Communications of Mathematical Education (한국수학교육학회지시리즈E:수학교육논문집)

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

DOI QR Code

A Comparative Study of Statistical Processes in Korean and U.S. Middle School Mathematics Textbooks

한국과 미국 중학교 수학 교과서의 통계적 문제해결과정 비교연구

  • Received : 2019.09.03
  • Accepted : 2019.10.10
  • Published : 2019.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

Comparing to the U.S. mathematics textbooks, this study examines the opportunity to learn statistical processes represented in mathematics textbooks reflecting 2015 revised curriculum. Analyzing four different kinds of Korean middle school mathematics textbooks and two kinds of corresponding U.S. textbooks for seventh graders, we found that the tasks dealing with all the phases of statistical processes were found only in the U.S. textbooks while not even one task in such a case was not observed in the Korean textbooks. To make matters worse, the proportion of the tasks dealing with only one phase of statistical processes was 93.3% of all the tasks in Korean textbooks. In terms of types of tasks, the types of tasks were very homogeneous in Korean textbooks, usually Types FPR or PR while more various types of tasks were found in the U.S. textbooks such as Types FRI, PRI, FR, or RI. In views of features of each phase in statistical processes, Korean textbooks heavily focused only on some particular statistical behaviors such as 'formulating a problem', 'collecting data', 'transforming data', and 'analyzing a part of data.' The findings of this study provide meaningful implications for improving statistics education and developing mathematics textbooks to enhance students' statistical thinking and problem-solving ability.

본 연구는 우리나라 2015 개정 수학과 교육과정에서 강조하고 있는 '통계적 문제해결과정'의 학습 기회를 교과서에서 어떻게 제공하고 구현하고 있는지 살펴보고 이의 개선 방안을 마련하고자 하나의 사례로서 미국 교과서와 비교 분석하였다. 우리나라 중학교 1학년 통계 단원의 학습 개념을 기준으로 미국 교과서에서 상응하는 단원을 선정하여 우리나라 중학교 1학년 교과서 4종과 미국 중학교 교과서 2종을 대상으로 비교 분석하였다. 그 결과, 단일과제에 통계적 문제해결과정의 전 단계를 포함하는 경우는 미국 교과서에서만 나타났을 뿐 한국 교과서에서는 찾아볼 수 없었으며 한국 교과서의 경우 총 4단계 중 오직 한 단계만을 제시하는 경우가 전체 문제의 93.3%로 나타났다. 또한 한국 교과서는 통계적 문제해결과정을 포함한 과제들이 대체로 비슷한 형태의 유형(FPR, PR 유형)으로 구성된 반면 미국 교과서는 이 외에도 다양한 과제 유형들(FRI, PRI, FR, RI)로 제시되고 있었다. 통계적 문제해결과정의 단계별 특징을 분석한 결과에서도 한국 교과서들은 각 단계에서 '문제 설정하기', '자료 수집하기', '자료 변환하기', '자료의 일부를 분석하기'와 같은 특정 하위 요소들이 집중적으로 다뤄지고 있었다. 이러한 연구 결과를 바탕으로 향후 통계교육에서의 통계적 문제해결과정 교육과 교과서 개선을 위한 시사점을 제시하였다.

Keywords

References

  1. Kang, O., Kwon E., Hwang H., Jeon D., Noh, J., Woo, H., ... Jung, K. (2018). Secondary mathematics 1. Seoul, Korea: Dong-A.
  2. Kang, H., Shin, B., Ko, E., Lee, D., Shim, S., Kim, J., Goo, N., Jung, I., Choi, K., Hong, J., & Lee, S. (2014). Research on improvement of mathematics curriculum for activation of statistics education. Seoul, Korea: Kofac.
  3. Go, S. M., Kim, M. S., Jung, J. K., & Cho, W. Y. (2017). Analysis of the problems in statistics units of middle school textbooks for the 3rd grade in terms of statistical literacy. School Mathematics, 19(4), 731-749.
  4. Ko, E. S., & Lee, K. H. (2010). A study on knowledge for the teaching of variability and reasoning about variation. Journal of Educational Research in Mathematics, 20(4), 493-509.
  5. Ko, E., Kang, H., Shin, B., Kim, E., Jung, S., Hong, C., Jee, Y., Lee, J., Ha, B., & Tak, B. (2017). Teacher Guidebook for Practical Statistics Education.. Korea: Kofac.
  6. Ko, E. S., & Park, M. S. (2017). Pre-service elementary school teachers’ statistical literacy related to statistical problem solving. School Mathematics, 19(3), 443-459.
  7. Ministry of Education (2015). Mathematics curriculum. Seoul, Korea: Ministry of Education.
  8. Kwon, N. Y., & Kim, J. H. (2017). Analysis on middle school mathematics curriculum of USA: Probability and statistics. Educational Research, 69, 95-120. https://doi.org/10.17253/swueri.2017.69..004
  9. Kim, G. Y., & Kim, R. Y (2019). Analyzing seventh graders' statistical thinking through statistical processes by phases and instructional settings. The Mathematical Education, 58(3), 459-481. https://doi.org/10.7468/MATHEDU.2019.58.3.459
  10. Kim, M. K., & Kim, H. W. (2011). A study on children's statistical thinking based on survey activities. School Mathematics, 13(1), 207-227.
  11. Kim, W., Cho M., Oh, J., Lim, S., Kim, D., Kang, S., ... Kim, Y. (2018). Secondary mathematics 1. Seoul, Korea: Visang.
  12. Kim, J. R., & Kim, Y. H. (2017). A study of the policy change of teacher' education in Korea with an analysis of America statistical literacy education. Journal of the Korean School Mathematics, 20(2), 163-186.
  13. Kim, H., Na, G., Lee, M., Lee, Y., & Kwon, Y. (2018). Secondary mathematics 1. Seoul, Korea: Sinsago.
  14. Ryu, H., Sunwoo, H., Shin, B., Jeong, D., Jang, Y., Sul, J., & Park, S. (2018). Secondary mathematics 1. Seoul, Korea: Chunjae.
  15. Bae, H. J. & Lee, D. H (2016). An analysis on statistical units of elementary school mathematics textbook. Journal of Elementary Mathematics Education in Korea, 20(1), 55-69.
  16. Song, S. E. (2019). The analysis of prospective mathematics teachers` capacity recognition and knowledge about statistical problem solving. Master's thesis. Ewha Womans University. Seoul, Korea.
  17. Oh, Y. Y., & Lee, M. Y. (2008). Exploring directions for improving elementary statistics education. The Journal of Korea Elementary Education, 19(1), 1-13. https://doi.org/10.20972/kjee.19.1.200807.1
  18. Oh, I. S. (2019). Statistical thinking level of ninth grade students using tongrami-centered for scatter diagram and correlation unit. Master's thesis. Korea National University of Education. ChungBuk, Korea.
  19. Woo, J. H. (2007). A Educational foundation on school mathematics. Seoul National University Publisher.
  20. Lee, K. H., & Ji, E. J. (2008). The study on didactic transposition for teaching statistical graphs - The comparison between the Korean and MiC's textbooks. The Journal of Educational Research in Mathematics, 18(3), 353-372.
  21. Lee, K. H., & Goo, N. Y. (2015). Use of technology in statstics and probability. In Ko, S. S.(Ed.), Technological tools in mathematics education(pp.285-313). Seoul, Korea: Kyungmoonsa..
  22. Lee, Y. K. (2009). The Effect of Project Classes on Statistical Teaching for First-Year Middle School Students. Master's thesis. Korea National University of Education. ChungBuk, KOREA.
  23. Lee, J. H., & Kim, W. K. (2011). Effects of Spreadsheet-used Instruction on Statistical Thinking and Attitude. The Mathematical Education, 50(2), 183-211.
  24. Lee, J., Choi, B., Kim, D., Lee, J., Kim, S., Won, Y., Kang, H., ... Kang, S. (2018). Secondary mathematics 1. Seoul: Chunjae
  25. Janh, A. R., & Kim, I. S. (2015). A Comparative Analysis on Statistical Reasoning Questions in Textbooks-focused on the first year of middle school. Journal of Science Education, 39(1), 1-10. https://doi.org/10.21796/jse.2015.39.1.1
  26. Ju, M. K., Kim, S. Y., Bae, K. T., Jeong, H. S., & Jung, S. Y. (2018). An Analysis of High School Students' Statistical Literacy: Students' Achievement and Difficulties of Statistical Inquiry. School Mathematics, 20(4), 661-683. https://doi.org/10.29275/sm.2018.12.20.4.661
  27. Chung, Y. O. et al. (2016). A comparative study of mathematics curriculum among the United States, Singapore, England, Japn, Australia, and Korea. Journal of Educational Studies in Mathematics, 26(3), 371-402.
  28. Ben-Zvi, D. & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions, and challenges. In D. Ben-Zvi & J. Garfield. (Eds.), The challenge of developing statistical literacy, reasoning and thinking. (pp. 3-15). Dordrecht, Netherlands: Kluwer.
  29. de Jong, J. A., Wijers, M., Bakker, A., Middleton, J. A., Simon, A. N., & Burrill, G. (2006). Mathematics in Context: Dealing with Data. Chicago, IL: Encyclopedia Britannica.
  30. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report pre-K-12. Alexandria, VA: American Statistical Association.
  31. 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
  32. Lappan, G., Phillips, E. D., Fey, J. T., & Friel, S. N. (2014a), Connected Mathematics 3: Grade 6. Upper Saddle River, NJ: Pearson.
  33. Lappan, G., Phillips, E. D., Fey, J. T., & Friel, S. N. (2014b), Connected Mathematics 3: Grade 7. Upper Saddle River, NJ: Pearson.
  34. Lappan, G., Phillips, E. D., Fey, J. T., & Friel, S. N. (2014c), Connected Mathematics 3: Grade 8. Upper Saddle River, NJ: Pearson.
  35. MacKay, R. J., & Oldford, R. W. (1994). Stat 231 Course Notes Fall 1994. Waterloo: University of Waterloo.
  36. MacKay, R. J., & Oldford, R. W. (2000). Scientific method, statistical method and the speed of light. Statistical Science, 15(3), 254-278. https://doi.org/10.1214/ss/1009212817
  37. Mooney, E. S. (1999). Development of middle school statistical thinking framework. Unpublished Doctoral Dissertation, Illinois state University.
  38. Mooney, E. S. (2002). A framework for characterizing middle school students' statistical thinking. Mathematical Thinking and Learning, 4, 23-64. https://doi.org/10.1207/S15327833MTL0401_2
  39. National Council of Teachers of Mathematics (2000). Principles and standards for mathematics. Reston, VA: The author.
  40. Newton, J., Dietiker, L., & Horvath, A.(2011). Statistics education in the United States: Statistical reasoning and the statistical process. In C. Batanero, G. Burrill, & C. Reading(Eds.), Teaching statistics in school mathematics - Challenges for teaching and teacher education (pp. 9-14). New York, NY: Springer.
  41. Pfannkuch, M. (2005). Thinking tools and variation. Statistics Education Research Journal, 4(1), 83-91.
  42. Polya, G. (1957). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
  43. Schield, M. (1999). Statistical literacy: Thinking critically about statistics. Of Significance, 1(1), 15-20.
  44. Schield, M. (2011). Statistical literacy: A new mission for data producers. Statistical Journal of the IAOS, 27(3), 173-183.
  45. Schoenfeld, A. H. (1987). What's all the fuss about metacognition? In A. H. Schoenfeld(Ed.), Cognitive science and mathematics education, 189-215. Hillsdale, NJ: Lawrence Erlbaum.
  46. Watson, J. M. (2002). Discussion: Statistical literacy before adulthood. International Statistical Review, 70(1), 26-30. https://doi.org/10.1111/j.1751-5823.2002.tb00337.x
  47. Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum.
  48. Wijers, M., de Lange, J., Bakker, A., Shafer, M. C., & Burrill, G. (2006). Mathematics in context: Insights into data.. Chicago, IL: Encyclopedia Britannica.
  49. Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248. https://doi.org/10.1111/j.1751-5823.1999.tb00442.x