Changing practice, changing minds, from arithmetical to algebraic thinking: An application of the concerns-based adoption model (CBAM)

Educational Studies in Mathematics

Volumn 72, Issue 2, 2009, Pages 161-183

  Tunks, Jeanne ^a   Weller, Kirk ^b  

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b FERRIS STATE UNIVERSITY   (United States)

Author keywords

Algebraic thinking; Concerns; Levels of use; Staff development; Teacher practice

Indexed keywords

EID: 70350374219     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-009-9189-x     Document Type: Article

References (38)

1. Anderson, S. (1997). Understanding teacher change: Revisiting the concerns based adoption model. Curriculum Inquiry, 27(3), 331-367. doi:10.1111/0362-6784.00057.
2. Beall, K. (Ed.).(2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
3. Burrill, G. (1997). Algebra for the twenty-first century. National Association of Secondary School Principals, 81(5), 11-16.
4. Burrill, G., Choate, J., Ferrini-Mundy, J., Monk, S., Moore-Harris, B., & Phillips, E. (1997). A framework for constructing a vision of algebra: A discussion document. Reston, VA: National Council of Teachers of Mathematics.
5. Carter, J., Ferrucci, B., & Yeap, B.-H. (2002). Developing algebraic thinking. Mathematics Teaching, 178, 39-41.
6. Chambers, D. (1994). The right algebra for all. Educational Leadership, 51(6), 85-86.
7. Christou, C., Eliophotou-Menon, M., & Philippou, G. (2004). Teachers' concerns regarding the adoption of a new mathematics curriculum: An application of CBAM. Educational Studies in Mathematics, 57(2), 157-176. doi:10.1023/B:EDUC.0000049271.01649.dd.
8. Cuevas, P., & Yeatts, K. (2001). Navigating through algebra in grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
9. Davidenko, S. (1997). Building the concept of function for students' everyday activities. Mathematics Teacher, 90(2), 144-150.
10. Day, R., & Jones, G. (1997). Building bridges to algebraic thinking. Mathematics Teaching in the Middle School, 2(4), 208-212.
11. Department for Education and Employment (DfEE). (2000). Mathematics: The national curriculum for England. London: DfEE.
12. Friel, S., Rachlin, S., & Doyle, D. (2002). Navigating through algebra in grades 6-8. Reston, VA: National Council of Teachers of Mathematics.
13. Hall, G., & Hord, S. (2001). Implementing change: Patterns, principles and potholes. Boston, MA: Allyn and Bacon.
14. Hall, G., & Loucks, S. (1978). Teacher concerns as a basis for facilitating and personalizing staff development. Teachers College Record, 80(1), 36-53.
15. Hall, G., Loucks, S., Rutherford, W., & Newlove, B. (1975). Levels of use of the innovation: A framework for analyzing innovation adoption. Journal of Teacher Education, 26(1), 52-56. doi:10.1177/002248717502600114.
16. Hamel, J., Dufour, S., & Fortin, D. (1993). Case study methods. Newbury Park, CA: Sage.
17. Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59-78. doi:10.1007/BF01284528.
18. Joyce, B., & Showers, B. (1980). Improving inservice training: The messages of research. Educational Leadership, 37(5), 379-385.
19. Kaput, J. (2000). Transforming algebra for an engine of inequity to an engine of mathematical power by algebrafying the K-12 curriculum. Arlington, VA: National Science Foundation (ERIC Document Reproduction Service No. ED444166).
20. rd Annual Meeting of the North American Chapter of the Psychology of Mathematics Education: Vol. 1 (pp. 99-108). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education (ED476613).
21. Kaput, J., & Blanton, M. L. (2003). Developing elementary teachers' "algebra eyes and ears. Teaching Children Mathematics, 10(2), 70-77.
22. th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Vol. 1 (pp. 22-29). Mérida, Mexico: Universidad Pedagógica Nacional.
23. Kieran, C., & Chalough, L. (1999). Prealgebra: The transition from arithmetic to algebra. In B. Moses (Ed.), Algebraic thinking: Readings from the NCTM's school-based journals and other publications (pp. 59-70). Reston, VA: National Council of Teachers of Mathematics.
24. Lodholz, R. (1999). The transition from arithmetic to algebra. In B. Moses (Ed.), Algebraic thinking: Readings from the NCTM's school-based journals and other publications (pp. 52-58). Reston, VA: National Council of Teachers of Mathematics.
25. Mason, J. (1996). Expressing generality and roots of algebra. In C. K. Bednarz, & L. Lee (Eds.), Approaches to algebra (pp. 65-86). Dordrecht: Kluwer.
26. Nathan, M., & Koedinger, K. (2000). An investigation of teachers' beliefs of students' algebra development. Cognition and Instruction, 18(2), 209-237. doi:10.1207/S1532690XCI1802_03.
27. Neilsen, L., & Turner, S. (1987). Intervention coaching for mathematics implementation: A CBAM application for school improvement. Florida Journal of Educational Research, 29(1), 73-100.
28. No Child Left Behind. (2002). Retrieved June 2007 from http://www.ed.gov/nclb/landing.jhtml.
29. th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education: Vol. 1 (pp. 2-21). Mérida, Mexico: Universidad Pedagógica Nacional.
30. Sfard, A. (1995). The development of algebra: Confronting historical and psychological perspectives. The Journal of Mathematical Behavior, 14(1), 15-39. doi:10.1016/0732-3123(95)90022-5.
31. Silver, E. A. (1995). Rethinking "algebra for all". Educational Leadership, 52(6), 30-33.
32. Stake, R. (1997). Case study methods in educational research: Seeking sweet water. In R. M. Jaeger (Ed.), Methods for research in education (2nd edn) (pp. 401-422). Washington, DC: American Educational Research Association.
33. th Annual Meeting of the International Group for the Psychology of Mathematics Education: Vol. 3 (pp. 121-128). Bergen, Norway: International Group for the Psychology of Mathematics Education (ERIC Document Reproduction Service No. ED 489538).
34. Tunks, J. (1999). Recommended and taught: The disparity in mathematics instruction. Curriculum and Teaching Dialogue, 1(1), 61-75.
35. th Annual Meeting of the International Group for the Psychology of Mathematics Education: Vol. 4 (pp. 417-424). Cape Town, South Africa: International Group for the Psychology of Mathematics Education (ERIC Document Reproduction Service No. ED 489597).
36. Warren, E. (2005). Patterns supporting the development of early algebraic thinking. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Theory, research and practice (Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia, MERGA-28): Vol. 2 (pp. 759-766). Melbourne: Mathematics Education Research Group of Australasia.
37. Wickett, M., & Burns, M. (2002). Lessons for algebraic thinking: Grades 6-8. Sausalito, CA: Math Solutions Publications.
38. Wickett, M., Kharas, K., & Burns, M. (2002). Lessons for algebraic thinking: Grades 3-5. Sausalito, CA: Math Solutions Publications.