Unfolding Teachers’ Interpretative Knowledge into Semiotic Interpretative Knowledge to Understand and Improve Mathematical Learning in an Inclusive Perspective

Abstract

In this article, grounded in the concept of interpretative knowledge (IK), which is well known in the literature, we introduce and discuss the construct of semiotic interpretative knowledge (SIK). This theoretical tool unfolds the interpretation of conceptual knowledge into a broader construct that intertwines the use of semiotic representations with the manifold aspects of mathematical learning. In the first part of the article, we first introduce Duval’s semio-cognitive approach, in which semiotics is the element characterizing the specific cognitive functioning of mathematics. On the basis of some classic examples from the relevant literature, we then show the necessity of introducing the semiotic component into IK to expand the interpretive power of the teacher. In the second part of the article, through the analysis of six episodes involving students with a specific learning disorder (SLD) engaged in mathematical activities, we show how the development of the teacher’s SIK emerges as a necessary condition for the implementation of inclusive teaching practices. This permits us to face the research question focused on how SIK allows us to understand the student’s behavior in a special needs educational context and provide effective feedback. In this sense, SIK is shown to be an intrinsic prerequisite of inclusive teaching, thus extending the concept of IK to the components of pedagogical content knowledge (PCK).