Epistemic and cognitive analysis of proportionality tasks from the algebraization levels perspective

In this article, we present the results of the evaluation phase of a training intervention with primary education prospective teachers on the subject of proportionality. The focus is on developing the epistemic and cognitive analysis competence of mathematical practices in problem solving. The prospective teachers first solve a mathematical task of inverse proportionality in several ways, then identify the mathematical practices employed in the resolutions, the objects and meanings, the difficulties, the levels of algebrization involved, and finally, perform the analysis of two solutions proposed by school pupils to a problem of direct proportionality. The results indicate that the future teachers’ knowledge about proportionality present deficiencies that can hinder the teaching of the subject. Likewise, it is concluded that developing the required professional knowledge and skills requires the application of longer training interventions