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Article

전자저널 논문

2018; 28(1): 1-26

Published online February 28, 2018 https://doi.org/10.29275/jerm.2018.02.28.1.1

Copyright © Korea Society of Education Studies in Mathematics.

A Comparative Study of the Mathematics Textbooks of Korea and the United States based on a Learning Trajectory for the Concept of Slope

중학교 기울기 개념에 대한 학습경로와 그에 따른 한국 수학 교과서와 미국의 CMP 교과서 비교

박종희, 이수진

Abstract

The understanding of the concept of slope in terms of the rate of change serves as the foundation for developing meaningful calculus concepts. The purpose of our study was two-fold: Firstly, we attempted to develop a learning trajectory for the slope of a linear function using the rate of change; secondly, we used the trajectory to compare Korean mathematics textbooks with those of the U.S. standard-based curriculum CMP. After developing a learning trajectory of slope for the linear function via an in-depth analysis of the past literature, we compared and contrasted the textbooks of the two countries. Specifically, we analyzed how the textbooks of the two countries defined and described the terminologies, how they introduced the slope concept including the way how slope was represented (e.g., double number line and strip diagram), and finally the affordance of the two different perspectives of proportional relationships. Our results suggest that a careful consideration of the method to introduce the slope concept, the consistency of the terminology usage and explanations, and the devising of instructional materials that enhance the student awareness of the invariant relationship between two quantities using proportional reasoning are imperative for students’ meaningful development of more advanced mathematics.

Keywords함수,기울기,비,비례,변화율,교과서 분석,학습 경로,function,slope,ratio,proportion,rate of change,analysis of textbooks,learning trajectory