September 14-18, 1996 Geneva, Switzerland


Empirical Aspects of Piaget's Epistemology:
Recent Findings from Rasch Analysis

Organiser and Chair: Trevor G Bond, James Cook University, Australia

Invited Discussant Leslie Smith, Lancaster University Great Britain

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Symposium Abstract
Empirical Aspects of Piaget's Epistemology: Recent Findings from Rasch Analysis

Three generations of researchers from four countries, Canada, the U S, Australia and the UK, use recent developments in measurement theory to examine the extent to which empirical data can inform Piaget's genetic epistemology. They conducted their research projects independently but commonly hold that empirical testing must fulfil two fundamental prerequisites before its evidence may be admitted for consideration: firstly, the psychological or educational test being used must interpret Piaget's theory in its own terms, and secondly, the statistical analyses must be sensitive to the expressly developmental nature of Piaget's explanatory account. Their carefully constructed research instruments are explicitly rooted in Piagetian theory, particularly as it is reported in Inhelder and Piaget (1955/1958); their focii range from one of Inhelder's tasks to Piaget's logico-mathematical model, from newly-conceptualised interview tasks, and class-tasks to pencil and paper versions, from traditional méthode critique administrations to multiple-choice formats. They recur to Rasch analysis techniques, one of the family of Item Response Theory models, for statistical interpretation of their data.

The ensuing data from these investigations take a range of forms from the right/wrong of multiple choice testing to the detailed procés-verbal of the Piagetian method. For each analysis, an appropriate Rasch technique was adopted. Given that Rasch principles make considerable demands on data with regard to both person and item performance characteristics, the fit of the data from each of the empirical investigations is remarkably good. The results provide confirmatory evidence concerning the scope and sequence of the cognitive developmental abilities described by Piaget as well as yielding precise quantitative estimates of the location of stages, the size of the horizontal décalage between related formal operational tasks, as well as the amount of cognitive development occuring over one and two year intervals during early adolescence. The results provide substantive quantitative evidence concerning the validity of key aspects of Piaget's oeuvre, the possibility of constructing reliable testing devices that validly represent Piagetian concepts and the suitability of Rasch analysis for developmental research. The discussion contextualizes this psychological research in terms of its relevance to Piaget's genetic epistemology.

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Unidimensionality in cognitive development

Gerald Noelting, Jean-Pierre Rousseau & Gino Coudé, Université Laval, Canada

In contrast to additive theories of development, where increase in the difficulty of a task is due to the progressive accumulation of details, Piaget's theory of development postulates that development is discontinuous. Once organised at a certain level, the whole task solution is reorganised when a new criterion is added. These aspects of Piaget's developmental model were investigated in an experiment involving the coding processes used by children of various ages to describe the structure of a range of poly-cubic objects : Coded Orthogonal Views.

A task was devised, involving cubes assembled in progressively complicated forms. The subject is asked to provide a coded diagram of the different poly-cubic objects given. For this, the child must first draw a two dimensional outline of the object and then add codes with legends, explaining the positions of the additional cubes of the object in the third dimension. The sequence of items is divided in three clusters explicitly derived from the Piagetian framework: intuitive period, concrete operational period and formal operational period. The resulting diagrams are scored as 'pass' or 'fail' and then analysed as to the strategy used to solve each problem. These strategies are ordered according to their complexity and categorised into Piagetian stages.

The inherent difficulty in research of this type is the difficulty of conveying qualitative observation in statistically sensitive and meaningful ways. We have addressed this difficulty by adopting the Rasch analytical model. In fact, the usefulness of Rasch analysis for studying results of Piagetian tasks is threefold: 1) It provides a hierarchical sequence of items according to difficulty, 2) It allows investigators to the assess fit of items to the Rasch model and to determine if items belong to the same latent trait. and 3) It reveals clustering of items of the same difficulty level, The hierarchical organisation of items, as a function of the difficulty of the item with respect to the latent trait, provides good support for the stage theory of cognitive development. Rasch applied to single tasks reveals a developmental sequence fitting the model. Moreover, the hierarchy obtained and the resulting gaps are coherent with the qualitative analysis made.
In the experiment undertaken, 278 subjects, aged between 6 and 16 years old, were subjected to the 22 items of the Coded Orthogonal Views task. Results were scored and submitted to Rasch analysis. The results obtained show clearly a correspondence between the Piagetian qualitative analyses and the (quantitative) statistical analysis. A graph revealing the difficulty-estimates of the items clearly shows the clustering of items for each stage with characteristic gaps between clusters of items at different stages. Results show equally that the sequence and gaps were obtained along a single developmental dimension. In all, remarkable correspondence was found between the quantitative hierarchical sequence revealed by Rasch analysis and the qualitative structural hierarchy postulated by the Piagetian cognitive developmental model.

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Revealing décalage and cognitive development quantitatively

Trevor G. Bond, James Cook University, Australia

Current research is demonstrating how measurement techniques based on Rasch analysis remain sensitive to principles underlying the collection and interpretation of Piagetian data. Brief examples of Rasch analyses applied to pencil and paper tests of formal operational ability as well as to interview transcripts derived from traditional méthode clinique investigation are held to demonstrate the utility of this statistical technique to Piagetian investigation. Two research projects were designed to develop quantitative estimations of two poorly researched aspects of Piaget's description of cognitive development during adolescence: cognitive growth and horizontal décalage.

Unfortunately, most developmental research is restricted to cross-sectional designs and it is difficult to infer if and when cognitive development takes place in any group of adolescents. To elucidate this problem with regard to Piagetian cognitive development two samples of secondary school students were assessed on a validated pencil and paper measure of formal operational thinking. This assessment was repeated after one year with the first sample and after two years with the second sample. Traditional statistical indices show the robust reliability of the test and affirm that statistically significant development had taken place over the intervening periods. More interesting however is the light that Rasch analysis shines on these data. As well as estimating growth in terms of substages of cognitive development, the analyses identify the subjects for whom growth did or did not take place and provides corroborating evidence for the account of formal operational thought provided by Inhelder and Piaget (1955/58).

Developmental psychologists, particularly those who research in the Anglo-American tradition of empiricism, often dismiss Piaget's horizontal décalage as a post hoc modification that has the effect of making Piagetian theory unfalsifiable. However, the use of validated Piagetian tests and developmentally sensitive Rasch analytical techniques allows precise estimates of the décalage that exists between two pencil and paper tasks of formal operational thought as well as between written and méthode critique versions of Inhelder's pendulum task. Given that horizontal décalage estimates from these investigations are consistently larger than the estimates for one- and two-year cognitive growth, significant implications for research methodology, educational interventions and Piagetian theory are canvassed.

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The development of negation--a Rasch-scaling approach

Ulrich Mueller & Willis Overton, Temple University, USA

The aim of this study was to examine the role the development of negations plays in the acquisition of class inclusion, implication, and the law of duality. Negations and the development of their frame of reference play an important role in class inclusion and implication. The failure to solve class inclusion and implication problems is due to the fact that the child is incapable of identifying the subclass A' by both its positive and its negative characteristics (A' = B.non-A). Children at the stage of concrete operations tend to have little difficulty solving class inclusion problems as long as concrete materials (picture cards) are provided. As soon as any concrete material is lacking, these children have the same problems in solving class inclusion problems as preoperational children have.

According to Piaget, it is not until formal operations are acquired that subjects will be able to solve inclusion problems on a purely verbal or propositional plane. The acquisition of propositional implication is due to a process of reflective abstraction by which the inclusion operation of the stage of concrete operations is transferred to a purely propositional plane at the stage of formal operational. At the stage of concrete operations, negation of a subclass A is restricted to its complement A' under the superordinate class. At the stage of formal operations the restriction on the scope of negation is lifted. The adolescent becomes capable of constructing a superordinate class C which includes the classes B and its complement B'. This allows the adolescent to broaden the scope of negation: The complement to A consists no longer only of A' but also includes all classes under B'. As a consequence, the adolescent becomes capable of understanding the "law of duality" (non-A= A'+ B' + etc.).

To study the development of negations, items were designed which tested for the understanding of negations within different frames of reference. In addition, tasks examining class inclusion, implication, and the law of duality were administered. Subjects were 120 primary and secondary school students. Rasch-analysis was used to assess whether the newly-designed negation task items measured one underlying dimension, and how success on the negation task was related to success on the inclusion and implication problems. The Rasch model was particularly suited for the analysis of these tasks. First, the Rasch model is an explicitly unidimensional model. Second, the Rasch model assesses how well each single item measures the underlying dimension and provides goodness of fit values for each item and person. Third, the distribution of the items along the dimension provides information as to whether those items designed to measure the same stage actually do so.

The items of the newly designed negation task generally fitted the Rasch model and distributed as expected. Joint fit analyses of the negation task, the class inclusion problems, the implication problems, along with the problems examining the understanding of the law of duality showed that most of the items fitted the expectations derived from the Rasch model. Misfitting items were examined in terms problems of item generations as well as problems for the Piagetian theoretical explanation. Overall, the results can be interpreted as providing evidence for the important role of the development of negation in solving class inclusion and implication problems.

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Integration and differentiation in longitudinal moral development data

Theo Dawson, University of California, Berkeley, USA

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Piaget's theory: Reculer pour mieux sauter

Leslie Smith, Lancaster University, Great Britain

Piaget's genetic epistemology has psychological implications. Perhaps because of this, the difference between an epistemological and a psychological account is easy to overlook. The application of psychological ideas, techniques and methods in the study of the development of children's knowledge in the actual world means that the psychological evaluation of Piaget's account is as necessary as it is important. But the outcome of this psychological evaluation does not settle the epistemological question which is central to Piaget's account. The psychological evaluation of Piaget's account is necessary, but not sufficient, since there are other questions in epistemology to address as well. The problem-shift due to Piaget is the realisation that certain problems in epistemology can be addressed empirically. Elsewhere, I have set out a case for regarding the development of necessary knowledge as the principal focus of Piaget's account (in my Necessary Knowledge). There is, however, a range of other epistemological questions.

To see the difference between epistemology and psychology, consider a specific case.

Question: 35 x 4 = ?
Answer A: 140
Answer B: 200
Does this question have a right answer? Is there one correct answer or several? Does A, or does B provide the right answer to this question?

Now it is pretty obvious that A is the right answer and B is wrong. Perhaps A is due to the use of "street mathematics" whilst B is due to "school mathematics"; but it could be the other way round since there is ample research in education to show that children have limited abilities to generalise. The research which documents the potency of such factors as content, context, and culture is clearly important - and fascinating as well. But issues relating to the generality of human understanding (across domain, contexts, culture) are quite different from issues relating to its universality. Quite simply, [A] - and [A] alone - is the right answer, so the question which also arises is: just how does the human understanding of this universal arise at all? From Plato to Putnam, universals have occupied centre-stage in epistemology. Piaget's account addresses the question: how do children acquire and develop a knowledge of universals? (Compare a standard conservation question: how do we acquire an understanding which is invariant to contextual changes?) Note well: such a question is quite distinct from the separate question about the generality of knowledge, once acquired. The point behind Piaget's question is that a universal is an abstract object knowledge of which is acquired through interactions in the actual world, so how is the (impoversished) stock of knowledge available in the actual world generative of the (rich) stock of knowledge of universals across 'possible worlds'?

Piaget's groupements and group structures are paradigm examples of abstract objects in this sense. They are not of course the only such examples. The argument set out by Inhelder & Piaget (1955/1958) is that there is a serial acquisition of such structures. It would be a triumph of human understanding if such structures really can be developed during childhood and adolescence just because a mathematical group is a universal structure, and a powerful one at that. This is one epistemological question which is central to Inhelder & Piaget's book. A consequential psychological question is that at the end of infancy, young children already have access to a group structure as displayed in practical intelligence. The problem of vertical décalage is thus with us. No doubt this problem is made especially acute due to factors related to generalisation. But in his 1941 paper in Archives de Psychologie, Piaget made it pretty clear that the former, rather than the latter, was his principal concern.

New evidence based on new ideas, techniques and methods is always welcome in and of itself, Since the Inhelder & Piaget account has had a mixed reception in the psychological domain, it offers an interesting opportunity. The application of Rasch analysis to this account in the generation of new empirical findings could provide clarification of existing psychological controversies. Even more important is the extent to which it provides the basis for new interpretations when Piaget's epistemology is at issue.

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