The present study aims to understand how the professional vision of prospective teachers (PTs) regarding whole-class reflective discussion develops as they explore a multimedia case (MC) in a mathematics teacher education course. The data come from the written productions of seven groups of PTs (N=15) related to whole-class discussion of one 6th grade lesson in two sections of the MC: first, they have focused on the teacher’s lesson plan and on her intentions for the whole-class discussion aiming at the students’ algebraic thinking; and in the second, they have analysed two video episodes of that lesson phase. The results show an integrated development of two processes of PTs’ professional vision – noticed events and the nature of the reasoning about them – with significant evolution from one section to another as they explore the MC. The study shows PTs’ alternative ways of accessing and making sense of the complexity of both ambitious and authentic teaching practices that can also be employed in at distance teacher education and mitigate the consequences of the impossibility to access the classrooms, such as that resulting from the recent COVID-19 pandemic.

O presente estudo tem como objetivo compreender a visão profissional sobre a comunicação no Ensino Exploratório desenvolvida por um grupo de futuros professores (FP) de Matemática numa disciplina da formação inicial. O contexto do estudo tem como elemento central a utilização de um caso multimídia que, dentre outras mídias, recorre ao vídeo para retratar episódios de uma aula de Matemática na perspectiva do Ensino Exploratório. Os dados dessa investigação qualitativa referem-se às respostas escritas dos FP em pequenos grupos e às discussões conjuntas nas sessões de formação voltadas à análise do caso. Os resultados evidenciam que os FP percebem os seguintes aspectos da comunicação: i) a promoção de interações dialógicas pela professora protagonista do caso para o desenvolvimento da tarefa matemática pelos alunos; e ii) o feedback da professora com base nas respostas dos alunos para o desenvolvimento da atividade matemática. O reconhecimento desses aspectos e os modos de raciocinar sobre eles expõem o desenvolvimento da visão profissional dos FP.

A teaching practice consistent with the development of students’ mathematical reasoning requires teachers to hold a profound understanding of mathematical reasoning. The aim of this research is to study the development of middle and secondary mathematics teachers’ understanding about the processes of generalizing and justifying in a professional development course. Data collection included observation of the course sessions, with video recordings, and document collection of teachers’ and their students’ productions. A qualitative in-depth analysis was carried out focusing on the ways and complexity of generalizing identified by the teachers. The results indicate that teachers progressively focus their attention on these reasoning processes, identifying and characterizing them. The way the course was designed and enacted appears to have contributed to enable the teachers to deepen their understanding of two central mathematical reasoning processes, generalizing and justifying, in addition to their ability to foster and identify such processes in the work with their students.

Classroom practice, as a process, involves multiple agents and their interactions within the classroom as a system. The process can be manifested in diverse formats and structures, and its effectiveness can be influenced by numerous factors both internal and external to the classroom. Research on (mathematics) classroom practice can thus take different perspectives, and much remains to be examined and understood as we all try to improve mathematics teaching and learning through classroom practice.