Knowledge Construction on Mathematics Problem Solving

수학 탐구학습에서 지식 형성에 대한 연구

  • 이중권 (동국대학교 수학교육과)
  • Published : 2004.08.01

Abstract

This study investigated three pre-service teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of pre- service teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

이 연구는 학과 과제와 기말 프로젝트에 있는 문제들 중에서 컴퓨터를 활용하여 수학적 문제 해결을 해 가는 세 명의 예비 교사를 연구 조사하였다 모든 연구 참여자들의 활동과 컴퓨터를 활용한 문제 해결 과정을 관찰하고 촬영하였다. 가능한 경우 예비 교사들의 탐구활동 전과 후 및 탐구활동 중에 개별적인 면담을 하였다. 자료수집 방법은 관찰, 면담, 현장 기록, 제출과제, 컴퓨터 작업, 오디오와 비디오 테이프를 사용하였다. 수학적 문제 해결 초기 단계에서는, 모든 연구 참여자들이 그래프와 데이터를 사용하여 모델 만들기, 사인 함수의 일반적 개념에 대하여 절차적 지식과 개념적 지식이 약하게 형성되어 있었으나 컴퓨터를 활용한 수학적 문제 해결 활동을 통하여 그들은 절차적 지식과 개념적 지식을 강하게 구성하였고 그들을 적절하게 연계시킬 수 있었다

Keywords

References

  1. The Architecture of Cognition Anderson, J.R.
  2. The Psychology of Memory Baddeley, A.D.
  3. Beyond the Information Given Bruner, J.S.
  4. Journal of Research in Science Teaching v.15 Concrete and formal piagetian stages and science concept attainment Canta, L.;Herron, J.
  5. International Journal of Instructional Media v.10 The program of systematic evaluation a brief review Dayer F.M.
  6. For the Learning of Mathematics v.1 The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques Ginsburg, H.E.
  7. The Journal of Educational Research v.94 no.3 Learning with dynamic geometry programs: Perspectives of teachers and learners Hannafin, R.D.;Burruss, J.D.;Little, C.
  8. Conceptual and Procedural Knowledge: the case of mathematics Conceptual and procedural knowledge in mathematics: An introductory analysis Hiebert, J.;Lefevre, P.
  9. Journal of Research in Science Teaching v.12 The effects of verbal and pictorial verbal information in science instruction Holliday, W.G.
  10. Unpublished doctoral dissertation, University of Georgia Student Representation and Understanding of Geometric Transformations with Technology Experience Jung, I.
  11. Journal of the Korea Society of Mathematics Education Series D v.5 no.1 Practical use of technology for mathematics education Kang, O.K.
  12. Handbook of Research on Mathematics Teaching and Learning Technology and mathematics education Kaput, J.J.
  13. The Psychology of Mathematical Abilities in School Children Krutetskii, V.A.
  14. Ethnography and Qualitative Design in Educational Research (2nd ed.) LeCompte, M.D.
  15. Curriculum and Evaluation Standards for School Mathematics National Council of Teachers of Mathematics
  16. Journal of Children's Mathematical Behavior v.5 Peaget's clinical method Opper, S.
  17. Mind Storms Papert, S.
  18. Journal of Educational Psychology v.68 Effect of graphic analogies of concepts in chemistry on learning and attitude Rigney, J.W.;Lutz, K.
  19. Elements of Episodic Memory Tulving, E.
  20. Handbook of Research on Mathematic Teaching and Learning Learning to think mathematically problem solving, metacogniton, and sense making in mathematics Schoenfeld, A.H.
  21. The Internet and Problem-Based Learning: Developing Solutions Through the Web Steipen, W.J.;Senn, P.R.;Steipen, W.C.
  22. The Geometric Supposer; What is it a case of ? For recitation to construction: Teachers change with new technologies Wish, M.S.;Houde, R.
  23. The Architecture of Cognition Anderson, J.R.
  24. The Psychology of Memory Baddeley, A.D.
  25. Beyond the Information Given Bruner, J.S.
  26. Journal of Research in Science Teaching v.15 Concrete and formal piagetian stages and science concept attainment Canta, L.;Herron, J.
  27. International Journal of Instructional Media v.10 The program of systematic evaluation a brief review Dayer, F.M.
  28. For the Learning of Mathematics v.1 The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques Ginsburg, H.E.
  29. The Journal of Educational Research v.94 no.3 Learning with dynamic geometry programs: Perspectives of teachers and learners Hannafin, R.D.;Burruss, J.D.;Little, C.
  30. Conceptual and Procedural Knowledge: the case of mathematics Hiebert, J.;Lefevre, P.
  31. Journal of Research in Science Teaching v.12 The effects of verbal and pictorial verbal information in science instruction Holliday, W.G.
  32. Unpublished doctoral dissertation, University of Georgia Student Representation and Understanding of Geometric Transformations with Technology Experience Jung, I.
  33. Journal of the Korea Society of Mathematics Education Series D v.5 no.1 Practical use of technology for mathematics education Kang, O.K.
  34. Handbook of Research on Mathematics Teaching and Learning Technology and mathematics education Kaput, J.J.
  35. The Psychology of Mathematical Abilities in School Children Krutetskii, V.A.
  36. Ethnography and Qualitative Design in Educational Research(2nd ed.) LeCompte, M.D.;Preissle, J.
  37. Curriculum and Evaluation Standards for School Mathematics National Council of Teachers of Mathematics
  38. Journal of Children's Mathematical Behavior v.5 Peaget's clinical method Opper, S.
  39. Mind Storms Papert, S.
  40. Journal of Educational Psychology v.68 Effect of graphic analogies of concepts in chemistry on learning and attitude Rigney, J.W.;Lutz, K.
  41. Elements of Episodic Memory Tulving, E.
  42. Handbook of Research on Mathematic Teaching and Learning Learning to think mathematically problem solving, metacogniton, and sense making in mathematics Schoenfeld, A.H.;D.A. Grouws(ed.)
  43. The Internet and Problem-Based Learning: Developing Solutions Through the Web Steipen, W.J.;Senn, P.R.;Steipen, W.C.
  44. The Geometric Supposer; What is it a case of? For recitation to construction: Teachers change with new technologies Wish, M.S.;Houde, R. ;J.L. Stewards(ed.);M. Yerushalmy(ed.);B. Wilson(ed.)