A Study on “Original Size” in 2nd Grade Elementary School Fractions Learning: Analysis of the Recognition Process of T-shaped Figures as “Original Size”

Abstract

The purpose of this study is to capture in detail the aspects seen in the learning of fractions in the second grade, and to illustrate, through case studies, the characteristics of children’s recognition of the “original size” and the transformation process of that recognition. For this purpose, we planned and implemented classroom practices for the fraction unit in the second grade, and based on the children’s aspects observed there, we conducted analysis and discussion. The analysis focused on the characteristics of children’s recognition of the “original size” pointed out three things: 1) Shapes like T-shapes are difficult to recognize as the “original size”, as they are not treated as the “original size” in arithmetic textbooks, 2) Visual coherence and an orderly arrangement are recognized as the “original size,” and 3) Dependence on previously learned methods of division influences the recognition of the “original size.” Moreover, the analysis focused on the process of recognizing the “original size” characterized the importance of engaging in concrete operations such as folding and stacking when recognizing the “original size”, as they are not treated as the “original size” in arithmetic textbooks.