The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

Development of Probabilistic Thinking of the Minority Students with Low Achievement & Low SES

교육소외 학생들을 대상으로 확률 이해수준에 관한 연구

  • Received : 2012.03.13
  • Accepted : 2012.08.24
  • Published : 2012.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

Since research has barely been done on the minority with low-achievement & low-SES in probability, this research attempted to search the change of their thinking level in the classes of probability and motivate them on the mathematical learning to feel confident in mathematics. We can say that the problems of the educational discriminations are due to the overlook on the individual conditions, situations, and environments. Therefore, in order to resolve some discrimination, 4 students who belonged to the minority group, engaged in the research, based on 10 units of the instructional materials designed for the research. As a result, for the student's thinking level, it was observed that they were improved from the 1st to the 3rd level in probability. Also, the researcher found that the adequate use of the encouragement, the praise, the direct explanation, and the scaffolding enabled them to prompt their learning motives and the increased responsibility on the learning. As time passed, the participants could share their mathematical knowledge and its concept with others, in the increased confidence.

Keywords

References

  1. 김수동․이화진․유준희․임재훈 (1998). 학습부진아 지도 프로그램 개발 연구, 서울: 한국교육과정평가원.
  2. 김애화․신동희․고상숙 (2010). 저소득층 학생, 학부모, 저소득층 학생을 가르치는 교사의 수학과 과학교수에 대한 인식. 한국교육, 37(2), 57-87.
  3. 김영희 (2002). 저소득층 청소년의 학교생활 적응에 관한 연구. 한국청소년개발원.
  4. 박용순 (2001). 빈곤과 자립, 서울: 학지사.
  5. 백정환 (2011). 교육소외 학생을 대상으로 담론을 통해 확률과 통계 교수 학습에 관한 사례 연구, 고2를 중심으로, 단국대학교 박사학위 논문.
  6. 백정환․고상숙 (2011). 교육소외 학생들을 위한 수업모형과 통계이해수준에 관한 연구, 한국수학교육학회지 시리즈 A <수학교육>, 50(3), 263-284.
  7. 신보미․이경화 (2008). 시뮬레이션을 활용한 확률 지식의 교수학적 변환, 수학교육학연구, 18(1), 25-50.
  8. 심정현 (2002). 문제중심수업이 개념 형성 및 수학적 성향에 미치는 효과, 한귝교원대학교 석사학위 논문.
  9. 우정호 (2007). 학교 수학의 교육적 기초, 서울: 서울대학교출판부.
  10. 유원섭 (2003). 저소득층 의료보장 제도의 현황과 과제, 월간 복지동향, 61, 12-16.
  11. 윤형철 (2009). 중학교 3학년 학생들의 확률적 사고 수준과 수준별 오개념에 대한 분석, 한국교원대학교 석사학위 논문.
  12. 이용구 (2005). 통계학의 이해. 서울: 율곡출판사.
  13. 최종덕 (1995). 부분의 합은 전체인가: 현대 자연 철학의 이해, 서울: 소나무 철학 문고.
  14. 한국교육개발원 (1987). 사고력 신장을 위한 프로그램 개발 연구(I), 서울: 한국교육개발원.
  15. 한국교육개발원 (1992). 교육의 본질 추구를 위한 수학교육 평가 체제 연구(III), 수학과 평가 도구 개발.
  16. 한국교육개발원 (2005). 도시 저소득층 평생학습 활성화 방안 연구, 서울: 한국교육개발원.
  17. Acredolo, C., O'Connor, J., Banks, L., & Horobin, K. (1989). Children's ability to make probability estimates: Skills revealed through application of Anderson' functional measurement methodology. Child Development, 60, 933-945. https://doi.org/10.2307/1131034
  18. Aiken, L. R. (1970). Attitudes toward mathematics: Review of Educational Research, 40, 551-596. https://doi.org/10.3102/00346543040004551
  19. Biggs, J. B., & Collis, K. F. (1991). Multimodal learning and intelligent behavior. In H. Rowe (Ed.), Intelligence: Reconceptionalization and measurement (pp.57-76). Hillsdale, NJ: Erlbaum.
  20. Boarler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239-258. https://doi.org/10.2307/749740
  21. Borovcnik, M. G., & Bentz, H. J. (1991). Empirical research in understanding probability. In R. Kapadia & M. Borovcnik (Eds.), Chance encounters: Probability in education (pp. 73-105). Dordrecht, The Netherland: Kluwer.
  22. Bourdieu, P. (1973). Cultural Reproduction and Social Reproduction. Richard Brown. 71-80.
  23. Byers, W. (2007). How mathematics think. Princeton, NJ: Princeton University Press.
  24. English, L. D. (1993). Children's strategies for solving two- and three-dimensional combinational problems. Journal for Research in Mathematics Education, 24, 255-273. https://doi.org/10.2307/749347
  25. Falk, R. (1987). Conditional probabilities: Insights and difficulties. In R. Davison & J. Swift(Eds.), Proceedings: The Second International Conference on Teaching Statistics(pp. 195-221). Victoria, Canada: University of Victoria.
  26. Fennema, E. & Sherman, J. A. (1977). Sex-related differences in mathematics achivement and related factor: A further study. Journal for Research in Mathematics Education, 9, 189-203.
  27. Fischbein, E. (1975). The Intuitive Sources of Probabilistic Thinking in Children. Dordrecht : D. Reidel Publishing Company.
  28. Fischbein, E. (1978). Intuition and Mathematical Education. Osnabrucher Schriftenzur Mathemarik.
  29. Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96-105. https://doi.org/10.2307/749665
  30. Fischbein, E., Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgements in children and adolescents. Educational Studies in Mathematics, 22, 523-549. https://doi.org/10.1007/BF00312714
  31. Freudenthal, H. (1991). Revisiting Mathematics Education. Dordrecht: Kluwer Academic Publishers.
  32. Green, D. (1986). Talking of probability. Mathematics and Applications, 20, 145-149.
  33. Huston, C. A., McLoyd, C. V., & Coll, G. C. (1995). Children and poverty: Issues in contemporary research. Child Development, 65(1), 275-282.
  34. Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' Probabailistic Thinking in Instruction. Journal for Research in Mathematics Education, 30(5), 487-519. https://doi.org/10.2307/749771
  35. Jones, G. A., Langrall, C. W., Thronton, C. A., & Mogil, A. T. (1997). A framework for assessing and nurturing young children's thinking in probability. Educational Studies in Mathematics, 32(2), 101-125. https://doi.org/10.1023/A:1002981520728
  36. Haladyna, T., Shaughnessy. J., & Shaughnessy, J. M. (1983). A casual Analysis of attitude toward mathematics. Journal for Research in Mathematics Education, 14(1), 19-29. https://doi.org/10.2307/748794
  37. Jones, G. A. (2005). Introduction. In G. A. Jones (Eds), Exploring probability in school : Challenges for teaching and learning(pp.1-12). USA: Springer.
  38. Jones, G. A., Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1999). Students' Probabilistic Thinking in Instruction. Journal for Research in Mathematics Education, 30(5), 487-519. https://doi.org/10.2307/749771
  39. McCoach, D., & Siegel, D. (2003). The school attitude assessment survey-revised: A new instrument to identify academically able students who underachieve. Educational and Psychological Measurement, 63, 414-429. https://doi.org/10.1177/0013164403063003005
  40. National Council of Teachers of Mathematics. (2003). A research companion to principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  41. National Council of Teachers of Mathematics. (1991). Professional Standards for Teaching Mathematics. Reston, VA: National Council of Teachers of Mathematics.
  42. National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
  43. Piaget, J., & Inhelder, B. (1975). The origin of the idea of chance in children. New York: W. W. Norton and Company.
  44. Pintrich, P. R., & de Groot, E. V. (1990). Motivation and self-regulated learning component If classroom academic performance. Journal of Education Psychology, 82(1), 33-40. https://doi.org/10.1037/0022-0663.82.1.33
  45. Polaki, M. V., Lefoka, P. J., & Jones, G. A. (2000). Developing a cognitive framework for describing and preparing Basotho students' probabilistic thinking, Boleswa Educational Research Journal. 17, 1-20.
  46. Polaki, M. V. (2005). Dealing with compound event. In G. A. Jones (Ed.), Exploring Probability in School: Challenges for Teaching and Learning. New York: Springer.
  47. Preckel, F., Holling, H., & Vock, M. (2006). Academic underachievement: Relationship with cognitive motivation, achievement motivation, and conscientiousness. Psychology in the Schools, 43(3), 401-411. https://doi.org/10.1002/pits.20154
  48. Rey, R. E., Suydam, M. N., Lindquist, M. M., & Smith, N. L. (1998). Helping children learn mathematics. NY: Simon & Schuster. 강문봉 외 (공 역) (1998). 초등수학 학습지도의 이해, 서울: 양서원.
  49. Saenz, C. (1998). Teaching probability for conceptual change. Educational Studies in Mathematics, 35, 233-254. https://doi.org/10.1023/A:1003182219483
  50. Scheaffer, L. R., Watkins, E. A., & Landwehr, M. J. (1998). What every high-school graduate should know about statistics. In S. P. Lajoie (Eds.), Reflections on statistics: Learning, teaching, and assessment in grades K-12(pp. 3-31). London: Lawrence Erlbaum Associates.
  51. Shaughnessy, J. M. (1992). Researches in probability and statistics: Reflections and direction. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 465-494). New York: Macmillan Publishing Company.
  52. Shaughnessy, J. M. (2003). Research on students' understandings of probability. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 216-226). Reston, VA: NCTM.
  53. Stake, R. E. (1995). The Art Of Case Study Research. Thousand Oaks, CA: SAGE publications, Inc. 홍용 희․노경주․심종희 역 (2000). 질적 사례 연구. 서울: 창지사.
  54. Tarr, J. E., & Jones, G. A. (1997). A framework for assessing middle school students' thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39-59. https://doi.org/10.1007/BF03217301
  55. Tarr, J. E., & Lannin, J. K. (2005). How can teachers build notions of conditional probability and independence? In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning. New York: Springer.