Mathematical representations in an algebraic problem in the initial training of primary school teachers

Abstract

Mathematical representations are increasingly taking a central role in mathematics education and in the planning of meaningful tasks that involve thinking and doing, rather than merely memorizing definitions and procedures. The guidelines that regulate mathematical activity, as well as key reference documents, highlight the knowledge and use of multiple representations as one of the core goals of mathematics learning, essential for achieving proficiency in the subject. In this context, the present study aims to identify the different types of mathematical representations used by higher education students, future primary school teachers, when solving an algebraic problem. This research follows a qualitative and interpretative approach, involving a total of sixty-eight students enrolled in a degree in Basic Education. The participants solved an algebraic problem and were subsequently asked to choose, from two alternative solutions to the same problem, the one that best aligned with their own way of thinking. Data collection instruments included students’ written work, observation, field notes, and audio recordings. The results show a predominant use of symbolic representations of an arithmetic nature, although with a lower-than-expected success rate. Algebraic symbolic representations were the least used and often led to incomplete solutions. Nevertheless, participants showed openness to other forms of representation different from their own, provided that explanations were offered and understanding was achieved.