The effect of metacognitive activity using CAS calculator on high school first grade mathematics slow-learners' achievement of Algebra

CAS 계산기를 활용한 메타인지 활동이 고등학교 1학년 수학학습부진아의 대수학업성취도에 미치는 영향

  • Published : 2009.02.28

Abstract

This paper observed the effect of CAS calculator usage while studying algebra on the achievement of low-achievement students. Participants were composed of 70 low-achievement tenth grade students from a high school located in a metropolitan city. That had never used a mathematics educational calculator before. Target participants were divided into two groups: an experiment group that studied activity papers with the aid of a CAS calculator, and a control group that studied the same activity papers using only paper-and-pencil. The content of the activity papers for the two groups was the same, but the structure differed. Content consisted of numbers and operations, equations and inequalities(character and expressions), and functions. Students in the experiment group exhibited matacognition learning using a CAS calculator. The two groups completed mathematics achievement tests both before and after the activity papers. Therefore, ANCOVA analysis results showed that compared to the pretest, results of the experiment group improved considerably more than the control group.

본 논문은 수학수업에서 점점 소외되고 있는 수학학습부진아가 대수학습에서 학업성취도를 신장시키기 위해 좀 더 나은 효과를 얻을 수 있는 방법을 모색하고자 하였다. 이를 위해 수학학습부진아를 선정하여 두 집단으로 나누었다. 한 집단은 처치집단으로 CAS 계산기를 사용하여 활동지를 학습하고, 다른 집단은 통제집단으로 지필을 사용하여 활동지를 학습하였다. 각 집단은 활동지를 통해서 메타인지 활동을 하였다. 수업 전과 후에 두 집단 모두 지필로 수학학업성취도를 실시하여 비교 분석한 결과, 처치집단이 통제집단보다 여러 가지 측면에서 더 나은 효과를 나타내는 것을 확인하였다.

Keywords

References

  1. 김인경, 대수학습에서 CAS 계산기를 활용한 메타인지 활동이 수학학습부진아의 수학학업 성취도에 미치는 영향, 한국교원대학교 대학원 박사학위논문, 2008.
  2. 김재찬, 메타인지 활동이 학습부진학생의 수학적 문제해결과 신념에 미치는 영향, 한국교원대학교 대학원 석사학위논문, 2004.
  3. 문성환, 메타인지적 수업에서 나타난 수학학습 태도와 학습과정의 특징 연구, 한국교원대학교 대학원 석사학위논문, 2006.
  4. 박정환, 우옥희, PBL(Problem-Based Learning)이 학습자의 메타인지 수준에 따라 문제해결 과정에 미치는 효과, 교육공학연구, 5 (1999) No.3, 55-81.
  5. 이경준, 학습부진아의 인지특성분석과 효율적인 교수전략탐색연구, 중앙대학교대학원 박사학위 논문, 1983.
  6. 이광상, 중학교에서의 메타인지적 수업이 수학적 문제해결에 미치는 효과, 한국교원대학교 대학원 석사학위논문, 1999.
  7. 이봉주, 문제해결 과정에서 메타인지적 활동 안내를 통한 고등학생의 메타인지 능력 활성화 가능성 탐색, 수학교육, 43 (2004) No.3, 217-231.
  8. 이양기, 메타인지적 사고를 향상시키기 위한 수업의 형태가 문제해결력에 미치는 영향 분석, 한국교원대학교 대학원 석사학위논문, 1997.
  9. 장선명, 반성활동에 초점을 둔 증명지도 사례연구-8단계를 중심으로, 한국교원대학교 대학원 석사학위논문, 2004.
  10. 조재영, 수학 교수활동 과정에서 학생의 메타인지적 능력 신장 방안 탐색, 한국교원대학교 대학원 박사학위논문, 1996.
  11. 최은희, 김민경, 메타인지 전략을 활용한 수업에서의 초등학생의 수학적 추론과 표현에 미치는 효과에 관한 연구, 교과교육학 연구, 10 (2006) No.1, 191-207.
  12. Artzt, A. F. & Armour-Thomas, E., Protocol analysis of group problem solving in mathematics : A cognitive-rnetacognitive frame-work for assessment, Boston, MA., In The Annual Meeting of the American Educational Research Association, (1990) 1-3. (ERIC Document Reprodution Service No. ED 320 927).
  13. Bennett, G., Calculus for general education in a computer classroom, The International DERIVE Journal, 2 (1995) No.2, 3-11.
  14. Blozy, T. A, An analysis of performance on calculus questions by students using CAS and Non- CAS graphing calculators, Doctoral Dissertation, Columbia University, 2002.
  15. Cuoco, A. & Levasseur, K., Classical Mathematics in the Age of CAS, In Fey. J. T., Cuoco, A, KIeran, C., McMullin, L., & Zbiek, R M.(Eds.), Computer Algebra Systems in Secondary School Mathematics Education, chapter 6, Reston, VA: National Council of Teachers of Mathematics, 2003.
  16. Dick, T. P., Dion, G. S., & Wright, C. L., Case Study: Advanced Placement Calculus in the Age of the Computer Algebra System, The Mathematics Teacher, 96 (2003) No.8.
  17. Dickman, S. J., Functional and Psychology inpulsivity : Personality and cognitive correlates, Journal of Personality and Social Psychology, 58 (1990) 95-102. https://doi.org/10.1037/0022-3514.58.1.95
  18. Dunham, P. H., Highlights from Research on Graphing Calculators, Proceedings of the T3 International Conference on Mathematics Education, 2000.
  19. Flavell, J. H., Cognitive development, NJ : Prentice-Hall, Inc., 1985.
  20. Flavell, J. H., Speculations about the nature and development of metacognition, In Weinert, F. E. & Kluwe, R. H.(Eds.), Metacognition, Motivation and Understanding, Lawrence Erlbaum Associates Publishers, 1987.
  21. Forrest-Pressley, D. L., MacKinnon, G. E., & Waller, T. G.(Eds.), Metacognition, cognition, and human performance : Instructional Practices (Vol. 2), NY : Academic Press, 1985.
  22. Garofalo, J. & Lester, F. K. Jr., Metacognition, cognitive monitoring, and mathematical performance, Journal for Research in Mathematics Education, 16 (1985) No.3, 163-176. https://doi.org/10.2307/748391
  23. Heid, M. K., Resequencing skills and concepts in applied calculus using the computer as a tool, Journal for Research in Mathematics Education, 19 (1988) No.1, 3-25. https://doi.org/10.2307/749108
  24. Heid, M. K. & Zbiek, R. M., A technology-intensive approach to algebra, The Mathematics Teacher, 88 (1995) No.8, 650-656.
  25. Hirschom, D. B. & Thompson, D. R., Technology and reasoning in algebra and geometry, The Mathematics Teacher, 89 (1996) No.2, 138-142.
  26. Kokol-Voljc, V., Exam Questions When Using CAS for School Mathematics Teaching, proceedings of the T3 World-Wide conference, Tokyo, Japan, 6-8 August, 2000.
  27. Llorens-Fuster, J., A mathematics course with DERIVE at technical colleges, The International DERIVE Journal, 2 (1995) No.2, 33-39.
  28. Mayes, R. L., Computer use in Algebra: And now the rest of the story, The Mathematics Teacher, 86 (1993) No.7, 38-541.
  29. Palmiter, J. R., Effects of computer algebra systems on concept and skill acquisition in calculus, Journal for Research in Mathematics Education, 22 (1991) No.2, 51-156.
  30. Schmidt, W. H., McKnight, C. C., et al., Facing the Consequences: Using TIMSS for a closer look at U. S. mathematics and science education, Dordrecht, Netherlands: Kluwer Academic Publishers, 1999.
  31. Schoenfeld, A. H., Mathematical problem solving, San Diego, CA : Academic Press, 1985.
  32. Schoenfeld, A. H., What's all the fuss about matacognition?, In Schoenfeld, A. H.(Ed.), Cognition Science and Mathematics Education, Hillsdale, NJ: Lawrence Erlbaum, (1987) 189-215.
  33. 대한수학교육학회, 8. 메타인지가 도대체 무엇인데 이야단인가- 제39회 수학교육학 집중세미나, 2002.
  34. Slife, B. D., Weiss, J., & Bell, T., Separability of metacognition and cognition: Problem solving in learning disabled and regular students, Journal of Educational Psychology, 77 (1985) No.4, 437-445. https://doi.org/10.1037/0022-0663.77.4.437
  35. Stewart, S., Concerns Relating to the CAS Use at University Level, Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia. Held at RMIT, Melbourne, 7-9 July, 2005.
  36. Taylor, M., Calculators and computer algebra systems-their use in mathematics examinations, The Mathematics Gazette, 79 (1995) No.4, 68-73. https://doi.org/10.2307/3619993
  37. Torgensen, J. K, The role of nonspecific factors in the task performance of learning-disabled children : A theoretical assessment, Journal of Learning Disabilities, 10 (1977) 27-34. https://doi.org/10.1177/002221947701000108
  38. Waits, B. K. & Demana, F., A Computer for All Students-Revisited, The Mathematics Teacher, 89 (1996) No.9, 712-714.
  39. Waits, B. K. & Demana, F., Calculators in Mathematics Teaching and Learning: Past, present and future, In Learning for a New Century: 2000 yearbook of the National Council of teachers of Mathematics. Chapter 5. Reston, VA: National Council of Teachers of Mathematics, 2000.