한국수학교육학회지시리즈A:수학교육 (The Mathematical Education)

  • 제55권1호
  • /
  • Pages.73-89
  • /
  • 2016
  • /
  • 1225-1380(pISSN)
  • /
  • 2287-9633(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지
DOI QR코드

DOI QR Code

중학생들의 수학적 문제제기 유형과 전략 분석

The analysis of middle school students' problem posing types and strategies

  • 투고 : 2015.07.20
  • 심사 : 2016.02.19
  • 발행 : 2016.02.28
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The purpose of this study was to analyze middle school students' problem posing types and strategies. we analyzed problems posed by 120 middle school students during mathematics class focused on problem posing activities in various aspects. Students' posed problems were classified into five types: not a problem(NP), non-math(NM), impossible(IM), insufficient(IN), sufficient(SU) and each of the posed problems. Students used three kinds of problem posing strategies such as goal manipulation(GM), assumption manipulation(AM), and condition manipulation(CM), and in posing one problem, one or more than two strategies were used. According to the prior studies, problem posing can contributes to the development of students' problem solving ability, creativity, mathematical aptitude, and a broader understanding of mathematical concepts. However, we found that some students had difficulties in posing problems or limited understandings of that. We hope the results of the study contribute to encouraging problem posing activities in mathematics instruction.

키워드

참고문헌

  1. 교육과학기술부 (2011). 수학과 교육과정. 서울: 교육과학기술부.(The Ministry of Education, Science and Technology (2011). Curriculum of mathematics department. Seoul: Ministry of Education, Science and Technology.)
  2. 도종훈 (2007). 학교수학에서 추측과 문제제기 중심의 수학적 탐구 활동 설계하기. 수학교육 46(1), 69-79.(Do, J. (2007). Designing mathematical activities centered on conjecture and problem posing in school mathematics. The Mathematical Education 46(1), 69-79.)
  3. 박미미, 이동환, 이경화, 고은성 (2012). 유추에 의한 문제제기 활동을 통해 본 통계적 개념 이해. 수학교육학연구 22(1), 101-115.(Park, M., Lee, D., Lee, K., & Ko, E. (2012). Understanding of statistical concepts examined through problem posing by analogy. The Journal of Education Research in Mathematics 22(1), 101-115.)
  4. 성태제, 시기자 (2006). 연구방법론. 서울: 학지사(Seong, T. J., & Si, K. J. (2006). Research methods. Seoul: Hakjisa.)
  5. 이상원 (2005). 문제제기 수업이 수학 문제해결력과 창의력에 미치는 효과. 수학교육 44(3), 361-374.(Lee, S. (2005). The effect of problem posing teaching on mathematical problem-solving ability and creativity. The Mathematical Education 44(3), 361-374.)
  6. 전미라, 허혜자 (1998). 문제제기 전략을 강조한 수업과 학업성취도와의 관계분석: 방정식을 중심으로. 대한수학교육학회 논문집 8(2), 709-722.(Jeon, M. & Heo, H. (1998). A study of the effects of problem posing strategies on mathematics achievement. Journal of the Korea society of Educational Studies in Mathematics 8(2), 709-722.)
  7. 한옥동, 박혜숙 (1997). 수학과 학습에의 문제제기 이론의 적용 효과 분석. 수학교육 36(1), 77-87.(Han, O. & Park, H. (1997). Analysis on the application effect of problem-posing in mathematics learning. The Mathematical Education 36(1), 77-87.)
  8. 한혜숙, 주홍연 (2014). 문제제기와 수학수업. 황혜정, 김진호, 고호경, 서보억(편저), 수학학습 지도 원리와 적용 (pp. 53-74). 서울: 경문사.(Han, H. & Joo, H. (2014). Problem posing and mathematics teaching. In H. Hwang, J. Kim, H. Ko, & B. Seo (Eds.), Principles and practice for teaching and learning mathematics (pp. 53-74). Seoul: Kyungmoonsa.)
  9. Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics 83(1), 37-55. https://doi.org/10.1007/s10649-012-9441-7
  10. Brown, S. I., & Walter, M. I. (1990). The art of problem posing. Hillsdale, NJ: Lawrence Erlbaum Associates.
  11. Cai, J., & Cifarelli, V. (2005). Exploring mathematical exploration: How do two college students formulate and solve their own mathematical problems?. Focus on Learning Problems in Mathematics 27(3), 43-72.
  12. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students' mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
  13. Dillon, J. T. (1982). Problem finding and solving. Journal of Creative Behaviour 16, 97-111. https://doi.org/10.1002/j.2162-6057.1982.tb00326.x
  14. Duncker, K., & Lees, L. S. (1945). On problem-solving. Psychological monographs, 58(5), i.
  15. Ellerton, N. F. (1986). Children's made-up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics 17, 261-271. https://doi.org/10.1007/BF00305073
  16. Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching. In A. J. Bishop, K. Clements, C. Keitel, J. Kilparick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 987-1053). Netherlands: Kluwer Academic Publishers.
  17. English, L. D. (1997). The development of fifth-grade children's problem abilities. Educational Studies in Mathematics 34, 183-217. https://doi.org/10.1023/A:1002963618035
  18. English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education 29(1), 83-106. https://doi.org/10.2307/749719
  19. Freudenthal, H. (1973). Mathematical as an educational task. Dordrecht: D. Reidel Publishing Company.
  20. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Hillsdale: Lawrence Erlbaum Associates.
  21. Leung, S. S. (1993). Mathematical Problem Solving: The influence of task formats, mathematics knowledge, and creative thinking. In I. Hirabayashi, N. Nohda, K. Shigematsu, & F. Lin (Eds.), Proceedings of the 17th International conference for the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 33-40). Tsukuba, Japan.
  22. Leung, S. S. (1996). Problem posing as assessment: Reflections and reconstructions. The Mathematics Educator 1(2), 159-171.
  23. Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralblatt fur Didaktik der Mathematik 97(3), 81-85.
  24. Leung, S. S. (2013). Teachers implementing mathematical problem posing in the classroom: Challenges and strategies. Educational Studies in Mathematics 83(1), 103-116. https://doi.org/10.1007/s10649-012-9436-4
  25. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  26. Polya, G. (1954). Mathematics and plausible reasoning (2 vols). Princeton, NJ: Princeton University Press.
  27. Polya, G. (1957). How to solve it (2nd ed.). New York: Doubleday.
  28. Rosenshine, B., Meister, C., & Chapman, S. (1996). Teaching students to generate questions: A review of the intervention studies. Review of Educational Research 66(2), 181-221. https://doi.org/10.3102/00346543066002181
  29. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics 14(1), 19-28.
  30. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt fur Didaktik der Mathematik 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
  31. Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1990). Thinking through mathematics: Fostering inquiry and communication in mathematics classrooms. New York: The College Board.
  32. Silver, E. A., Mamona-Downs, J., Leung, S., & Kenney, P. A. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education 27(3), 293-309. https://doi.org/10.2307/749366
  33. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Melbourne: Mathematics Education Research Group of Australasia.
  34. Torrance, E. P. (1966). Torrance tests of creative thinking. Princeton: Personal Press.
  35. Yuan, X., & Sriraman, B. (2010). An exploratory study of relationships between students' creativity and mathematical problem posing abilities. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5-28). Rotterdam: Sense Publishers.

피인용 문헌

  1. 수학적 문제제기 활동을 반영한 수업이 고등학교 1학년 학생들의 수학 학업 성취도 및 수학 교과에 대한 정의적 특성에 미치는 영향 vol.32, pp.3, 2016, https://doi.org/10.7468/jksmee.2018.32.3.385