The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
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A study on the understanding of limitations of experiential viewpoints for 9th grade students

증명에서 경험적 관점의 한계에 대한 중학교 3학년 학생들의 이해 연구

  • Received : 2014.12.31
  • Accepted : 2015.02.22
  • Published : 2015.02.28
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Abstract

The mathematical object is conceptual. Thus we can not prove the property of mathematical object in experimental viewpoint but in conceptual viewpoint. We performed the experiment for 28 middle school students to investigate whether they understand this. As a result, the majority of student didn't cognize the limit of experimental method. We had also individual interviews with four students. As results, one student was exactly cognizing the limit of experimental method, but he couldn't prove logically. The others didn't cognize the limit of experimental method. They thought that the proposition was already true regardless of the error. And one of them even thought that to be equal approximately was the same of to be equal exactly. Also, one student has confused between the experimental viewpoint and the conceptual viewpoint. This implies that it is necessary to help students understand the limit of experimental method.

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References

  1. 교육과학기술부 (2010a) 초등학교 수학 4-1. 서울: 두산동아.(The Ministry of Education, Science and Technology (2010a). Elementary school mathematics 4-1. Seoul: Dusandonga.)
  2. 교육과학기술부 (2010b) 초등학교 수학 4-2. 서울: 두산동아.(The Ministry of Education, Science and Technology (2010b). Elementary school mathematics 4-2. Seoul: Dusandonga)
  3. 교육과학기술부 (2011). 수학과 교육과정. 교육과학기술부 고시 제 2011-361호 [별책 8].(The Ministry of Education, Science and Technology(2011). Curriculum of mathematics department. Notification No. 2011-301 of the Ministry of Education, Science and Technology [the extra number 8])
  4. 김부윤, 정경미 (2007). 수학 교실에서 나타나는 극단적 교수 현상에 대한 고찰. 수학교육 논문집 21(3), 407-430.(Kim, B.Y., Jeong, K.M (2007). Review on the Extreme Didactic Phenomena in the Mathematical Class. Communications of Mathematics Education 21(3), 407-430.)
  5. 김양희 (2008). 기하증명과정에서 발생하는 오류 분석: 중학교 8-나 도형의 성질을 중심으로. 연세대학교 교육대학원 석사학위논문.(Kim, Y.H. (2008). A study on error patterns of middle school students in proof geometry : around the field of geometry at mathematics 8-second grade in middle school. Master's thesis, YSU.)
  6. 나귀수 (2011). 수학 영재 학생들의 발견과 증명에 대한 연구. 수학교육학연구 21(2), 105-120.(Na, G.S. (2011). Analysing the Processes of Discovery and Proof of the Mathematically Gifted Students. The Journal of Education Research in Mathematics, 21(2), 105-120.)
  7. 류성림 (1998). 전형식적 증명의 의의와 교수학적 의의에 관한 연구. 대한수학교육학회 논문집 8(1), 313-326.(Ryu, S.R. (1998). A study on the meaning of preformal proof and its didactical significance. Journal of the Korea Society of Educational Studies in Mathematics 8(1), 313-326.)
  8. 류성림, 정창현 (1993). 중학생의 기하 증명 능력과 오류에 대한 연구. 수학교육 32(2), 137-149.(Ryu, S.R, Jeong, C.H. (1993). A Study on Proof-Writing Abilities and Errors of Middle School Students in Geometry. The Mathematical Education 32(2), 137-149.)
  9. 이준열, 최부림, 김동재, 송영준, 윤상호, 황선미 (2009). 중학교 수학 2. 서울: 천재교육.(Lee, J.Y., Choi, B.R., Kim, D.J., Song, Y.J., Yoon, S.H., & Hwang, S.M. (2009). Middle school mathematics 2. Seoul: Chunjae education.)
  10. 이호철 (2007). 중학교 기하 증명과정에서 학생들이 보이는 오류분석: 8-나의 사각형의 성질중심으로. 단국대학교 교육대학원 석사학위논문.(Lee, H.C. (2007). A study on the analysis of errors in proof of middle school geometry. Master's thesis, DKU.)
  11. 장혜원 (1997). 수학 학습에서의 표현 및 표상에 관한 연구: 표상 모델 개발을 중심으로. 서울대학교 박사학위논문.(Chang, H.W. (1997). A Study on the Representations in Mathematics Learning - Focused on the Development of a Representation Model -. Doctoral dissertation, SNU.)
  12. 홍인선 (2002). 중학생의 기하 증명에 관한 의식과 증명과정의 오류 경향 연구: 제주도 중3 학생을 중심으로. 제주대학교 교육대학원 석사학위논문.(Hong, I.S. (2002). A Study on the Attitude about the Proof-writing and Error patterns of Middle school students in Geometry : around the 3rd year students of Middle School in Jejudo. Master's thesis, JJU.)
  13. 홍진곤, 권석일 (2004). 전형식적 증명의 교수학적 의미에 관한 고찰. 수학교육 43(4), 381-390.(Hong, J.G., Kwon, S.I. (2004). On the Didactical Meaning of Preformal Proofs. The Mathematical Education 43(4), 381-390.)
  14. Balacheff, N. (1988). Aspects of proof in pupil's practice of school mathematics. In D. Pimm(Ed.), Mathematics, teachers and children. London: The Open University, 216-235.
  15. Branford, B. (1908). A Study of Mathematical Education, Oxford: Clarendon Press.
  16. Blum, W., & Kirsch, K. (1991). Preformal Proving: Example and Reflections. Educational Studies in Mathematics, 22, 183-203. https://doi.org/10.1007/BF00555722
  17. Fischbein, E. (1993). The Theory of Figural Concepts, Educational Studies in Mathematics 24, 139-162. https://doi.org/10.1007/BF01273689
  18. Miyazaki, M. (2000). Levels of Proof in Lower Secondary School Mathematics, Educational Studies in Mathematics, 41, 47-68. https://doi.org/10.1023/A:1003956532587
  19. Semadeni, Z. (1984). Action Proof in Primary Mathematics Teaching and in Teacher Training. For the Learning of Mathematics, 4(1), 32-34.
  20. Skemp, R. R. (1987). The Psychology of Learning Mathematics. Lawrence Erlbaum Associates, Inc. New Jersey. 황우형 역 (1998). 수학학습심리학. 서울: 민음사.
  21. Van Hiele, P. M. (1986). Structure and insight - A theory of mathematics education, Academic press.