DOI QR코드

DOI QR Code

수학적 문제 해결 연구에 있어서 미래 연구 주제: 델파이 기법

Future Research Topics in the Field of Mathematical Problem Solving: Using Delphi Method

  • Kim, Jin-Ho (Department of Mathematics Education, Daegu National University of Education) ;
  • Kim, In-Kyung (Department of Mathematics Education, College of Education, Cheongju University)
  • 투고 : 2011.07.25
  • 심사 : 2011.08.26
  • 발행 : 2011.08.31

초록

1980년대 이후로 현재까지 수학적 문제해결은 수학교육학의 주요 연구 주제 중의 하나로 자리매김하고 있다. 초창기에는 문제 그 자체에 대한 연구, 학습자들이 문제를 해결하는 방법 및 메타인지에 대한 연구, 교수학습 방법에 대한 연구 등 다양한 방법에서 연구가 진행되었으며, 최근 들어서는 문제해결을 통한 수학교육 및 모델링을 통한 문제해결이 연구자들의 관심을 끌고 있다. 이처럼 문제해결과 관련된 연구주제들은 변하면서도 지속적으로 연구자들의 관심을 끌고 있다. 따라서, 수학적 문제해결 영역에서 미래에 어떤 주제들이 더 연구될 필요가 있는지를 델파이를 기법을 통해서 알아보았다.

Mathematical problem solving have placed as one of the important research topics which many researcher have been interested in from 1980's until now. A variety of topics have been researched: Characteries of problem; Processes of how learners to solve them and their metaoognition; Teaching and learning practices. Recently, the topics have been shifted to mathematical learning through problem solving and the connection of problem solving and modeling. In the field of mathematical problem solving where researcher have continuously been interested in, future research topics in this domain are investigated using delphi method.

키워드

참고문헌

  1. 강옥기, 신성균, 강완, 류희찬, 정은실, 박교식, 우정호(1985), 수학과 문제해결력 신장을 위한 수업 방법 개선 연구. 한국교육개발원 연구보고 RR 85-9.
  2. 강옥기, 정은실, 박교식, 강문봉 (1989). 수학적 사고력 신장 프로그램 개발을 위한 방안 탐색: 초등학교 산수과를 중심으로. 한국교육개발원 연구보고 RM 89-11.
  3. 교육과학기술부 (2007). 초등학교 교육과정 해설 총론. 서울: 대한교과서 주식회사.
  4. 교육과학기술부 (2009). 초등학교 교육과정 해설 총론. 서울: 교육과학기술부.
  5. 교육과학기술부 (2010). 수학 4-1: 교사용지도서. 서울: 두산동아(주).
  6. 교육부 (1997). 제7차 교육과정 해설 총론. 서울: 대한교과서 주식회사.
  7. 교육부 (1989). 수학 4-1. 서울: 교육부.
  8. 구광조, 전평국, 강완 (1996). 수학교육 개혁 방안에 관한 연구. 한국교원대학교 교과교육공동연구소, 연구보고 RR 94-1.
  9. 권정은, 최재호 (2008). 우리나라 초등수학교육 연구의 동향 분석. 한국초등수학교육학회지, 12(2), 149-163.
  10. 길양숙 (1991). 문제 해결 전략 지도에 관한 연구 동향. 교육학연구, 29(4), 94-109.
  11. 김진락 (1992). 수학과 교육과정의 개발과 체제에 관한연구. 한국교원대학교 미간행 박사학위논문.
  12. 김진숙 (1997). 초등학교 수학교과서 문장제에 대한 문제해결 관점에서의 연구. 이화여자대학교 미간행 박사학위논문.
  13. 김진호 (2010). 모든 학습자가 수학수업에 참여하는 교수.학습 행위. 초등수학교육, 13(1), 13-24.
  14. 류성림, 최창우, 남승인, 김상룡, 최재호, 김진호 (2011). 수학 문제해결 교육 어떻게 할 것인가. 서울: 양서원.
  15. 류희찬, 권성룡, 김남균 (2005). 현행 수학 교과서와 미국의 개혁 교과서의 비교 분석: 모델링과 테크놀로지를 중심으로. 교과교육 활성화 방안 연구, 4(3), 891-992.
  16. 박교식 (1996). 우리나라 초등학교의 수학 교수 . 학습에서 볼 수 있는 몇 가지 특징. 수학교육학연구, 6(2), 99-113.
  17. 박교식 (2001). 제7차 초등학교 수학과 교육과정에서의 문제해결 관련 내용의 분석. 학교수학, 3(1), 1-23.
  18. 박교식 (2005). 한국수학교육학: 논문 해제 III. 서울:경문사.
  19. 방승진, 이상원, 황동주 (2002). 초등학교 수학 문제해결 교육에 관한 연구. 수학교육논문집, 14, 1-25.
  20. 방정숙, 김상화 (2006). 문제해결과 관련된 제7차 초등학교 수학과 교육과정 및 교과용 도서 분석. 학교수학, 8(3), 341-364.
  21. 백석윤 (1993). 수학 문제해결 교육과 연구에 대한 반성적 일고. 대한수학교육학회 논문집, 3(2), 59-68.
  22. 성인서 (1987). 교사, 학생이 수학문제 해결에서 사용하는 전략에 관한 연구. 수학교육, 26(1), 11-19.
  23. 소경희 (2000). 우리나라 교육과정 개정에 있어서 총론과 각론의 괴리 문제에 대한 고찰. 교육과정연구, 18(1), 201-218.
  24. 신성균, 강문봉, 황혜정 (1993). 수학과 문제해결력 신장을 위한 교수-학습 자료 개발 연구. 한국교육개발원 연구보고 RR 93-13.
  25. 양인환 (1991). 수학적 문제해결에서의 소집단활동의 인지적 효과 분석. 한국교원대학교 미간행 박사학위논문.
  26. 이부다, 김진호 (2010). 구성주의 지식관이란 관점에서 초등학교 수학교과서 분석. 한국학교수학회논문집, 13(3), 415-442.
  27. 이종성 (2001). 델파이 방법. 서울: 교육과학사.
  28. 정인수 (2003). 수학적 문제해결 지도에서 교사의 역할에 대한 분석. 한국교원대학교 미간행 석사학위논문.
  29. 조경원, 김경자, 노선숙 (2000). 창조적 지식기반사회의 교육과정 개발 연구를 위한 초.중등학교 교육과정 실태조사. 교육과학연구, 31(2), 1-530.
  30. 황치홍 (2001). 수학교육에서 문제해결의 교육과 연구 경향의 분석. 서울교육대학교 미간행 석사학위논문.
  31. 황혜정 (2007). 수학적 모델링의 이해. 학교수학, 9(1), 65-97.
  32. Anderson, J. R. (1976). Language, memory, and thought. Hillsdale, NJ: Lawrence Erlbaum Associates.
  33. Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93(4), 373-397. https://doi.org/10.1086/461730
  34. Baroody, A. (1993). Problem solving, reasoning and communication. New York, NY: Merrill.
  35. Baroody, A. (1998). Fostering children's mathematical power. Mahwah, NJ: Lawrence Erlbaum Associates.
  36. Branca, N. A. (1980). Problem solving as a goal, process, and basic skill. In S. Krulik, & R. E. Reys (Eds.), Problem solving in school mathematics (pp. 3-8). Reston, VA: NCTM Press.
  37. Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.)(2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.
  38. Burns, M. & Wickett, M. (2001). Lessons for extending multiplication to grades 4-5. Sausalito, CA: Math Solutions Publication.
  39. Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In F. Lester & R. Charles (Eds.), Teaching mathematics through problem solving (pp. 241-253). Reston, VA: NCTM Press.
  40. Cai, J. (2010). Commentary on problem solving heuristics, affect, and discrete mathematics: A representational discussion. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 251-258). New York, NY: Springer.
  41. Chi, T., Feltovich, P., Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5(2), 121-152. https://doi.org/10.1207/s15516709cog0502_2
  42. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in education research. Educational Researcher, 32(1), 9-13. https://doi.org/10.3102/0013189X032001009
  43. Custer, R. L., Scarcella, J. A., & Stewart, B. R. (1999). The modified Delphi technique: A rotational modification. Journal of Vocational and Technical Education, 15(2), 1-10.
  44. English, L., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 263-290). New York, NY: Springer.
  45. Gainsburg, J. (2006). The mathematical modeling of structural engineers. Mathematical Thinking and Learning, 8(1), 3-36. https://doi.org/10.1207/s15327833mtl0801_2
  46. Garofalo, J., & Lester, F. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163-176. https://doi.org/10.2307/748391
  47. Gok, T. (2010). The general assessment of problem solving processes and metacognition in physics education. Eurasian Journal of Physics and Chemistry Education, 2(2), 110-122.
  48. Goldin, G. A., & McClintock, C. E. (1979/1984). Task variables in mathematical problem solving. Philadelphia, PA: Franklin Institute Press.
  49. Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307. https://doi.org/10.1016/S0959-4752(97)00006-6
  50. Hamilton, E. (2007). What changes are needed in the kind of problem solving situations where mathematical thinking is needed beyond school? In R. Lesh, E. Hamilton, & J. Kaput (Eds.), Foundations for the future in mathematics education (pp. 1-6). Mahwah, NJ: Lawrence Erlbaum Associates.
  51. Hiebert, J., Thomas P., Carpenter, E., Fennema, K., Fuson, P., et al. (1996). Problem solving as a basis for reform in curriculum and instruction: the case of mathematics. Educational Researcher, 25(4), 12–21. https://doi.org/10.3102/0013189X025004012
  52. Hino, K. (2007). Toward the problem-centered classroom: Trends in mathematical problem solving in Japan. ZDM Mathematics Education, 39(5-6), 503-514. https://doi.org/10.1007/s11858-007-0052-1
  53. Hsu, C., & Sandford, B. (2007). The Delphi technique: Making sense of consensus. Practical Assessment, Research & Evaluation, 12(10), 1-7.
  54. Kamii, C. (1994). Young children continue to reinvent arithmetic: 3rd grade. New York: Teachers College Press
  55. Kaplan, L. M. (1971). The use of the Delphi method in organizational communication: A Case study. Unpublished master's thesis, The Ohio State University, Columbus.
  56. Kilpatrick, J. (1969). Problem solving and creative behavior in mathematics. In J. W. Wilson & L. R. Carey (Eds.), Reviews of recent research in mathematics education. Studies in Mathematics Series, Vol. 19 (pp. 153-187). Stanford, CA: School Mathematics Study Group.
  57. Kilpatrick, J. (1985). A retrospective account of the past 25 years of research on teaching mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (1-15). Hillsdale, NJ: Lawrence Erlbaum.
  58. Kim, J. (2002). Analysis of strategies for problem solving presented in elementary school mathematics textbooks. 학교수학, 4(4), 565-580.
  59. Krulik, S., & Rudnick, J. A. (1995). The new sourcebook for teaching reasoning and problem solving in elementary school. Boston: Allyn and Bacon.
  60. Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. Chicago: University of Chicago Press.
  61. Lesh, R. E. (2010). New directions for research on mathematical problem solving. http://www.merga. net.au/documents/keynote32006.pdf.
  62. 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
  63. Lester, F. K. (Eds.) (2003). Teaching mathematics through problem solving. Reston, VA: NCTM Press.
  64. 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.
  65. Levin, H. (1976). Educational reform: Its learning? In M. Carnoy & H. M. Levin (Eds.), The limits of educational reform (pp. 23-51). New York: Longman.
  66. Lindquist, M. M. (1989). It's time to change. In P. R. Trafton, & A. P. Shulte (Eds.), New directions for elementary school mathematics (pp. 1-13). Reston, VA: NCTM Press.
  67. Ludwig, B. (1997). Predicting the future: Have you considered using the Delphi methodology? Journal of Extension, 35(5), 1-4.
  68. Mayer, R. E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, 26(1-2), 49-63.
  69. Mayer, R. E., & Wittrock, M. C. (2006). Problem solving. In P. A. Alexander and P. H. Winne (Eds.), Handbook of educational psychology (2nd Ed.) (pp. 287-303). Mahwah, NJ: Lawrence Erlbaum Associaties.
  70. NCTM (1980a). Problem solving in school mathematics. Reston, VA: The Author.
  71. NCTM (1980b). An agenda for action: Recommendations for school mathematics of the 1980s. Reston, VA: The Author.
  72. NCTM (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: The Author.
  73. NCTM (2000). Principles and standards for school mathematics. Reston, VA: The Author
  74. Phi Delta Kappa (1984). Handbook for conducting future studies in education. Blppmington, IN: The Author.
  75. Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
  76. Polya, G. (1954). Mathematics and plausible reasoning. Princeton, NJ: Princeton University Press.
  77. Polya, G. (1981). Mathematical discovery. New York: Wiley.
  78. Schoen, H. L., & Charles, R. I. (Eds.) (2003). Teaching mathematics through problem solving: 6-12. Reston, VA: NCTM Press.
  79. Schoenfeld, A. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
  80. Schoenfeld, A. (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.
  81. Schoenfeld, A. (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
  82. Schoenfeld, A. H. (2006). Mathematics teaching and learning. In: P. A. Alexander, & P. H. Winne (Eds.), Handbook of educational psychology (2nd edition) (pp. 479–510). Mahwah, NJ: Erlbaum.
  83. Schroeder T. L., & Lester, F. K. (1989). Developing understanding in mathematics via problem solving. In P. R. Trafton, & A. P. Shulte (Eds.), New directions for elementary school mathematics (pp. 31-42). Reston, VA: NCTM Press.
  84. Senk, S., & Thompson, D. (Eds.). (2003). Standards -oriented school mathematics curricula. Mahwah, NJ: Erlbaum.
  85. Silver, E. (1985). Research on teaching mathematical problem solving. In E. A. Schoenfeld (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247-295). Hillsdale, NJ: Lawrence Erlbaum Associates.
  86. Silver, E. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
  87. Simon, H. A., & Newell, A. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.
  88. Skemp, R. R. (1987). The psychology of learning mathematics. London: Penguin Books.
  89. Stacy, K. (2007). Trends in researching and teaching problem solving in school mathematics in Australia: 1997-2000. In E. Pdhkonen (Ed.), Problem solving around the world (pp. 45-53). University of Turku, Finland
  90. Wickett, M., Ohanina, S., & Burns, M. (2002). Lessons for introducing division: Grades 3-4. Sausalito, CA: Math Solutions Publication.
  91. Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties? Learning and Instruction, 7(4), 329-338. https://doi.org/10.1016/S0959-4752(97)00007-8
  92. Yousuf, M. I. (2007). Using expert's opinions through Delphi technique. Practical Assessment, Research & Evaluation, 12(4), 1-8.
  93. Zawojewski, J. S., Hjalmarson, M. A., Bowman, K. J., & Lesh, R. (2008). A modeling perspective on learning and teaching in engineering education. In J. S. Zawojewski, H. A. Diefes-Dux, & K. Bowman (Eds.), Models and modeling in engineering education. Rotterdam: Sense Publishers.
  94. Zawojewski, J., & McCarthy, L. (2007). Numeracy in practice. Principal Leadership, 7(5), 32–38.

피인용 문헌

  1. 연속적으로 공변하는 두 양에 대한 추론의 차이가 문제 해결에 미치는 영향 vol.55, pp.3, 2011, https://doi.org/10.7468/mathedu.2016.55.3.251
  2. 수학적 문제해결역량을 위한 평가 문항의 조건과 그 실제 vol.57, pp.2, 2011, https://doi.org/10.7468/mathedu.2018.57.2.111