The Korea Society Of Educational Studies In Mathematics

Current Issue

Journal of Educational Research in Mathematics - Vol. 30 , No. 2

[ Article ]
Journal of Educational Research in Mathematics - Vol. 29, No. 2, pp.209-226
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 31 May 2019
Received 15 Mar 2019 Reviewed 14 May 2019 Accepted 17 May 2019

Duality of the Area Ratio in Similar Figures: Procept and Proceptual
Park, Moon Hwan* ; Yoo, Jae-Geun**,
*Professor, Chuncheon National University of Education, South Korea (
**Teacher, Hongcheon Middle School, South Korea (

Correspondence to : Teacher, Hongcheon Middle School, South Korea,


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.

Keywords: procept, proceptual, similar ratio, area ratio

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