The synergy between the semiocognitive operations of the Theory of Semiotic Representation Registers:a study on the teaching of geometry

Abstract

Mathematics teaching is often centered around calculations in problem-solving tasks, neglecting other forms of language. Based on Raymond Duval’s Theory of Semiotic Representation Registers, language plays a vital role in the socialization and communication of knowledge and is fundamental in mathematics for representing its elements and semi-cognitive operations—a crucial aspect of student learning. Thus, this study seeks to identify the contributions of Duval’s Theory of Semiotic Representation Registers (TSRR) in understanding the role of language through the synergy among semi-cognitive operations: geometric gazes, geometric apprehensions, and discursive functions. The research follows the principles of Didactic Engineering as described by Michèle Artigue, adopting a qualitative approach. The theoretical framework highlights the decisive role of figural and natural representations in solving tasks involving three-dimensional figures, as they induce the activation of semi-cognitive operations in the construction of mathematical discourse. We conclude that the synergy among semi-cognitive operations significantly contributes to the development of geometric understanding, as well as to the identification of learning difficulties encountered by students during these activities. This study highlights the need for further research on this topic, particularly in the context of teacher training for basic education.