Engenharia Didática para a Teoria do Resíduo: Análises Preliminares, Análise a Priori e Descrição de Situações-Problema

Abstract

O presente escrito aborda elementos de ordem teórico-conceitual, característicos de um design de investigação em Didática da Matemática, com o escopo de assinalar uma discussão e a possibilidade do ganho de conhecimentos didático-metodológicos acerca da Teoria do Resíduo. Dessa forma, tendo em vista extensa literatura, com influência da vertente de pesquisa francesa, descrevem-se com maior ênfase, as etapas de análise preliminar, análise a priori de uma Engenharia Didática - ED, com atenção especial dedicada à concepção e a modelização de duas situações-problema. Por intermédio de uma perspectiva afetada pela Teoria das Situações Didáticas – TSD, o trabalho aborda quatro etapas dialéticas, relativas ao planejamento teórico de uma experimentação, que promovem um debate científico envolvendo professor, alunos e um saber matemático específico, significado e mobilizado por intermédio da visualização (com o uso da tecnologia), e do entendimento tácito preliminar de determinadas propriedades fundamentais na Teoria dos Resíduos. Outrossim, o trabalho acentua o caráter epistemologicamente intrincado da referida teoria matemática, fato que justifica um olhar pormenorizado e cientificizado, proporcionado por uma proposta de ED.Palavras-chave: Engenharia Didática. Teoria do Resíduo. Análises Preliminares.AbstractThis writing deals with conceptual and theorical order elements, characteristic of a particular design of research in the Didactics of Mathematics, varygin between offering a discussion and the possibility of a gain of didactical and methodological knowledge of the Residue Theory. Thus, aiming at extensive literature, with the French research, the preliminary stages nominated preliminary and a priori analysis of a Didactical Engineering – DE are described with a greater emphasis, with especial attention dedicated to the design and modeling of two didactic situations. Thus through a perspective affected by the Theory of Didactic Situations – TDS, the present work addresses four dialectical steps, regarding the theorical planning related to experimentation, with the goal to promote a scientific debate involving the teacher, students and a specific mathematical knowledge, signified and mobilized through the visualization (with the using of technology) and a tacit understanding of certain fundamental properties in the Residue Theory. Furthermore, the work emphasizes the mathematical character of a epistemological complex theory, which justifies a careful and scientific look provided by the present ED proposal.Keywords: Didactic Engineering. Theory of Residue. Preliminary Analysis.

Software GeoGebra as a Proposal for Mathematical Modeling Problems

“…To achieve the objectives of this work, we used Didactic Engineering (DE) as a methodology to guide the research path, in its first two phases -preliminary analysis and a priori analysis -considering the fact that this work consists of ongoing research. DE was chosen because, according to Alves and Dias (2019), it is a methodology that brings an alternative from a systematic perspective of preparation, design, planning, modeling and allows the execution and replication of structured teaching sequences.…”

Didactic Engineering and Learning Objects: A Proposal for Teaching Parabolas in Analytical Geometry

“…To structure this article, we adopted Didactic Engineering (DE) as a methodology in its first two phasespreliminary analysis and a priori analysisgiven the character of theoretical research in the format of the didactic proposal of this work. According to Alves and Dias [8], DE is a method that brings alternatives from a systematic perspective of preparation, conception, planning, modelling, in addition to the possibility of executing and/or replicating structured teaching sequences.…”