Structural Sense Expressed by a Group of Pre-service Mathematics Teachers When They Resolve Factorization Tasks

Abstract

The Costa Rican mathematics curriculum promotes the development of algebraic skills in secondary education students. This has a direct impact on the initial training of teachers, which should include the promotion of various capacities related to the structural sense. This article delves into the structural sense manifested by 20 pre-service teachers, when they solve mathematical tasks on factoring polynomials. The research is descriptive and corresponds to an instrumental study of cases. The analysis considered three main categories adapted from theoretical proposals on the structural sense, which highlight the recognition of algebraic structures in their simplest form, composite form, and the manipulation of various structures. Results show that strengths in the structural sense of these teachers have been identified when they solve tasks with familiar algebraic structures. Add to this, weaknesses are evident when they solve tasks with composite structures, these weaknesses are intensified when they face tasks that involve the use of various manipulations in algebraic structures.