Grade 8 Students’ Mathematical Reasoning: Conjectures, generalizations and justifications

Abstract

This article aims to understand how conjectures, generalizations, and justifications of grade 8 students are characterized when solving algebraic tasks, in the context of a teaching experiment that emphasizes the promotion of mathematical reasoning. Adopting a qualitative and interpretative approach we used the students’ written and oral answers of grade 8 students when solving algebraic tasks in the context of a teaching experiment based on the promotion of mathematical reasoning. As a result, we highlight the emergence of several conjectures and empirical generalizations, with some theoretical/structural/symbolic generalizations. We also highlight the use of empirical justifications, with a few examples, selected cases, and generic examples, and some episodes of justifications by external conviction, both by symbolic manipulations and by the look of the arguments. In addition, we emphasize that the discussion around empirical generalizations benefits the mobilization of other forms of justification that were not based only on the use of examples.

Keywords
Mathematical reasoning; Conjecture; Generalization; Justification; Algebra