The Mathematical Education (한국수학교육학회지시리즈A:수학교육)

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

DOI QR Code

Preservice Secondary Mathematics Teachers' Statistical Literacy in Understanding of Sample

중등수학 예비교사들의 통계적 소양 : 표본 개념에 대한 이해를 중심으로

  • Received : 2016.09.25
  • Accepted : 2017.02.21
  • Published : 2017.02.28
Download PDF
⟨ Previous Next ⟩

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.

Keywords

References

  1. 강현영 (2012). 통계적 소양의 교육적 의미 고찰, 한국수학사학회지, 25(4), 121-137. Kang, H.Y. (2012). Study of the educational meaning of Statistical Literacy. The Korean Journal for History of Mathematics, 25(4), 121-137.
  2. 강현영, 신보미, 고은성, 이동환, 심송용, 김정자, 구나영, 정인수, 최경식, 홍지혜 (2014). 통계교육 활성화를 위한 수학 교육과정 개선 방안 연구. 한국과학창의재단. 연구보고 2014A039. Kang, H.Y., Shin, B., Ko, E.S., Lee, D.H., Sim, S., Kim, J.J., Ku, N.Y., Jeong, I.S., Choi, K.S., & Hong. J.H. (2014). Research on improvement of mathematics curriculum for activation of statistics education. Research Report. Korea Foundation for the Advancement of Society and Creativity.
  3. 고은성 (2012). 통계적 변이성 사고 요소 간의 관계 연구. 학교수학, 14(4), 495-516. Ko, E.S. (2012). The Relationships among Components of Thinking related to Statistical Variability. School Mathematics, 14(4), 495-516.
  4. 고은성 (2015). 현 초중고 통계교육 연구 진행 현황 및 과제. 통계청(편.). 미래사회, 이제 통계적 소양이다 (pp.83-100). 대전: 통계청. Ko. E.S. (2015). The status quo and the issues of statistics education research in school mathematics. Statistics Korea (Eds.). Statistics literacy for the future society. Daejeon: Statistics Korea.
  5. 고은성, 이경화 (2011). 예비교사들의 통계적 표집에 대한 이해. 수학교육학연구, 21(1), 17-32. Ko, E.S. & Lee, K.H. (2011). Pre-service Teachers' Understanding of Statistical Sampling. Journal of Educational Research in Mathematics, 21(1), 17-32.
  6. 교육부 (2015). 수학과 교육과정. 교육부 고시 제2015-74호 [별책 8] Ministry of Education. (2015). Mathematics Curriculum. Bulletin of MOE No. 2015-74 [Seperate Volume #8]
  7. 구나영, 탁병주, 강현영, 이경화 (2015). 표본 지도에 대한 고찰: 국외 교육과정 분석을 중심으로. 학교수학, 17(3), 515-530. Ku, N.Y., Tak, B., Kang, H.Y., & Lee, K.H. (2015). A Study on the Teaching Sample - An Analysis of Foreign Curriculum. School Mathematics, 17(3), 515-530.
  8. 이강섭 (2003). 교원양성기관의 통계분야 교육과정에 대한 기본 자료. 수학교육논문집, 15, 59-64. Lee. K.S. (2003). Basic data on the curriculum of the statistics for teacher education. Communications of Mathematical Education, 15, 59-64.
  9. 이경화 (2015). 우리나라 초중고 통계교육의 실제와 방향. 통계청(편.). 미래사회, 이제 통계적 소양이다 (pp.27-43). 대전: 통계청. Lee. K.H. (2015). The location and direction of statistics education research in Korea. Statistics Korea (Eds.). Statistics literacy for the future society. Daejeon: Statistics Korea.
  10. 이영하 (2014). 인문학으로 풀어 쓴 통계교육 원론. 서울: 이화여자대학교출판부. Lee Y. (2014). Principles of statistics education in terms of humanities. Seoul: Ewha Woman's University Press.
  11. 이영하, 신수영 (2011). 초.중.고등학교 확률과 통계 단원에 나타난 표본개념에 대한 분석. 수학교육학연구, 21(4), 327-344. Lee, Y. & Shin, S. (2011). Features of sample concepts in the probability and statistics chapters of Korean mathematics textbooks of grades 1-12. Journal of Educational Research in Mathematics, 21(4), 327-344.
  12. 이영하, 심효정 (2003). 확률.통계 연구에 대한 수학교육학적 고찰: <수학교육>에 게재된 논문을 중심으로. 수학교육, 42(2), 203-218. Lee, Y. & Sim, H.J. (2003). A Trend analysis on the educational research of the probability and statistics: Focused on papers published in , the journal of Korea Society of Mathematical Education. The Mathematical Education, 42(2), 203-218.
  13. 이은희, 김원경 (2015). 국내외 통계교육 연구동향 비교분석. 수학교육, 54(3), 241-259. Lee, E.H. & Kim, W.K. (2015). A comparative analysis on research trends of statistics education between Korea and overseas. The Mathematical Education, 54(3), 241-259.
  14. 정한영 (1995). 통계학사 개론. 춘천: 한림대학교출판부. Chung, H.Y. (1995). Introduction to Statistics History. Chuncheon: Hallim University Press.
  15. 지은정 (2011). 자료의 분포와 표본추출 상황에서 변이성 개념 지도. 박사학위논문, 한국교원대학교. Ji, E.J. (2011). Instruction on the concept of variability in the data distributions and sampling situations. Doctoral Dissertation. Korea University of Education.
  16. 탁병주, 구나영, 강현영, 이경화 (2014). 표본 개념에 대한 고찰: 역사적 분석을 중심으로. 학교수학, 16(4), 727-743. Tak, B., Ku, N.Y., Kang, H.Y., & Lee, K.H. (2014). A Study on the Concept of Sample by a Historical Analysis. School Mathematics, 16(4), 727-743.
  17. Bar-Hillel, M. (1979). The role of sample size in sample evaluation. Organizational Behavior and Human Performance, 24(2), 245-257. https://doi.org/10.1016/0030-5073(79)90028-X
  18. Ben-Zvi, D. & Garfield, J. (2010). 통계적 소양, 추론, 사고: 목표, 정의, 난제. In D. Ben-Zvi & J. Garfield (Eds.). 통계적 사고의 의미와 교육 (이경화 외 9인역), (pp.3-17) 서울: 경문사. (원저 2004년 출판)
  19. Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291-303. https://doi.org/10.1007/s10649-015-9593-3
  20. Coffey, D. (2013). Pearson Mathematics 8: Student Book. Frenchs Forest: Pearson Education Australia.
  21. delMas, R.C. (2002). Statistical literacy, reasoning, and learning: A commentary. Journal of Statistics Education, 10(3).
  22. Franklin, C.G., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education report. Alexandria: American Statistical Association
  23. Gal, I. (2002). Adults' statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25. https://doi.org/10.1111/j.1751-5823.2002.tb00336.x
  24. Garfield, J., delMas, R.C., & Chance, B. (2003). The Web-based ARTIST: Assessment resource tools for improving statistical thinking. In annual meeting of the American Educational Research Association, Chicago.
  25. Garfield, J., Le, L., Zieffler, A., & Ben-Zvi, D. (2015). Developing students' reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88(3), 327-342. https://doi.org/10.1007/s10649-014-9541-7
  26. Groth, R.E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for research in Mathematics Education, 38(5), 427-437.
  27. Groth, R.E., & Bergner, J.A. (2005). Pre-service elementary school teachers' metaphors for the concept of statistical sample. Statistics education research Journal, 4(2), 27-42.
  28. Hill, H.C., Blunk, M.L., Charalambous, C.Y., Lewis, J.M., Phelps, G.C., Sleep, L., & Ball, D.L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. https://doi.org/10.1080/07370000802177235
  29. Kahneman, D. & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430-454. https://doi.org/10.1016/0010-0285(72)90016-3
  30. Lipson, K. (2003). The role of the sampling distribution in understanding statistical inference. Mathematics Education Research Journal, 15(3), 270-287. https://doi.org/10.1007/BF03217383
  31. Moore, D.S. (1990). Uncertainty. In L.S. Steen (Ed.). On the Shoulders of Giants: New Approaches to Numeracy (pp.95-137). Washington, DC: National Academy Press.
  32. Moore, D.S., & Notz, W.I. (2009). 논쟁거리로 배우는 통계학 (심규박, 조태영, 신미경 역), 서울: 홍릉과학출판사. (원저 2005년 출판)
  33. Noll, J.A. (2007). Graduate teaching assistants' statistical knowledge for teaching. Ph.D. dissertation. Portland State University.
  34. Noll, J.A. (2011). Graduate teaching assistants' statistical content knowledge of sampling. Statistics Education Research Journal, 10(2), 48-74.
  35. Pfannkuch, M. (2008). Building sampling concepts for statistical inference: A case study. ICME-11 Proceedings, Monterrey, Mexico, July 2008.
  36. Pfannkuch, M., Arnold, P., & Wild, C.J. (2015). What I see is not quite the way it really is: students' emergent reasoning about sampling variability. Educational Studies in Mathematics, 88(3), 343-360. https://doi.org/10.1007/s10649-014-9539-1
  37. Reading, C., & Shaughnessy, J.M. (2010). 변이에 대한 추론. In D. Ben-Zvi & J. Garfield (Eds.). 통계적 사고의 의미와 교육 (이경화 외 9인 역), (pp.239-270) 서울: 경문사. (원저 2004년 출판)
  38. Ridgway, J., Nicholson, J., & McCusker, S. (2011). Developing statistical literacy in students and teachers. In C., Batanero, G. Burrill, & C. Reading (Eds.). Teaching Statistics in School Mathematics:Challenges for Teaching and Teacher Education. New York: Springer.
  39. Rubin, A., Bruce, B., & Tenney, Y. (1990). Learning about sampling: Trouble at the core of statistics. In D. Vere-Jones(Eds.). Proceedings of the third international conference on teaching statistics. (Vol. 1, pp.314-319). Voorburg: International Statistical Institute.
  40. Rumsey, D.J. (2002). Statistical literacy as a goal for introductory statistics courses. Journal of Statistics Education, 10(3), 6-13.
  41. Saldanha, L. & Thompson, P. (2002). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51, 257-270. https://doi.org/10.1023/A:1023692604014
  42. Shaughnessy, J.M. (2007). Research on statistics learning. Second handbook of research on mathematics teaching and learning, 957-1009.
  43. Sullivan, P., Clarke, D., & Clarke, B. (2013). Teaching with tasks for effective mathematics learning. New York: Springer.
  44. Sullivan, P., Zevenbergen, R., & Mousley, J. (2003). The Contexts of mathematics tasks and the context of the classroom: Are we including all students?. Mathematics Education Research Journal, 15(2), 107-121. https://doi.org/10.1007/BF03217373
  45. Torok, R., & Watson, J. (2000). Development of the concept of statistical variation: An exploratory study. Mathematics Education Research Journal, 12(2), 147-169. https://doi.org/10.1007/BF03217081
  46. Wallman, K.K. (1993). Enhancing statistical literacy: Enriching our society. Journal of the American Statistical Association, 88, 1-8.
  47. Watson, J.M. (1997). Assessing Statistical Thinking Using the Media. In I. Gal & J. B. Garfield (Eds.). The Assessment Chanllenge in Statistics Education (pp.107-121). Amsterdam: IOS Press.
  48. Watson, J.M. (2000). Preservice mathematics teachers' understanding of sampling: Intuition or mathematics. Mathematics Teacher Education and Development, 2(1), 121-135.
  49. Watson, J.M. (2010). 표본에 대한 추론. In D. Ben-Zvi & J. Garfield (Eds.). 통계적 사고의 의미와 교육 (이경화외 역 pp.329-351) 서울: 경문사. (원저 2004년 출판)
  50. Watson, J.M. (2013). 학교에서 어떤 통계를 배워야 하지? 통계적 소양의 성장과 목표 (박영희 역). 서울: 경문사. (원저 2006년 출판)
  51. Watson, J.M., Kelly, B.A., Callingham, R.A., & Shaughnessy, J.M. (2003). The measurement of school students' understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1-29. https://doi.org/10.1080/0020739021000018791
  52. Watson, J.M. & Moritz, J.B. (2000a). Developing concepts of sampling. Journal for Research in Mathematics Education, 31, 44-70. https://doi.org/10.2307/749819
  53. Watson, J.M. & Moritz, J.B. (2000b). Development of understanding of sampling for statistical literacy. Journal of Mathematical Behavior, 19, 109-136. https://doi.org/10.1016/S0732-3123(00)00039-0
  54. Wild. C.J. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10-26.

Cited by

  1. 국내 수학 교사교육 연구의 동향 분석: 2000년 이후 게재된 한국수학교육학회의 학술지 논문을 중심으로 vol.58, pp.1, 2017, https://doi.org/10.7468/mathedu.2019.58.1.121
  2. Enhancing Preservice Teachers’ Key Competencies for Promoting Sustainability in a University Statistics Course vol.12, pp.21, 2017, https://doi.org/10.3390/su12219051