Promoting mathematical reasoning: exploration tasks in practice as a curriculum component

Abstract

This article presents results from an investigation on mathematical reasoning, through the implementation of Exploring and Developing Learning and Teaching Tasks, in mathematics teacher education. The study is part of a larger project, guided by the implementation of studies in mathematics education with the objective of designing an intervention in a mathematics course that articulates the practice of mathematics teaching and the hours of practice as a curricular component. It relies on case studies, and design experiments focused on learning processes from exploration tasks with the goal of identifying and documenting reasoning processes and changes in the learning environment and fostering new beliefs about the nature of mathematics teaching. The experiment involved future mathematics teachers who are taking hours of Practice as a Curricular Component (PCC). The role that mathematical representations play in understanding, organizing, and planning instructional sequences is highlighted. The results highlight the importance of exploratory tasks, which favor collaborative environments in the training process and direct attention to aspects of the content, and propose an innovation in the classroom dynamics, giving protagonism to the students, and can also develop inductive reasoning based on the identification of patterns, building their own visual or numerical schemes that perform a double function of understanding and recording. Deductive reasoning based on mathematical definitions and properties using algebraic representation to formulate conjectures was also used by the university graduates.