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## 전자저널 논문

2020; 30(특별호): 213-227

Published online August 31, 2020 https://doi.org/10.29275/jerm.2020.08.sp.1.213

## An Analysis of Fifth and Sixth Graders’ Algebraic Thinking about Reverse Fraction Problems

JeongSuk Pang1, SeonMi Cho2, Minsung Kwon3

*Professor, Korea National University of Education, South Korea
**Teacher, Seoul Sungsan Elementary School, South Korea
***Professor, California State University at Northridge, USA

Correspondence to:Email: jeongsuk@knue.ac.kr, halifax01@naver.com, minsung.kwon@csun.edu

### Abstract

In light of a growing emphasis on the relationship between fractional knowledge and algebraic thinking, the purpose of this study was to compare algebraic thinking about reverse fraction problems between fifth graders who had not been taught fraction division and sixth graders who had been taught fraction division. For this purpose, we conducted cognitive interviews with 30 students (15 fifth graders and 15 sixth graders) who used different solution methods in a paper-and-pencil test dealing with reverse fraction problems. We analyzed their algebraic thinking in terms of problem structure reasoning, generalization-representation, and justification. The results showed that fifth graders could generalize their solution methods but sixth graders who learned only the algorithm of fraction division had difficulties with generalization and justification. However, sixth graders who reasoned about the problem structure demonstrated proficiency in algebraic thinking. Although some students used the same solution methods in the paper-and-pencil test, they had different capacities in generalizing, representing, and justifying them during the cognitive interviews. The results of this study provide implications for teaching fraction operations in a way that develops algebraic thinking by attending to the mathematical structure and relation.

KeywordsReverse fraction, Algebraic thinking, Reasoning the problem structure, Generalization, Representation, Justification

### Vol.32 No.2 2020-08-31

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly