Um estudo da gênese documental de professores para função de uma variável real com várias sentenças matemáticas

Abstract

This research focused on the formation of mathematics teachers for the teaching of function with the Documentational Approach to Didactics (DAD) and Instrumental Orchestration (IO) as the theoretical framework and as research subjects’ teachers from public and private schools of basic education. The objective of the investigation was to study how the construction of documents to introduce the study of function with a collective of teachers in a continuing education can boost the professional development of this group. For this purpose, the reflective investigation methodology was used, which has five principles. The first three are dedicated to long-term follow-ups, inside and outside the classroom and reflective of the documentation work, while the last two, focused on the extensive collection of material resources used and produced and the permanent confrontation of teachers' opinions regarding their documentary work. To try to answer specific challenges caused by the problem, preliminary studies of a historical, epistemological and didactic nature were initially carried out, which brought to the fore details about the formation of the formal definition of function and its overlap with the Piecewise Defined Function (PDF). Such studies allowed to structure the continuing education that was organized to be developed in two phases: one called preparation and a second, strictly linked to the first, called execution. The preparation phase aimed to map the participants' resources and knowledge about teaching function, as well as to understand the structure of their resource system, while the execution phase was aimed at experiencing a set of situations made possible by IOs, in order to elaborate, apply and criticize a Sequence of Educational Situations (SES), having as a background the appropriation of a model to introduce the teaching of function from the PDF. The results obtained during the preparation phase made it possible to understand the structure of the research subjects' resource system and the identification of their knowledge made it possible to interpret their choices in introducing the teaching of the theme. The monitoring of the situations experienced by the subjects throughout the execution phase, allowed to identify documentary schemes and classes of situations mobilized for the construction of documents, as well as to infer about their professional development. Regarding the objective of the investigation, it can be said that the study of document construction was observed when the participants resolved, elaborated, applied or criticized the SSE, concluding that the documentary genesis was adequate to accompany the professional development of participants in continuing education