Raciocínio matemático e as oportunidades de aprendizagem profissional do professor que ensina matemática: o papel e as ações do formador

Abstract

This research arose from professional and personal motivations related to the role of the trainer of mathematics teachers, particularly in light of the need to understand how mathematical reasoning (MR) develops in training interactions and how the trainer’s role, actions, and practices can enhance this process. Based on this practical and investigative concern, the central objective of the study was to understand how the actions of mathematics teacher educators contribute to creating opportunities for professional learning regarding the essential understandings of MR. The research approach is qualitative and interpretive, grounded in the analysis of discursive episodes produced during the four meetings analyzed as part of a training process. The setting consisted of collaborative meetings in which Basic Education teachers solved Professional Learning Tasks (PLTs) and discussed problem-solving strategies, identifying RM processes based on records of students’ practice. The participants were Basic Education teachers from Paraná, facilitated by the trainers, whose role constitutes a central part of the phenomenon under study. Data collection involved audio and video recordings, full transcripts of the discussions, written records by the teachers, and notes taken by the trainers. The analysis was guided by categories derived from the trainer’s actions and practices as proposed in the literature, linked to RM processes. The results revealed that the trainer’s role and actions are related to their professional knowledge, including their mathematical, didactic, and pedagogical knowledge, as well as their knowledge of mathematics education and training experiences. The identified actions-inviting, clarifying, revisiting, expanding, paraphrasing, contrasting, and questioning-functioned as formative interventions capable of transforming teachers’ spontaneous interactions into evidence of conjecture, generalization, inquiry into “why,” and the beginning of justifications. These actions structured the discourse, made validity criteria explicit, and created OAPs directly related to the development of RM. As a complement to the results and conclusions highlighted in the research analyses, this educational product presents a training plan for instructors consisting of a theoretical-practical guide for developing MR in teachers who teach mathematics.