O DESENVOLVIMENTO DO RACIOCÍNIO MATEMÁTICO COM BASE NA RESOLUÇÃO DE TAREFAS EXPLORATÓRIAS: UM ESTUDO COM ALUNOS DO 7º ANO DO ENSINO FUNDAMENTAL DE UMA ESCOLA DO CAMPO

Abstract

This research corresponds to a teaching experiment involving the implementation of task-based approaches in an Exploratory Teaching context, considering the perspectives of Rural Education in the teaching of mathematics. The aim is to enhance the mathematical reasoning processes of 7th-grade elementary school students in a rural municipal school located in Guarapuava, Paraná. While the development of mathematical reasoning skills is considered relevant in the curriculum guidelines, tasks designed with this specific intention are seldom observed in the classroom. Therefore, our research poses the following question: 'What contributions are evident from Exploratory Teaching experiences in the classroom for fostering the development of mathematical reasoning among 7th-grade rural elementary school students?'.The main objective of the research was to understand the possibilities of developing Mathematical Reasoning in students of the 7th year of Elementary School through Exploratory Teaching practices. To achieve this goal, we examined the key processes of mathematical reasoning that students engaged in during the resolution of four exploratory tasks. Data were gathered in the classroom through participant observation, audio/video recordings, and the maintenance of a logbook.". The analysis, of a qualitative and interpretative nature, took place based on the triangulation between the students' written and oral productions, the theoretical framework adopted and the current curricular guidelines. As a result, we identified the processes of conjecturing, generalizing and justifying, respectively inherent to the types of abductive, inductive and deductive reasoning referring to the first and fourth tasks and we verified the processes of conjecturing and justifying associated with the types of abductive and deductive reasoning in the execution of the second and third tasks. In terms of the learning outcomes, many students expressed their comprehension of regularities, numerical and algebraic expressions, measurements, area equivalences of plane figures, and representations involving rational numbers. These results point to the development of students' mathematical reasoning in na Exploratory Teaching context.