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ERIC Number: EJ859722
Record Type: Journal
Publication Date: 2009-Mar
Pages: 6
Abstractor: ERIC
Reference Count: 6
ISSN: ISSN-0025-5785
Breaking the Equation
Stylianides, Andreas J.
Mathematics Teaching, n213 p9-14 Mar 2009
A proof's potential to promote understanding and conviction is one of the main reasons for which proof is so important for students' learning of mathematics. Unless students realise the limitations of empirical arguments as methods for validating mathematical generalisations, they are unlikely to appreciate the importance of proof in mathematics. In this article, the author describes working with students on a journey to appreciate the difference between being convinced and "proof". The author describes and discusses a mathematics lesson in a high-attaining Year 10 class that aims to help the students begin to realise the limitations of empirical arguments. The lesson is an adapted version of one developed by a research project in the context of a university course. The lesson is approximately 60 minutes long and is taught over two consecutive 45-minute periods. It involves three activities: (1) the Squares Problem; (2) the Circle and Spots Problem; and (3) the "Monstrous Counterexample" illustration. (Contains 5 figures.)
Association of Teachers of Mathematics. Unit 7 Prime Industrial Park, Shaftesbury Street, Derby, DE23 8YB, UK. Tel: +44-1332-346599; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Grade 10; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: United Kingdom