Prospective Primary School Teachers’ Competence for the Cognitive Analysis of Students’ Solutions to Proportionality Tasks

Abstract

In order to foster the learning of mathematics, the teacher must be able to analyse and assess the students’ mathematical activity. The explicit recognition of objects and processes involved in mathematical practices is a competence that the teacher should develop. This cognitive analysis competence allows the teacher to understand the processes of mathematical learning, to foresee conflicts of meanings and to establish different possibilities for institutionalising the mathematical knowledge involved. In this article we present the results of the evaluation phase of a training intervention with eighty-eight prospective primary school teachers, which aims to promote and assess the competence for the cognitive analysis of students’ solutions to proportionality tasks. To this end, we proposed the prospective teachers to interpret different students’ solution strategies for a problem, recognise the mathematical elements (languages, concepts, propositions, procedures and arguments) put at stake in each strategy, and to analyse the algebraic character of the mathematical practices involved in them. The results reveal the prospective teachers’ limitations for the analysis and assessment of non-usual resolution strategies, the identification of key mathematical objects and the discrimination of arithmetic and algebraic activity in the students’ solutions. The improvement of the results requires the following actions: to allow prospective teachers to become acquainted with different forms of reasoning that can be applied in proportionality situations, delve more deeply into the algebraic character of mathematical activity, and extend the number and variety of situation problems that prospective teachers can analyse and discuss.