A network of notions, concepts and processes for fractions and rational numbers as an interpretation of Didactical Phenomenology

Abstract

International audience

One of the main purposes of the research project that is being carried out in Mexico consists on building, from Filloy's point of view, a Local Theoretical Model (LTM) for fractions and rational numbers. For this purpose, four components of the LTM have to be constructed: models of formal competence, teaching models, models for the cognitive processes and models of communication. In this paper, a network of notions, concepts and processes for fractions and rational numbers that constitutes a fundamental part of the models of formal competence is described. This network was structured taking into account five mathematical processes grounded on Freudenthal's specimen of Didactical Phenomenology of fractions.