How to understand a theorem?

被引：3

作者：

Abramovitz, Buma ^{[1
]}

Berezina, Miryam ^{[1
]}

Berman, Abraham ^{[2
]}

Shvartsman, Ludmila ^{[1
]}

机构：

[1] Ort Braude Coll, Dept Math, POB 78, IL-21982 Karmiel, Israel

[2] Techn Israel Inst Technol, Dept Educ Technol & Sci, Technion City, IL-32000 Haifa, Israel

来源：

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY | 2009年 / 40卷 / 05期

关键词：

theorem; assumptions; conclusions; counterexamples; self learning;

D O I：

10.1080/00207390902759618

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

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.

引用

页码：577 / 586

页数：10

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