O campo multiplicativo no âmbito institucional: das praxeologias sábias às ensinadas

Abstract

The present study aims to analyze the multiplicative conceptual field in the institutional scope, from the wise mathematical praxeologies concerning the referred object of study in question to its didactic transposition in terms of knowledge to teach in the school institution. To this end, in the light of the Conceptual Fields Theory and the Anthropological Theory of the Didactic, we conducted a descriptive analytical study of praxeological organizations inherent in two mathematical works from the academic-scientific literature, the institutional conditions imposed in the curricular design prescribed to basic education in connection with the multiplicative field materialized in the Common National Curricular Base and, finally, an analysis of the diffusion of mathematical objects constituting the multiplicative field in terms of competences/conceptions inherent to the respective praxeological organizations arranged in a collection of mathematics textbooks for the initial years of schooling approved by the National Textbook Plan for the year 2019 for the municipal education system of Belém do Pará. We point to the need of a convergence between nuances related to epistemologicalconceptual aspects of mathematical objects and their relations with cognitive processes between subject and mathematical object in face of the diffusion of didactic-mathematical paxeologies in the school institutional scope.