How a standards-based mathematics curriculum differs from a traditional curriculum: With a focus on intended treatments of the ideas of variable

ZDM - International Journal on Mathematics Education

Volumn 41, Issue 6, 2009, Pages 777-792

  Nie, Bikai ^a   Cai, Jinfa ^a   Moyer, John C ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b MARQUETTE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960488563     PISSN: 18639690     EISSN: 18639704     Source Type: Journal    
DOI: 10.1007/s11858-009-0197-1     Document Type: Article

References (50)

1. Bailey, R., Day, R., Frey, P., Howard, A. C., Hutchens, D. T., McClain, K., et al. (2006a). Mathematics: Applications and concepts (teacher wraparound edition), course 1. Columbus, OH: The McGraw-Hill Company.
2. Bailey, R., Day, R., Frey, P., Howard, A. C., Hutchens, D. T., McClain, K., et al. (2006b). Mathematics: Applications and concepts (teacher wraparound edition), course 2. Columbus, OH: The McGraw-Hill Company.
3. Bailey, R., Day, R., Frey, P., Howard, A. C., Hutchens, D. T., McClain, K., et al. (2006c). Mathematics: Applications and concepts (teacher wraparound edition), course 3. Columbus, OH: The McGraw-Hill Company.
4. Booth, L. R. (1988). Children's difficulty in beginning algebra. In A. F. Coxford (Ed.), The Ideas of algebra, K-12 (pp. 8-19). Reston, VA: NCTM.
5. Cai, J. (1995). A cognitive analysis of US and Chinese students' mathematical performance on tasks involving computation, simple problem solving, and complex problem solving. Journal for Research in Mathematics Education Monographs Series, 7. Reston, VA: National Council of Teachers of Mathematics.
6. Cai, J. (2003). What research tells us about teaching mathematics through problem solving. In F. Lester (Ed.), Research and issues in teaching mathematics through problem solving (pp. 241-254). Reston, VA: National Council of Teachers of Mathematics.
7. Cai, J. (2004a). Introduction to the special issue on developing algebraic thinking in the earlier grades from an international perspective. The Mathematics Educator (Singapore), 8(1), 1-5.
8. Cai, J. (2004b). Why do U.S. and Chinese students think differently in mathematical problem solving? Exploring the impact of early algebra learning and teachers' beliefs. Journal of Mathematical Behavior, 23, 135-167.
9. Cai, J., Lew, H. C., Morris, A., Moyer, J. C., Ng, S. F., & Schmittau, J. (2005). The development of students' algebraic thinking in earlier grades: A cross-cultural comparative perspective. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 37(1), 5-15.
10. Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatment of arithmetic average in U.S. and Asian school mathematics textbooks. School Science and Mathematics, 102(8), 391-404.
11. Cai, J., & Moyer, J. C. (2006). A conceptual framework for studying curricular effects on students' learning: Conceptualization and design in the LieCal Project. Newark, DE: The University of Delaware.
12. Collins, W., Dritsas, L., Frey-Mason, P., Howard, A. C., McClain, K., Molina, D. D., et al. (1998a). Mathematics: Applications and connections, course 1. Columbus, OH: The McGraw-Hill Company.
13. Collins, W., Dritsas, L., Frey-Mason, P., Howard, A. C., McClain, K., Molina, D. D., et al. (1998b). Mathematics: Applications and connections, course 2. Columbus, OH: The McGraw-Hill Company.
14. Collins, W., Dritsas, L., Frey-Mason, P., Howard, A. C., McClain, K., Molina, D. D., et al. (1998c). Mathematics: Applications and connections, course 3. Columbus, OH: The McGraw-Hill Company.
15. Dowling, P. (1996). A sociological analysis of school mathematics text. Educational Research in Mathematics, 31, 389-415.
16. Ginsburg, M., & Clift, R. (1990). The hidden curriculum of preservice teacher education. In W. R. Houston & J. R. Flanders (Eds.), Handbook of research on teacher education (pp. 450-465). New York: Macmillan Publishing Company.
17. 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.
18. 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.
19. Herman, R., Boruch, R., Powell, R., Fleischman, S., & Maynard, R. (2006). Overcoming the challenges: A response to Alan H. Schoenfeld's "What doesn't work". Educational Researcher, 35(2), 22-23.
20. Jackson, P. W. (Ed.). (1992). Handbook of research on curriculum. New York: Macmillan Publishing Company.
21. Janvier, C. (1996). Modeling and the initiation to algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 225-236). The Netherlands: Kluwer Academic Publishers, Dordrecht.
22. Kieran, C. (1988). Two different approaches among algebra learners. In A. F. Coxford (Ed.), The ideas of algebra, K-12 (pp. 91-96). Reston, VA: NCTM.
23. Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students' understanding of core algebraic concepts: Equivalence and variable. Zentralblatt fuer Didaktik der Mathematik (International Journal on Mathematics Education), 37(1), 69-76.
24. Kulm, G., Morris, K., & Grier, L. (1999). Middle grades mathematics textbooks: A benchmark-based evaluation. Washington, DC: American Association for the Advancement of Science: Project 2061. Available: http://www.project2061.org/publications/textbook/mgmth/report/default.htm. [04/15/09].
25. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002a). Variables and patterns. Upper Saddle River, NJ: Prentice Hall.
26. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002b). Moving straight ahead. Upper Saddle River, NJ: Prentice Hall.
27. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002c). Thinking with mathematical models. Upper Saddle River, NJ: Prentice Hall.
28. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002d). Looking for Pythagoras. Upper Saddle River, NJ: Prentice Hall.
29. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002e). Growing, growing, growing. Upper Saddle River, NJ: Prentice Hall.
30. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002f). Frogs, fleas, and painted cubes. Upper Saddle River, NJ: Prentice Hall.
31. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002g). Say it with symbols. Upper Saddle River, NJ: Prentice Hall.
32. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002h). Getting to know connected mathematics: An implementation guide. Upper Saddle River, NJ: Prentice Hall.
33. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002i). Lesson planner for Grades 6, 7, and 8. Upper Saddle River, NJ: Prentice Hall.
34. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2002j). Data about us. Upper Saddle River, NJ: Prentice Hall.
35. Lappan, G., Fey, J. T., Fitzgerald, W. M., Friel, S. N., & Phillips, E. D. (2006). The shapes of algebra. Upper Saddle River, NJ: Prentice Hall.
36. 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.
37. Moyer, J. C., Huinker, D., & Cai, J. (2004). Developing algebraic thinking in the earlier grades: A case study of the U.S. The Mathematics Educator (Singapore), 8(1), 6-38.
38. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
39. National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
40. National Council of Teachers of Mathematics. (1995). Assessment standards for school mathematics. Reston, VA: Author.
41. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
42. National Research Council (NRC). (2004). On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. Washington, DC: The National Academies Press.
43. Ng, S. F. (2004). Developing algebraic thinking: A case study of the Singaporean primary school curriculum. The Mathematics Educator (Singapore), 8(1), 39-59.
44. Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H., Wiley, D. E., Cogan, L. S., et al. (2002). Why schools matter: A crossnational comparison of curriculum and learning. San Fransisco, CA: Jossey-Bass.
45. Schoenfeld, A. H. (2006). What doesn't work: The challenge and failure of the works clearinghouse to conduct meaningful reviews of studies of mathematics curricula. Educational Researcher, 35(2), 13-21.
46. Schoenfeld, H. A., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, 81(6), 420-427.
47. Senk, S. L., & Thompson, D. R. (2003). Standards-based school mathematics curricula: What are they? What do students learn?. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
48. Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford (Ed.), The Ideas of algebra, K-12 (pp. 8-19). Reston, VA: NCTM.
49. Wheeler, D. (1996). Backwards and forwards: Reflections on different approaches to algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 317-325). The Netherlands: Kluwer Academic Publishers, Dordrecht.
50. Wu, H. (1997). The mathematics education reform: Why you should be concerned and what you can do. American Mathematical Monthly, 104, 946-954.