# 역사-발생적 접근을 통한 논증 기하 학습의 직관적 수준에 대한 고찰

• Published : 2003.06.01

#### Abstract

This study investigated tile intuitive level of justification in geometry, as the former step to the aximatization, with concrete examples. First, we analyze limitations that the axiomatic method has in tile context of discovery and the educational situation. This limitations can be supplemented by the proper use of the intuitive method. Then, using the histo-genetic analysis, this study shows the process of the development of geometrical thought consists of experimental, intuitive, and axiomatic steps. The intuitive method of proof which is free from the rigorous axiom has an advantage that can include the context of discovery. Finally, this paper presents the issue of intuitive proving that the three angles of an arbitrary triangle amount to 180$^{\circ}$, as an example of the local systematization.

#### References

1. 수학과 교육과정 교육부
2. 論證の意義の理解に關する發達的硏究 國宗進
3. 서울대학교 박사학위논문 증명의 본질과 지도 실제의 분석 나귀수
4. 수학교육 박성택
5. 중학교 수학 7-나 조태근(외)
6. 서울대학교 박사학위논문 증명의 구성요소 분석 및 학습-지도 방향 탐색 서동엽
7. 학교수학의 교육적 기초 우정호
8. 서울대학교 석사학위논문 대뇌반구의 기능분화를 고려한 수학 학습-지도에 관한 연구 유재근
9. 구장산술/주비산경 차종천(역)
10. 학교수학 1-1 중학교 수학에서 평행공리의 의미 최영기
11. Die Logik oder die Kunst des Denkens Arnauld
12. Developments in School Mathematics Education around the World - Proceedings of the UCSMP ICME v.2 A Study of Students' Proving Processes at the Junior High School Level Balacheff;Wirszup(ed.);Streit(ed.)
13. Proceedings of the 6th International Conference for PME Difficulties and Errors in Geometric Proofs by Grade 7 Pupils Becker;Vermandel(ed.)
14. A Study of Mathematical Education Branford
15. Arbeitsgemeinschaft f. Forschung des Landes Nordrhein-Westfalen v.Heft 7 Nicolas Bourbaki und die heutige Mathematik Cartan
16. American Scientist v.61 Should We Teach 'Modern Mathematics'? Dieudonne
17. For the Learning of Mathematics v.3 no.2 Intuition and Proof Fischbein
18. Educational Studies in Mathematics v.12 no.1 Aspects of Proving: A Clinical Investigation of Process Galbraith
19. Euclidean & Non-Euclidean Geometries Greenberg
20. The thirteen books of Euclid`s Elements with introduction and commentary Heath
21. Using History to Teach Mathematics - An International Perspective Euclid vs. Lin Hui; A Pedagogical Reflection Horng;Katz(ed.)
22. 數學敎育學의 觀點 A Study on Intuition in Mathematics Education Koyama
23. Educational Studies in Mathematics v.27 Making the Transition to Formal Proof Moore
24. Using History to Teach Mathematics - An International Perspective Mesopotamian Mathematics; Some Historical Background Robson;Katz(ed.)
25. Educational Studies in Mathematics v.22 On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin Sfard
26. Using History to Teach Mathematics - An International Perspective An Excursion in Ancient Chinese Mathematics Siu;Katz(ed.)
27. A History of the Teaching of Elementary Geometry Stamper
28. For the Learning of Mathematics v.8 no.3 Two Kinds of 'Elements' and the Dialectic between Synthetic-deductive and Analytic-genetic Approaches in Mathematics Steiner
29. American Scientist v.59 Modern' Mathematics: An Educational and Philosophic Error? Thom