Syntactic and semantic reasoning in mathematics teaching and learning

David Easdown

Abstract

This paper discusses a variety of examples in errors in mathematical reasoning, the source of which is due to the tension between syntax (form of mathematical expression) and semantics (underlying ideas or meaning). The paper suggests that heightened awareness of syntactic and semantic reasoning, and consequent resolution of the tension and errors in particular cases, may lead to enhanced mathematics learning outcomes, robustness and creativity.

Keywords: mathematical reasoning, syntax, semantics.

AMS Subject Classification: Primary 97C30.