Skip to main content

A comparison of Korean and American secondary school textbooks: the case of quadratic equations

Educational Studies in Mathematics volume 85, pages 241–263 (2014)Cite this article

Abstract

This study compares quadratic equations sections of Korean and American textbooks. The number of topics, contents and mathematics items were analyzed. The results show Korean students learn some topics relatively earlier than American students. American textbooks include more problems requiring explanations and various representations and problems requiring higher level cognitive demand. This result could indicate that textbooks might not be the reason for American and Korean students’ performances in international comparative studies. More studies analyzing other standards based textbooks and teaching practice might be needed to have further understanding of mathematics education in two countries.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Notes

  1. Since CPMP does not contain worked examples with complete solutions, we did not compute the percentage.

References

  • Cai, J. (1995). A cognitive analysis of U.S. and Chinese students’ mathematical performance on tasking involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education (Monograph series 7). Reston, VA: National Council of Teachers of Mathematics.

  • Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students’ solving process-constrained and process-open problems. Mathematical Thinking and Learning, 2, 309–340.

    Article  Google Scholar 

  • Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatments of arithmetic average in U.S. and Asian school mathematics. School Science and Mathematics, 102, 391–404.

    Article  Google Scholar 

  • Cai, J., Nie, B., & Moyer, J. C. (2010). The teaching of equation solving: Approaches in standards-based and traditional curricula in the United States. Pedagogies: An International Journal, 5, 170–186.

    Article  Google Scholar 

  • Charalambous, C., Delaney, S., Hui-Yu, H., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12, 117–151.

    Article  Google Scholar 

  • Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf

  • Fan, L., & Zhu, Y. (2007). Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks. Educational Studies in Mathematics, 66, 61–75.

    Article  Google Scholar 

  • Ferrini-Mundy, J., & Schmidt, W. H. (2005). Research commentary: International comparative studies in mathematics education: Opportunities for collaboration and challenges for researchers. Journal for Research in Mathematics Education, 36, 164–175.

    Google Scholar 

  • Fey, J. T., Schoen, H. L., Watkins, A. E., Hirsh, C. R., & Hart, E. W. (2008). Core-plus mathematics: Contemporary mathematics in context, course 3. Columbus: Glencoe/McGraw-Hill.

    Google Scholar 

  • Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19–25.

    Google Scholar 

  • Fuson, K. C., Stigler, J. W., & Bartsch, K. B. (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, 449–456.

    Article  Google Scholar 

  • Garner, R. (1992). Learning from school texts. Educational Psychologist, 27, 43–53.

    Article  Google Scholar 

  • Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59–78.

    Article  Google Scholar 

  • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J. K., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study, (NCES 2003-013 Revised). Washington, DC: U.S. Department of Education, National Center for Education Statistics.

    Google Scholar 

  • Hiebert, J., Stigler, J., Jacobs, J., 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, 27(2), 111–132.

    Article  Google Scholar 

  • Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30, 393–425.

    Article  Google Scholar 

  • Hirsch, C. R., Fey, J. T., Hart, E. W., Schoen, H. L., & Watkins, A. E. (2007). Core-plus mathematics: Contemporary mathematics in context, course 1. Columbus: Glencoe/McGraw-Hill.

    Google Scholar 

  • Hirsch, C. R., Schoen, H. L., Fey, J. T., Watkins, A. E., & Hart, E. W. (2007). Core-plus mathematics: Contemporary mathematics in context, course 2. Columbus: Glencoe/McGraw-Hill.

    Google Scholar 

  • Judson, T. W., & Nishimori, T. (2005). Concepts and skills in high school calculus: An examination of a special case in Japan and the United States. Journal for Research in Mathematics Education, 36, 24–43.

    Google Scholar 

  • Kang, O. K., Jung, S., & Lee, H. (2008). Joonghakyo Soohak 9-Ga [Middle School Mathematics 9-A]. Seoul: Dusan.

    Google Scholar 

  • Kang, O. K., et al. (2001). Godunghakyo Soohak 10-Ga [High School Mathematics 10-A]. Seoul: Joongang Education.

    Google Scholar 

  • Kang, H., et al. (2007). Joonghakyo Soohak 9-Ga [Middle School Mathematics 9-A]. Seoul: Joongang Education.

    Google Scholar 

  • Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317–326.

    Article  Google Scholar 

  • Korean Textbook Research Foundation (KTRF) (1998). A study on making list of all textbooks published in Korea since 1945 and studying how to collect these textbooks. Seoul: KTRF.

  • Kramer, S. L., & Keller, R. (2008). A brief report: An existence proof: Successful joint implementation of the IMP curriculum and a 4 × 4 block schedule at a suburban U.S. high school. Journal for Research in Mathematics Education, 39, 2–8.

    Google Scholar 

  • Leung, F. K. S. (2005). Some characteristics of East Asian mathematics classrooms based on data from the TIMSS 1999 video study. Educational Studies in Mathematics, 60, 199–215.

    Article  Google Scholar 

  • 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, 234–241.

    Article  Google Scholar 

  • Lins Lessa, M. M. (1995). A balança de dois pratos versus problemas verbais na iniciação à algebra [Two-pan scale versus verbal problems in introductory algebra] (Unpublished master’s thesis). Universidade Federal de Pernambuco, Recife, Brazil.

  • MacGregor, M., & Stacey, K. (1993). Cognitive models underlying students’ formulation of simple linear equations. Journal for Research in Mathematics Education, 24, 217–232.

    Article  Google Scholar 

  • MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11-15. Educational Studies in Mathematics, 33, 1–19.

    Article  Google Scholar 

  • 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, 443–460.

    Google Scholar 

  • Ministry of Education (MOE) in Korea. (2007). The seventh national mathematics curriculum. Seoul: MOE.

  • National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.

  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

  • Renkl, A. (2002). Worked-out examples: Instructional explanations support learning by self-explanations. Learning and Instruction, 12, 529–556.

    Article  Google Scholar 

  • Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 61(5), 61–66.

    Google Scholar 

  • Riordan, J. E., & Noyce, P. E. (2001). The impact of two standards-based mathematics curricula on student achievement in Massachusetts. Journal for Research in Mathematics Education, 32, 368–398.

    Article  Google Scholar 

  • Schliemann, A. D., Carraher, D. W., Brizuela, B., & Jones, W. (1998). Solving algebra problems before algebra instruction. Paper presented at the Second Meeting of the Early Algebra Research Group, Medford, MA.

  • Schmidt, W. H. (2005). A vision for mathematics. Educational Leadership, 61(5), 6–11.

    Google Scholar 

  • Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H. C., Wiley, D. E., Cogan, L. S., et al. (2001). Why schools matter: A cross national comparison of curriculum and learning. San Francisco: Jossey-Bass.

    Google Scholar 

  • Schoen, H. L., & Hirsch, C. R. (2003a). Responding to calls for change in high school mathematics: Implications for collegiate mathematics. American Mathematical Monthly, 110(2), 109–123.

    Article  Google Scholar 

  • Schoen, H. L., & Hirsch, C. R. (2003b). The core-plus mathematics project: Perspectives and student achievement. In S. Senk & D. Thompson (Eds.), Standards-oriented school mathematics curricula: What are they? What do students learn? (pp. 311–344). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Seeley, C., & Schielack, J. F. (2007). A look at the development of algebraic thinking in curriculum focal points. Mathematics Teaching in the Middle School, 13, 266–269.

    Google Scholar 

  • Son, J., & Senk, S. (2010). How standards curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74, 117–142.

    Article  Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in standards classrooms. American Educational Research Journal, 33, 455–488.

    Article  Google Scholar 

  • Steinberg, R., Sleeman, D., & Ktorza, D. (1990). Algebra students knowledge of equivalence of equations. Journal for Research in Mathematics Education, 22, 112–121.

    Article  Google Scholar 

  • Stevenson, H. W., & Bartsch, K. (1992). An analysis of Japanese and American textbooks in mathematics. In R. Leetsman & H. J. Walberg (Eds.), Japanese educational productivih (pp. 103–134). Greenwich, CT: JAI Press.

  • Stigler, J., Fuson, K., 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, 153–171.

    Article  Google Scholar 

  • Stigler, J. W., & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 65(1), 12–16.

    Google Scholar 

  • 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, 315–322.

    Article  Google Scholar 

  • Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. (2008). The impact of middles grades mathematics curricula and the classroom learning environment on student achievement. Journal for Research in Mathematics Education, 39, 247–280.

    Google Scholar 

  • Wagner, S. (1981). Conservation of equation and function under transformations of variable. Journal for Research in Mathematics Education, 12, 107–118.

    Article  Google Scholar 

  • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Westbury, I. (1992). Comparing American and Japanese achievement: Is the United States really a low achiever? Educational Researcher, 21(5), 18–24.

    Article  Google Scholar 

  • Wu, M. (2006). A comparison of mathematics performance between East and West: What PISA and TIMSS can tell us. 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 (pp. 227–238). New York: Springer.

    Google Scholar 

  • Yim, J., et al. (2001). Godunghakyo Soohak 10-Ga [High School Mathematics 10-A]. Seoul: Doosan.

    Google Scholar 

  • Zhu, Y., & Fan, L. (2006). Focus on the representation of problem types in intended curriculum: A comparison of selected mathematics textbooks from mainland China and the United States. International Journal of Science and Mathematics Education, 4, 609–626.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Iowa, Iowa City, IA, USA

    Dae S. Hong & Kyong Mi Choi

Authors
  1. Dae S. Hong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kyong Mi Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dae S. Hong.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hong, D.S., Choi, K.M. A comparison of Korean and American secondary school textbooks: the case of quadratic equations. Educ Stud Math 85, 241–263 (2014). https://doi.org/10.1007/s10649-013-9512-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-013-9512-4

Keywords

  • Comparative study
  • Textbook analysis
  • Cognitive demand of mathematics items