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Article

전자저널 논문

2019; 29(2): 227-250

Published online May 31, 2019 https://doi.org/10.29275/jerm.2019.5.29.2.227

Copyright © Korea Society of Education Studies in Mathematics.

Conceptual Analysis for Solving a Missing Value Problem Using a Proportional Relationship

비례 관계를 이용한 미지값 문제해결과정에 대한 개념적 분석

신재홍, 이수진

Abstract

The aim of this scheme-theoretic study is to present a conceptual analysis on how arithmetic knowledge of whole number and fraction can be used in various solutions to a missing value problem involving a proportional relationship. The missing value problem analyzed in this study is the type of problem in which literature reports that students have difficulties reasoning with quantitative structures embedded. Four schemes (splitting scheme for composite units, iterative fraction scheme, unit-segmenting scheme with a remainder, and general iterative fraction scheme for composite units) and four operations (splitting operation for composite units, splitting operation, unit-segmenting operation, and equipartitioning operation) emerged as essential constructs in solving of the missing value problem using different ways. Our conceptual analysis of the problem suggests that students’ proportional reasoning would be developed as their partitive and quotitive division knowledge is reorganized by embedding the concept of fractions as measurable extents.

Keywords비례 추론,미지값 문제,개념적 분석,스킴과 조작,합성 단위에 대한 스플리팅 조작,proportional reasoning,missing value problem,conceptual analysis,schemes and operations,splitting operation for composite units

Journal Info

Korea Society of Education Studies in Mathematics

Vol.32 No.1
2019-05-31

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly

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