Professional learning opportunities regarding mathematical reasoning: a model for categorization

Abstract

Since teachers' knowledge of mathematical reasoning (MR) directly influences their classroom practices, the research that resulted in this study was developed from a training process aimed at teachers who teach mathematics, which explored this topic. Therefore, the objective of this study is to understand the professional learning opportunities (PLO) regarding MR, their processes and understandings experienced by a teacher participating in a training process during the planning, development and reflection stages of a lesson. The nature of the study is qualitative and interpretive, and the analysis focused on the moments of interaction of the aforementioned teacher during the planning, development and reflection stages of a lesson for the early years of elementary school. Different PLO on RM were highlighted, either stated by the teacher or inferred from the data at each of these stages. As a result, a model was proposed for categorizing PLO, which were segmented into two groups: Specialized Knowledge of MR and Pedagogical Knowledge of MR, the latter organized into two categories: Knowledge of MR and teaching and Knowledge of MR and students. The conclusion is that the promotion of formative actions that focus on PLO in relation to MR can result in a breakthrough in the students' learning process and in improved proficiency in learning mathematics.