A Semiotic Perspective of Mathematical Activity: The Case of Number

摘要

A semiotic perspective on mathematical activity provides a way of conceptualizing the teaching and learning of mathematics that transcends and encompasses both psychological perspectives focussing exclusively on mental structures and functions, and performance-focussed perspectives concerned only with student' behaviours. Instead it considers the personal appropriation of signs and the underlying meaning structures embodying relationships between signs. It is concerned with patterns of sign use and sign production, including individual creativity in sign use, and the underlying social rules and contexts of sign use. It is based on the concept of a semiotic system, comprising signs, rules of sign production, and an underpinning meaning structure. This theorisation is applied to the learning of number, from counting to calculation. Historical, foundational and developmental (i.e., learning) perspectives are explored and contrasted. It is argued that in each of these domains, the dominant significant activity concerns the production of sequences of signs.