Mathematics in the middle: Measure, picture, gesture, sign, and word

Abstract

Argues that mathematics can best be learned and taught as an integral component of a larger sense-making resource system which also includes natural language and visual representation. Formal and social semiotic perspectives are used to show how natural language, mathematics, and visual representations form a single unified system for meaning-making in which mathematics extends the typological resources of natural language to enable it to connect to the more topological meanings made with visual representations. Concludes that the mathematics curriculum and education for mathematics teaching need to give students and teachers much greater insight into the historical contexts and intellectual development of mathematical meanings, as well as the mathematics with natural language and visual representation.