Conceptual thinking of fractions: the Davydovian mode of teaching organization

Abstract

This article was produced in the context of teaching organization from a historical and dialectic perspective. More specifically, its main reference is the developmental teaching proposed by Davýdov and his collaborators. The specification can be expressed in the following research question: what are the manifestations of the movement of conceptual thinking of fractions in the particular tasks in textbooks and teacher’s guides, when their reference is the Davydovian mode of teaching organization? In this bibliographical research, the analyzed data represents a sample of five particular tasks taken from the 5th Year textbook, based on Davýdov’s proposal and accompanied by the teacher’s guide. The first three tasks reveal the movement of reduction from the concrete to the abstract; the remaining tasks reveal the movement of thought as an ascension from the abstract to the concrete. This study reveals that the processes of reduction and ascension direct thinking towards the acquisition of the essential relations constituting the concept of fractions. Essence manifests in the measurement problem which creates the need for a division of the unit of measurement that will establish an intermediary unit. Both movements are characterized by mediated processes leading thinking into the abstraction and generalization of the inner connections constituting the law and cause of the concept.