기하 증명 구성에 나타나는 학생들의 사고과정 탐색
Exploring students’ thinking in proof production in geometry
0
조회
0
다운로드
5
인용
0
참고문헌
키워드
초록
This study aims to explore secondary students’ thinking while doing proof in geometry. Two secondarystudents were interviewed and the interview data were analyzed. The results of the analysis suggest that thetwo students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles tosolve a given problem, b) being confused about the rules of similar and congruent triangles, and c) beingconfused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the resultsrevealed that a relatively low achieving student has tendency to rely on intuitive information such as visualrepresentations.
Abstract
This study aims to explore secondary students’ thinking while doing proof in geometry. Two secondarystudents were interviewed and the interview data were analyzed. The results of the analysis suggest that thetwo students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles tosolve a given problem, b) being confused about the rules of similar and congruent triangles, and c) beingconfused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the resultsrevealed that a relatively low achieving student has tendency to rely on intuitive information such as visualrepresentations.
참고문헌 (17)
- 권지현, "중학교 수학 교과서에 제시된 기하영역의 수학 과제 분석", 수학교육, 52(1), pp.111~128 (2013), 한국수학교육학회
- 나귀수, "기하 개념의 이해와 적용에 관한 소고", 수학교육학연구, 7(2), pp.349~358 (1997)
- 이지현, "일상적 정의에서 수학적 정의로의 이행 - 영재 중학생들의 점과 선의 정의 인식 -", 수학교육, 50(4), pp.429~440 (2011), 한국수학교육학회
- 한인기, "한국과 러시아의 7~8학년 수학교과서 도형영역에 나타난 직관적 정당화와 엄밀한 증명", 수학교육, 44(4), pp.541~554 (2005), 한국수학교육학회
- Balacheff, N., "Aspects of proof in pupils’ practice of school mathematics. Mathematics", Teachers and Children, 216, pp.235~240 (1988)
- Chazan, D., "High school geometry students' justification for their views of empirical evidence and mathematical proof", Educational Studies in Mathematics, 24(4), pp.359~387 (1993)
- Dimakos, G., "Developing a proof-writing tool for novice lyceum geometry students", Teaching of Mathematics, 10(2), pp.87~106 (2007)
- Harel, G., "Students' understanding of proofs : A historical analysis and implications for the teaching of geometry and linear algebra", Linear Algebra and its Applications, 302(303), pp.601~613 (1999)
- Harel, G., "Students’ proof schemes : Results from exploratory studies", Research in Collegiate Mathematics Education III, 7, pp.234~282 (1998)
- Healy, L., "A study of proof conceptions in algebra", Journal for Research in Mathematics Education, 31, pp.396~428 (2000)
- Heinze, A., "Teaching and learning proof across the grades", pp.191~203 (2009), Routledge
- Herbst, P. G., "Teaching geometry with problems : Negotiating instructional situations and mathematical tasks", Journal for Research in Mathematics Education, 37(4), pp.313~ (2006)
- Mammana, C., "Perspectives on the teaching of geometry for the 21st century" (1998), Kluwer
- National Council of Teachers of Mathematics, "Principles and standards for school mathematics" (2000), National Council of Teachers of Mathematics
- Schoenfeld, A. H., "When good teaching leads to bad results : The disasters of"well-taught"mathematics courses", Educational Psychologist, 23, pp.145~166 (1988)
- Van hiele levels and achievement in secondary school geometry, "Usiskin, Z.", CDASSG, ~ (1982)
- Waring, S., "Can you prove it? Developing concepts of proof in primary and secondary schools" (2000), Mathematical Association