Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: The case of fraction division

ZDM - International Journal on Mathematics Education

Volumn 41, Issue 6, 2009, Pages 809-826

  Li, Yeping ^a   Chen, Xi ^a   An, Song ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Cross national study; Fraction computation; Mathematics curriculum; Textbook analysis

Indexed keywords

EID: 84867463854     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-009-0177-5     Document Type: Article

References (45)

1. Abels, M., Wijers, M., & Pligge, M. (2008). Revisiting numbers. In Wisconsin Center for Educational Research & Freudenthal Institute (Ed.), Mathematics in context. Chicago: Encyclopedia Britannica, Inc.
2. American Association for the Advancement of Science. (2000). Middle grades mathematics textbooks: A benchmarks-based evaluation. Washington, DC: American Association for the Advancement of Science.
3. Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatment of arithmetic average in US and Asian school mathematics textbooks. School Science and Mathematics, 102, 391-404.
4. Collins, W., Howard, A. C., Drisaa, L., McClain, K., Frey, P., Molina, D., et al. (1999). Mathematics: Applications and connections. Course 1. New York: McGraw-Hill Glencoe. Curriculum and Textbook Research Institute-Elementary Textbook.
5. Development Committee. (2006). Shuxue, liunianjie Shangce [Mathematics, Sixth grade (1)]. Beijing: People's Education Press.
6. Delaney, S., Charalambous, C. Y., Hsu, H. Y., & Mesa, V. (2007). The treatment of addition and subtraction of fractions in Cypriot, Irish, and Taiwanese textbooks. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st conference of the international group for the psychology of mathematics education (Vol. 2, pp. 193-200). Seoul: PME.
7. Dossey, J. O., Mullis, I. V. S., Lindquist, M. M., & Chambers, D. L. (1988). The mathematics report card: Are we measuring up?. Princeton: Educational Testing Service.
8. Education Development Center, the Seeing and Thinking Mathematics Project (2005). MathScape: Course 1. New York: McGraw-Hill Glencoe.
9. 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.
10. Flanders, J. (1994). Student opportunities in grade 8 mathematics: Textbook coverage of the SIMS test. In I. Westbury, C. A. Ethington, L. A. Sosniak, & D. P. Baker (Eds.), In search of more effective mathematics education: Examining data from the IEA Second International Mathematics Study (pp. 61-93). Norwood, NJ: Ablex.
11. 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, 449-456.
12. Griffiths, H. B., & Howson, A. G. (1974). Mathematics: Society and curricula. London: Cambridge University Press.
13. Howson, G. (1995). Mathematics textbooks: A comparative study of grade 8 texts. Vancouver: Pacific Educational Press.
14. Kazumatu, S., Okata, I., Machita, S., Aoyanagi, M., Kiyozawa, I., et al. (2007). Minna to manabu shogakkou Sansuu 6nen (gei) (Everybody learning: Elementary arithmetic, sixth grade, 2). Tokyo: Gakkou Tosho Kabushiki Kaisha.
15. Lappan, G., Fey, J. T., Fizgerald, W. M., Friel, S. N., & Phillips, E. D. (2008). Bits and pieces 2: Using fraction operations. In Michigan State University (Ed.), Connected mathematics project. Boston: Person Prentice Hall.
16. 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.
17. Li, Y. (2007a). Curriculum research to improve teaching and learning. School Science and Mathematics, 107, 166-168.
18. Li, Y. (2007b). Curriculum and culture: An exploratory examination of mathematics curriculum materials in their system and cultural contexts. The Mathematics Educator, 10(1), 21-38.
19. Li, Y. (2007c). Curriculum and cognition: A study on math problems. Academic Exchange Quarterly, 11(2), 86-91.
20. Li, Y. (2008a). Transforming curriculum from intended to implemented: 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: Information Age Publishing.
21. Li, Y. (2008b). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13, 546-552.
22. Li, Y., & Kulm, G. (2008). Knowledge and confidence of preservice mathematics teacher: The case of fraction division. ZDM-The International Journal on Mathematics Education, 40, 833-843.
23. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates.
24. 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.
25. McKnight, C. C., Crosswhite, F. J., Dossey, J. A., Kifer, E., Swafford, J. O., Travers, K. J., et al. (1987). The underachieving curriculum: Assessing US school mathematics from an international perspective. Champaign: Stipes.
26. Murata, A. (2008). Mathematics teaching and learning as a mediating process: The case of tape diagrams. Mathematical Thinking and Learning, 10, 374-406.
27. Nakahara, T., Azemori, T., Sakitani, S., Hirabayashi, I., Ida, S., et al. (2007). Shogakkou Sansuu 6nen (gei) (Elementary Arithmetic, sixth grade, 2). Osaka: Osaka Shoseki Kabushiki Kaisha.
28. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
29. National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: US Department of Education.
30. Reys, B. (Ed.). (2006). The intended mathematics curriculum as represented in state-level curriculum standards. Charlotte: Information Age.
31. Romberg, T. A. (1992). Problematic features of the school mathematics curriculum. In P. W. Jackson (Ed.), Handbook of research on curriculum (pp. 749-788). New York: Macmillan.
32. Schmidt, W. H., Houang, R., & Cogan, L. (2002). A coherent curriculum-The case of mathematics. American Educator, Summer, 2002, 1-18.
33. Schmidt, W. H., McKnight, C. C., & Raizen, S. A. (1997). A splintered vision: An investigation of US science and mathematics education. Dordrecht: Kluwer Academic Press.
34. Schmidt, W. H., McKnight, C. E., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many visions, many aims (Vol. 1): A crossnational investigation of curricular intentions in school mathematics. Dordrecht: Kluwer Academic Press.
35. Steen, L. A. (2007). How mathematics counts. Educational Leadership, 65(3), 8-14.
36. Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Charlotte: Information Age Publishing.
37. 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, 153-171.
38. 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.
39. Sugiyama, Y. (1987). Comparison of word problems in textbooks between Japan and the US. In J. P. Becker & T. Miwa (Eds.), Proceedings of US-Japan seminar on problem solving. Carbondale: Board of Trustees, Southern Illinois University.
40. Sugiyama, Y., Itaka, S., Ito, S., Aoyanagi, K., Nakano, Y., et al. (2007). Shinhen, Atarashi Sansuu 6 (New arithmetic) 6(1). Tokyo: Tokyo Shoseki Kabushiki Kaisha.
41. Sun, L., Wang, L., Lin, G., Chen, C., Li, X., et al. (2007). Shuxue, liunianji Shangce [Mathematics, sixth grade (1)]. Jiangsu, China: Jiangsu Education Publisher.
42. 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 in the world of textbooks. Dordrecht: Kluwer.
43. Westbury, I. (1992). Comparing American and Japanese achievement: Is the United States really an underachiever? Educational Researcher, 21(5), 18-24.
44. Willoughby, S. S. (1984). Mathematics for 21st century citizens. Educational Leadership, 41, 45-50.
45. Xia, M., Li, W., Chen, G., Li, J., & Liang, M. (2004). Shuxue, dishiyice [Mathematics, Vol. 11]. Zhejiang, China: Zhejiang Education Publisher.