Apresentamos neste artigo uma discussão sobre as decisões didáticas, analisando a influência dos fatores decisionais do tipo história didática no ensino das expressões algébricas. Tratase de um recorte de uma pesquisa de Doutorado desenvolvida no campo da Didática da Matemática. Para tanto, abordamos essa problemática por meio da teorização e pesquisas acerca das decisões didáticas, com base no modelo dos níveis da atividade do professor, proposto por Margolinas ( 2002), e do modelo dos fatores decisionais, a partir de Bessot (2018). Elegemos como sujeitos da pesquisa um professor do Ensino Fundamental de uma escola pública, e seus alunos, e como saber matemático, as expressões algébricas. Os resultados obtidos apontam que o processo envolvendo as decisões didáticas pode ocorrer de forma coordenada, sem contradição entre os sujeitos participantes (professor-alunos), desde que os fatores decisionais do tipo história didática sejam identificados como responsáveis por influenciar tais decisões. Os fatores decisionais do tipo história didática fazem parte de forma predominante no processo que determina a tomada de decisão do professor, em especial, no nível 0 da sua atividade. Palavras-chave: Decisões didáticas. Fatores decisionais. História didática. Expressões algébricas.

The Dynamics of the Didactic Contract in the Teaching of Calorimetry by Situation-Problem Resolution: The Simultaneousness of Two ContractualRelationships. In this study, we seek to analyze the didactic contract in the elaboration and application of a didactic intervention centered on the resolution of problem situations. The proposed methodology was composed of a mini-course for in-service chemistry professors and PIBID scholarship students working in the 2 nd year of High School, with the purpose of instrumentalizing them for the construction and application of didactic interventions based on problem-solving with the chemical content that they would be working in the classroom. Later we accompanied the teacher Luiza in the application of her didactic intervention. In this article, we present one of the three situations of analysis that we carried out: the simultaneity of two contractual relations existing when the teacher applies the intervention in the classroom. The data revealed the maintenance of the didactic contract established in the mini course, which continues to be valid parallel to the didactic relationship that the teacher establishes with her students in the classroom.

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RésuméLe but de cet article est d'analyser, de manière comparative, les livres didactiques et les praxéologies mises en place par les enseignants dans leur pratique pédagogique, concernant l'enseignement des équations polynomiales du premier degré. Cette étude est faite dans le cadre de la théorie anthropologique du didactique (TAD) proposée par Yves Chevallard et ses collaborateurs (1999, 2002, 2009, 2010). La méthodologie est basée sur une approche ethnographique qualitative, dans laquelle les organisations mathématiques et didactiques de trois enseignants sont analysées en les comparant à celles des livres de référence. Les résultats indiquent qu'il existe une certaine conformité entre les praxéologies à enseigner, proposées par les auteurs des manuels scolaires et les praxéologies effectivement enseignées par les professeurs en classe. Les enseignants sont les organisateurs des tâches, des techniques et de la technologie de complexité croissante (FONSECA, 2004) qui sont rendus routinières ou problématiques en classe. La résolution d’une équation polynomiale du premier degré du type ax+b=c a été le point commun des trois professeurs, bien que deux des trois enseignants aient aussi travaillé des équations du type a1x+b1=a2x+b2.Mots-clés : Livres didactiques, Équations polynomiales du premier degré, Théorie Anthropologique du didactique.AbstractThe aim of this article was to analyze, comparatively, praxeologies in didactic books and praxeologies carried out by the teacher, concerning the teaching of polynomial equations of the first degree. This study is done within the framework of the Anthropological Theory of Didactics (ATD), proposed by Yves Chevallard and his collaborators (1999, 2002, 2009, 2010). The methodology consists of a qualitative ethnographic approach, in which the mathematical and didactic organizations of three teachers were compared with those of their reference books. The results indicate that there is some conformity between the praxeologies to be taught, proposed by the authors of the textbooks, and the praxeologies effectively taught by the teachers in the classroom. Teachers are the organizers of tasks, techniques, and technology of increasing complexity (FONSECA, 2004) that are made routine or problematic in the classroom. The resolution of a first-degree polynomial equation of the type ax+b=c was the common point among the three teachers, although two of the three teachers also worked on equations of the type a1x+b1=a2x+b2.Keywords: Didactic books, Polynomial equations of the first degree, Anthropological theory of didactics.