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담론적 관점에서 히스토그램의 의미와 과제 발문 분석

Analysis of the meaning of histogram and questioning in histogram tasks from a discursive perspective

  • 투고 : 2023.05.01
  • 심사 : 2023.05.23
  • 발행 : 2023.05.31

초록

본 연구에서는 담론적 관점에서 우리날 중학교 1학년 교과서 3종과 미국 CMP 교과서 담론에서 생성된 히스토그램의 의미를 분석하는 한편, 히스토그램 과제의 통계적 문제해결 단계별 발문의 특징을 조사하여 향후 히스토그램에 관한 교과서 담론 개선에 구체적인 아이디어를 제공하고자 한다. 분석 결과 첫째, 국내 교과서와 미국 CMP 교과서에서 히스토그램을 정의하는 방식의 차이가 있었고, 둘째, 교과서에서 히스토그램의 의미를 구성하는 담론적 구조는 다양했다. 셋째, 히스토그램 과제에 반영된 통계적 문제해결 단계가 제한적이었고, 넷째, 국내 교과서와 미국 CMP 교과서의 히스토그램 과제 발문에서 학생들에게 요구하는 활동에 차이가 나타났다. 이를 바탕으로 히스토그램을 정의하는 과정과 과제의 발문 개선에 대한 아이디어를 제안하고자 한다.

The objective of this study is to explore the meaning generated through discourse in three different types of 1st-grade middle school textbooks in Korea and CMP textbook in the United States, specifically focusing on histograms. Through a discursive perspective, the study aims to analyze the characteristics of questioning within the stages of statistical problem-solving found in histogram tasks. The findings highlight several significant points. Firstly, variations exist in the definitions of histograms between Korean and US CMP textbooks. Secondly, diverse discursive structures contribute to the interpretation and understanding of histograms in textbooks. Thirdly, limitations are observed in the stages of statistical problem-solving reflected in histogram tasks. Lastly, distinctions are identified in the types of questioning employed in histogram tasks between Korean and US CMP textbooks. Building on these insights, the study suggests concrete ideas for enhancing the process of defining histograms and refining the questioning in histogram tasks.

키워드

과제정보

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-R2021321).

참고문헌

  1. Alshwaikh, J. (2011). Geometrical diagrams as representation and communication: A functional analytic framework [Doctoral dissertation, University of London].
  2. Alshwaikh, J. (2016). Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse, Research in Mathematics Education, 18(2), 165-181. https://doi.org/10.1080/14794802.2016.1177580
  3. Bae, H., & Lee, D. (2016). An analysis on statistical units of elementary school mathematics textbook. Journal of Elementary Mathematics Education in Korea, 20(1), 55-69.
  4. Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools [Doctoral dissertation, Utrecht University]. https://dspace.library.uu.nl/handle/1874/893
  5. Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D. (2020). Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education (GAISE) report II. American Statistical Association.
  6. Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning, and thinking(1st ed.). Springer. https://doi.org/10.1007/1-4020-2278-6
  7. Bruno, A., & Espinel, M. C. (2009). Construction and evaluation of histograms in teacher training. International Journal of Mathematical Education in Science & Technology, 40(4), 473-493. https://doi.org/10.1080/00207390902759584
  8. Cooper, L. L., & Shore, F. S. (2008). Students' misconceptions in interpreting center and variability of data represented via histograms and stem-and-leaf plots. Journal of Statistics Education, 16(2), 1-13. https://doi.org/10.1080/10691898.2008.11889559
  9. Cooper, L. L., & Shore, F. S. (2010). The effects of data and graph type on concepts and visualizations of variability. Journal of Statistics Education, 18(2), 1-16. https://doi.org/10.1080/10691898.2010.11889487
  10. Derouet, C., & Parzysz, B. (2016). How can histograms be useful for introducing continuous probability distributions? ZDM Mathematics Education, 48(6), 757-773. https://doi.org/10.1007/s11858-016-0769-9
  11. 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: A pre-K-12 curriculum framework. American Statistical Association.
  12. Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32(2), 124-158. https://doi.org/10.2307/749671
  13. Gal, I. (2002). Adults' statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1-25. https://doi.org/10.2307/1403713
  14. Garfield, J. & Ben-Zvi, D (2007). How students learn statistics revisited: a current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372-396. https://doi.org/10.1111/j.1751-5823.2007.00029.x
  15. Garfield, J. & Ben-Zvi, D. (2008). Developing students' statistical reasoning: Connecting research and teaching practice. Springer.
  16. Hwang, H. J., Na, K. S., Choi, S. H., Park, K. M., Jang, J. H., & Seo, D. Y. (2019). New Perspectives on Mathematics Education 1 (Revised and Enlarged Edition). Moonumsa.
  17. Hwang, S., Kang, B., Yoon, G., Lee, K., Jang, H., Jung, J., & Cho, S. (2018). Middle school mathematics 1. Mirae-N.
  18. Jacobbe, T., & Horton, R. (2010). Elementary school teachers' comprehension of data displays. Statistics Education Research Journal, 9(1), 27-45. https://doi.org/10.52041/serj.v9i1.386
  19. Kang, O., Kwon, E., Hwang, H., Jeon, D., Noh, J., Woo, H., Yun, S., Lee, H., Yoo, S., Yun, H., Hong, C., & Jung, K. (2018). Middle school mathematics 1. Doosan Dong-A.
  20. Kang, H., Shin, B., Ko, E., Lee, D., Shim, S., Kim, J., Ku, N., Jung, I., Choi, K., & Hong, J. (2014). Research on improvement of mathematics curriculum for activation of statistics education [Research report No. 2014A039]. Korea Foundation for the Advancement Science & Creativity
  21. Kaplan, J. J., Gabrosek, J. G., Curtiss, P., & Malone, C. (2014). Investigating student understanding of histograms. Journal of Statistics Education, 22(2), 1-30. https://doi.org/10.1080/10691898.2014.11889701
  22. Kaplan, J., Lyford, A., & Jennings, J. K. (2018). Effects of question stem on student descriptions of histograms. Statistics Education Research Journal, 17(1), 85-102. Retrieved from https://iase-web.org/documents/SERJ/SERJ17(1)_Kaplan.pdf. https://doi.org/10.52041/serj.v17i1.177
  23. Kim, E., & Lee, S. (2019). Statistics and Probability Education. Kyungmoonsa.
  24. Kim, D., Park, T., Song, S., Lim, C., Yoo, Y., & Yeo, I. (2019). Research report on the improvement of elementary and middle school statistics education curriculum. Korean Statistical Society. http://www.kss.or.kr/bbs/board.php?bo_table=pds_data&wr_id=119
  25. Kim, D., Shin, J., Lee, J., Lim, W., Lee, Y., & Choi, S. (2019). Conceptualizing discursive teaching capacity: A case study of a middle school mathematics teacher. Schol Mathematics, 21(2), 291-318. http://doi.org/10.29275/sm.2019.06.21.2.291
  26. Kim, W., Choi, S., & Kim, D. (2018a). A discursive approach to analysis of definition of graph in first year middle school textbooks. Communications of Mathematical Education, 32(3), 407-433. http://doi.org/10.7468/jksmee.2018.32.3.407
  27. Kim, W., Choi, S., & Kim, D. (2018b). Reconstruction and application of an analytic framework for discursive approach to interpretations of graph -The case of a Korean textbook and CMP-. The Mathematical Education, 57(4), 433-452. https://doi.org/10.7468/mathedu.2018.57.4.433
  28. Kim, S., & Kang, H. (2020). Exploring ways to improve statistics curriculum by analyzing secondary curriculum in foreign countries. School Mathematics, 22(3), 631-650. https://doi.org/10.29275/sm.2020.09.22.3.631
  29. Kim, B., & Kim, Y. (2019). Comparisons of the revised mathematics curriculum between korea and japan: focusing on statistics. Journal of Learner-Centered Curriculum and Instruction, 19(3), 495-523. http://dx.doi.org/10.22251/jlcci.2019.19.3.495
  30. Kim, S. (2019). Exploration of foreign curriculums for the improvement of the Korean middle school statistical curriculum: Focusing on learning elements in Korea, the United States, Singapore, and Japan. Journal of the Korean School Mathematics Society, 22(4), 501-520. http://doi.org/10.30807/ksms.2019.22.4.008
  31. Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305-325. https://doi.org/10.1007/S10649-013-9529-8
  32. Kress, G. & Van Leeuwen, T. (2006). Reading images: The grammar of visual images. Routledge.
  33. Lappan, G., Phillips, E. D., Fey, J. T., & Friel, S. N. (2014). Connected Mathematics 3 Grade 6. Pearson Education.
  34. Leavy, A. (2006). Using data comparison to support a focus on distribution: Examining preservice teacher's understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89-114. Retrieved from http://iase-web.org/documents/SERJ/SERJ5(2)_Leavy.pdf. https://doi.org/10.52041/serj.v5i2.502
  35. Lee, J., & Rim, H. (2021). Analysis of textbooks on statistical problem-solving process and statistical literacy. Journal of the Korean School Mathematics Society, 24(2), 191-216. http://doi.org/10.30807/ksms.2021.24.2.002
  36. Lee, K., Yoo, Y., & Tak, B. (2021). Towards data-driven statistics education: an exploration of restructuring the mathematics curriculum. School Mathematics, 23(3), 361-386. http://doi.org/10.29275/sm.2021.09.23.3.361
  37. Lee, Y., & Choi, J. (2008). An analysis of statistics chapter of the grade 7's current textbook in view of the distribution concepts. Journal of Educational Research in Mathematics, 18(3), 407-434.
  38. Marriott, J., Davies, N., & Gibson, L. (2009). Teaching, learning and assessing statistical problem solving. Journal of Statistics Education [Online], 17(1),
  39. Ministry of Education. (2015). Mathematics curriculum (Annex 8 to Education Notice No. 2015-74). Ministry of Education.
  40. Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants(pp. 95-137). National Academy Press.
  41. Morgan, C. (2016). Studying the role of human agency in school mathematics. Research in Mathematics Education, 18(2), 120-141. https://doi.org/10.1080/14794802.2016.1176595
  42. Morgan, C., & Sfard, A. (2016). Investigating changes in high-stakes mathematics examinations: a discursive approach. Research in Mathematics Education, 18(2), 92-119. https://doi.org/10.1080/14794802.2016.1176596
  43. National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. NCTM.
  44. O'Halloran, K. L. (2015). The language of learning mathematics: A multimodal perspective. The Journal of Mathematical Behavior, 40(Part A), 63-74. https://psycnet.apa.org/doi/10.1016/j.jmathb.2014.09.002
  45. Park, J. H. (2015). On the supplementation of teaching informative text producing. Korean Writing Association, 24, 89-111.
  46. Park, J. (2016). Communicational approach to study textbook discourse on the derivative. Educational Studies in Mathematics, 91(3), 395-421. https://doi.org/10.1007/s10649-015-9655-6
  47. Park, Y. (2016). An analysis of contents on statistics in elementary mathematics textbooks according to 2009 mathematics curriculum for elementary school. Journal of Elementary Mathematics Education in Korea, 20 (1), 17-34.
  48. Ryu, H., Sunwoo, H., Shin, B., Jung, D., Jang, Y., Seo, S., & Park, S. (2018). Middle school mathematics 1. Cheonjae Education.
  49. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.
  50. Song, I., & Choi, S. (2023). The power of seeing the world clearly: Statistical perspective. Bartleby.
  51. Stevens, S. P., & Palocsay, S. W. (2012). Identifying addressable impediments to student learning in an introductory statistics course. INFORMS Transactions on Education, 12(3), 124-139. https://doi.org/10.1287/ited.1120.0085.
  52. Tak, B., & Kim, D. (2020). An analysis on error types of graphs for statistical literacy education: Ethical problems at data analysis in the statistical problem solving. Journal of Elementary Mathematics Education in Korea, 24(1), 1-30.
  53. Watson, J. M. (1997). Assessing statistical thinking using the media. In I. Gal & J. B. Garfield (Eds.), The assessment challenge in statistics education (pp. 107-121). IOS Press and The International Statistical Institute.
  54. Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Lawrence Erlbaum Associates.
  55. Woo, J. H. (2017). The educational foundation of school mathematics (Vol. 3). Seoul National University Press.