A Constructivist Interpretation of Formal Operations

Abstract

Piaget’s logical model of formal operations is problematic since it is unclear how Piaget’s logic should be understood. In a recent review, Braine and Rumain conclude that neither of the two available interpretations is adequate. Under one interpretation, formulae which should be compatible are incompatible in Piaget’s logic. Under the other interpretation, formulae which should be incompatible are compatible in Piaget’s logic. A constructivist interpretation is outlined so as to overcome these weaknesses. It is proposed that the attribution of formal operational thinking depends upon an individual’s generalization of classificatory abilities which are present during concrete operations. Each of the formal operations has a unique specification in terms of the 16 patterns inherent in such classifications. Access to formal operations does not require conscious awareness of propositional symbolism. The interpretation is shown to be minimally adequate in avoiding the objections which invalidate existing interpretations. The interpretation is taken to exemplify two features of Piaget’s constructivism, namely the differentiation and integration of understanding which has a modal character.

Modelling the psychological structure of reasoning

“…A framework of possible relations between phenomena based on combinations of observations thus mediates the discovery of the factual relationship between phenomena, and the development of this framework demarcates propositional from concrete reasoning (Inhelder and Piaget 1958, chaps. 16-17;Smith 1987, sec. Piaget's Logic: A Constructivist Interpretation).…”

What the Pendulum Can Tell Educators about Children’s Scientific Reasoning

“…In particular, the GLT problems are related to discrimination between concrete and formal levels of operational ability (Parsons 1958;Smith 1987). A further consequence of Rasch analytic procedures is that, since item difficulty estimates are obtained for test items on the two measurement procedures, it is possible to make a comparison of those estimates relative to stage estimates of item difficulties, as stipulated by the test developers.…”

Revising the Logic of Operations as a Relevance Logic: From Hypothesis Testing to Explanation

“…1982;Par sons. 1960;Smith. 1987], Several proposals have shown that these criticisms can be hand led, to some extent, by interpreting the formal operational logic consistently as a quantifica tional logic [Braine and Rumain, 1983;Lei ser.…”

“…1987], Several proposals have shown that these criticisms can be hand led, to some extent, by interpreting the formal operational logic consistently as a quantifica tional logic [Braine and Rumain, 1983;Lei ser. 1982;Parsons, 1960] and considering In helder and Piaget's application of the binaryoperations in characterizing reasoning on such tasks as the rod flexibility or pendulum problems to represent changing states of knowledge in the course of the problem solu tion, particularly in regard to the set of actual, i.c., observed, combinations of events and the set of possible combinations, for any given hypothesis about the relationship among the relevant variables [Leiser, 1982;Smith, 1987], In addition to these specific proposals. Piaget's nonstandard use of symbolic logic can be defended on the grounds that standard logics require modification if they are to serve as competence models.…”