Between the Announced and the Realized: the “Confusions” Present in the Productions of the XI and XII Encontro Nacional de Educação Matemática regarding Mathematical Research Tasks

Abstract

Assuming the aspects of qualitative research, this article explains an analysis of the works that focused on Mathematical Investigation as a subject of study and which were published in editions XI and XII of the Encontro Nacional de Educação Matemática - ENEM. In order to identify, in these works, possible misunderstandings in understanding what are Mathematical Research tasks and to elucidate some differences between them and the other types of mathematical tasks, we ask: the “confusions” between Mathematical Research tasks and other types of tasks used for teaching mathematics are present in the work on Mathematical Research in the editions of XI and XII ENEM? Are there specifics that make it possible to distinguish a Mathematical Investigation task from Mathematical Modeling tasks? What about troubleshooting tasks? What about exercises? As a synthesis of the perceived and articulated we affirm that, in the editions of XI and XII ENEM, there was the presence of misconceptions in the conception of what are Mathematical Research tasks, sometimes confused with the other types of tasks, in most cases, with the tasks of Mathematical Modeling. Among the perceived differences, we affirm that the Mathematical Investigation tasks have an open structure and are located in exclusively mathematical contexts. The problems are presented in real and semi-real contexts, with closed enunciative structure and without pre-established direction and questioning. Mathematical Modeling tasks are structurally open, situated in almost exclusively real context, and are usually composed of news, videos, and other resources that bring out a non-mathematical theme to investigate. We emphasize the need for care and attention to theory, assuming different methodologies to organize mathematics teaching, so that the theoretical and methodological aspects announced are consistent with the practice.