Skip to main content
Log in

How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Textbooks play an important part in the design of instruction. This study analyzed the presentation of fractions in textbooks designed for the elementary grades in Kuwait, Japan, and the USA. The analysis focused on the physical characteristics of the books, the structure of the lessons, and the nature of the mathematical problems presented. Findings showed USA and Kuwaiti mathematics textbooks are larger than Japanese textbooks; this larger size is consistent with a great deal of repetition. The Japanese texts do not address fractions until the third grade; they use linear models and connect fractions with measurement. In the USA and Kuwait, fractions are introduced in the first grade. The Harcourt text uses concrete material to help students learn fraction procedures. For the Kuwaiti series, the lessons depend on using some pictorial representation of the area model to illustrate fraction ideas. All these textbooks focus on standard algorithms as the main computational methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Alajmi, A. (2009). Addressing computational estimation in the Kuwaiti curriculum: Teachers’ views. Mathematics Teacher Education, 12(4), 263–283.

    Article  Google Scholar 

  • Alajmi, A., & Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65(1), 77–94.

    Article  Google Scholar 

  • Alajmi, A., & Reys, R. (2010). Examining eighth grade students’ recognition and interpretation of reasonable answers. International Journal of Science and Mathematics Education, 8(1), 117–139.

    Article  Google Scholar 

  • Andrews, G. A., McLeod, C. J., Bennett, M. J., Newman, V., Burton, M. G., Roby, T., et al. (2007a). Harcourt math. (Grade 1). Orlando: Harcourt.

    Google Scholar 

  • Andrews, G. A., McLeod, C. J., Bennett, M. J., Newman, V., Burton, M. G., Roby, T., et al. (2007b). Harcourt math. (Grade 2). Orlando: Harcourt.

    Google Scholar 

  • Andrews, G. A., McLeod, C. J., Bennett, M. J., Newman, V., Burton, M. G., Roby, T., et al. (2007c). Harcourt math. (Grade 3). Orlando: Harcourt.

    Google Scholar 

  • Andrews, G. A., McLeod, C. J., Bennett, M. J., Newman, V., Burton, M. G., Roby, T., et al. (2007d). Harcourt math. (Grade 4). Orlando: Harcourt.

    Google Scholar 

  • Andrews, G. A., McLeod, C. J., Bennett, M. J., Newman, V., Burton, M. G., Roby, T., et al. (2007e). Harcourt math. (Grade 5). Orlando: Harcourt.

    Google Scholar 

  • Arab Bureau of Education for the Gulf States. (2005a). Mathematics for fourth grade. Kuwait: Alriyadi Publication.

    Google Scholar 

  • Arab Bureau of Education for the Gulf States. (2005b). Mathematics for fifth grade. Kuwait: Alriyadi Publication.

    Google Scholar 

  • Arab Bureau of Education for the Gulf States. (2006a). Mathematics for first grade. Kuwait: Alriyadi Publication.

    Google Scholar 

  • Arab Bureau of Education for the Gulf States. (2006b). Mathematics for second grade. Kuwait: Alriyadi Publication.

    Google Scholar 

  • Arab Bureau of Education for the Gulf States. (2006c). Mathematics for third grade. Kuwait: International Group Press.

    Google Scholar 

  • Beaton, A., Mullis, I., Martin, M., Gonzalez, E., Kelly, D., & Smith, T. (1996). Mathematics achievement in the middle school years: IEA’s Third International Mathematics and Science Study (TIMSS). Chestnut Hill: TIMSS International Study Center, Boston College.

    Google Scholar 

  • Behr, M. J., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ration, proportion. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). New York: Macmillan.

    Google Scholar 

  • Bezuk, N., & Cramer, K. (1989). Teaching about fractions: What, when and how? In P. Trafton (Ed.), New directions for elementary school mathematics: 1989 Yearbook (pp. 156–167). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Carter, J., Li, Y., & Ferrucci, B. (1997). A comparison of how textbooks present integer addition and subtraction in China and the United States. The Mathematics Educator, 2(2), 197–209.

    Google Scholar 

  • Charalambous, C., Delaney, S., Hsu, H., & Mesa, M. (2010). A Comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning: An International Journal, 12(2), 117–151.

    Article  Google Scholar 

  • Chaval, K., & Reys, R. (2008). Effective use of manipulatives across elementary grade levels: Moving beyond isolated pockets of excellence to school-wide implementation. Journal of Mathematics Education Leadership, 10(1), 3–8.

    Google Scholar 

  • Education Market Research. (2005). Mathematics market, grades K-12: Teaching methods, textbooks/materials used and needed, and market size. Rockaway Park: Education Market Research.

    Google Scholar 

  • Flanders, J. R. (1987). How much of the content in mathematics is new? Arithmetic Teacher, 35(1), 18–23.

    Google Scholar 

  • Flanders, J. R. (1994). Textbooks, teachers, and the SIMS test. Journal for Research in Mathematics Education, 25(3), 260–278.

    Article  Google Scholar 

  • Fuson, K., Stigler, J., & Bartsch, K. (1988). Brief report: 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(4), 449–456.

    Article  Google Scholar 

  • Ginsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005). What the United States can learn from Singapore’s world-class mathematics system (and what Singapore learn from the United States): An exploratory study. American Institutes for Research. Retrieved from http://www.air.org/news/documents/Singapore.htm.

  • Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., & Frenwald, S. (2008). Highlights from TIMSS 2007: Mathematics science Achievement of U.S. fourth—and eighth—grade Students in an international context (NCES 2009–001 Revised). Washington: National Center for Education Statistics, US Department of Education.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hirsch, C., Lappan, G., Reys, B., & Reys, R. (2005). Curriculum as a focus for improving school mathematics. Mathematicians and Education Reform Forum Newsletter, 18(1), 1. 6–7, 12–14.

    Google Scholar 

  • Jones, D. L. (2004). Probability in middle grades mathematics textbooks: An examination of historical trends, 1957–2004. Unpublished doctoral dissertation, University of Missouri, Columbia, MO.

  • Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4–27.

    Google Scholar 

  • Kulm, G. (1999). Evaluating mathematics textbooks. Basic Education, 43(9). Retrieved November 2, 2006, from http://www.project2061.org/publications/articales/ articles/cbe.htm.

  • Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Charlotte: Information Age Publishing.

    Google Scholar 

  • Leinwand, S., & Ginsburg, A. (2007). Learning from Singapore math. Educational Leadership, 65(3), 31–35.

    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(1), 234–4.

    Article  Google Scholar 

  • Mullis, I., Martin, M., Beaton, A., Gonzalez, E., Kelly, D., & Smith, T. (1997). Mathematics achievement in the primary school years. IEA's third international mathematics and science study (TIMSS). Chestnut Hill: TIMSS, International Study Center, Boston College.

    Google Scholar 

  • National Mathematics Panel Report. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington: United States Department of Education.

    Google Scholar 

  • National Research Council. (2001). In J. Kilpatrick, J. Swafford, & B. Findell (Eds.), Adding it up: Helping children learn mathematics. Washington: National Academy Press.

    Google Scholar 

  • Porter, A. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3–14.

    Article  Google Scholar 

  • Porter, A. (2006). Curriculum assessment. In J. Green, G. Camilli, & P. Elmore (Eds.), Handbook of complementary methods in education research (pp. 141–159). Mahwah: Erlbaum.

    Google Scholar 

  • Reys, B., Reys, R., & Koyama, M. (1996). The development of computation in three Japanese primary-grade textbooks. The Elementary School Journal, 96(4), 423–437.

    Article  Google Scholar 

  • Robitaille, D. F., & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 687–709). New York: Macmillan.

    Google Scholar 

  • Schmidt, W., McKnight, C., & Raizen, S. (1997). A splintered vision: An investigation of U.S. science and mathematics education. Boston: Kluwer.

    Google Scholar 

  • Shimahara, N. K., & Sakai, A. (1995). Learning to teach in two cultures: Japan and The United States. New York: Garland.

    Google Scholar 

  • Stein, M., Remillard, J., & Smith, M. (2007). How curriculum influences students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557–628). Charlotte: Information Age.

    Google Scholar 

  • Tokyo Shoseki. (2006a). Mathematics for elementary school (Grade 3). Tokyo: Tokyo Shoseki Co., Ltd.

    Google Scholar 

  • Tokyo Shoseki. (2006b). Mathematics for elementary school (Grade 4). Tokyo: Tokyo Shoseki Co., Ltd.

    Google Scholar 

  • Tokyo Shoseki. (2006c). Mathematics for elementary school (Grade 5). Tokyo: Tokyo Shoseki Co., Ltd.

    Google Scholar 

  • Tyson-Bernstein, H., & Woodward, A. (1991). Nineteenth century policies for twenty-first century practice: The textbook reform dilemma. In P. G. Altbach, G. P. Kelly, H. G. Petrie, & L. Weis (Eds.), Textbooks in American society: Politics, policy, and pedagogy. Albany: State University of New York Press.

    Google Scholar 

  • Valverde, G. A., 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. Boston: Kluwer.

    Google Scholar 

  • Watanabe, T. (2001a). Content and organization of teacher’s manuals: An analysis of Japanese elementary mathematics teacher’s manuals. School Science and Mathematics, 101(4), 194–205.

    Article  Google Scholar 

  • Watanabe, T. (2001b). Let’s eliminate fraction instruction from primary curriculum. Teaching Children Mathematics, 8(2), 70–72.

    Google Scholar 

  • Watanabe, T. (2003). Teaching multiplication: An analysis of elementary school mathematics teachers’ manuals from Japan and the United States. The Elementary School Journal, 104(2), 111–125.

    Article  Google Scholar 

  • Watanabe, T. (2006). The teaching and learning of fractions: A Japanese perspective. Teaching Children Mathematics, 12(7), 368–374.

    Google Scholar 

  • Wearne, D., & Kouba, V. L. (2000). Rational numbers. In E. A. Silver & P. A. Kenny (Eds.), Results from the Seventh Mathematics Assessment of the National Assessment of Educational Progress (pp. 163–191). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Weiss, I. R., Pasley, J. D., Smith, P. S., Sanilower, E. R., & Heck, D. J. (2003). Looking inside the classroom: A study of K-12 mathematics and science education in United States. Chapel Hill: Horizon Research.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amal Hussain Alajmi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alajmi, A.H. How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educ Stud Math 79, 239–261 (2012). https://doi.org/10.1007/s10649-011-9342-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-011-9342-1

Keywords

Navigation