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중등수학 예비교사들의 통계적 소양: 표본 개념에 대한 이해를 중심으로

Preservice Secondary Mathematics Teachers’ Statistical Literacy in Understanding of Sample

이경화|구나영|강현영|탁병주
한국수학교육학회|2017.02|수학교육 (The Mathematical Education)|제56권 제1호|pp. 19-39|DOI https://doi.org/10.7468/mathedu.2017.56.1.19

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키워드

statistical literacy통계교육통계적 소양statistics education표본대표성표집변이성sample representativenesssampling variability

초록

Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don’t appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers’ understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson’s statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

Abstract

Taking samples of data and using samples to make inferences about unknown populations are at the core of statistical investigations. So, an understanding of the nature of sample as statistical thinking is involved in the area of statistical literacy, since the process of a statistical investigation can turn out to be totally useless if we don’t appreciate the part sampling plays. However, the conception of sampling is a scheme of interrelated ideas entailing many statistical notions such as repeatability, representativeness, randomness, variability, and distribution. This complexity makes many people, teachers as well as students, reason about statistical inference relying on their incorrect intuitions without understanding sample comprehensively. Some research investigated how the concept of a sample is understood by not only students but also teachers or preservice teachers, but we want to identify preservice secondary mathematics teachers’ understanding of sample as the statistical literacy by a qualitative analysis. We designed four items which asked preservice teachers to write their understanding for sampling tasks including representativeness and variability. Then, we categorized the similar responses and compared these categories with Watson’s statistical literacy hierarchy. As a result, many preservice teachers turned out to be lie in the low level of statistical literacy as they ignore contexts and critical thinking, expecially about sampling variability rather than sample representativeness. Moreover, the experience of taking statistics courses in university did not seem to make a contribution to development of their statistical literacy. These findings should be considered when design preservice teacher education program to promote statistics education.

참고문헌 (54)

  1. 강현영, "통계적 소양의 교육적 의미 고찰", 한국수학사학회지, 25(4), pp.121~137 (2012), 한국수학사학회
  2. 통계교육 활성화를 위한 수학 교육과정 개선 방안 연구, "강현영", 한국과학창의재단, ~, pp.연구보고 2014A039 (2014)
  3. 고은성, "통계적 변이성 사고 요소 간의 관계 연구", 학교수학, 14(4), pp.495~516 (2012), 대한수학교육학회
  4. 고은성, "미래사회, 이제 통계적 소양이다", pp.83~100 (2015), 통계청
  5. 고은성, "예비교사들의 통계적 표집에 대한 이해", 수학교육학연구, 21(1), pp.17~32 (2011), 대한수학교육학회
  6. , 2015
  7. 구나영, "표본 지도에 대한 고찰: 국외 교육과정 분석을 중심으로", 학교수학, 17(3), pp.515~530 (2015), 대한수학교육학회
  8. 이강섭, "교원양성기관의 통계분야 교육과정에 대한 기본 자료", 수학교육논문집, 15, pp.59~64 (2003)
  9. 이경화, "미래사회, 이제 통계적 소양이다", pp.27~43 (2015), 통계청
  10. 이영하, "인문학으로 풀어 쓴 통계교육 원론" (2014), 이화여자대학교출판부
  11. 이영하, "초·중·고등학교 확률과 통계 단원에 나타난 표본개념에 대한 분석", 수학교육학연구, 21(4), pp.327~345 (2011), 대한수학교육학회
  12. 이영하, "확률·통계 연구에 대한 수학교육학적 고찰 : <수학교육>에 게재된 논문을 중심으로", 수학교육, 42(2), pp.203~218 (2003), 한국수학교육학회
  13. 이은희, "국내외 통계교육 연구동향 비교 분석", 수학교육, 54(3), pp.241~259 (2015), 한국수학교육학회
  14. 정한영, "통계학사 개론" (1995), 한림대학교출판부
  15. 지은정, "자료의 분포와 표본추출 상황에서 변이성 개념 지도", 박사, 수학교육, pp.2011
  16. 탁병주, "표본 개념에 대한 고찰: 역사적 분석을 중심으로", 학교수학, 16(4), pp.727~743 (2014), 대한수학교육학회
  17. Bar-Hillel, M., "The role of sample size in sample evaluation", Organizational Behavior and Human Performance, 24(2), pp.245~257 (1979)
  18. 2010, , ~
  19. Ben-Zvi, D., "Learning to reason from samples", Educational Studies in Mathematics, 88(3), pp.291~303 (2015)
  20. Coffey, D., "Pearson Mathematics 8: Student Book" (2013), Pearson Education Australia
  21. delMas, R. C., "Statistical literacy, reasoning, and learning: A commentary", Journal of Statistics Education, 10(3) (2002)
  22. Guidelines for assessment and instruction in statistics education report, "Franklin, C. G.", American Statistical Association, ~ (2007)
  23. Gal, I., "Adults' statistical literacy : Meanings, components, responsibilities", International Statistical Review, 70(1), pp.1~25 (2002)
  24. Garfield, J., "The Web-based ARTIST: Assessment resource tools for improving statistical thinking", annual meeting of the American Educational Research Association (2003)
  25. Garfield, J., "Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking", Educational Studies in Mathematics, 88(3), pp.327~342 (2015)
  26. Groth, R. E., "Toward a conceptualization of statistical knowledge for teaching", Journal for research in Mathematics Education, 38(5), pp.427~437 (2007)
  27. Groth, R. E., "Pre-service elementary school teachers’ metaphors for the concept of statistical sample", Statistics education research Journal, 4(2), pp.27~42 (2005)
  28. Hill, H. C., "Mathematical knowledge for teaching and the mathematical quality of instruction : An exploratory study", Cognition and Instruction, 26(4), pp.430~511 (2008)
  29. Kahneman, D., "Subjective probability : A judgment of representativeness", Cognitive Psychology, 3(3), pp.430~454 (1972)
  30. Lipson, K., "The role of the sampling distribution in understanding statistical inference", Mathematics Education Research Journal, 15(3), pp.270~287 (2003)
  31. Moore, D. S., "On the Shoulders of Giants: New Approaches to Numeracy", pp.95~137 (1990), National Academy Press
  32. Moore, D. S., "논쟁거리로 배우는통계학" (2009), 홍릉과학출판사
  33. Noll, J. A., "Graduate teaching assistants’statistical knowledge for teaching", Ph.D, pp.2007
  34. Noll, J. A., "Graduate teaching assistants’statistical content knowledge of sampling", Statistics Education Research Journal, 10(2), pp.48~74 (2011)
  35. Pfannkuch, M., "Building sampling concepts for statistical inference: A case study", ICME-11 Proceedings (2008)
  36. Pfannkuch, M., "What I see is not quite the way it really is : students’emergent reasoning about sampling variability", Educational Studies in Mathematics, 88(3), pp.343~360 (2015)
  37. 2010, , 239~270
  38. Ridgway, J., "Teaching Statistics in School Mathematics:Challenges for Teaching and Teacher Education" (2011), Springer
  39. Rubin, A., "Proceedings of the third international conference on teaching statistics. Vol. 1", pp.314~319 (1990), International Statistical Institute
  40. Rumsey, D. J., "Statistical literacy as a goal for introductory statistics courses", Journal of Statistics Education, 10(3), pp.6~13 (2002)
  41. Saldanha, L., "Conceptions of sample and their relationship to statistical inference", Educational Studies in Mathematics, 51, pp.257~270 (2002)
  42. Shaughnessy, J. M., "Second handbook of research on mathematics teaching and learning", pp.957~1009 (2007)
  43. Sullivan, P., "Teaching with tasks for effective mathematics learning" (2013), Springer
  44. Sullivan, P., "The Contexts of mathematics tasks and the context of the classroom : Are we including all students?", Mathematics Education Research Journal, 15(2), pp.107~121 (2003)
  45. Torok, R., "Development of the concept of statistical variation : An exploratory study", Mathematics Education Research Journal, 12(2), pp.147~169 (2000)
  46. Wallman, K. K., "Enhancing statistical literacy : Enriching our society", Journal of the American Statistical Association, 88, pp.1~8 (1993)
  47. Watson, J. M., "The Assessment Chanllenge in Statistics Education", pp.107~121 (1997), IOS Press
  48. Watson, J. M., "Preservice mathematics teachers’understanding of sampling : Intuition or mathematics", Mathematics Teacher Education and Development, 2(1), pp.121~135 (2000)
  49. 2010, , ~
  50. Watson, J. M., "학교에서 어떤 통계를 배워야 하지? 통계적 소양의 성장과 목표" (2013), 경문사
  51. Watson, J. M., "The measurement of school students' understanding of statistical variation", International Journal of Mathematical Education in Science and Technology, 34(1), pp.1~29 (2003)
  52. Watson, J.M., "Developing concepts of sampling", Journal for Research in Mathematics Education, 31, pp.44~70 (2000)
  53. Watson, J.M., "Development of understanding of sampling for statistical literacy", Journal of Mathematical Behavior, 19, pp.109~136 (2000)
  54. Wild. C. J., "The concept of distribution", Statistics Education Research Journal, 5(2), pp.10~26 (2006)

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