음수의 교수 현상학적 연구

• 영문명: A Study on the didactical phenomenology of the negative numbers
• 발행기관: 대한수학교육학회
• 저자명: 우정호 최병철
• 간행물 정보: 『수학교육학연구』제13권 1호, 29~55쪽, 전체 27쪽
• 주제분류: 사회과학 > 교육학
• 파일형태: PDF
• 발행일자: 2003.02.28

영문 초록

In the school mathematics, the negative numbers have been instructed by means of intuitive models(concrete situation models, number line model, colour counter model), inductive-extrapolation approach, and the formal approach using the inverse operation relations. These instructions on the negative numbers have caused students to have the difficulty in understanding especially why the rules of signs hold. It is due to the fact that those models are complicated, inconsistent, and incomplete. So, students usually should memorize the sign rules. In this study we studied on the didactical phenomenology of the negative numbers as a foundational study for the improvement of teaching negative numbers. First, we analysed the formal nature of the negative numbers and the cognitive obstructions which have showed up in the historic-genetic process of them. Second, we investigated what the middle school students know about the negative numbers and their operations, which they have learned according to the current national curriculum. The results showed that the degree they understand the reasons why the sign rules hold was low. Third, we instructed the middle school students about the negative number and its operations using the formal approach as Freudenthal suggest-ed. And we investigated whether students understand the formal approach or not. And we analysed the validity of the new teaching method of the negative numbers. The results showed that students didn't understand the formal approach well. And finally we discussed the directions for improving the instruction of the negative numbers on the ground of these didactical phenomenological analysis.

목차

Ⅰ. 서언

Ⅱ. 음수의 본질

Ⅲ. 현행 교과서에 따른 지도 결과의 분석

Ⅳ. 형식적 접근에 의한 음수의 지도

Ⅴ. 요약 및 논의

참고문헌

〈부록〉

키워드

교수학적 현상학 음수 연산 형식적 접근 부호 규칙 didactical phenomenology negative numbers operation formal approach rules of signs