Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course

Abstract

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.

Student Teachers’ Motivation toward Participation in the Professional Development Programs

“…Similarly, a variety of previous studies [14,21,[51][52][53][54][55][56] confirmed that the role of intrinsic motivation in stimulating student teachers and motivating them to develop their learning practices and performance through participation in training programs is due to their passion for the teaching profession rather than being influenced by any external incentives. Likewise, student teachers' motivation was not based on tangible foundations but rather was based on a preference to be persistent teachers to develop their instructional performance.…”

The effect of conceptual understanding principles-based training program on enhancement of pedagogical knowledge of mathematics teachers

“…Based on professional development course, Santos et al (2022) indicated that the course had an effect on enabling teachers to deepen their understanding of the processes of generalization and justification, and their ability to enhance these processes with their students. In addition, Goos et al (2021) recognized a change in the knowledge of mathematics teachers and their ability to teach more advanced mathematics, and they recorded teaching practices consistent with the developed curriculum that adopted problem solving, after they were exposed to an in-service training program (professional diploma) in mathematics.…”

Gestão e Formação de Professores na Educação Básica

“…Para que professores desenvolvam uma prática de ensino com foco no raciocínio matemático, experiências no âmbito da formação inicial são de suma importância para que as prerrogativas sobre o raciocínio matemático sejam agregadas à sua prática pedagógica, quer seja a partir do confronto com situações concretas que envolvam de forma explícita o raciocínio matemático, quer seja pela experimentação de estratégias distintas e de forma específica, ao examinar trabalhos desenvolvidos por alunos (Vieira; Serrazina, 2020).…”

“…Nesse tópico, os indicadores educacionais apontam para o progressivo aumento das matrículas, com um pequeno decréscimo -de 92,7%, em 2019, para 91,6% em 2022 na faixa de 4 e 5 anos -na última Pesquisa Nacional por Amostra de Domicílios (Pnad). No conjunto do histórico da oferta, é possível reconhecer conquistas na ampliação da oferta, ainda incipientes se cotejarmos com as metas do Plano Nacional de Educação (BRASIL, 2014), de modo a evidenciar a necessidade de investimentos nessa etapa (Alves;Côco, 2014;Côco et al, 2015;Vieira;Côco, 2019).…”

“…No entanto, uma maior diversidade no processo formativo dos envolvidos, promoverá uma melhor qualidade na formação, bem como introduzirá novas perspectivas culturais, entre outros aspectos. Neste sentido, a mobilidade transnacional docente, em particular, pode contribuir para a pluralidade dos sistemas educativos, no local de trabalho e na sociedade em geral (Sobhi;Locatelli, 2015).…”