Joining the pieces of a puzzle: dialectical perspectives and the documentational genesis in the initial formation of Mathematics teachers

Abstract

This article aims to illustrate the Documentational Genesis considering a real situation of planning and implementation of a class experienced by a pre-service math teacher from the perspective of the three dialectic instrumentation/instrumentalization, “mother” resource/“child” resource and productive activity/constructive activity. The real situation referred to one of the studies analyzed during the post-doctoral internship of the first author at UFPE and at ENS/Ifé de Lyon, between 2016 and 2018. To reread the data, we listed three guiding questions: What does the student rely on in terms of resources? What are the reasons for her choices? What are the learnings in the formative process? As a theoretical and methodological framework, we rely on the Documentational Approach to Didactics. In the analysis of instrumentation and instrumentation dialectics, we had answers to the questions: what does the student rely on in terms of resources? What are the adaptations? and we look at the resources used from the task document. In this study we also identified the “mother” and “child” resources. In the study of these two dialectics, we infer the birth of a system of student resources built to teach triangle classification with Geogebra. In the productive activity/constructive activity dialectic, we had answers for the questions: what were the reasons for her choices? and what were the learnings in the formative process? when we analyzed the operational invariants of the scheme for creating a task. The study of task versions was essential to identify knowledge, beliefs and learning of the prospective teacher.