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Syntactic and semantic reasoning in mathematics teaching and learning

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Abstract:

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

Keywords: mathematical reasoning; semantics; syntax

Document Type: Research Article

DOI: https://doi.org/10.1080/00207390903205488

Affiliations: School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia

Publication date: 2009-01-01

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