Teachers’ Practical Argumentation on the Teaching of the Pythagorean Theorem

Abstract

Delving into teaching reflection on practice and the underlying argumentation are key aspects for teacher professional development. Our interest in this study is focused on the role played by the Didactic Suitability Criteria in the analysis of the practical argumentation of a group of teachers during their reflection on a mathematical teaching and learning process. Methodologically, it is a case study conducted in a training course to foster teacher reflection involving eight Brazilian practising mathematics teachers who designed, implemented, and redesigned a lesson with the Pythagorean theorem. In this article, we analysed the practical argumentation emerging from teaching reflection, for which we proposed an adaptation of Toulmin’s model incorporating the Didactic Suitability Criteria construct to structure and represent the emerging practical arguments, and whose use was exemplified in two episodes of practical argumentation. The main result is that Didactic Suitability Criteria allowed us to: (a) reinterpret the dialogues that contained the participating teachers’ practical argumentation, in terms of some of the criteria, components, and indicators of this construct; (b) infer the participating teachers’ beliefs and values in their proposals of actions; and (c) nuance the relationship between the warrant and the action of each practical argument for the choice of certain actions in decision-making.