Historical artefacts, semiotic mediation and teaching proof

Abstract

This paper illustrates two examples of contexts for approaching validation, framed by a research program on semiotic mediation in the mathematics classroom. The question of how to approach theoretical reasoning, a major problem in mathematics education, is especially difficult when physical, truly tangible, artefacts are in play. Whenever a student is given a mathematical task to solve by using some artefact, in the solution process the student displays intense, observable semiotic activity (gazing, gesturing, writing, speaking, drawing and so on). A major aim of mathematics teaching is to foster the students' construction of the relationship between those produced signs and mathematical signs. The two examples show the successful introduction of physical artefacts at both the primary and secondary levels as tools of semiotic mediation in the process of mathematical validation. © 2010 Springer-Verlag US.