Constructing meanings of mathematical registers using metaphorical reasoning and models

Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This paper investigates how a mathematics teacher made use of models and metaphors to construct mathematical meanings within a transformational shift between less- and more-mathematical language. The Peircian model of semiosis was employed to identify the conceptual relationships in the metaphors and to analyse possible discrepancies between the literal meaning of metaphors, the teacher's intended meaning and the targeted mathematical concepts. The findings indicate that the syntactic, semantic, and pragmatic features of the language used in mathematics teaching play a significant role in student learning. Teachers' knowledge of students' prior understanding of mathematical meaning of related concepts and their knowledge of examples, models, and language that are pedagogically preferable jointly affect the quality of teaching.