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기하 증명에서 중학생들의 시각의존적 비약 인식에 대한 연구

A Study on Secondary School Student's Recognition of Vision-dependent Jump in the Geometry Proof

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주제분류수학

초록

Although a figure expression has a role of mediator in the geometry proof, it is not admitted to prove based on a vision-dependent feature. This study starts from the problem that although a figure expression has an important role in the geometry proof, a lot of students don't understand the limit of vision-dependent feature in the figure expression. We will investigate this problem to understand cognitive characteristic of students. Moreover, we try to get the didactical implications. To do this, we investigate the cognitive ability for a limit of vision-dependent feature, targeting a class of middle school seniors And we will have a personal interview with four students who show a lack of sense of limit of vision-dependent feature in the figure expression and two students for who it is difficult to judge that they don't understand the limit of vision-dependent feature in the figure expression. We will observe and analyzed the cognitive characteristic of six students. Based on the analysis, we will finally discuss on the didactical implications to help students understand the limit of vision-dependent feature in the figure expression.

Abstract

Although a figure expression has a role of mediator in the geometry proof, it is not admitted to prove based on a vision-dependent feature. This study starts from the problem that although a figure expression has an important role in the geometry proof, a lot of students don't understand the limit of vision-dependent feature in the figure expression. We will investigate this problem to understand cognitive characteristic of students. Moreover, we try to get the didactical implications. To do this, we investigate the cognitive ability for a limit of vision-dependent feature, targeting a class of middle school seniors And we will have a personal interview with four students who show a lack of sense of limit of vision-dependent feature in the figure expression and two students for who it is difficult to judge that they don't understand the limit of vision-dependent feature in the figure expression. We will observe and analyzed the cognitive characteristic of six students. Based on the analysis, we will finally discuss on the didactical implications to help students understand the limit of vision-dependent feature in the figure expression.

참고문헌 (14)

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  2. 柳成林, "중학생의 幾何 證明 能力과 誤謬에 대한 연구", 석사, 수학교육학, pp.1994
  3. 류성림, "수학교육에서 ‘증명의 의의’에 관한 연구", 한국수학교육학회지 시리즈 A <수학교육>, 37(1), pp.73~85 (1998)
  4. 서동엽, "증명의 구성요소 분석 및 학습지도방향 탐색 : 중학교 수학을 중심으로", 박사, 수학교육, pp.1999
  5. 이준열, "중학교 수학 2" (2009), 천재교육
  6. Dreyfus, T., "Learning and Teaching Geometry, K - 12 - NCTM 1987 Yearbook" (1987), NCTM
  7. Duval, R., "Perspectives on the teaching of geometry for the 21th Century" (1998), Kluwer
  8. Fischbein, E., "Proof and certitude in the development of mathematical thinking", Proceedings of the Sixth International Conference for the Psychology of Mathematical Education, pp.128~136 (1982), PME
  9. Hershkowitz, R., "Children's Concept in Elementary Geometry - a reflection of teacher's concepts?", 8th Conference of the International Group for Psychology of Mathematics Education, pp.63~70 (1984)
  10. Martin, W. G., "Proof Frames of Preservice Elementary Teachers", Journal for Research in Mathematics Education, 20(1), pp.41~51 (1989)
  11. Mesquita, A. L., "On the Utilization of Non-standard Representations in Geometrical Problems", 18th Conference of the International Group for Psychology of Mathematics Education, pp.271~278 (1994)
  12. Parzysz, B., "Representation of Space and Students' Conceptions at High School Level", Educational Studies in Mathematics, 22, pp.575~593 (1991)
  13. Williams, E., "An Investigation of Senior High School Students' Understanding of the Nature of Mathematical Proof", Journal for Research in Mathematics Education, 11(3), pp.165~176 (1990)
  14. Zazkis, R., "Sets, Subsets and the Empty set: Students' Constructions and Mathematical Convertions", J I of Computers in Mathematics and Science Teaching, 16(1), pp.133~169 (1997)

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