Can the sandwiches be split? The semiotic representation registers and concrete materials in teacher training

Abstract

Even in higher education, the many ways to represent fractions and the plurality of their meanings can be a challenge. Thus, this article explores the results from an excerpt from a didactic sequence in the context of teacher training, applied in two classes – one in the second and another in the fifth semester – of the undergraduate program in Mathematics at a public university. The results were analyzed from the perspective of the Theory of Registers of Semiotic Representation, the use of concrete material in teaching and the learning of fractions. The goal of the sequence was to introduce a possibility for the teaching of fractions using fraction bars (concrete material) and the Problem-Solving Methodology, as well as to assess the potentialities and limitations of the developed material. In this context, this text brings an analysis of the data collected from the audiovisual resources and the participants’ written notes referring to the first generating problem. Based on Bardin’s content analysis, three categories were designed, which allowed us to understand how the undergraduate students transit between different representation register forms and how the fraction bars may influence problem solving. Among the results, we highlight that the bars were useful for both the verification of the solutions and the interpretation of the problem. We also observed that, with some exceptions, the students mastered algebraic procedures but had a difficult time with the formation and representation of the situation in the other registers.