A generalization of Piaget's logical-mathematical model for the stage of formal operations

Abstract

The Piagetian logical-mathematical model for the stage of formal operations is presented. Weaknesses and limitations of the model are depicted and then a generalization of the model is presented along with a set of assumptions based on a hierarchial stage-theoretic view of formal thought with which the generalization complied. The Boolean algebraic structure of combinatorial thinking and the regular Boolean permutation group structure of hypothetico-deductive thinking are discussed. The method of designating the formal transformations in the groups descriptive of formal thought using the symmetric-difference operation is cited. The method of positive intersection generators is then employed to indicate the primitive formal transformations proper to a level of formal thought. The two smallest proposed groups descriptive of formal thought with their respective generators are displayed. Comparisons of the generalization with the Piagetian model are then instituted indicating the greater scope, adequacy, and sufficiency of the generalization in the explanation of formal operations. The usefulness of the generalization is indicated in various ways such as in the designation of the formal transformation used by an individual in a hypotheticodeductive situation.