 [ Article ]
Journal of Educational Research in Mathematics - Vol. 30, No. 2, pp.353-374
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 May 2020
Received 10 Apr 2020 Revised 15 May 2020 Accepted 15 May 2020

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

Yoo, Jae-Geun* ; Yi, Jung-A**, ; Park, Moon Hwan*** ; Chang, Hyewon****
*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

Correspondence to: Teacher, Pungduck high school, South Korea, cantatamath@hanmail.net

## 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.

## Keywords:

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

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