PROBLEMS INVOLVING COUNTEREXAMPLES FOR THE DEVELOPMENT OF MATHEMATICAL REASONING IN THE 7TH GRADE OF MIDDLE SCHOOL

Abstract

This paper presents the results of qualitative and interpretative research on mathematical reasoning in Middle School. The study follows the Design-Based Investigation - (DBI) method. It aims to identify whether problems involving counterexamples, addressed according to the Methodology of Teaching-Learning-Assessment of Mathematics through Problem Solving, can contribute to the development of mathematical reasoning in 7th-grade Middle School. To obtain empirical data, a problem was applied to two trios of students in this grade at a school in the city of Maringá, in Paraná. Data were collected through audio recordings of the dialogue between the trios and written records of the students when solving the problem and analyzed, showing the mathematical reasoning processes mobilized by the students in solving the problem. The results indicated that the following mathematical reasoning processes were mobilized: conjecturing, exemplifying, justifying, and validating.