Transition to higher education: a case study on the contributions of semiotic representations

Abstract

This study aimed at investigating the contributions of semiotic representations to the understanding of mathematical concepts necessary for the learning of Differential and Integral Calculus I. Sixteen students enrolled in a Mathematics Course at a public university in Rio Grande do Sul participated in the research. The qualitative approach research, of case study, used the Didactic Engineering as research and teaching methodology. The theoretical contributions are anchored in the Registers of Semiotic Representation Theory. In a preliminary study, a diagnostic evaluation was applied, the result of which showed gaps, originating from Basic Education. After the preliminary analyses, a teaching sequence was elaborated and applied, and the activities address basic math contents.the data analysis was based on the triple analysis suggested by Raymond Duval, and the comparison with the a priori analysis. through the analysis, it can be inferred that the semiotic representations mobilized during the resolution of the activities have contributed to: a greater domain in the establishment of relations between the algebraic and graphical representations of functions, a better resourcefulness in the reading and interpretation of graphs, advances in the factoring and simplification of expressions, advances in the resolution of inequalities, the understanding of the concept of domain and its implications in the graph of function, as well as the understanding of the concept of function and the intuitive notion of limit.