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## 전자저널 논문

2020; 30(2): 281-305

Published online May 31, 2020 https://doi.org/10.29275/jerm.2020.05.30.2.281

Copyright © Korea Society of Education Studies in Mathematics.

## 중학교 1학년 학생들의 비례 추론과 공변 추론의 관계 비교·분석

JongHee Park1, Soo Jin Lee2

*Teacher, Cheonan Yonggok Middle School, South Korea, cyber-iris@hanmail.net
** Professor, Korea National University of Education, South Korea, sjlee@knue.ac.kr

*천안용곡중학교 교사, **한국교원대학교 교수

Correspondence to:1) 본 연구는 제1저자의 2019년 박사학위 논문의 내용을 토대로 재구성, 수정 및 보완하여 작성하였음.
†corresponding author

Received: April 6, 2020; Revised: May 13, 2020; Accepted: May 14, 2020

### Abstract

To understand the relationship between students’ proportional reasoning and covariational reasoning, clinical interview was conducted with four 7th grade students. Students participated in four interviews each of which took about three-four hours. The analysis of the data suggests the following results: First, all four students conceived ratio as ‘internalized ratio’ but how they reasoned with the ratio concept were somewhat different, which were categorized into three different types of proportional reasoning. Secondly, there were differences in how the four students conceived two quantities in graph construction and interpretation tasks. Specifically, two of the four students showed ‘coordination of values’ level, one showed ‘chunky continuous covariational reasoning’, and the other showed ‘smooth continuous covariational reasoning’. Thirdly, there was little relationship as to how students conceived ratio and how they reasoned with quantities in function task. All four students perceived the continuity of function in various ways. We have finalized our study by suggesting students" ways of partitioning and iterating of two quantities in proportion and function tasks as potential theoretical constructs to distinguish how students reason.

Keywordsproportional reasoning, covariational reasoning, proportion, function, constant comparative method

### Vol.32 No.1 2020-05-31

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly