Inter-relações entre Domínios Matemáticos: a integração do NAG em um modelo praxeológico alternativo

In this paper, which objective is to discuss the conditions of implementation of an alternative praxeological model – APM, based on interrelationships between mathematical domains, we present epistemological-historical aspects of three major mathematical domains, and some basic notions of didactics anthropology, to subsequent presentation of characteristics of an MPA. A cut is made for three mathematical domains, namely: numeric-algebraic and geometric – NAG. We consider these NAG interrelationships by using them in two task examples. The study under * Doutor em Didática da Matemática pela Université de Montpellier II (UM2-França). Professor permanente no Programa de Pós-Graduação em Ensino, Filosofia e História das Ciências da Universidade Federal da Bahia (UFBA), Salvador, Bahia, Brasil. E-mail: lmsfarias@ufba.br. ** Doutor em Matemática pela Universidade de São Paulo (USP). Professor no Instituto de Ciências Exatas e Naturais da Universidade Federal de Rondonópolis (UFR), Rondonópolis, Mato Grosso, Brasil. E-mail: bittencourt@ufr.edu.br *** Doutor em Ensino, Filosofia e História das Ciências pela Universidade Federal da Bahia (UFBA). Professor no Centro das Ciências Exatas e das Tecnologias da Universidade Federal do Oeste da Bahia (UFOB), Barreiras, Bahia, Brasil. E-mail: edmo.carvalho@ufob.edu.br. ISSN 1980-4415 DOI: http://dx.doi.org/10.1590/1980-4415v35n69a25 Bolema, Rio Claro (SP), v. 35, n. 69, p. 529-548, abr. 2021 530 discussion is an offshoot of an investigation into interrelationships between mathematical domains in the re (construction) of praxeological models. The method was inspired by the praxeological analysis, notion of the Anthropological Theory of Didactics proposed by Yves Chevallard. The APM-NAG proposition is viable in institutional practices if attention is given to the type of task to be proposed, which places it at the center of the discussion of alternative praxeological models as opposed to dominant ones.