Education of Primary School Mathematics (한국수학교육학회지시리즈C:초등수학교육)

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

DOI QR Code

A Comparative Analysis of the Mathematics Curriculum on Time-related Contents: Focusing on Korea, Japan, Australia, the United States, and Finland

시각과 시간에 대한 수학과 교육과정 국제 비교 연구: 한국, 일본, 호주, 미국, 핀란드를 중심으로

  • Received : 2021.07.05
  • Accepted : 2021.07.20
  • Published : 2021.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

This study implemented a comparative analysis of the international mathematics curriculum on time learning. It aimed the improvement of challenges students facing when they learn time. As a preliminary step, I reviewed the previous literature on teaching and learning of time, and based on this, I drew five issues that require to be considered for better time learning. The coverage of time contents and the learning periods of respective time contents were compared across the mathematics curriculum of Korea, Japan, Australia, the United States, and Finland. The textbook cases of those countries were analyzed with a special focus on the five issues. The results showed that the Korean curriculum assigned time learning contents compressively during short periods compared to other countries. responded to the issues on teaching and learning of time, several improvement ideas were deduced from textbook cases of other countries. Implications for the curriculum reform were discussed underlying the results.

이 연구는 시간 관련 학습에서의 어려움 개선을 목적으로 하는 시각과 시간에 대한 수학과 교육과정 국제 비교연구이다. 이를 위해 먼저 시간 관련 내용의 교수·학습과 관련된 선행 문헌을 검토하고 교수·학습 개선을 위해 고려해야 할 이슈들을 도출하였다. 한국, 일본, 호주, 미국, 핀란드의 수학과 교육과정에서 시각과 시간 내용의 범주 및 학습 시기를 비교하고, 선행 문헌 검토를 통해 도출된 이슈들을 중심으로 각국의 교과서 사례를 분석하였다. 그 결과, 우리나라는 학교 수학에서 시각 및 시간 내용을 다른 나라보다 짧은 시간 동안 압축적으로 다루고 있었다. 시간 관련 교수·학습 이슈별로 우리나라가 참고할 만한 개선 아이디어들을 다른 나라 교과서 사례 분석을 통하여 제시하였다. 결과를 바탕으로 시각과 시간 내용에 관한 우리나라 교육과정의 개선에 참고할 시사점을 제언하였다.

Keywords

References

  1. Ko, H. K., Chang, K-Y., & Lee, G. C. (2016). A comparative analysis of the middle school mathematics curriculum in Korea and Australian. Journal of Educational Research in Mathematics, 26(2), 309-331.
  2. Ministry of Education. (1997). Mathematics curriculum. Seoul: Daehan Textbook Inc.
  3. Ministry of Education. (2015). Mathematics curriculum. Sejong, South Korea: Author.
  4. Ministry of Education. (2017a). Mathematics 2-2. Seoul: Chunjae Education Inc.
  5. Ministry of Education. (2017b). Mathematics 2-2 teachers' guidebook. Seoul: Chunjae Education Inc.
  6. Ministry of Education. (2021. April 20). Launching discussion of the future curriculum with the citizen. Press release of Ministry of Education. Retrieved from https://www.moe.go.kr/boardCnts/view.do?boardID=294&boardSeq=84176&lev=0&searchType=null&statusYN=W&page=1&s=moe&m=020402&opType=N
  7. Kwon, M. (2019). Second grade elementary school students' understanding of time and elapsed time. Journal of Educational Research in Mathematics, 49(4), 741-760. https://doi.org/10.29275/jerm.2019.11.29.4.741
  8. Kwon, O. N., Lee, K., Lee, A., & Han, C. (2019). A comparative study on the external & internal structure of mathematics curriculum between Korea and Japan: Focusing on the aspects of recent revisions. Mathematics Education, 58(2), 187-223.
  9. Na, G. S., Park, M., Kim, D-W., Kim, Y., & Lee, S. J. (2017). Exploring the direction of mathematics education in the future age. Journal of Educational Research in Mathematics, 28(4), 437-478. https://doi.org/10.29275/jerm.2018.11.28.4.437
  10. Ministry of Education. (1963). Elementary school curricum. Seoul, Korea: Author.
  11. So, K-H. (2017). Analysis of Trend in Comparative Education Research Related to Curriculum in the 「Korean Journal of Comparative Education」from Postcolonial perspectives. Korean Journal of Comparative Education, 27(4), 23-44. https://doi.org/10.20306/kces.2017.27.4.33
  12. Yun, E. (2015). 2015 global education policy information 7-2016 Finnish national core curriculum reform: endless journey to joy of learning. Seoul: Korean Educational Development Institute.
  13. Cho, Y. M., & Lim, S. H. (2010). A study on textbooks of South Korea, Singapore, and Japan Focused on the teaching of the time. Journal of Elementary Mathematics Education in Korea, 14(2), 421-440.
  14. Choi, H., Kim, B., & Kim, S. (2017). The fourth industrial revolution trend ①: Japan's fourth industrial revolution policy and implications. Trends and Issues, 30. Science & Technology Policy Institute.
  15. Han, C. (in press). Realization of signifiers and mathematics understanding: Focused on the elapsed time. Mathematics Education.
  16. Acredolo, C. (1989). Assessing children's understanding of time, speed, and distance interrelations. In I.Levin & D. Zakay (Eds.), Time and human cognition: A life-span perspective (pp. 219-257). Amsterdam, The Netherlands: Elsevier Science.
  17. Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2012). Australian Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/
  18. Banilower, E. R., Smith, P. S., Malzahn, K. A., Plumley, C. L., Gordon, E. M., & Hayes, M. L. (2018). Report of the 2018 NSSME+. Horizon Research, Inc.
  19. Basic Education Curriculum Material Development Centre. (2001). National mathematics curriculum standards at the compulsory education level. Beijing, China: Beijing Normal University.
  20. Bock, K., Irwin, D. E., Davidson, D. J., & Levelt, W. J. M. (2003). Minding the clock. J ournal of Memory and Language, 48, 653-685. https://doi.org/10.1016/S0749-596X(03)00007-X
  21. Boulton-Lewis, G., Wilss, L., & Mutch, S. (1997). Analysis of primary school children's abilities and strategies for reading and recording time from analogue and digital clocks. Mathematics education research journal, 9(2), 136-151. https://doi.org/10.1007/BF03217308
  22. Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40. https://doi.org/10.3316/QRJ0902027
  23. Bruno, R., Johnson, J., & Simon, J. (1988). Perception of time by students with and without learning disabilities. Focus on Learning Problems in Mathematics, 10(2), 15-27.
  24. Burny, E. (2012). Time-related competences in primary education. Unpublished Doctoral dissertation, Ghent University.
  25. Burny, E., Valcke, M., & Desoete, A. (2009). Towards an agenda for studying learning and instruction focusing on time-related competencies in children. Educational Studies, 35(5), 481-492. https://doi.org/10.1080/03055690902879093
  26. Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33, 352-378. https://doi.org/10.2307/4149958
  27. Dixon, J. K., Larson, M., Burger, E. B., Sandoval-Martinez, M. E., & Leinwand, S. J. (2015a). Go math! grade 1 volume 2: Student edition. Orlando, FL: Houghton Mifflin Harcourt Publishing Company.
  28. Dixon, J. K., Larson, M., Burger, E. B., Sandoval-Martinez, M. E., & Leinwand, S. J. (2015b). Go math! grade 3 volume 2: Student edition. Orlando, FL: Houghton Mifflin Harcourt Publishing Company.
  29. Earnest, D. (2015). From number lines to graphs in the coordinate plane: Investigating problem solving across mathematical representations. Cognition and Instruction, 33(1), 46-87. https://doi.org/10.1080/07370008.2014.994634
  30. Earnest, D. (2017). Clock work: How tools for time mediate problem solving and reveal understanding. Journal for Research in Mathematics Education, 48(2), 191-223. https://doi.org/10.5951/jresematheduc.48.2.0191
  31. Earnest, D. (2019). The invisible quantity: time intervals in early algebra/La cantidad invisible: los intervalos de tiempo en el algebra temprana. Infancia y Aprendizaje, 42(3), 664-720. https://doi.org/10.1080/02103702.2019.1615199
  32. Earnest, D. (2021). About time: Syntactically-guided reasoning with analog and digital clocks. Mathematical Thinking and Learning, DOI: 10.1080/10986065.2021.1881703
  33. Earnest, D., & Chandler, J. (2021). Making time: words, narratives, and clocks in elementary mathematics. Journal for Research in Mathematics Education, 52(4), 407-443. https://doi.org/10.5951/jresematheduc-2021-0020
  34. Earnest, D., Gonzales, A. C., & Plant, A. M. (2018). Time as a measure: Elementary students positioning the hands of an analog clock. Journal of Numerical Cognition, 4(1), 188-214. https://doi.org/10.5964/jnc.v4i1.94
  35. Ellis, A. B. (2007). Connections between generalizing and justifying: Students' reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194-229.
  36. Finnish National Board of Education (2016). National core curriculum for basic education 2014. Helsinki, Finland: Author.
  37. Friedman, W. J., & Laycock, F. (1989). Children's analog and digital clock knowledge. Child Development, 60(2), 357-371. https://doi.org/10.1111/j.1467-8624.1989.tb02721.x
  38. Hackenberg, A. J. (2010). Students' reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383-432. https://doi.org/10.1080/07370008.2010.511565
  39. Han, C. (2020). Making sense of time-telling classroom: Interplay of cognition, instruction, and tools. Unpublished doctoral dissertation, Seoul National University.
  40. Heck, D. J., Weiss, I. R., & Pasley, J. D. (2011). A priority research agenda for understanding the influence of the common core state standards for mathematics. Chapel Hill, NC: Horizon Research, Inc.
  41. Kamii, C., & Russell, K. A. (2010). The older of two trees: Young children's development of operational time. Journal for Research in Mathematics Education, 41(1), 6-13. https://doi.org/10.5951/jresematheduc.41.1.0006
  42. Kamii, C., & Russell, K. A. (2012). Elapsed time: Why is it so difficult to teach? Journal for Research in Mathematics Education, 43(3), 296-315. https://doi.org/10.5951/jresematheduc.43.3.0296
  43. Korvorst, M., Roelofs, A., & Levelt, W. J. (2007). Telling time from analog and digital clocks: A multiple-route account. Experimental Psychology, 54(3), 187-191. https://doi.org/10.1027/1618-3169.54.3.187
  44. Lakoff, G., & Nunez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York, NY: Basic Books.
  45. Lloyd, G. M., Cai, J., & Tarr, J. E. (2017). Issues in curriculum studies: evidence-based insights and future directions. In J. Cai (Ed.), Compendium for research in mathematics education. Reston, VA: National Council of Teachers of Mathematics.
  46. Long, K., & Kamii, C. (2001). The measurement of time: Children's construction of transitivity, unit iteration, and conservation of speed. School Science and Mathematics, 101(3), 125-132. https://doi.org/10.1111/j.1949-8594.2001.tb18015.x
  47. Males, L. M., & Earnest, D. (2015, April). Opportunities to learn time measure in elementary curriculum materials. In D. Earnest, L. M. Males, C. Rumsey, & R. Lehrer (Discussants), The measurement of time: Cognition, instruction, and curricula. Symposium conducted at the 2015 Research Conference of the National Council of Teachers of Mathematics, Boston, MA.
  48. Meeuwissen, M., Roelofs, A., & Levelt, W. J. (2004). Naming analog clocks conceptually facilitates naming digital clocks. Brain and Language, 90(1-3), 434-440. https://doi.org/10.1016/S0093-934X(03)00454-1
  49. Monroe, E. E., Orme, M. P., & Erickson, L. B. (2002). Working cotton: Toward an understanding of time. Teaching Children Mathematics, 8(8), 475-479. https://doi.org/10.5951/TCM.8.8.0475
  50. Moore, K. C., & Carlson, M. P. (2012). Students' images of problem contexts when solving applied problems. The Journal of Mathematical Behavior, 31, 48-59. https://doi.org/10.1016/j.jmathb.2011.09.001
  51. Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. Boston College, TIMSS & PIRLS International Study Center.
  52. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  53. National Governors Association [NGA] Center for Best Practices & Council of Chief State School Officers [CCSSO] (2010). Common core state standards for mathematics. Washington, DC: Authors.
  54. O'Brien, H., & Purcell, G. (2016). Math plus 3 stage 2 student book. South Melbourne, Australia: Oxford University Press Australia.
  55. Piaget, J. (1969). The child's conception of time. New York, NY: Ballantine Books.
  56. Reys, B., Reys, R., & Rubenstein, R. (Eds.). (2010). Mathematics curriculum: Issues, trends, and future directions, 72nd yearbook of the National Council of Teachers of Mathematics. Reston, VA: NCTM.
  57. Smith III, J. P., & Barrett, J. E. (2017). Learning and teaching measurement: coordinating quantity and number. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 355-385). Reston, VA: National Council of Teachers of Mathematics.
  58. Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H., Wiley, D. E., Cogan, L. S., & Wolfe, R. G. (2001). Why schools matter: A cross-national comparison of curriculum and learning. San Francisco, CA: OSSEY-BASS.
  59. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York, NY: Cambridge University Press.
  60. Siegler, R. S., & McGilly, K. (1989). Strategy choices in children's time-telling. In I. Levin & D. Zakay (Eds.), Time and human cognition: A life-span perspective (pp. 185-218). Amsterdam, Netherlands: Elsevier.
  61. Siegler, R. S., & Richards, D. D. (1979). Development of time, speed, and distance concepts. Developmental psychology, 15(3), 288-298. https://doi.org/10.1037/0012-1649.15.3.288
  62. Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Reston, VA: National Council of Teachers of Mathematics.
  63. Thomas, M. C. (2018). A matter of time: An investigation into the learning and teaching of time in the middle primary years. Unpublished doctoral dissertation, Australian Catholic University.
  64. Thompson, P. W. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. H. Schoenfeld, & J. J. Kaput (Eds.), Research in collegiate mathematics education: Issues in mathematics education (pp. 21-44). Providence, RI: American Mathematical Society.
  65. Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421-456). Reston, VA: National Council of Teachers of Mathematics.
  66. Trethewey, A. R. (1976). Introducing comparative education. Rushcutters Bay, Australia: Pergamon Press.
  67. Vlaams Verbond voor het Katholiek Onderwijs. (1998). Mathematics curriculum standards [Wiskunde Leerplan]. Brussel, Belgium: VVKBaO.
  68. Williams, R. F. (2004). Making meaning from a clock: Material artifacts and conceptual blending in time-telling instruction. Unpublished doctoral dissertation, University of California, San Diego.
  69. Williams, R. F. (2012). Image schemas in clock-reading: Latent errors and emerging expertise. Journal of the Learning Sciences, 21(2), 216-246. https://doi.org/10.1080/10508406.2011.553259
  70. 文部科學省. (2008a). 小學校學習指導要領. 文部科學省.
  71. 文部科學省. (2008b). 小學校學習指導要領解說 算數編. 文部科學省.
  72. 文部科學省. (2008c). 小學校學習指導要領解說 總則編. 文部科學省.
  73. 文部科學省. (2017a). 小學校學習指導要領. 文部科學省.
  74. 文部科學省. (2017b). 小學校學習指導要領解說 算數編. 文部科學省.
  75. 文部科學省. (2017c). 小學校學習指導要領解說 總則編. 文部科學省.
  76. 大久保和義 외 24명. (2016a). しょうがく さんすう1. 東京: 敎育出版.
  77. 大久保和義 외 24명. (2016b). 小學 算數 3上. 東京: 敎育出版.