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Research Article

The Problem of Discontinuous Method of Mathematical Teaching: A Case on Concept of Continuity

Jung Won

Department of Science Studies and Center for Science and Culture, Jeonbuk National University

Published: December 2013 · Vol. 35 No. 3 · pp. 521-542
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Abstract

Combining history of mathematics with mathematical education is oneof broadly discussed topics of mathematical education. Since the stages ofdevelopment of students’ mathematical notion resemble the historicalintroduction of new mathematical ideas, the potential effectiveness of integratinghistory with classroom education is very large. This article surveys some effortsto apply history of mathematics to education and suggests one possible topicwhich can be adapted in university mathematics class. Many students who majorin natural science or engineering in Korea have a difficulty in understandinguniversity mathematics. One of the reasons which causes such a difficulty is theintroducing whole new method never used in high school mathematics class.
That method is so called ε-δ method. This article shows that ε-δ methodcame to be used through long and hard efforts of the 17th, 18th and 19thcentury mathematicians who wanted to establish rigor in calculus and the mainfigures were Euler, d’Alembert, and Cauchy. Also this article asserts thatexplaining historical development of ε-δ method will help students overcomingdifficulties due to discontinuous method of mathematical teaching.
Keywords: mathematical teachinghistory of mathematicsε-δ methodCauchy