한국수학교육학회지시리즈D:수학교육연구 (Research in Mathematical Education)

  • 제22권3호
  • /
  • Pages.153-174
  • /
  • 2019
  • /
  • 1226-6191(pISSN)
  • /
  • 2287-9943(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
권호 표지
DOI QR코드

DOI QR Code

Alignment between National College Entrance Examinations and Mathematics Curriculum Standards: A Comparative Analysis

  • Hong, Dae S. (University of Iowa) ;
  • Bae, Yejun (University of Iowa) ;
  • Wu, Yu-Fen (University of Iowa)
  • 투고 : 2019.09.03
  • 심사 : 2019.09.19
  • 발행 : 2019.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Measuring alignment of various educational components is an important issue in educational research because with aligned educational system, we can have clear expectations about what to teach and assess. In this study, we examined the alignment between mathematics curriculum standards and college entrance examinations from Korea and China. The results indicate that curriculum standards and high stakes assessments from both countries are not well aligned to each other. Their Surveys of Enacted Curriculum (SEC) indices were lower than what previous studies have found and the critical values (Fulmer, 2011; Liu & Fulmer, 2008; Liu et al., 2009). There are several topics that are not assessed in both countries' national assessments. Also, discrepancies between the most frequently covered topics in the curriculum standards and the most frequently assessed mathematical topics in the national assessments caused topic level misalignment. We also found misalignment in cognitive level. Both national assessments included more perform procedures and demonstrate understanding items than their respective curriculum standards. Thus, previous findings about the inclusion of more items with higher cognitive demand in assessments is only partially true for either country. With these results, it is difficult to say that whether mathematical topics in the curriculum standards appropriately represent and support students to do well on the CSAT and the NCEE or that the mathematical items in the CSAT and the NCEE validly assess students' level of mathematical understanding.

키워드

참고문헌

  1. Au, W. (2007). High-stakes testing and curricular control: A qualitative metasynthesis. Educational Researcher, 36(5), 258-267. doi:10.3102/0013189x07306523
  2. Beck, M. D. (2007). Review and other views: "Alignment" as a psychometric issue. Applied Measurement in Education, 20(1), 127-135. doi:10.1080/08957340709336733
  3. Bhola, D. S., Impara, J. C., & Buckendahl, C. W. (2003). Aligning tests with states' content standards: Methods and issues. Educational Measurement: Issues and Practice, 22(3), 21-29. doi:doi:10.1111/j.1745-3992.2003.tb00134.x
  4. Cai, J. (2005). U.S. and Chinese teachers' constructing, knowing, and evaluating representations to teach mathematics. Mathematical Thinking and Learning, 7(2), 135-169. doi:10.1207/s15327833mtl0702_3
  5. Cai, J., & Nie, B. (2007). Problem solving in Chinese mathematics education: Research and practice. ZDM, 39(5), 459-473. doi:10.1007/s11858-007-0042-3
  6. Fulmer, G. W. (2011). Estimating critical values for strength of alignment among curriculum, assessments, and instruction. Journal of Educational and Behavioral Statistics, 36(3), 381-402. doi:10.3102/1076998610381397
  7. Fulmer, G. W., Tanas, J., & Weiss, K. A. (2018). The challenges of alignment for the Next Generation Science Standards. Journal of Research in Science Teaching, 55(7), 1076-1100. doi:doi:10.1002/tea.21481
  8. 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. Retrieved from Chapel Hill, NC: http://www.horizon-research.com/reports/2011/CCSSMresearchagenda/research_agenda.pdf
  9. Herman, J. L., & Webb, N. M. (2007). Alignment methodologies. Applied Measurement in Education, 20(1), 1-5. doi:10.1080/08957340709336727
  10. Herman, J. L., Webb, N. M., & Zuniga, S. A. (2007). Measurement issues in the alignment of standards and assessments. Applied Measurement in Education, 20(1), 101-126. doi:10.1080/08957340709336732
  11. Hong, D. S. (2011). Best known problem solving strategies in ‘high-stakes’ assessments. International Journal of Mathematical Education in Science and Technology, 42(6), 823-829. doi:10.1080/0020739X.2011.562321
  12. Hong, D. S., & Choi, K. M. (2011). Korean college entrance exams: An inside look. The Mathematics Teacher, 105(3), 208-213. doi:10.5951/mathteacher.105.3.0208
  13. Hong, D. S., & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: The case of quadratic equations. Educational Studies in Mathematics, 85(2), 241-263. doi:10.1007/s10649-013-9512-4.
  14. Hong, D. S., & Choi, K. M. (2018). A comparative analysis of linear functions in Korean and American standards-based secondary textbooks. International Journal of Mathematical Education in Science and Technology, 49(7), 1025-1051. doi:10.1080/0020739X.2018.1440327
  15. Hong, D. S., Choi, K. M., Runnalls, C., & Hwang, J. (2018). Do textbooks address known learning challenges in area measurement? A comparative analysis. Mathematics Education Research Journal, 30(3), 325-354. doi:10.1007/s13394-018-0238-6
  16. Hwang, H., & Han, H. (2014). Current national mathematics curriculum. Hackensack, UNITED STATES: World Scientific Publishing Co Pte Ltd.
  17. Liang, L. L., & Yuan, H. (2008). Examining the alignment of Chinese national physics curriculum guidelines and 12th-grade exit examinations: A case study. International Journal of Science Education, 30(13), 1823-1835. doi:10.1080/09500690701689766
  18. Liu, X. (1996). Mathematics and science curriculum change in the People's Republic of China. Lewiston, NY: Edwin Mellen.
  19. Liu, X., & Fulmer, G. (2008). Alignment between the science curriculum and assessment in selected NY State regents exams. Journal of Science Education and Technology, 17(4), 373-383. doi:10.1007/s10956-008-9107-5
  20. Liu, X., Zhang, B., Liang, L. L., Fulmer, G., Kim, B., & Yuan, H. (2009). Alignment between the physics content standard and the standardized test: A comparison among the United States-New York State, Singapore, and China-Jiangsu. Science Education, 93(5), 777-797. doi:doi:10.1002/sce.20330
  21. Lu, Q., & Liu, E. (2012). Alignment between high school biology curriculum standard and the standardised tests of four provinces in China. Journal of Biological Education, 46(3), 149-164. doi:10.1080/00219266.2011.645855
  22. Lv, S.-h., & Cao, C. (2018). The evolution of mathematics curriculum and teaching materials in secondary schools in the twenty-first century. In Y. Cao & F. K. S. Leung (Eds.), The 21st century mathematics education in China (pp. 147-169). Berlin, Heidelberg: Springer Berlin Heidelberg.
  23. Ma, H., Fulmer, G. W., Liang, L. L., Chen, X., Li, X., & Li, Y. (2013). An alignment analysis of junior high school chemistry curriculum standards and city-wide exit exams in China. In M.-H. Chiu, H.-L. Tuan, H.-K. Wu, J.-W. Lin, & C.-C. Chou (Eds.), Chemistry education and sustainability in the global age (pp. 157-169). Dordrecht: Springer Netherlands.
  24. Martone, A., & Sireci, S. G. (2009). Evaluating alignment between curriculum, assessment, and instruction. Review of Educational Research, 79(4), 1332-1361. doi:10.3102/0034654309341375
  25. Ministry of Education in Korea. (2011). The mathematics curriculum standards. Retrieved from Seoul, Korea: http://ncic.go.kr/mobile.revise.board.list.do
  26. Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). The TIMSS 2011 international results in mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.
  27. Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Retrieved from Boston College: http://timssandpirls.bc.edu/timss2015/international-results/
  28. Nam, J. (2014). Mathematics test in the CSAT. In J. Kim & H. Han (Eds.), Mathematics education in Korea (pp. 289-306). Hackensack, NJ: World Scientific Publishing.
  29. Newton, J., & Kasten, S. (2013). Two models for evaluating alignment of state standards and assessments: Competing or complementary perspectives? Journal for Research in Mathematics Education, 44(3), 550-580. doi:10.5951/jresematheduc.44.3.0550
  30. Organisation for Economic Cooperation and Development [OECD]. (2015). Database-PISA 2015. Retrieved from http://www.oecd.org/pisa/pisa-2015-results-infocus.
  31. Polikoff, M. S. (2015). How well aligned are textbooks to the Common Core Standards in Mathematics? American Educational Research Journal, 52(6), 1185-1211. doi:10.3102/0002831215584435
  32. Polikoff, M. S., Porter, A. C., & Smithson, J. (2011). How well aligned are state assessments of student achievement with state content standards? American Educational Research Journal, 48(4), 965-995. doi:10.3102/0002831211410684
  33. Resnick, L. B., Rothman, R., Slattery, J. B., & Vranek, J. L. (2004). Benchmarking and alignment of standards and testing. Educational Assessment, 9(1-2), 1-27. doi:10.1080/10627197.2004.9652957
  34. Schmidt, W. H., & Prawat, R. S. (2006). Curriculum coherence and national control of education: issue or non-issue? Journal of Curriculum Studies, 38(6), 641-658. doi:10.1080/00220270600682804
  35. Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525-559. doi:10.1080/0022027042000294682
  36. Son, J.-W., & Hu, Q. (2016). The initial treatment of the concept of function in the selected secondary school mathematics textbooks in the US and China. International Journal of Mathematical Education in Science and Technology, 47(4), 505-530. doi:10.1080/0020739X.2015.1088084
  37. Son, J.-W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117-142. doi:10.1007/s10649-010-9229-6
  38. Tu, R. (2018). Primary and secondary mathematics selective examinations. In Y. Cao & F. K. S. Leung (Eds.), The 21st century mathematics education in China (pp. 453-478). Berlin, Heidelberg: Springer Berlin Heidelberg.
  39. Tyler, R. (1949). Basic principles of curriculum and instruction. In. Chicago: University of Chicago Press.
  40. Valverde, G., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht, Netherlands: Kluwer.
  41. Wang, L., Liu, Q., Du, X., & Liu, J. (2018). Chinese mathematics curriculum reform in the twentyfirst century. In Y. Cao & F. K. S. Leung (Eds.), The 21st century mathematics education in China (pp. 53-72). Berlin, Heidelberg: Springer Berlin Heidelberg.
  42. Webb, N. L. (1997a). Criteria for alignment of expectations and assessments in mathematics and science education. Madison, WI: University of Wisconsin-Madison, Wisconsin Center for Education Research.
  43. Webb, N. L. (1997b). Determining alignment of expectations and assessments in mathematics and science education. NISE Brief, 1(2), 1-8.
  44. Webb, N. L. (1999). Alignment of science and mathematics standards and assessments in four states (Research Monograph No. 18). Madison, WI: University of Wisconsin-Madison, National Institute for Science Education.
  45. Webb, N. L. (2007). Issues related to judging the alignment of curriculum standards and assessments. Applied Measurement in Education, 20(1), 7-25. doi:10.1080/08957340709336728