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학생중심의 문제해결 모형 개발 및 효과 분석

Development and Analysis of Effect for Problem Solving Model of Student-based

  • Jung, Chan Sik (Myeongseok Elementary School) ;
  • Roh, Eun Hwan (Department of Mathematics Education, Chinju National University of Education)
  • 투고 : 2014.03.16
  • 심사 : 2014.04.10
  • 발행 : 2014.04.30

초록

학교수학에 있어 문제해결은 오래전부터 강조되어 오고 있으며, 학생들의 문제해결력 신장을 위해 다양하고 많은 연구들이 진행되고 있다. 하지만 이러한 연구와 노력에도 불구하고 수학에 대한 학생들의 수준차는 초등학교 입학 후 얼마 지나지 않아 나타나기 시작한다. 학생들은 소극적이며 무언가에 의존하려 하며, 실패한 일에 대해서는 발전의 메커니즘을 적용하지 못하고, 문제해결의 주체는 문제를 해결하는 학생 본인이어야 함에도 불구하고 교사는 문제해결을 돕는다는 명목 하에 자꾸만 개입하게 된다. 본 연구에서는 다른 사람이나 어떤 것의 도움 없이 학생 스스로 해결하여야 한다는 것을 기본 전제로 학생중심의 문제해결 모형을 개발하고 이에 대한 효과성을 검토하고 논의함으로써 문제해결을 원하는 학생과 교사 모두에게 문제해결에 대한 새로운 접근의 필요성을 인식시키는 계기를 마련하고자 하였다.

Problem Solving has been emphasized for recent decades, and many research case studies have been used to improve students' Problem Solving abilities. However, the gap of students' abilities can be easily shown after enrollment into school in spite of scholar's attempt to reduce students' level of differentiation. Besides, it is clear that teachers have been too readily assisting students' and not allowing them to acquire the process of Problem Solving, and this may be due to impatience. Therefore, students seem to show signs of the dependent tendency towards teachers and other materials. This tendency easily allows students' to depend on teaching resources without attempting any developmental mechanism of Problem Solving. The presupposition of this study is that every student must solve a problem without any assistance, and also this study is to provide new cognitive strategies for both teachers and students who want to solve their problems by themselves through the process of visible Problem Solving. After applying the student-based problem-solving model by this study, it was found to be effective. Therefore this will lead to the improvement of the Problem Solving and knowledge acquisition of students.

키워드

참고문헌

  1. 강문봉 (1997). 의식화가 수반된 문제해결 수업 모형. 대한수학교육학회 논문집, 7(1), 133-143.(Kang, M. B. (2008). The instructional models for developing mathematical problem solving abilities and consciousness. Journal of Educational Research in Mathematics, 7(1), 133-143.)
  2. 교육과학기술부 (2008). 초등학교 교육과정 해설(IV) 수학, 과학, 실과. 광주: 한솔사.(Ministry of Education, Science and Technology (2008). Elementary school curriculum manual IV: Mathematics, Science, Practical Course. Gwangju: Hansol Press.)
  3. 김부윤.이영숙 (2003). 우리나라에서의 수학적 문제 해결연구. 한국수학교육학회지 시리즈 A <수학교육>, 42(2), 137-157.(Kim, B. Y. & Lee, Y. S. (2003). A Study of Mathematical Problem Solving in Korea. Journal of the Korean Society of Mathematical Educational Series A, , 42(2), 137-157.)
  4. 김연식.허혜자 (1995). 수학불안 요인에 관한 연구. 대한수학교육학회 논문집, 5(2), 111-128.(Kim, Y. S. & Heo, H. J. (1995). A Study on Antecedents of Mathematics Anxiety in High School Students. Journal of Educational Research in Mathematics, 5(2), 111-157.)
  5. 김영채 (1999). 창의적 문제해결 : 창의력의 이론, 개발과 수업. 서울: 교육과학사.(Kim, Y. C. (1999). Creative Problem Solving : Theory of creativity, development and teaching. Seoul: Kyoyookbook Publishers.)
  6. 김진호.김인경 (2011). 수학적 문제 해결 연구에 있어서 미래 연구 주제 : 델파이 기법. 한국수학교육학회지 시리즈 C <초등수학교육>, 14(2), 187-206.(Kim, J. H. & Kim, I. K. (2011). Future Research Topics in the Field of Mathematical Problem Solving: U sing Delphi Method. Journal of the Korean Society of Mathematical Educational Series C, , 14(2), 187-206.)
  7. 신현성.김경희 (1999). 수학적 문제해결 . 서울. 경문사.(Sin, H. S. & Kim, K. H. (1999). Mathematical problem solving. Seoul: Kyungmoon Publishers.)
  8. 이종희.김기연 (2008). 창의적 하위 요소 탐색 및 수학영재의 창의적 문제해결 모델 개발. 대한수학교육학회지 <학교수학>, 10(4), 583-601.(Lee, C. H. & Kim, K. Y. (2008). A Case study on the Effects of Mathematically Gifted Creative Problem Solving Model in Mathematics Learnings for Ordinary students. Journal of Korea Society of Educational Studies in Mathematics, , 10(4), 583-601.)
  9. 정은실 (1995). Polya의 수학적 발견술 연구. 서울대학교대학원 교육학 박사학위 논문.(Jeong, E. S. (1995). A Study on Polya's Mathematical Heuristics. Ph.D. thesis, Seoul National University of Education.)
  10. 정찬식.노은환 (2009). 수학영재아의 문제해결 과정에 따른 사례 연구. 한국수학교육학회지 시리즈 A <수학교육> , 48(4), 455-467.(Jung, C. S. & Roh, E. H. (2009). Case Study : An analysis on Problem Solving Processes of Gifted Math Students. Journal of the Korean Society of Mathematical Educational Series A, , 48(4), 455-467.)
  11. 전평국.정인수 (2003). 수학적 문제해결 지도에서 교사의 역할에 대한 분석. 한국수학교육학회지 시리즈 C <초등수학교육>, 7(1), 1-14.(Jeon, P. G. & Jeong, I. S. (2003). An Analysis on Teachers' Role in Teaching Mathematical Problem Solving. Journal of the Korean Society of Mathematical Educational Series C, , 7(1), 1-14.)
  12. 片桐重男 (1988). 이용율.성현경.정동권.박영배 공역(1997). 수학적인 생각.태도와 그 지도I-수학적인 생각의 구체화. 서울: 경문사.(片桐重男 (1988). Lee, Y. Y.; Seong, H. G.; Jeong, D. G. & Park, Y. B. Common Translation (1997). Mathematical thinking attitude and the teaching I-Specification of mathematical thinking. Seoul: Kyungmoon Publishers.)
  13. 한국교육개발원 (1985). 수학과 문제해결력 신장을 위한 수업방법 개선 연구. 한국교육개발원 연구보고 RR 85-9.(Korean Education Development Institute (1985). Problem Solving Ability for Mathematics Improvement of teaching methods. KEDI, RR 85-9.)
  14. 한인기.꼴랴긴 (2006). 문제해결의 이론과 실제. 서울: 승산.(Han, I. K. & Yu.M. Kolyagin (2006). Theory and practice of problem solving. Seoul: Seungsan Publishers.)
  15. Burton, L. (1984). Thinking things through problem solving in mathematics. Basil Backwel Limited : 24-27.
  16. Charles, R. I. & Lester, F. K. (1982). Teaching problem solving : what why & how. CA: Dale Seymour Publications.
  17. English, L. & Sriraman, B. (2010). Problem solving for the 21st century. In b. Srirman & L. English (Eds.), Theories of mathematics education (pp. 263-290). New York, NY: Springer.
  18. Hatfield, L. L. (1978). Mathematical Problem Solving, Geogia Center for the Study of Learning and Teaching Mathematics.
  19. Kilpatrick, J. (1985). "Reflection and recursion", Educational studies in Mathematics, 16 : 1-26.
  20. Krulik, S. E. & Rudnick, J. A. (1984). A Sourcebook for teaching problem solving. Boston : Allyn and Bacon, Inc.
  21. Krulik, S. E. & Rudnick, J. A. (1987). Problem solving : A handbook for teachers. Boston : Allyn and Bacon, Inc.
  22. Lester, F. K. (1980). "Research on Mathematical Problem Solving" In: Richard Schumway(Ed.), Research in Mathematics Education : 286-323. Reston, Va., National Council of Teachers Mathematics.
  23. Lester, F. K. (1994). "Musings about mathematical problem-solving research : 1970-1994, Journal for Research in Mathematics Education 25(6) : 660-675. https://doi.org/10.2307/749578
  24. Lester, F. K. & Kehle, P. E. (2003). From problem solving to modeling: The evolution of thinking about research on complex mathematical activity. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 501-518). Mahwah, NJ: Lawrence Erlbaum Associates.
  25. National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA : NCTM.
  26. National Council of Teacher of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.(류희찬.조완영.이경화.나귀수.김남균.방정숙 공역. 2007. 학교수학을 위한 원리와 규준. 서울: 경문사.)
  27. Philip J. Davis.Reuben Hersh. (1981). The Mathematical Experience(양영오.허빈 공역. 1995. 수학적 경험. 서울: 경문사.)
  28. Polya, G. (1945). How to Solve It: A New Aspect of Mathematical Method. Princeton and Oxford: Princeton University Press.(우정호 역. 2008. 어떻게 문제를 풀 것인가?-수학적 사고 방법, 서울: 교우사.)
  29. Polya, G. (1971). Mathematical Discovery, Vol.I, John Wiley & Som, Inc.(우정호.정영옥.박경미.이경화.김남희.나귀수.임재훈 공역. 2005. 수학적발견(I), 서울: 경문사.)
  30. Schoenfeld, A. H. (1985). Mathematical Problem Solving. New York: Academic Press, Inc.
  31. Schoenfeld, A. H. (1988). The Teaching and Assessing of Mathematical Problem Solving, Vol.3, NCTM : 82-92.
  32. Schoenfeld, A. H. (1992). Learning to think mathematically. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.334-370). New York, NY: Macmillan Publishing Co.
  33. Schoenfeld, A. H. (2007). Problem solving in the United States, 1970-2008: Research and theory, practice and politics. ZDM Mathematics Education, 39(5-6), 537-551. https://doi.org/10.1007/s11858-007-0038-z
  34. Schroeder, T. L. & Lester, F. K. (1989). Developing understanding in mathematical via problem solving. In P. R. Trafton, A. P. Shulte(Ed.) New directions for elementary school mathematics, NCTM : 31-42.
  35. Skemp, R. R. (1987). The Psychology Learning Mathematics. Lawreence Erlbaum Associates, Inc.(황우형 역. 2008. 수학학습 심리학, 서울: (주)사이언스북스.)

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