earticle

영어

This study was intended to suggest realistic knowledge for learning and teaching the optimization problems in regional inequalities using GeoGebra. For this purpose, learning material that is adequate to apply GeoGebra was developed and applied to experimental teaching. At first, through reviewing previous studies about learning of the optimization problems in regional inequalities, it is found that the concept of level curve is essential in studying the content. So analysis was conducted for the concept of level curve and development of the concept based on APOS theory that explains the development of understanding mathematical concept as the construction of mental structures: action, process, object. From the reviewing cases of utilizing GeoGebra for math class, availability of certain functions of GeoGebra like coordinate indicating function, drawing graph, dragging graph, and slider emerged as suitable teaching methods to understand the level curve. As a result, learning materials of activities with GeoGebra was designed so that student's understanding of the level curve can be improved. Secondly, the effects of using GeoGebra in teaching optimization problems in regional inequalities were investigated by analyzing the feature of learning・teaching through the developed learning materials. The analysis was conducted focusing on the change in level of student's understanding of the level curve. The followings are the results of this study. Through the concrete activities with GeoGebra, students' were able to understand the meaning of level curve, the variability of k in the expression f(x,y)=k, and relation between k and level curve f(x,y)=k. During the class with GeoGebra activities, students could correct their misconception and understand the reason why the maximum and minimum values are assumed only on the boundary of the area of solution of inequalities.

한국어

본 연구에서는 GeoGebra를 활용한 부등식 영역의 최대 최소 문제의 지도 과정에서 나타나는 학생들의 등고선 개념에 대한 이해 수준의 특징을 분석하였다. 또한 부등식 영역의 최대・최소 학습 지도에서 GeoGebra의 활용이 학생들의 수학적 사고에 미치는 영향과 함께 교실 수업에서 GeoGebra의 활용을 위한 시사점을 알아보았다. 연구의 결과로 첫째, 연구대상 학생들 중에서 주희는 등고선 개념에 대해서 과정 수준, 혜민이와 다영이는 행동 수준의 특성을 보였다. 둘째, 부등식 영역의 최대・최소 지도에서 GeoGebra의 활용은 학생들의 등고선 개념의 이해 수준을 향상시킬 수 있었다. 또한 GeoGebra의 활용을 통해 학생들은 목적함수의 의미를 파악할 수 있었으며, 목적함수식에서의 변수적 측면을 이해하고, 최댓값과 최솟값이 경계에서만 나오는 이유를 알 수 있었다.