Prospective primary school teachers' competence for analysing the difficulties in solving proportionality problem

In this paper, we describe the design, implementation and results of a formative intervention, meant to develop prospective primary school teachers' competence in the analysis of the difficulties emerging in the resolution of proportionality tasks. Solving problems by different methods, identifying the knowledge put at stake in each problem and taking this information into account to recognize the difficulties that pupils may encounter in solving the problems using each strategy are essential aspects of the epistemic and cognitive facets of didactic-mathematical knowledge. The experience has been carried out with a sample of 88 prospective primary school teachers during the third year of their studies, by applying a didactic model that includes work in teams, institutionalization, and assessment of the individual learning achieved. To analyse the participants' responses, we used some theoretical and methodological tools of the onto-semiotic approach in mathematics education. The identification of pupils' potential difficulties in addressing problem-solving, based on the objects involved in the mathematical activity, was a challenging task for prospective teachers. The difficulties most frequently identified by the prospective teachers were those concerned with understanding the statement requirements, or the problem-situations context, and the mathematical procedures involved in the resolution of the task. They did not discriminate the difficulties according to the resolution strategies. Time constraints conditioned the degree of learning achieved. We conclude that it is necessary that teacher education programs consider this type of didactical analysis and should be articulated with situations focused on developing other complementary knowledge and competencies.