A didactic proposal for teaching factorization cases of expressions of the form ax²+by+cx+ay+exy+f through Mathigon

Abstract

This paper presents the results of research conducted in a classroom setting with eighth-grade students in a public school in Argentina. The experience aimed, within the framework of an algebra course, to introduce the design and results of the implementation of a didactic proposal designed to establish relationships between expressions of the form ax<sup>2</sup>+by+cx+ay+exy+f, with a, b ∈ N and c, d, e, f ∈ Z, as a product of factors through the virtual manipulative Mathigon. The evidence collected leads to the identification that algebraic work using virtual manipulatives allows students to give a different meaning to mathematics, explore various forms of representation, and construct their own knowledge.