O processo de delineamento de uma trajetória de ensino e de aprendizagem: reflexões para o ensino de matemática

Abstract

His paper describes and analyzes a research with a Trajectory of Teaching and Learning (TEA) applied to students enrolled in the 6th year of Elementary School. In this research, we aimed to reflect on aspects of mathematics teaching that emerge for the teacher in delineating a Trajectory of Teaching and Learning for the 6th year of Elementary Education in the light of Realistic Mathematical Education. The approach to teaching Realistic Mathematics Education (RME) was selected and based on authors who study it. The approach to teaching Realistic Mathematics Education was selected and based on authors who study it. This research has a qualitative character of interpretative character in which it was used three cycles of iteration of the Research of Development (Design Research) for implementation, application and review of the TEA. Tasks in the design process were excluded, included, and altered to make them fit for the students for whom they were intended. The final version of the TEA consists of thirteen mathematical tasks that, in common, have the context of low floors and approach mathematical knowledge classified in different structuring contents. Two tasks that compose the TEA were selected to make a particularized descriptive analysis. By systematically reflecting the conduct of the teacher-researcher in the process of delineating two of the selected tasks, it was verified that the confrontation between expectations and the reality of the students' way of dealing with tasks; the decision-making of the teacher-researcher in the face of the students' difficulties during the lessons; the enhancement of the RME principles in the tasks statements were aspects that emerged in the design process of the TEA for the 6th year of Elementary Education in the light of Realistic Mathematical Education. The Educational Product from this research is composed of the tasks of the TEA and orientations of how to conduct, in the classroom in light of the RME.