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전자저널 논문

2020; 30(2): 353-374

Published online May 31, 2020 https://doi.org/10.29275/jerm.2020.05.30.2.353

Copyright © Korea Society of Education Studies in Mathematics.

Alternative Method of Irrational Numbers Using Approximate Fractions and Slopes of Straight Lines in a Spreadsheet Environment

스프레드시트 환경에서 근사 분수와 직선의 기울기를 이용한 무리수의 대안적 지도법

Jae-Geun Yoo1, Jung-A Yi2, Moon Hwan Park3, Hyewon Chang4

* Teacher, Hongcheon middle school, South Korea, kuki122@chol.com
**Teacher, Pungduck high school, South Korea, cantatamath@hanmail.net
***Professor, Chuncheon National University of Education, South Korea, pmhwan@cnue.ac.kr
****Professor, Seoul National University of Education, South Korea, hwchang@snue.ac.kr

*홍천중학교 교사, **용인풍덕고등학교 교사, ***춘천교육대학교 교수, ****서울교육대학교 교수

Correspondence to:†corresponding author

Received: April 10, 2020; Revised: May 15, 2020; Accepted: May 15, 2020

Abstract

The purpose of this study was to explore the possibility of interconnection between non-fractional representation and non-circular decimal representation in irrational teaching and learning of school mathematics and to examine the possibility of field application. First, through the analysis of previous studies, it was found that the core of understanding irrational concepts is the intuitive perception of convergence and the inference of acyclicity. And through mathematical analysis, we confirmed that finite decimal sequences and approximate fractional sequences should be learning contents. In this regard, we applied engineering tools in teaching and learning activity of irrational numbers and analyzed the process by which engineering tools become learners’ mathematical tools and then learning occurs, that is, instrument genesis. As a result, in the activity of finding finite fractions of square roots, students gained a meaningful understanding by focusing on the meaning of square root symbols and square roots as objects from inputting functions and operations and using drag. And in the activity to solve the task ‘Can a graph cross a grid point?’, Students could infer the acyclicity of the decimal representation of irrational numbers by observing the approximate fraction as the slope. Thus, this study is expected to be a basic reference of teaching and learning of irrational numbers to construct a mental image of real numbers completeness axiom.

Keywordsirrational number, fractional representation, instrumental genesis, teaching experiment, slopes of straight lines, a spreadsheet environment

Journal Info

Korea Society of Education Studies in Mathematics

Vol.32 No.2
2020-05-31

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly

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