Tecendo redes cognitivas entre a formação matemática do pedagogo e o pensamento algébrico: reflexões a partir de grupos focais

Abstract

Faced with the changes and reforms that have taken place in the structure of teaching in Brazil in relation to the teaching of algebra in the early years of elementary school, teacher training for the development of algebraic thinking has commonly been related to the practice of solving calculations with little or no meaning for the student, so before dealing with the students' understanding of this subject it is necessary to discuss how teacher training can be improved. Our aim was to analyze the mathematical training of teachers in terms of the development of algebraic thinking, focusing on the knowledge objects that make up the algebra thematic unit of the National Common Core Curriculum (BNCC) through focus groups. In this context, we started with the following question: given the obligations imposed by the curriculum and the limited number of studies aimed at teacher training for the development of algebraic thinking, what practices can be reflected on in order to develop better learning? The methodology used involved basic participant research based on a qualitative and exploratory case study approach. As a structure, we used the theoretical assumptions of the Fedathi Sequence (FS) to mediate with the course participants, using the logbook as a resource for the observations made and research into bibliographic sources to structure and systematize the theoretical elements. As an information-gathering technique, based on the pedagogues' perceptions and experiences of how they understood and mediated algebraic thinking, we used face-to-face and non-face-to-face focus groups in three versions of the same extension course that took place in 2020, 2021 and 2022, independently, respectively with nineteen, twenty and in the last version six pedagogues from the public school system. In addition to the knowledge objects contained in the BNCC, the training courses covered the teachers' knowledge of algebraic thinking, their mediation practices with their students and how the teachers' continuing education has been carried out. As a result, we identified that the teachers associated the teaching of algebraic thinking with the use of letters as unknowns, their mediation practices were carried out in the way they understood when they were students and the continuing training offered did not allow them to rework the specific knowledge acquired in Basic Education. As a result of the actions developed in the extension courses, it was possible to mitigate these difficulties in teacher training to the point of highlighting as results that; there is a need to rethink the process of continuing teacher training so that it is constant in the practice of teachers, that its objectives are focused on the training of mathematical researchers, both for pedagogical and specific knowledge and that this process is accompanied by an institutional structure that gives them the conditions to promote this change concomitant with their performance as a teacher. That said, we conclude that these results will contribute to reflection and the development of policies for continuing teacher training with regard to the development of algebraic thinking with their students.