고등학교 수학교과 과정에서 무한개념의 이해

Abstract

This thesis starts from the historical background and the rigorous definition of infinity from calculus. We compare it from the intuitive definition which is dealt in highschool mathematics. We also final some teaching skills to help our students to understand the concept of infinity effectively.

As results, we found the following,

First, teachers should give sufficient explanations and show various examples to the subjects in which students may have confusion.

Second, the functional aspects such as calculation skills should be emphasized rather than rigorousness in teaching analysis. Logical explanations should be given to the extent that helps student to understand basic concepts of infinity. In mathematics, the concept of infinity is very important as it is fundamental to the theory of continuous functions, differentiation and integration. But it is also true that the rigorous definitions of limit, continuity, differentiation and integration are not appropriate in highschool mathematics education. So those concepts are introduced somewhat intuitively in highschool education, and as, a result, students may have some confusion in learning analysis. In some cases, ambiguous definitions are the main factors for students to make some mistakes.

Third, highschool mathematics education should enlarge the scope of thingking abilities of students about infinity and limit.