Aspectos do raciocínio matemático desenvolvidos a partir de um estudo de aula nos anos iniciais do ensino fundamental

Abstract

This dissertation aims to understand which aspects of mathematical reasoning are mobilized by fourth-grade students in Elementary School during an inquiry lesson developed within the con- text of a Lesson Study focused on the fundamental mathematical operations. The research fo- cuses on students’ mathematical learning, seeking to identify the reasoning processes that emerge from solving an exploratory task proposed for the inquiry lesson. The Lesson Study was devel- oped within the context of initial teacher education, involving sixth-semester students of a Bach- elor’s Degree in Pedagogy at a community higher education institution in Western Santa Cata- rina, Brazil. In this context, the students collaboratively planned, implemented, and reflected on the lesson, which was conducted with a fourth-grade class in Elementary School. Data were col- lected through observation of the inquiry lesson, video and audio recordings, students’ written productions, and field notes. The empirical material was analyzed using Content Analysis, based on Bardin’s approach, seeking to identify evidence of the aspects of mathematical reasoning mo- bilized by the students during the inquiry lesson. The results were organized into four analytical categories: resolution strategies, mathematical reasoning processes, communication of mathe- matical ideas, and construction of meanings. In the first category, the students were found to mobilize different strategies, such as mental calculation, written records, conventional algo- rithms, manipulable materials, and different forms of representation, making choices, adapting, and reorganizing their procedures. In the second category, conjectures, justifications, validations, and generalizations were identified, with the mobilization of heuristic, deductive, and, at times, abductive reasoning, evidencing the progressive construction of relationships among mathemat- ical concepts. In the third category, working in pairs and engaging in collective discussions were found to foster the sharing, comparison, and negotiation of strategies, the explicit articulation of procedures, and the shared construction of mathematical knowledge. In the fourth category, the construction of meanings was found to be supported by students’ prior knowledge, the strategies and representations they mobilized, the characteristics of the tasks, the use of manipulable mate- rials, and pedagogical mediation. Overall, the results demonstrate that mathematical reasoning develops dynamically and progressively and is fostered by learning situations that promote ex- ploration, inquiry, communication, and reflection. The research contributes to discussions on mathematical learning in the early years of Elementary School and highlights the potential of Lesson Study as a formative process, both for understanding students’ learning and for improving mathematics teaching.