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Article

전자저널 논문

2019; 29(1): 143-156

Published online February 28, 2019 https://doi.org/10.29275/jerm.2019.2.29.1.143

Copyright © Korea Society of Education Studies in Mathematics.

Is the Limit Process Commutative with the Division Operation?

극한과 나눗셈 연산은 교환이 가능한가?

백승주, 최영기

Abstract

This study has analyses reasons why students perceive as ‘a ratio of limit’, even though they have been taught dy/dx and instantaneous velocity as ‘the limit of a ratio’ in school mathematics. The recognition of dy/dx as ‘a ratio of limit’ is related to the view of non-standard analysis through the accepting and use of infinity and infinitesimal as numbers. Historical findings have shown that this is similar to Leibniz"s notion of calculus. This study suggests that students may have different understanding from textbooks due to different interpretations in areas where experiences cannot reach, suggesting that they are paradigmatic rather than misconceptions. Similarly, we suggest that an intuitive teaching emphasized in the mathematics classroom be reconsidered in calculus that deals with infinity and infinitesimal.

Keywords비의 극한,극한의 비,패러다임,비표준해석학,Leibniz,직관,limit of a ratio,a ratio of limit,paradigm,nonstandard analysis,intui

Journal Info

Korea Society of Education Studies in Mathematics

Vol.32 No.2
2019-02-28

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly

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