Sentidos e significados das operações de multiplicação e divisão com alunos dos anos iniciais: um estudo a partir de atividade orientadora de ensino

Abstract

This study explored the meaning and significance students experience when teaching multiplication and division in schools. We used Historical-Cultural Theory as a foundation, with an emphasis on Activity Theory and Teaching Orientation Activity (TEA). The study was guided by the following question: What are the meanings and significance of multiplication and division concepts expressed by elementary school students? The research, related to the teaching and learning of mathematics, was developed in a school setting using a qualitative approach. Participants were third- and fourth-grade elementary school students from 2022 to 2023.The analysis instruments used were episodes and scenes recorded through filming of activities produced by the teacher and developed by the students, written records made by the students and the teacher as well. We based our theory on authors such as Boyer (1996), Caraça (1951), Eves (2004), Ifrah (2007), Kopnin (1978), Leontiev (1978), Moura (2004, 2010), Vygotsky (2005, 2009, 2010).To compile the information, we used the theoretical and methodological assumptions of ESL, where students actively participate in the proposed Learning Trigger Situations (LTS), seeking solutions to their respective problems. The exchange of letters between the character Emília and the students was what mobilized the students to solve the problems posed by Emília, and thus were able to experience, with due respect, part of the historical process of multiplication and division constituted by different human cultures.We argue that through SDA, we can foster students' expressions of sense and meaning, which can then be used to connect them to mathematical meanings. When we work through SDA, we can consider children's imagination, as sense and meaning can manifest in ways that enable students to form mathematical concepts. Working with multiplication and division from a non-linear perspective enabled students to develop the need and motivation to engage in the process of thinking about mathematical concepts meaningfully. We concluded that mathematics instruction, when guided by autonomy and dialogue, enables meaningful learning, in which students assign meaning and significance to concepts, transforming the classroom into a space for discovery and learning. In this sense, we hope that this study will inspire other teachers to develop practices that prioritize and value the strategies used by students in solving problem situations, favoring the manifestation of the senses and meanings of mathematical concepts in the school context.