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전자저널 논문

2019; 29(2): 209-226

Published online May 31, 2019 https://doi.org/10.29275/jerm.2019.5.29.2.209

Copyright © Korea Society of Education Studies in Mathematics.

Duality of the Area Ratio in Similar Figures: Procept and Proceptual

닮은 도형에서 넓이비의 이중성: 과정-개념과 과정화-개념화

박문환, 유재근

Abstract

Tall expressed the three worlds of mathematics using a diagram, and discussed the role of the ‘blending forms’ combining ‘embodied forms’ and ‘symbolic forms’ in the development of individual thinking. According to Tall’s viewpoint, ‘procept’ and ‘proceptual’ are distinguished. The ‘blending form’ proposed by Tall can be reinterpreted in regards to ‘procept’ and ‘proceptual’. Based on the two perspectives of ‘procept’ presented in textbooks through didactical transformation and ‘proceptual’ that the students are actually learning, this study investigated the relationship between similarity ratio and area ratio in the 2015 revised mathematics textbooks. Consequently, most textbooks exhibited ‘procept’ in the exploring task and the generalizing process of area ratios between similar figures. However, the ‘symbolic form’ described in the textbook proved to be insufficient to provide the students with opportunity to explore ‘proceptual’. Particularly, it was discussed Klein’s similarity transformation as a means to supplement the ‘embodied forms’. As a result of this study, it was established that the didactical transformation considering both ‘procept’ and ‘proceptual’ was required. The results of this study could be extended to offer pedagogical implications for school mathematics.

Keywords과정-개념,과정화-개념화,닮음비,넓이비,procept,proceptual,similar ratio,area ratio

Journal Info

Korea Society of Education Studies in Mathematics

Vol.32 No.2
2019-05-31

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly

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