How to understand a theorem?

Authors: Abramovitz, Buma¹; Berezina, Miryam¹; Berman, Abraham²; Shvartsman, Ludmila¹

Source: International Journal of Mathematical Education, Volume 40, Number 5, January 2009 , pp. 577-586(10)

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Abstract:

In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more of the theorem's assumptions are not fulfiled? What assumptions are necessary and which are sufficient? According to the students' opinion and the test results the developed approach was successful.

Keywords: theorem; assumptions; conclusions; counterexamples; self learning

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00207390902759618

Affiliations: 1: Department of Mathematics, Ort Braude College, Karmiel, 21982, Israel 2: Department of Education in Technology and Science, Technion-Israel Institute of Technology, Technion City, Haifa, 32000, Israel

Publication date: 2009-01-01

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