In his final works, Piaget suggested formalizing the developmental processes operating in different fields in terms of the mathematical theory of morphisms and categories. This new approach is used to account for the stages of development in two distinct fields: the understanding of the concept of inclusion observed via quantification tasks and the resolution of complex additive problems in arithmetic. We shall demonstrate that the distinction between intramorphic, intermorphic and transmorphic levels proposed by Piaget accounts for the stages of development in these two fields as well as for numerous empirical facts which have been considered incompatible with the earlier structuralist approach. As Piaget suggested, the main difficulty which children encounter in trying to resolve inclusion and additive problems is indeed the transition from state-oriented to transformation-oriented reasoning.

Keywords:
Correspondences, Morphisms, Class inclusion, Arithmetic problem solving
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© 1997 S. Karger AG, Basel
1997
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