대수 증명에서 종속적 일반성의 인식 및 특정수 전이에 관한 연구
Study on recognition of the dependent generality in algebraic proofs and its transition to numerical cases
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
Algebra deals with so general properties about number system that it is called as ‘generalized arithmetic’. Observing students’ activities in algebra classes, however, we can discover that recognition of the generality inalgebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play animportant role in algebraic proofs. Many studies show that students have experienced some difficulties inrecognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, studentsalso have a difficulty in making a transition from algebraic proof to numerical cases which have the samestructure as the proof. This study investigates whether middle school students can recognize dependentgenerality and make a transition from proofs to numerical cases. The result shows that the participants of thisstudy have a difficulty in both of them. Based on the result, this study also includes didactical implications forteaching the generality of algebraic proofs.
Abstract
Algebra deals with so general properties about number system that it is called as ‘generalized arithmetic’. Observing students’ activities in algebra classes, however, we can discover that recognition of the generality inalgebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play animportant role in algebraic proofs. Many studies show that students have experienced some difficulties inrecognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, studentsalso have a difficulty in making a transition from algebraic proof to numerical cases which have the samestructure as the proof. This study investigates whether middle school students can recognize dependentgenerality and make a transition from proofs to numerical cases. The result shows that the participants of thisstudy have a difficulty in both of them. Based on the result, this study also includes didactical implications forteaching the generality of algebraic proofs.
참고문헌 (15)
- 김남희, "변수 개념의 교수학적 분석 및 학습-지도 방향 탐색", 박사, 수학교육, pp.1997
- 김남희, "변수(문자)의 의미 이해를 위한 고찰", 대한수학교육학회 논문집, 7(1), pp.345~356 (1997)
- 반혜진, "문자 및 변수지도 시 발생하는 오개념의 분석", 석사, 수학교육, pp.2006
- 유혜민, "변수개념에 관련된 대수적 인지장애의 예와 지도방안 : 중학교 2학년, 중학교 3학년을 중심으로", 석사, 수학교육전공, pp.2013
- 이준열, "중학교 수학 1" (2009), 천재교육
- 이준열, "중학교 수학 익힘책 1" (2009), 천재교육
- 이준열, "중학교 수학 익힘책 2" (2009), 천재교육
- 이준열, "중학교 수학 익힘책 3" (2009), 천재교육
- 장혜원, "기하 정리의 일반성 인식을 위한 동적기하환경의 활용", 수학교육학연구, 23(4), pp.585~604 (2013), 대한수학교육학회
- Lee, L., "Approaches to algebra: Perspectives for research and teaching", pp.87~106 (1996), Kluwer academic publishers
- Mason, J., "Approaches to algebra: Perspectives for research and teaching", pp.65~86 (1996), Kluwer academic publishers
- Mason, J., "Questions about mathematical reasoning and proof in schools", Reasoning, explanation and proof in school mathematics and their place in the intended curriculum: proceedings of the QCA international seminar (2002)
- Mason, J., "Generic examples : seeing the general in the particular", Educational Studies in Mathematics, 15, pp.227~289 (1984)
- Radford, L., "Approaches to algebra: Perspectives for research and teaching", pp.107~111 (1996), Kluwer academic publishers
- Usiskin, Z., "The ideas of algebra, K-12. 1988 NCTM yearbook", pp.8~19 (1988)