conservation of liquids; in the first and second posttests after training, 18 remained nonconservers, 7 were intermediate, and 3 became conservers. Sinclair concluded that linguistic training did not lead to progress in conservation. If it did anything, it aided some children who had already acquired conservation t o give clearer verbal justifications. That is, language t nining facilitated rapid verbal coding and the efficient storage and retention of information (Inhelder er al., 1974, p. 215). Piaget has often commented that although cognitive structures develop in a

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fail-1y fixed order. their rate of development can be affected by social and cultural experience. The same is true for conservation, and cross-cultural eviilerice is cited that points t o such differences in rate of acquisition. In one such instance, I’iaget, noting the way the comparative form is used in French and English (Sinclair found they were the same), observed that Turkish, which lacks :i w n i p a r ~ h l ecomparative form, is apparently associated with later acquisition of coiiscrvation t h a n is observed in Geneva. Sevinc and Turner (in press) purS I I ~ I I tliis observation with two groups of bilingual migrant Cypriote children residing in London-one predominantly Creek-speaking, the other predciiiiinantly Turkish-speaking. The Greek comparative is comparable to the English: the Turkish is different. A third group of native English speakers was ;rlso studied. (Subjects ranged from 4 t o 1 I years of age.) The Creek and Turkish subjects thus shared the same migrant Cypriote bilingual cultural background hilt dit‘fered in comparative type, whereas the English and Greek children t1it‘ti.i-edi n cultural experience but were similar in their linguistic use of comparatives. The children all spoke English, however, which confounds the results t o sonic extent in that they all had common knowledge of the comparative in English. The subjects were administered a linguistic pretest in their native language, based on Sinclair’s assessment of conservation language (see Sinclair-de %wart, 1‘367) delineating scalar (“much”) and vector (comparative-“more”) knowledge in the three groups, as well as three types of cognitive task: conservat i o n (six tasks), seriation. and multiple classification (nine matrices). (Cognitive tcsis were also conducted in the child’s native language.) The results showed that native laIiguage affects cognitive performance in consistent ways. English and Greek, which similarly code object attributes and differences with scalars (de,, and vectors (comparatives), yield organizations of concrete operations .,iiiptivcs) in c1:issification and conservation tasks. For Greek subjects, attainment of coiiiparativcs was predictive of (correlated with) conservation. Turkish has only m e forni for both classification and comparative relations; for the Turkishspeaking subjects, then, there was an overlapping of classification and conservat i m skills, and mastery of the comparative forni was found to be nonprcdictive of conservation performance. The authors suggested that language is neither a necessary nor sufficient condition f o r conservation. They held instead that language has a contributory role in cognitive development, a role nevertheless less influential than “maturation.” An additional finding is that the Turkish children, allhougli they are poorer than the others in conservation, far exceeded them in multiple classification skills. Why this occurred, or how the structure of thc ‘Turkish lexicon can account f o r it. is not discussed. The various ways language is used in conservation experiments lead t o a number of questions concerning its effects on conservation. These have been addressed in a number of studies, sometimes as a subsidiary rather than principal focus. Beilin (1964, I965), for example, showed that the child’s knowledge of ~

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comparatives (“more,” “less”) and terms of equivalence (“same,” “different”) were not understood equally well by children in conservation experiments. Children who understood ‘‘same number” on pretest were more likely t o conserve on number, length, and area tests both before and after training than those who did not understand the expressions. Children were also found t o understand “more” better than “less,” a finding which has now been extensively investigated in nonconservation contexts (e.g., Donaldson & Balfour, 1968; Palermo, 1973; Weiner, 1974). Beilin (1 968) later proposed that a noncomparative meaning of “more” is understood (as “addition to”) by children before they understand the comparative sense (as “more than”), which in turn is understood before the conserved sense (“more in spite of appearing like less, or equal to”). Bloom (1970) also showed that a noncomparative sense of “more” precedes the comparative, although “more” was said t o be understood first as “repetition.” A study by Pratoomraj and Johnson (1966) on the role of different types of questions employing different lexical ternis-“more,” ‘‘less,’’ “same,” “different”-showed that with three types of conservation task, i.e., prediction, judgment, and explanation, variation in the type of question (lexical term) had little effect on performance, whereas the type of task did. Griffiths et al. (1967), in contrast, hold that lack of knowledge of comparatives can interfere with conservation performance. Going in another direction, Shantz and Sigel(l967) tested the effects on conservation of labeling of object attributes in addition t o learning simple classification skills. Such labeling plus classification proved successful, but it was not clear whether this was due t o attribute labeling or to classification skill learning. Lumsden and Kling (1969) found that training for “bigger” led t o improvement in size conservation, but with older rather than younger subjects (7 years, 6 months versus 6 years, 6 months). They propose that teaching concepts should not be pursued prior to the child’s being able t o handle their appropriate verbal representations. A study by Russell (1975) was concerned with whether verbal competence is a reflection of the level of “operational” or “cognitive equilibrium,” although it was conducted not with conservation as such but with a task involving comprehension of the phrase “sanie amount of room.” The subject was presented first with a standard figure and had to choose one with the same amount of room from a set of comparison figures. In an alternative task he was required t o adjust an apparatus of fixed width and variable height t o a standard. Following the pretest, subjects were trained in one of two procedures (manipulative or conceptual) and posttested. Successful and unsuccessful subjects were given manipulative training plus corrective feedback in which they transferred squares or cubes t o selected figures “with a little help from the experimenter.” Conceptual training was verbal and was intended to “redraw” the chld’s concept of area and volume and t o “discourage” the interpretation of “same amount” as same shape or length. There was also variation in two-dimensional (area) and three-dimen-

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sional figures (volumes). Five-year-old subjects, in the pretest, tended t o interpret “sanie amount” as height when they varied tlie test figure t o conform t o the standard; they interpreted it as “same shape” when they selected from comparison shapes. The latter intcrpretation is questionable, however, since the data o n which it is based were not from tlie “coi-rwt” choices of the same shape (which were chosen at just about chance level) but from those close to it (which are statistically “dominant” when tlie correct choices are omitted from the statistical analysis). Russell also reported that conceptual training was effective in one condition, whereas manipulation training was not effective at all. However, when pretest differences arc cquated in an analysis of covariance, conceptual training was also ineffective. The most stable finding from the study was that 5-year-old subjects misinterpret the conservation expression ‘‘same amount of room” when tested in a nonconservatiori context. Russell, in light of other results, attributes the child’s difficulties to other than “sein:uitic” failure. The author holds that tlie notion that conservation failure I-esults from lack of knowlcdge of the meaning of words is too simplistic. Me asserts instead that the failure is inore basic and is related either t o a lack of cognitive operations (Piaget’s explanation) or 3 source related to tlie child’s “consciousness.” Another study combines relatiorial term training (“more,” “less,” “same”) with “language activation” [in fact, rule instruction; the rule given was: “The water is the same height and tlie glasses are the same width, therefore the glasses have the same amount of water” (Hamel, Van Der Veer, & Westerhof, 1972)l. Conservers were bettei- than nonconservei-s on a pretest of relational terms. After training, there were fewer relational term errors on the posttests and concomitantly substantial improvement in performance: 15 of 20 pretest conservers conserved on two posttests, as did 4 nonconservers and 1 control subject. Justifications also changed with conservation change. Hamel supports what he believes to bc Bruner’s position on identity, but offers as justification an argument that sounds more like Piaget’s. Haniel makes no distinction between levels or types of identity (i.e., object versus operational), which taken together with the confounding of rule instruction and lexical training leaves the results ambiguous. One feature of Bruner’s views merits attention here since it concerns language. Bruner cuntends that in the course of development the child increasingly fits his experience t o his language so that the verbal representation of objects and events enables the child t o acquire concepts and operations. The key to his “instrumental functionalism” is the notion of progressive change in the forms of representation that increasingly facilitate and extend the power of thought. The forms of representation~eiiactive,ikonic, and symbolic-involve different instruments of both representation and expression. Symbolic representation, the most advanced form of representation, is primarily linguistic, and speech is its princi-

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pal expression. Bruner’s experiments on conservation (Bruner et al., 1966) are interpreted as demonstrating that the linguistic representation of particular perceptual relationships results in resistance t o the effects of misleading perceptual cues (as in the screening experiments in conservation). The Genevans (Inhelder et al., 1974) argue, however, that Bruner’s verbal training combined with other procedures directs attention t o relevant features of the experiment, the result of which is correct local response (pseudoconservation) but not true operational change. The resistance t o misleading perceptual cues that linguistic representation provides is seen by Beilin (1969) as a form of algorithm learning in which the acquired linguistic algorithm provides the child with a processing procedure for dealing with perceptual and conceptual inputs. The notion of representation-bound cognitive structure is also held by Aebli (1970) and Steiner (1974). Their view is that the form (media) in which objects are represented affects their comprehension. Aebli suggests for example that the (linguistic) form in which the Piagetian “clinical” interview is conducted prestructures the problem posed by the experimenter (Steiner, 1974, p. W S ) , and affects the ease with which cognitive structures are achieved in Genevan experiments. C. SUMMARY

The research on lexical training and lexical effects on conservation indicates first that lexical training as such does not improve conservation performance, except t o a minor degree. When combined with verbal-rule instruction it appears t o be effective, but this may be more a consequence of verbal-rule instruction than lexical training. There does, however, appear t o be a relation between knowledge of comparative terms and conservation knowledge. Whether or not the relation is as originally posited by Piaget, the proposition that lexical knowledge is intimately tied t o acquisition of cognitive operations does not get strong support. Sinclair’s research suggests that conservers have a more complex linguistic structure than nonconservers, and this structure allows the use of comparatives b y conservers. But conservation performance clearly does not depend entirely upon such structures, since they d o not reflect the logical rule relation basic t o conservation itself. Instead, these linguistic structures reflect a larger complex of logical relations associated with concrete operational knowledge. For this reason training in the lexicon is not successful in leading t o conservation performance, but conservation rule instruction is successful. Although cross-cultural studies to some extent encourage the view that different languages relate t o cognitive functions differently, the case of Turkish is puzzling. The lack of a differentiated comparative form should lead t o poorer performance in conservation, as is in fact the case, but why an undifferentiated

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set of terms is associated with superior multiple classification is not clear. To date, n o clear pattern emerges from cross-cultural study of language-cognitive relations (Click, 1975). Research on the lexicon and conservation suggests a note of caution, however. It indicates that studies of conservation (or other cognitive functions) require an assessment of the child’s knowledge of the technical lexicon of the experiment. If the child lacks comprehension of the terms used, either the procedures have t o be capable of testing knowledge without the terms or an examination has t o be made of how acquisition of the terms relates t o the acquisition of the cognitive process in question. We have shown elsewhere (Beilin, 1975) that the acquisition and development of the number lexicon (cardinal, ordinal, determinate, and indeterminate number words) is generally related to the development of number conceptualization but that it is not a one-to-one relation. The studies reviewed here on the relation between lexical knowledge and conservation performance confirm this view. The lexical-conservation relations exposed in research by Sinclair and others show a relation between lexical knowledge and conservation, but the relation is not one-to-one. That is, conservation acquisition is not strictly and necessarily dependent upon linguistic knowledge, and lexical knowledge is not directly dependent upon cognitive operations. The nature of the relation is not one that assigns t o language an exclusive performance function (representational) or competence function (operational); its role in conservation is bound up with both, as the data on verbal-rule instruction suggest.

VI. Summary of Results and Theoretical Considerations The most evident conclusion to draw from the substantial research on verbalrule instruction is that it leads to effective change in conservation performance. Since many of the investigators employed strong criteria, including specific and nonspecific transfer, delayed posttests, judgmental and justification criteria (although justifications could clearly be artifactual since they are often cognitively similar to the training rules), and change measures, the evidence appears strong that the changes that occur reflect operatory change, although not necessarily in all experiments. The possibility of operational change is admitted by the Genevans: “we d o not deny that verbal training can sometimes result in truly operatory acquisitions” (Inhelder et al., 1974, p. 11 6); however, the consequences of such a possibility for Piaget’s theory are not developed. In contrast t o the strong evidence in favor of verbal-rule instruction, the evidence for positive effects of lexical training is weak. Only the verbal statement of rule

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relations among relevant lexical itenis that encapsulates or can be said to parallel hypothesized internal cognitive structures affects cognitive change significantly. The theoretical explanations proposed for the efficacy of verbal rule instruction follow, though on the whole there has been little speculation as t o why rule instruction is effective. A. SOCIAL LI ARNING T I E O R Y

The position espoused by Zimmerman and Rosenthal (1974b) is a neobehaviorist formulation that holds that a modeling “display” when “accompanied by symbolic codes . . . which provide a ninemonic summary of the rule governed response [enhances] concept attainment and retention. . .” (p. 39). Rules or rule structures are learned by creating “an arrangement and consolidation of behavioral components which allow the person to better adapt to environmental demands” (p. 39). Learning is said to occur not as a probability learning function but in “an integrated gestalt-like fashion” (p. 39). Association, by way of familiarity and plausibility, plays il role, but Zimniernian and liosenthal question a simple stimulus-response association explanation. Thus, the gradual, incremental conditioning view of‘ classical behaviorism is rejected for “abstract paradigms rapidly and holistically acquired” (p. 39). More specifically, the young child, according t o Zimmerman and Lanaro (1974) is said t o first acquire a “tionconservation rule” through observation of adults. That is, quantitative judgnients first reflect perceptual saliences rather than quantitative properties. When the child approaches 7 years of age, his verbal repertoire expands in describing dimensions (taller, bigger), and coordinations are learned more easily thrcugh verbal explanation. Verbal instruction directs the child to ignore irrelevant attributes and to attend to relevant attributes, though nonverbal learning can occur to the same level using many more instances. Inasmuch as such nonverbal learning is not naturally available, verbal instruction beconies more effective. Generalization, when it occurs, is based on stimulus characteristics (stimulus and response associations) and not logical structures. Conservation is seen, then, as a socially mediated form of rule learning in which social agents define the nature of the rules and how they can be applied. Dkcalage in turn is attributed to I’requency in modeling and use (e.g., number is better known; weight less so) ancl to difficulty of verification (number is less difficult to verify than weight). Some types of conservation are not known because prerequisite learning skills huve not been acquired. The long period of nonconservation is accounted f o r by tlie fact that conservation is not a typical rule to be learned. It is rarely encouiitered or seen applied as a nonverbal rule. In addition, the verbal skills of youtig children are far from developed.

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This form of empiricist theory, which owes much to A. Bandura, is a far cry from classical conceptions of behaviorism; it offers, however, an example of theoretical “eclecticism” in the bad sense of the term. As Reese and Overton (1970) point out, one of the paradigmatic requirements of a theory is consistent meaning in its constructs. In this instance, behavioristic theory requires that all behavior, covert or overt, function alike. Zimmerinan and Rosenthal treat “rule” as though it functions like real behavior, when it does not. Thus, the theory attempting to satisfy both cognitive and behavioristic theories satisfies neither. In spite of Zimmerman and Rosenthal’s conception of learning as “abstract paradigms rapidly and holistically acquired,” the theory is not a developmental theory in the Piagetian sense, in that it defines developnient as a function of learning rather than the reverse. A limitation of the theory in addition t o its self-defeating eclectism is that its stress on the significant role of the model is not generally borne out by the data reviewed here. The critical element in the model’s verbal behavior is the rule statement itself, that is, its form, content, and meaning rather than the model’s behavior. B. REPRESENTATIVE ITJNCTIONALISM

Bruner’s “instrumental conceptualism” (Bruner et aL, 1966) is based on the thesis that linguistic forms provide the symbolic representation of conceptual relations and that these are utilized in and define the nature of thought. Forms of representation are defined by Piaget as necessary for thought as well, but his emphasis differs from Bruner’s. Bruner asserts that our knowledge of the world is based on a “constructed model of reality” (p. 319). The axiomatic structures of this model are to some extent given in the “innate nature” of the three techniques for representing or “modeling” reality: action, imagery, and symbolism. The second tenet of Bruner’s thesis is that models of reality develop as a function of the uses t o which they have been put by the culture and by the individuals who use them. Man grows “by the process of internalizing the ways of acting, imagining and symbolizing that exist in his culture, ways that amplify his powers” (p. 320). In conservation, the linguistic system, as the symbolic form of representation, maps or translates the primitive idea of the identity of a substance (or “conservation in action”) into linguistic judgments. Thus, “ideas” exist first in action, and by implication language training has the effect of facilitating the mapping of one system onto another. Bruner’s instrumental conceptualism applied t o the acquisition of conservation differs from Piaget’s conception not so much over the role of linguistic representation per se (although they do differ in this regard) as in Bruner’s view of conservation as little more than identity of substance plus representation. The Genevans look on Bruner’s experiments as doing little more than creating pseudoconservations through the use of linguistic forms tied t o

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semilogical structures. The suggestion that cognitive growth proceeds b y internalizing the language-in-use of the culture implies that conservation has more of a social and cultural origin than Piagct's constructivist thesis allows. There are at least two limitations t o Bi-uner's view of linguistic represeiitation. The first relates t o the implication that symbolic thought requires linguistic representation for its occurrence; the second refers t o the emphasis on the internalization of cultural uses o f linguistic forms. In our view, the evidence [not reviewed here, but see Beilin (1975)] supports the Piagetian position that the origin of symbolic thought is not in language and that symbolic behavior (in play, for example) is not necessarily limited by o r dependent upon linguistic representation. Bruner's view of symbolization is so limiting as t o deny to imagery and t o action (such as gesture) a symbolic function, a position which also appears to be contrary t o the evidence (Piaget & lnhelder, 1971). Thus, although language is the symbolic representational systerns par excellence, it is not sufficient to account for the effectiveness of verbal-rule instruction in forming cognitive structures, since in Bruner's theory at least language does not account for the origin of these structures but only has a mapping function. C. LINGUISTIC STRUCTURALISM

The Genevans interpret linguistic methods of instruction as helping the child t o focus his attention on particular probleni attributes; as far as thev are concerned, the artifacts of the experiment facilitate response so that it simulates operatory behavior. This account is denied by the evidence reviewed here in that truly operatory response, evaluated by the sanie criteria used by the Genevans. is shown t o be the consequence of verbal-rule instruction. Although the possibility of true operatory acquisition by linsuistic means is not denied by the Genevans, n o attempt is made to account for it and evidence is in fact marshaled against it, consistent with earlier Piagetian views of the relation between language and thought. Piaget's and apparently Sinclair's views of the relation between language and cognition have changed, however, and we propose a theoretical account that is consistent with their more recent position. Piaget in this regard says in his preface t o Ferriero ( I07 1 ): Regarding t h e problem of rel~itiiin~ between the cognitive operations o r prcopcrations and language, it can be said . . . that the forrncr do n o t direct thc latter . . . according t o a one way action, b t i t that I h c progressions of Ianguagc ai-c duc t o :I regulatory or organizing mecliclnisiii intcrnal to [ i t ] and a t the sanic time coordinate with other forms of the siitiic pro acting at the canre 1c.vcl i n othcr domains; t h e logico-iiiatheinatic~il operation or prcopcration constitutes t h c n simultaneously the result of \\ 1i;it is i n c'oniiiion t o thc diverse eqtiilibrations and thc structural crystallization of this functioning in the domains whcre it becomes an end in itself: classification foi classification. seriation for scriation, etc. with

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This statement suggests the following: (1) Cognitive operations and preoperations d o not direct language or language acquisition as a one-way relation (as in fact the Genevans had previously asserted). (2) What directs language acquisition is a regulating and organizing mechanism that has a counterpart in the regulating mechanisms in other (nonlinguistic) domains of behavior. These partially independent and at the same time coordinate mechanisms are the manifestations of a more abstract system. (3) Logicomathematical operations and preoperations manifest these more abstract structures when there is a need for them. These abstract structures are evident in classification, seriation, and other behaviors that embody the logicomathematical operations of inclusion, order relations, etc. (4) Cognitive structures do not derive then from linguistic structure, nor apparently d o linguistic structures derive from cognitive systems. They both derive from a more abstract system of regulations and organizations conimon t o all domains. The foregoing statement by Piaget, brief as it is, reflects an important development in his views on language, for it makes language less dependent on cognition for its structure. This partial autonomy implies the possibility that operational structures can be constructed in language independent of nonlinguistic cognition. Piaget’s new position illuminates (if it does not fully account for) the fact that verbal-rule instruction leads t o operational conservation, as will be indicated short1y . D. VERBAL-RULE INSTRUCTION: THEORY

There are three ways in which language intervenes in cognitive development. One relates t o linguistic representation in the sense suggested by Bruner. Language, as a conventional sign system (or symbol system for Bruner), is said by Piaget t o provide the means for representing concepts and conceptual relations. Language can thus map onto other forms of representation (e.g., imagery), or it may map onto existing or emerging cognitive structures (i.e., sensorimotor schemes or preoperations). In the latter instances structures formed in the process of cognitive construction are given linguistic expression or representation. Cognitive acquisition or construction in this case is not due t o language 3This is a slightly edited version of a translation made by Barbara Lust.

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itself; the manifestation of language is only a concomitant to structural attainments. The Genevan experiments (Inhelder et al., 1974), as well as others, show the way that the linguistic system maps onto operational structures as verbal justifications parallel the child’s conservation judgments. The successful experiments on verbal-rule instruction suggest two additional functions for language. One involves transient algorithmic learning. In this instance, coded representations in the form of rule statements of the ostensible underlying mechanisms of conservation (or any other logical structures) act as algorithms or processing routines for organizing various perceptual inputs. The generality of the rule determines the extension of the class of instances to which the algorithm applies. The critical question is not whether an algorithm in linguistic form will work, since it requires only that the child have sufficient linguistic competence to form an internal linguistic representation; rather, the question is whether the algorithm can function as an operatory scheme. In younger children (around 5 years of age) the algorithm will be a transient acquisition because there is no adequate cognitive system to accommodate to this linguistic acquisition. (In Piaget’s terms there is partial assimilation without accommodation.) The algorithm functions for a while as a placeholder in the processing system of cognitive structures. Unless the system undergoes sufficient change (in development or learning) to generate operatory structures that could accommodate to the algorithmic structures and integrate with them, the linguistic rule structures so acquired in training (or otherwise) will extinguish. The other possibility is that rule instruction mobilizes previously unintegrated cognitive structures or operations so that they may be brought to bear on the conservation problems at hand. In this sense rule instruction generates cognitive conflict to induce such coordinations. Piaget and Sinclair apparently d o not believe that such coordinations can occur without disequilibrium or cognitive conflict. There is no logical reason, however, why a verbal rule at variance with the subject’s available strategies may not generate such conflict and lead to coordinations that result in new operational schemes. This view requires little change in prevailing Piagetian theoiy. There is still another possibility, however, which does require a more radical change, because it views the language-thought relation differently from the representational role attributed by Piaget to language in the past. In this case, the linguistic algorithms generated by verbal rule instruction are not transient but lead t o true operatory schemes. This occurs in those instances in which the learner is sufficiently advanced in cognitive level so that available operatory structures can acconiniodate the schemes embodied in linguistic rules. This is based on the assumption that the linguistic system can generate structures that do not necessarily have their origin in nonlinguistic cognition. Piaget, as shown in the passage quoted earlier (Section VI, C), proposes now that the linguistic system does not depend on nonlinguistic cognitive operations for all of

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its structure. Instead, the cognitive system and the linguistic system are both semiotic instruments that derive from a common, more abstract form of structure, and by implication each system has properties unique unto itself. As a consequence, language schemes can parallel cognitive schemes without merely mapping onto them-although such mapping is also possible. Thus, in our view linguistic structures derived from their own internally regulated mechanisms may embody operatory schemes just as reasonably as nonlinguistic cognition. Verbalrule instruction that mimics such structures may either anticipate true operatory structures or lead directly to their assimilation into the child’s existing operational or preoperational schemes. Inasmuch as linguistic and cognitive systems share a common origin in more abstract logical structure, there is no reason why there cannot be complementary or reciprocal assimilation and accommodation. In sum, the verbal-rule instruction experiments provide the evidence for concluding that operational structures can be induced or constructed by verbal means, and Piaget’s more recent views of the relation between language and thought provide the theoretical basis for accounting for the evidence.

REFERENCES Aebli, H. Piaget, and beyond. Ititerchange, 1970, 1, 12-24. Apostel, L. Logique et apprentissage. In L. Apostel, A. R. Jonckheere, & B. Matalon, Logique, apprentissage et prohahilit&. (Etudes d%pist&mologiegdndtique. Vol. 8.) Paris: Presses Universitaires de France, 1959. Pp. 1-138. Beilin, H. Perceptual-cognitive conflict in the development of an invariant area concept. Journal of Experimental Child Psychology, 1964, I , 208-226. Beilin, H. Learning and operational convergence in logical thought development. Journal of Experimental Child Psychology, 1965, 2, 3 17-339. Beilin, 1-1. Cognitive capacities of young children: A replication. Science, 1968, 162, 920-921. Beilin, 13. Stimulus and cognitive transformation in conservation. In D. Elkind & J . 13. I:lavell (Eds.), Studies in cognitive developnrent: Essays in honor of Jean Piaget. London and New York: Oxford University Press, 1969. Beilin, H. The training and acquisition of logical opcrations. In M. F. Rosskopf, L. P. Steffe, & S. Taback (Eds.), Piagetian cognitive-deI,elopment research and mathematical education. Washington, D.C.: National Council o f Teachers of Mathematics, 1971. (a) Beilin, H. Developrnental stages and developmental processes. In D. R. Green, M. P. Ford, & G . B. Flamer (Eds.), Measurement and Piaget. New York: McGraw-Hill, 1971. (b) Beilin, H. Studies in the cognitive hasis of language dei~eloprnent. New York: Academic Press, 1975. Beilin, H. Creating cognitive structure through training. In G. Steiner (led.), Twentiethcentury psychology. Vol. 7 . Piaget arid beyond. Bern: Kinder, in press. Beilin, H., & Franklin, I. Logical operations in area and length measurement: Age and training effects. Child Dei~elopment,1962, 33, 607-61 8. Binct, A. The perception of lengths and numbers in some small children. In R. EL Pollock &

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M. W. Brenner (Eds.), The experimental psychology of Alfred Binet. New York: Springer Publ., 1969. (Originally published in Revue philosophique, 1890, 30, 68-81.) Bloom, L. Language development: Form and function in emerging grammars. Cambridge, Mass.: MIT Press, 1970. Blum, A. H., & Adcock, C. Successful number conservation. Paper presented at the annual meeting of the American Educational Research Association, Los Angeles, February 1969. Braine, M. D. S. The ontogeny of certain logical operations: Piaget’s formulation examined by nonverbal means. Psychological Monographs, 1959, 73, No. 5 (Whole No. 475). Brainerd, C. J. The age-stage issue in conservation acquisition. Psychonornic Science, 1972, 29,115-117. Brainerd, C. J. Judgments and explanations as criteria for the presence of cognitive structures. Psychological Bulletin, 1973, 79, 172-179. Brainerd, C. J . Postmortem on judgments, explanations and Piagetian cognitive structure. Psychological Bulletin, 1974, 81, 70-71. Brainerd, C. J., & Allen, T. W. Experimental inductions of the conservation of ‘first-order’ quantitative invariants. Psychological Bulletin. 1971, 75, 128-144. Brainerd, C. J., & Hooper, F. A methodological analysis of developmental studies of identity conservation and equivalence conservation. Psychological Bulletin, 1975, 82, 725-737. Bruner, J . S., Olver, R. R., Greenfield, P. M., et al. Studies in cognitive growth. New York: Wiley, 1966. Bryant, P. Perception and understanding in young children. New York: Basic Rooks, 1974. Carlson, J. S. The effects of levels of verbal instruction and overt activity on the attainment of conservation of substance. Dissertation Abstracts, 1967, 28(1-A), 118. (a) Carlson, J. S. Effects of instruction on the concept of conservation of substance. Science Education, 1967,51, 138-145. (b) Donaldson, M., & Balfour, C . Less is more: A study of language comprehension in children. British Journal of Psychology, 1968, 5 9 , 4 6 1 4 7 1 . Elkind, D. Piaget’s conservation problems. Child Development, 1967, 38, 15-27. Ferriero, E. Les relations temporelles duns le langage de l’enfant. Geneva: Librarie Droz, 1971. Figurelli, J. C., & Keller, H. R. The effects of training and socio-economic class upon the acquisition of conservation concepts. Child Development, 1972, 43, 293-298. Flavell, J . H. The developmental psvcholog,v of Jean Piaget. Princeton, N.J.: Van Nostrand, 1963. Click, J. Cognitive development in cross-cultural perspective. In F. D. Horowitz (Eds.), Review of child development research. Vol. 4. Chicago: University of Chicago Press, 1975. Greitzer, G., & Jeffrey, W. Negative effects of the pretest in training conservation of length. Developmental Psychology, 1973, 9, 435. Griffiths, J. A., Shantz, C. U., & Sigcl. 1. E. 4 methodological problem in conservation studies: The use of relational terms. Child Development, 1967, 38, 841-848. Gruen, G. E. Note on conservation: Methodological and definitional considerations. Child Development, 1966, 37, 971-983. Hamel, B. R., & De Witt, S. The role of language-level in conservation-acquisition. Scandinavian Journal of Educational Research, 197 I , 1 3-20. Hamel, B. R., & Riksen, B. 0. M. Identity, reversibility, verbal rule instruction and conservation. Developmental Psychology, 1973, 9, 66-72.

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Mainel, B. K., Van I>er Veer, M. A. A,, & Westerhof, R. Identity, language activation training and conservation. British Journal of Educational Psychology, 1972,42, 186-1 91. Inhelder, B., Sinclair, I{., & Bovet, M. Apprentissage e l structures de la connaissance. Paris: Presses Universitaires de France, 1974. (Learning and the developrnent o f cognition. Cambridge, Mass. : Harvard University Press, 1974.) Lister, C. M. The development of ESN children’s understanding of conservation in a range of attribute situations. British Journal of’Edrccationa1 I’sycholog.~, I972,42, 14-22. Lunisden, E. A,, & Kling, J. K. The relevance of an adequate concept of “bigger” for investigations of size conservation: A methodological critique. Journal of Experimental Child Psycliology, 1969, 8, 82-91. Mehler, J., & Bever, T. G. Cognitive capacity of very young children. Science, 1967, 158, 141-142. Miller. S. A. Extinction of conservation: A methodological and theoretical analysis. MerrillPalrner Quarterly, 1971, 17, 319-334. Miller, S. A,, & Lipps, L. Extinction of conservation and transitivity of weight. Journal of Experimental Child Psyckolog~,,1973, 16, 3 8 8 4 0 3 . Morf, A. Apprentissage d’une structure logique concrete (inclusion): Effets e t limites. In A. Morf, J. Smedslund, V. Bang, & J. I;.WohlwiU, L’Apprentissagc. des structures logiques. (Etudes d’dpistdrnologie gdndtique. Vol. 9.) Paris: Presses Universitaires de France, 1959. Moynahan, E., & Glick, J. Relation between identity conservation and equivalence conservation within four conceptual domains. Dei~elopmerztalPs.vchology, 1972,6, 247-25 1. Oleron, P., & Thong, T. L’Acquisition dcs conservations I’apprentissage. A n n & Psychologique, 1968,68, 549-575. Overbeck, C., & Schwartz, M. Training in conservation of weight. .loirrnal of Experinfental Child Pswhology, 1970, 9, 253-264. Palermo, D. S. More about less: A study of language comprehension. Journal of‘ Verhal Learriing arid Verbal Behavior, 1973, 12, 21 1-221. Peters, D. L. Verbal mediators and cue discrimination in the transition from nonconscrvation to conservation of number. Child Developmerrf, 1970, 41, 707-721. Piaget, J. The construction ofreality in the child. New York: Basic Books, 1954. (a) Piaget, J. Language and thought from a genetic point of view. Acta Ps?.chologica, 1954, 10, 88--98. (b) Piagct, J. Assimilation et connaissance. In J. Jonckheere, B. Mandelbrot, & J. Piaget, La lecture de [‘experience. (Etudes d%pisr&ridogicgt’tidtiqiie. Vol. 5.) Paris: Presses Universitaires de France, 1958. Piaget, J. Apprentissage e t connaissance (part one). In P. GrCco & J. Piaget, Apprentissage ef connaissance. (Etudes d’&pistemologic getzetique. Vol. 7.) Paris: Presses Universitaires de I:rance, 1959. Pp. 21-67. (a) Piaget, J. Apprentissage e t connaissance (part two). In M. Goustard, P. GrCco, B. Matalon, & J . Piaget, La logique des apprenrissages. (Btlitles d’bpisthnlologie gddtiqiic. Vol. 10.) Paris: Presses Universitaircs de I:rance, 1959. Pp. 159-1 88. (b) Piaget, J. Introduction. In P. GrCco Cpr J . l’iaget, Appretitissagc et connaissaizcc. (Efiides d’dpisfdnzologie gdndriquc. Vol. 7.) Paris: Presses Universitaires de France. 1959. Pp. 1-20. (c) Piaget, J. Play, dreams and inzitation in childhood. New Y o r k : Norton, 1962. (Original edition: La forination du symbol, 1946.) Piaget, J . Development and learning. I n R. 1:. Ripple & V. N. Rockcastle (Eds.), Piaget rediscovered: A report of the confcvetrce on cognitive studies and cirrric~ilrrnzdevelop ment. Ithaca, N.Y.: School of Education, Cornell University, 1964.

Constructing Cognifii’eOperations Linguistically

105

Piaget, J . 012 the development o f )rrcniorj’ arid identity. Barre, Mass.: Clark University Press and Barre Publishers, 1968. Piaget, J. Biologji and knowledge. C‘hicago: University o f Chicago Press, 1971. (Original French edition: 1967.) Piaget, J., & Inhelder, B. Mental i i i f q y r i , in r/ie child. London: Routledge & Kegan Paul, 1971. (Original French edition: 1966.) Piaget, J., & Inhelder, B. The child’s co?rstrfrctiofz of quantifies. London: Routledge & Kegan Paul, 1974. (Original Swiss edition: 1941 .) Pratoomraj, S., & Johnson, R. C. K i n d s of questions and types of conservation tasks as related t o children’s conservation responses. Child Developnient, 1966, 37, 343-35 3. Reese, H. W., & Overton, W. I,’. Models of clevclopnient and theories of development. In L. R. Goulet & P. 13. Baltes (Eds.), I.if‘-spaii dcvelopniental psychologv: Research arid theory. New York: Academic Press. 1970. Reese, H. W., & Schack. M. L. Commcnts 011 Brainerd’s criteria for cognitive structures. Psychological Bulletin, 1974, 81. 67 69. Roscnthal, T. L., & Zimmerman, 1%. I . klodcling by exemplification and instruction in training conservation, Developrricritnl Ps>droloRy, 1972, 6, 3 9 2 4 0 1 . Russell, J. The interpretation of conservation instructions by five-pear-old children. Journal o f Child Psychology atzd Psychiatry, 1975, 16, 233-244. Sevinc, M., & Turner, C. Language and tlic htructure of cognitive development. Interriational Journal ofPsychology, 1976, 1 l ( 4 ) . Shantz, C. U., & Sigel, I . E , Logical oper~itionsand concepts o f conscrvation in children: A training study. USOL Report, Meriill-l’almcr Institute, Detroit, Michigan. Final Report, June 1967. Siegler, R. S. Inducing a general coirscrvation o f liquid quantity concept in young children: Use of a basic rule and feedback. I’erc~epriccilarid Motov Skills, 1973, 3 7 , 4 4 3 4 5 2 . Siegler, K. S., & Liebert, R. M. f’ffects 01’ presenting relevant rules and complete feedback o n the conservation of liquid q u ; i n t i t y t . Dei7eloprnental psycho log.^^, 1972, 7, 133-138. e n tla pensbe. Paris: LDunod, Sinclair-de Zwart, H. Acquisitior7 drr /atiqncqc, et d P ~ ~ ~ l o p p r t n dc 1967. Sjoberg, L., Noijer, B., & Olson, I . ‘I caching conservation of weight by nieans of verbal 1970, 11, 266-273. instructions. Scatrdiriaviari Joiirnnl o / 13>~c/tolo,qi8, Smedslund, J . Apprentissage de la notioil de la conservation et de la transitivitk du poids. In A. Morf, J. Sniedslund, V. l3ang. X J . I , . \lolilwill, L’Apprentissagr des structitres logiqires. (Etudes d’dpistdrnologic Kc’ircitiqirc‘. Vol. 9.) Paris: Presses Universitaires de France, 1959. Pp. 85-1 24. Smedslund, J. The acquisition of conservation of. substance and weight in children: I. 1961, 2, 1 1-20. ( a ) Introduction. Scandinavian Jorrrtial o f Psj’dio/o,q>~. Smedslund, J. 11. External reinforcement of conservation of weight and the operations of addition and subtraction. Scandiriai’iair .Joirriial ofPs,vcholo,yy, 196 I,2, 71-84. (b) Smedslund, J. 111. Extinction of con\crv;ition o f weight acquired “normally” and by nieans of empirical controls o n a balnncc. Scaritlirravian Journal of Psj~chology, 1961, 2, 85-87. (c) Smedslund, J. IV. An attempt at extinction o f t h c visual components of thc weight concept. Scandinaviati Journal of’Psyc.holoS\7, 1961. 2, 153-155. (d) Smedslund, J. V. Practice in conflict .;ituntions without external reinforcement. ScandiHQViQnJournal OfPSyChO[OgJ’, 1 96 1 , 2. 156-1 60. (e) Smedslund, J. VI. Practice on continiioits versus discontinuous material in problem situa-

106

Harry Beilin

tions without external reinforcement. Scandinavian Journal of Psychology, 1961, 2, 203-210. (f) Smith, I. The effects of training procedures upon t h e acquisition of conservation of weight. Child Development, 1968, 39,5 15-5 26. Steiner, G . On the psychological reality of cognitive structures: A tentative synthesis of Piaget’s and Bruner’s theories. Child Development, 1974, 45, 891-899. Sullivan, E. V. Transition problems in conservation research. Journal of Genetic Psychology, 1969,115,41-54. Waghorn, L., & Sullivan, E. V. The exploration of transition rules in conservation of quantity (substance) using film mediated modeling. Acta PsycholoKica, 1970, 32, 65-80. Weiner, S. L. On the development of more and less. Journal of Experimental Child Psychology, 1974, 17, 271-287. Wohlwill, J. F. Un essai d’apprentissage dans le domaine de la conservation du numbre. In J. Smedslund, V. Bang, & J. F. Wohlwill, L ‘Apprentissage des structures logiques. (Etudes d’dpist6mologie g6n6tique. Vol. 9.) Paris: Presses Universitaires de France, 1959. Pp. 125-35. Wohlwill, J. F., & Lowe, R. C. Experimental analysis of the development of conservation of number. Child Development, 1962, 33, 153-167. Zimiles, H. A note on Piaget’s concept of conservation. Child Development, 1963, 34, 691-695. Zimmerman, B. J., & Lanaro, P. Acquiring and retaining conservation of length through modeling and reversibility cues. Merrill-Palmer Quarterly, 1974, 20, 145-162. Zimmerman, B. J., & Rosenthal, T. L. Conserving and retaining equalities and inequalities through observation and correction. Developmental Psychology, 1974, 10, 260-268. (a) Zimmerman, B. J., & Rosenthal, T. L. Observational learning of rule-governed behavior by children. Psychological Bulletin, 1974, 81, 2 9 4 2 . (b)