그래프의 형식적 정의와 항등함수에 대한 학생의 표현과 의미에 대한 연구

Abstract

The aim of this study is to analyze students' expressions explaining the formal definition of graphs and the identity function, and to explore the meaning underlying the expressions. To this end, we conducted clinical interviews with three first-year high school students. The data analyzed in this study are a portion of the data of 20 clinical interviews conducted for 6-7 sessions per student. As a result of the study, it was revealed that in order to understand the formal definition of a graph, meaning must be constructed through the process of mentally coordinating images of ordered pairs, set-builder notation, and function definition. The three students were unable to construct a formal definition of a graph, simply by understanding ordered pairs, set-builder notation, and function definitions. In addition, in the process of constructing the initial meaning of the identity function, an attempt to connect the meaning of the identity expression was confirmed. Based on the results of this study, we discussed the process of students understanding the formal definition of a graph and the understanding process of identifying the image of the identity function and the image of the identity expression. We finalized by suggesting implications. First, the teacher should design the class considering the coordination of three images related to ordered pair, set-builder notation, and function definition. Second, teachers should consider that there may be cases where students understand the concept of the identity function in connection with the identity expression. Finally, teachers need to plan various activities in class so that students can construct sufficient conceptual images to understand the concepts of functions.