A Comparative Analysis of
Geometry Education on Curriculum
Standards, Textbook Structure, and
Textbook Items between the U.S.
and Korea

Kyong Mi Choi; Hye-Jin Park

doi:10.12973/eurasia.2013.947a

A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea

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Kyong Mi Choi ¹ ^* , Hye-Jin Park ²

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¹ University of Iowa, USA² University of Hawaii at Manoa, USA^* Corresponding Author

Abstract

This study compares American and Korean curriculum standards, textbooks, and geometry items to help explain the consistent differences that have been found between the achievement levels of U.S. and Korean students in the Program for International Student Assessment (PISA) mathematics. Since PISA measures the mathematical proficiency of 15-year-old students, this study focuses primarily on 8th-grade curriculum standards and textbooks. The findings provide valuable information for curriculum designers and textbook editors to help improve the quality of geometry curricula and textbooks. Teachers can also use these findings to assess the proficiency levels of items in the textbooks they use, so that they can develop lesson plans appropriate to the ability of their students and select relevant problems for their classes.

Keywords

PISA
geometry
mathematics textbook
item difficulty
mathematics curriculum

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2013, Volume 9, Issue 4, 379-391

https://doi.org/10.12973/eurasia.2013.947a

Publication date: 14 Dec 2013

Article Views: 2661

Article Downloads: 1416

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References

Afari, E., Aldridge, J., Fraser, B. (2012) Effectiveness of using games in tertiary-level mathematics classrooms. International Journal of Science and Mathematics Education, 10, 1369–1392.
Battista, M. T. (2007). The development of geometric and spiral thinking. In F. K. Lester Jr. (ed.), Second handbook of research on mathematics teaching and learning (pp. 843— 908). Charlotte, NC: Information Age.
Cai, J. (2001). Improving mathematics learning: Lessons from cross-national studies of U.S. and Chinese students. Phi Delta Kappan, 82(5), 400-405.
Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended Treatments of Arithmetic Average in U.S. and Asian School Mathematics Textbooks. School Science and Mathematics, 102(8), 391--404.
Cogan, L. S., & Schmidt, W. H. (1999). What we’ve learned from the TIMSS: Middle school math reform. Available online at: http://ustimss.msu.edu/midmathreform.html.
Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers' learning. Elementary School Journal, 103(3), 287--311.
Connected Math Project (2006). Connected math project. Michigan State University. Available online at: http://showmecenter.missouri.edu/showme/cmp.shtm l, accessed July 9, 2008.
Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347--362.
Education Market Research (2002, October). K-12 market size and growth rates. Available online at: http://www.edmarket.com/r_c_archives/display_article.php?article_id =46, accessed July 10, 2008.
Ernest, P. (1996). The negative influence of "Progressive" ideas on school mathematics. Mathematics in School, 25(2), 6--7.
Fan, L., & Zhu, Y. (2007). Representation of Problem-Solving Procedures: A Comparative Look at China, Singapore, and American Mathematics Textbooks. Educational Studies in Mathematics, 66(1), 61--75.
Fujita, T., & Jones, K. (2002). The bridge between practical and deductive geometry: Developing the "geometrical eye." In D. Cockburn and E. Nardi (eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, Vol 2 (pp. 384--391). Norfolk, UK: University of East Anglia
Fujita, T., Jones, J., & Kunimune, S. (2009). The design of textbooks and their influences on students' understanding of 'proof' in lower secondary school. In Fou-Lai Lin, Feng-Jui Hsieh, Gila HAnna, Michael de Villiers (eds.), Proceedings of the ICMI Study 19th Conference: Proof and Proving in Mathematics Education (Vol 1, pp. 172—177). Taipei, Taiwan: National Taiwan Normal University.
Fuson, K. C., Stigler, J. W., & Bartsch, K. (1988). Grade placement of addition and subtraction topics in Japan, mainland China, the Soviet Union, Taiwan, and the United States. Journal for Research in Mathematics Education, 19(5), 449--456.
Garelick, B. (2006). Miracle math: A successful program from Singapore tests the limits of school reform in the suburbs. Education Next, 6(4).
Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1--38.
Ginsburg, A., Cooke, G., Leinwand, S., Noell, J., & Pollock, E. (2005). Reassessing U.S. international mathematics performance: New findings from the 2003 TIMSS and PISA Washington, DC: American Institutes for Research.
Haggarty, L., & Pepin, B. (2002). An Investigation of Mathematics Textbooks and their Use in English, French and German Classrooms: who gets an opportunity to learn what? British Educational Research Journal, 28(4), 567--590.
Hechinger, J. (2006). Arithmetic problem: New report urges return to basics I teaching math. Available online at: http://online.wsj.com/article/SB115802278519360136.html.
Herbel-Eisenmann, B. A. (2007). From Intended Curriculum to Written Curriculum: Examining the "Voice" of a Mathematics Textbook. Journal for Research in Mathematics Education, 38(4), 344--369.
Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M. et al. (2005). Mathematics Teaching in the United States Today (and Tomorrow): Results From the TIMSS 1999 Video Study. Educational Evaluation and Policy Analysis, 27(2), 111--132.
Howson, A. G. (1995). Mathematics textbooks: a comparative study of grade 8 texts. Vancouver, Canada: Pacific Educational Press.
Institute of Education Sciences (2003). American performance in mathematics literacy and problem solving. Available online at: http://nces.ed.gov/surveys/pisa/pisa2003highlights_2. asp, accessed July 7, 2008.
Jennings, S. and Dunne, R. (1996). A critical appraisal of the National Curriculum by comparison with the French experience. Teaching Mathematics and its Applications, 15(2), 49--55.
Kim, H. (1993). A Comparative Study between an American and a Republic of Korean Textbook Series" Coverage of Measurement and Geometry Content in First through Eighth Grades. School Science and Mathematics, 93(3), 123--126.
Korean Department of Education. (1999). Je chilcha suhak kyoyuk kwajung [The 7th National Mathematics Curriculum Standards for the 8th grade] Seoul, Korea: Korean Department of Education.
Lappan, G., Fey, J. T., Fitgerald, W., Friel, S. N., & Phillips, E. D. (2006). Connected Mathematics 2- Grade 8th Student Textbook. Boston, MA: Upper Saddle River, NJ: Prentice Hall.
Leung, F. K. S. (2005). Some characteristics of East Asian mathematics classrooms based on data from TIMSS 1999 video study. Educational Studies in Mathematics, 60(2), 199--215.
Li, Y. (2008). What teachers need to do and what they learned in the United States and China. In Z. Usiskin, & E. Willmore (Eds.), Mathematics curriculum in pacific rim countries - China, Japan, Korea, and Singapore (pp. 183-195). Charlotte, NC: Information Age.
Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234--241.
Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32(2), 443--460.
McKnight, C. C., Crosswhite, F. J., Dossey, J. A., Kifer, E., Swafford, J. O., Travers, K. J., & Cooney, T. J. (1987). The underachieving curriculum: Assessing U.S. school mathematics from an international perspective. Champaign, IL: Stipes.
Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco, CA: Jossey-Bass.
National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
NCTM (2000). Principles and Standards for Mathematics. Reston, VA: NCTM.
NCTM (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: a quest for coherence. Reston, VA: NCTM.
OECD (2003). The PISA 2003 Assessment Framework - Mathematics, Reading, Science and Problem Solving Knowledge and Skills. Paris: OECD.
OECD (2004). Learning for Tomorrow's World: First Results from PISA 2003. Paris: OECD.
OECD (2005). PISA 2003 technical report. Paris: OECD.
OECD (2010). PISA 2009 results: What students know and can do - student performance in reading, mathematics and science. Paris: OECD.
Park, K., & Leung, F. K. S. (2006). A comparative study of Arithmetic Problems in China, England, Japan, Korea, and the United States. In F.K.S. Leung, K.-D. Graf, & F. J. Lopez-Real (eds.), Mathematics Education in Different Cultural Traditions - A Comparative Study of East Asia and the West (Vol. 9, pp. 227--238) New York, NY: Springer.
Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why Mathematics Textbooks Matter. Educational Leadership, 61(5), 61--66.
Schmidt, W. H., McKnight, C. E., Valverde, G.A., Houng, R.T., & Wiley, D.E. (1997). Many visions, many aims: A cross-national investigation of curricula intentions in school mathematics. Dordrecht, The Netherlands: Kluwer.
Schoenfeld, A. (1983). Beyond the purely cognitive: Belief systems, social cognitions, and metacognitions as driving forces in intellectual performance. Cognitive Science, 7, 329--363.
Senk, S. L., & Thompson, D. R. (2003). Standard-based school mathematics curricula: What are they? what do students learn? Mahwah, NJ: Erlbaum.
Silver, E. (2009). Cross-national comparisons of mathematics curriculum materials: What might we learn? ZDM, 41(6), 827-832. doi: 10.1007/s11858-009-0209-1
Snider, V. E. (2004). A Comparison of Spiral versus Strand Curriculum. Journal of Direct Instruction, 4(1), 29--39.
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.
Stake, R. E. (2000). Case studies. In N. K. Denzin and Y. S. Lincoln (eds), Handbook of qualitative research (pp. 435-- 454). Thousand Oaks, CA: Sage.
Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3(3), 153--171.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: The Free Press.
Stigler, J. W., Lee, S.-y., Lucker, G. W., & Stevenson, H. W. (1982). Curriculum and achievement in mathematics: A study of elementary school children in Japan, Taiwan, and the United States. Journal of Educational Psychology, 74(3), 315-322.
Sweller, J., & Cooper, G.A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Istruction, 2, 59--89.
Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. J. (2008). The Impact of Middle-Grades Mathematics Curricula and the Classroom Learning Environment on Student Achievement. Journal for Research in Mathematics Education, 39(3), 247--280.
Yang, S. G., Park, Y. S., Park, W. S., Bae, J. S., Sung, D. H., Lee, S. G. et al. (2001). Chunghakgyo Suhak 8-Na [Middle School Mathematics 8-B]. Seoul, Korea: Gumsung.

How to cite this article

APA

Choi, K. M., & Park, H.-J. (2013). A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea. Eurasia Journal of Mathematics, Science and Technology Education, 9(4), 379-391. https://doi.org/10.12973/eurasia.2013.947a

Vancouver

Choi KM, Park HJ. A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea. EURASIA J Math Sci Tech Ed. 2013;9(4):379-91. https://doi.org/10.12973/eurasia.2013.947a

AMA

Choi KM, Park HJ. A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea. EURASIA J Math Sci Tech Ed. 2013;9(4), 379-391. https://doi.org/10.12973/eurasia.2013.947a

Chicago

Choi, Kyong Mi, and Hye-Jin Park. "A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea". Eurasia Journal of Mathematics, Science and Technology Education 2013 9 no. 4 (2013): 379-391. https://doi.org/10.12973/eurasia.2013.947a

Harvard

Choi, K. M., and Park, H.-J. (2013). A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea. Eurasia Journal of Mathematics, Science and Technology Education, 9(4), pp. 379-391. https://doi.org/10.12973/eurasia.2013.947a

MLA

Choi, Kyong Mi et al. "A Comparative Analysis of Geometry Education on Curriculum Standards, Textbook Structure, and Textbook Items between the U.S. and Korea". Eurasia Journal of Mathematics, Science and Technology Education, vol. 9, no. 4, 2013, pp. 379-391. https://doi.org/10.12973/eurasia.2013.947a