Enseñanza y aprendizaje de la función lineal : un estudio desde la teoría modos de pensamiento

Abstract

The research work we presented, made reference to a study related to the process to understand the linear function (FL), evidenced in students of ninth grades, at a public educational institution in Medellin, considering as a theoretical referent the modes of thinking by Ana Sierpinska (2000) and as a methodological design, The Art of Case Study Research by Stake (2010). The research problem originated, starting from some difficulties identified in the mathematical competences, which according to the national curriculum must reach young people from the interpretation, reasoning-argumentation and formulation-performance, being closely related to the mathematical object researched in the investigation. Other difficulties that are detected, are directly related to the way in which this object has been addressed in the educational context, where priority has been given to the geometric and arithmetic interpretation, leaving aside the structural analysis that seeks to take into account the properties and axioms that define it. In the current research, this last approach is precisely the one that we want to highlight in the understanding of the FL, through the investigation of the articulating elements between the three modes of thinking FL- Synthetic-Geometric FL, Analytical-Arithmetic FL and Analytical -Structural FL- to thus contribute to the deep understanding of the FL concept, where the student can understand the FL in the three modes, defined explicitly as follows: Synthetic-Geometric FL described as a straight line, Analytical-Arithmetic FL expressed as the general equation of the straight line and Analytic-Structural FL described as a locus.