Mathematical Reasoning Processes Mobilized by Calculus Students in Tasks Involving Graphic Representations

Abstract

Acknowledging the importance of reasoning development as a basic competence in learning Differential and Integral Calculus, this work is aimed at understanding the mathematical reasoning processes of students in this discipline, in the process involving the investigation of task resolution that contains the coordinated analysis of changes that happen in two interdependent variables. Adoptin a qualitative perspective of an interpretative nature, with the principles of Design-Based Research, we use the written protocol and audio recordings of the work of three groups of students when solving task involving the creation, interpretation, and reflection about graphics. As a result, we highlight a process construction of conjectures supported by mathematical knowledge that they already had, in the perception of relationships present in the task or, still, in common sense. In addition, we emphasize the search for reasons for validation or refutation, at which time students recovered knowledge they already had or built new mathematical knowledge, with the elaboration of new conjectures or improvement of an already elaborated on, new investigations and attempts to justify. Finally, we highlight the role played by the discussion among students, as well the potential and limitations of the tasks.

Keywords
Mathematics teaching; Differential and Integral Calculus Teaching; Mathematical Reasoning; Covariacional Reasoning