A Comparison of Geometry Problems in Middle-Grade Mathematics Textbooks from Taiwan, Singapore, Finland, and the United States

1 | National Chiayi University, Graduate Institute of Mathematics and Science Education, Department of Education |

2 | National Central University, Graduate Institute of Statistics |

3 | Graduate Institute of Mathematics and Science Education, National Tsing Hua University, Graduate Institute of Mathematics and Science Education |

**CORRESPONDING AUTHOR**

Tzu-Ling Wang

Graduate Institute of Mathematics and Science Education, National Tsing Hua University, Graduate Institute of Mathematics and Science Education, No.521, Nan-Da Rd., 30014 Hsinchu City, Taiwan

Graduate Institute of Mathematics and Science Education, National Tsing Hua University, Graduate Institute of Mathematics and Science Education, No.521, Nan-Da Rd., 30014 Hsinchu City, Taiwan

Publish date: 2017-06-15

EURASIA J. Math., Sci Tech. Ed 2017;13(7):2841–2857

KEYWORDS

TOPICS

ABSTRACT

**Background:**

This study analyzed geometry problems in four middle-grade mathematics textbook series from Taiwan, Singapore, Finland, and the United States, while exploring the expectations for students’ learning experiences with these problems.

**Material and methods:**

An analytical framework developed for mathematics textbook problem analysis had three dimensions: representation forms, contextual features, and response types.

**Results:**

The results showed that Taiwanese and Singaporean textbooks contained more problems in combined form, whereas Finnish and the American textbooks contained more problems in verbal and visual forms. The problem distribution across various representation forms was more balanced in the Finnish and Singaporean textbooks than in the Taiwanese and American textbooks. Most problems were non-application and close-ended problems compared to other application and open-ended problems. The Taiwanese textbooks contained the lowest proportion of real-world problems, whereas the American textbooks contained the highest proportion of open-ended problems.

**Conclusions:**

Implications of this study’s findings for textbook developers and future research directions are discussed.

REFERENCES (60)

1.

Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), 239–261.

2.

Altman, D. G. (1991). Practical statistics for medical research. London: Chapman & Hall.

3.

American Association for the Advancement of Science. (2000). Middle grades mathematics textbooks: A benchmarks-based evaluation. Washington DC: AAAS.

4.

Beaton, A. E., Mullis, I. V. Martin, M. O., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1996). Mathematics achievement in the middle school years: IEA’s third international mathematics and science study (TIMSS). Boston, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College.

5.

Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Durán, R., Smith-Reed, B., & Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663–689.

6.

Cai, J. (1995). A cognitive analysis of U.S. and Chinese students’ mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education Monograph, 7, 1–160.

7.

Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students’ solving of process- constrained and process-open problems. Mathematical thinking and Learning, 2(4), 309–340.

8.

Cai, J., & Cirillo, M. (2014). What do we know about reasoning and proving? Opportunities and missing opportunities from curriculum analyses. International Journal of Educational Research, 64, 132-140.

9.

Cai, J., Wang, N., Moyer, J. C., & Nie, B. (2011). Longitudinal investigation of the curriculum effect: An analysis of student learning outcomes from the LieCal Project. International Journal of Educational Research, 50(2), 117–136.

10.

Charalambous, C. Y., Delaney, S., Hsu, H.-Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117–151.

11.

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 & Technology Education, 9(4), 379–391.

12.

Delil, H. (2006). An analysis of geometry problems in 6-8 grades Turkish mathematics textbooks (Unpublished master’s thesis). Middle East Technical University, Ankara.

13.

Ding, M., & Li, X. (2010). A comparative analysis of the distributive property in U.S. and Chinese elementary mathematics textbooks. Cognition and Instruction, 28(12), 146–180.

14.

Doyle, W. (1983). Academic work. Review of Educational Research, 53, 159–199.

15.

Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23(2), 167–180.

16.

Dufour-Janvier, B., Berdnarz, N., & Belanger, M. (1987). Pedagogical considerations concerning the Problem of representation. In C. Janvier (Eds.), Problems of representations in the teaching and learning of Mathematics (pp.109–122). Hillsdale, NJ: Lawrence Erlbaum Associates.

17.

Fan, L. (1999). Applications of arithmetic in US and Chinese textbooks: A comparative study, In G. Kaiser, E. Luna & I. Huntley (Eds.), Studies in mathematics education series: II. International comparisons in mathematics education (pp. 151–162). London: Falmer Press.

18.

Fan, L., & Zhu, Y. (2000). Problem solving in Singaporean secondary mathematics textbooks. The Mathematics Educator, 5(1/2), 117–141.

19.

Fan, L., Chen, J., Zhu, Y., Oiu, X., & Hu, Q. (2004). Textbook use within and beyond Chinese classrooms: A study of 12 secondary schools in Kunming and Fuzhou of China. In F. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics (pp. 228–261). Singapore: World Scientific.

20.

Fan, L., Zhu, Y., & Miao, Z. (2013). Textbooks research in mathematics education: Development, status and direction. ZDM, 45, 633–646.

21.

Greeno, J. G. (1991). Number sense as situated knowing in a conceptual domain. Journal of Research in Mathematics Education, 22(3), 170–218.

22.

Grishchenko, S. (2009). A comparative analysis of word problems in selected United States and Russian first grade textbooks (Unpublished doctoral dissertation). University of California, Santa Barbara.

23.

Gu, L., Huang, R., & Marton, F. (2004). Teaching with Variation: An effective way of mathematics teaching in China. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 309–345). Singapore: World Scientific.

24.

Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (Vol. 1, pp. 371–404). Charlotte, NC: Information Age Publishing.

25.

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.

26.

Husén, T. (Ed.). (1967). International study of achievement in mathematics: A comparison of twelve countries (Vol. 2). New York: John Wiley & Sons.

27.

Kang Hsuan Educational Publishing Group. (2010). Mathematics textbook 1A-6B. Taiwan: Kang Hsuan.

28.

Kolovou, A., van den Heuvel-Panhuizen, M., & Bakker, A. (2009). Non-routine problem solving tasks in primary school mathematics textbooks: A needle in a haystack. Mediterranean Journal for Research in Mathematics Education, 8(2), 31–68.

29.

Kwon, O. N., Park, J. S., & Park, J. H. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7(1) 51–61.

30.

Lappan, S., Fey, J. T., Fitzgerald, W., Friel, S., & Phillips, E. D. (1996). A guild to the connected mathematics curriculum: Getting to know connected mathematics. Palo Alto, CA: Dale Seymour.

31.

Laurinoli, T., Lindroos-Heinänen, R., Luoma-aho, E., Sankilampi, T., Selenius, R., Talvitie, K. & Vähä-Vahe, O. (2008). Laskutaito 7–9. Helsinki, Finland: WOSY.

32.

Leung, K. S. F. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51.

33.

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.

34.

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.

35.

Ministry of Education in Singapore. (2001). Mathematics syllabus lower secondary, Singapore: Curriculum Planning and Development Division, Ministry of Education.

36.

Mullis, I., Martin, M.O., Foy, P. & Arora, A. (2012). TIMSS 2011 International results in mathematics. Chestnut Hill, MA, USA: TIMSS & PIRLS International Study Center, Lynch School of Education, Boston College.

37.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: NCTM.

38.

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

39.

National Research Council. (2001). Helping children learn mathematics. Washington, DC: National Academy Press.

40.

Organization for Economic Co-operation & Development (OECD). (2013). PISA 2012 results: What students know and can do: Student performance in mathematics, reading and science (Vol. I). Paris: OECD.

41.

Özer, E., & Sezer, R. (2014). A comparative analysis of questions in American, Singaporean, and Turkish mathematics textbooks based on the topics covered in 8th grade in Turkey. Educational Sciences: Theory and Practice, 14 (1), 411–421.

42.

Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why Mathematics Textbooks Matter. Educational Leadership, 61(5), 61–66.

43.

Riley, M. S., Greeno, J. G., & Heller, J. I. (1983). Development of children’s problem–solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153–196). New York: Academic Press.

44.

Rivette, K., Grant, Y., Ludema, H., & Rickard, A. (2003). Connected mathematics project: Research and evaluation summary. Upper Saddle River, NJ: Prentice Hall.

45.

Stanic, G., & Kilpatrick, J. (1988). Historical perspective on problem solving in the mathematics curriculum. In R. Charles & E. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1–22). Reston: National Council of Teachers of Mathematics.

46.

Stein, M. K., & Smith, M. S. (2010). The influence of curriculum on students’ learning. In B. J. Reys, R. E., Reys, & R. Rubenstein (Eds.), Mathematics curriculum: Issues, trends, and future directions (pp. 351–362). Reston: National Council of Teachers of Mathematics.

47.

Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268–275.

48.

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.

49.

Sun, Y., Kulm, G., & Capraro, M. M. (2009). Middle grade teachers’ use of textbooks and their classroom instruction. Journal of Mathematics Education, 2(2), 20–37.

50.

Sweller, J., Chandler, P., Tierney, P., & Cooper, M. (1990). Cognitive load as a factor in the structuring of technical material. Journal of Experimental Psychology: General, 119, 176–192.

51.

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

52.

Teh, K. S., & Loh, C. Y. (2007). New syllabus Mathematics 1 (6th ed.). Singapore: Shinglee.

53.

Törnrros, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327.

54.

van Zanten, M., & van den Heuvel-Panhuizen, M. (2014). Freedom of design: The multiple faces of subtraction in Dutch primary school textbooks. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 231–259). Heidelberg: Springer.

55.

Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics 89(1), 41–65.

56.

Xin, Y. P. (2007). Word problem solving tasks in textbooks and their relation to student performance. Journal of Educational Research, 100(6), 347–359.

57.

Yang, D. C., & Lin, Y. C. (2016). Examining the differences of linear systems between Finnish and Taiwanese textbooks. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1265–1281.

58.

Yang, D. C., Reys, R. E., & Wu, L. L. (2010). Comparing how fractions were developed in textbooks used by the 5th- and 6th-graders in Singapore, Taiwan, and the U.S.A. School Science and Mathematics, 110(3), 118–127.

59.

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(4), 609–626.

60.

Zhu, Y., & Fan, L. (2004). An analysis of the representation of problem types in Chinese and US mathematics textbooks. Paper accepted for ICME-10 Discussion Group 14, 4-11 July: Copenhagen, Denmark.

Related articles