A collective case study of the influence of teachers' beliefs and knowledge on error-handling practices during class discussion of mathematics

Journal for Research in Mathematics Education

Volumn 42, Issue 1, 2011, Pages 2-38

  Bray, Wendy S ^a  

^a UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Discourse analysis; Qualitative methods; Reform in mathematics education; Teacher beliefs; Teacher knowledge; Teaching practice

Indexed keywords

EID: 79551583850     PISSN: 00218251     EISSN: None     Source Type: Journal    
DOI: 10.5951/jresematheduc.42.1.0002     Document Type: Article

References (60)

1. Aguirre, I, & Speer, N. M. (2000). Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behavior, 18,327-356.
2. Ambrose, R., Phillip, R., Chauvot, J., & Clement, L. (2003). A web-based survey to assess prospective elementary school teachers' beliefs about mathematics and mathematics learning: An alternative to Likert scales. In N. A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 2003 joint meeting of PME and PMENA (Vol. 2, pp. 33-39). Honolulu, HI: CRDG, College of Education, University of Hawaii.
3. Ball, D. L., Lubienski, S. T, & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers' mathematical knowledge. In V Richardson (Ed.), Handbook of research on teaching (4th ed., pp. 433-456). Washington, DC: American Educational Research Association.
4. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59,389-407.
5. Bell, M., Bell, J., & Hartfield, R. (1993). Everyday mathematics: Third grade. Chicago, IL: SRA/McGraw-Hill.
6. Borasi, R. (1994). Capitalizing on errors as "springboards for inquiry": A teaching experiment. Journal for Research in Mathematics Education, 25, 166-208.
7. Borko, H., & Livingston, C. (1989). Cognition and improvisation: Differences in mathematics instruction by expert and novice teachers. American Educational Research Journal, 26,473-498.
8. Borko, H., & Putnam, R. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 673-708). New York: Macmillan.
9. Bray, W. S. (2008). A study of teacher transitions to a reform-based mathematics curriculum in an urban school: The interaction of beliefs, knowledge, and classroom practices (Doctoral dissertation, The University of North Carolina at Chapel Hill, 2007). Dissertation Abstracts International, 68A, 11
10. Calderhead, J. (1996). Teachers: Beliefs and knowledge. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 709-725). New York: Macmillan.
11. Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19-32). Mahwah, NJ: Erlbaum.
12. Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28,258-277.
13. Cooney, T. J., & Shealy, B. E. (1997). On understanding the structure of teachers' beliefs and their relationship to change. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 87-109). Mahwah, NJ: Erlbaum.
14. Cooney, T. J., Shealy, B. E., & Arvold, B. (1998). Conceptualizing belief structures of preservice mathematics teachers. Journal for Research in Mathematics Education, 29,306-333.
15. Empson, S. B. (2001). Equal sharing and the roots of fraction equivalence. Teaching Children Mathematics, 7,421-425.
16. Empson, S. B., & Junk, D. L. (2004). Teachers' knowledge of children's mathematics after implementing a student-centered curriculum. Journal of Mathematics Teacher Education, 7,121-144.
17. Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V R., & Empson, S. B. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27,403-434.
18. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
19. Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children's mathematical thinking in Everyday Mathematics classrooms. Journal for Research in Mathematics Education, 30, 148-170.
20. Franke, M., Fennema, E., & Carpenter, T. P. (1997). Changing teachers: Interactions between beliefs and classroom practice. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 255-282). Mahwah, NJ: Erlbaum.
21. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225-256). Charlotte, NC: Information Age.
22. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Hawthorne, NY: Aldine de Gruyter.
23. Green, T. F. (1971). The activities of teaching. New York: McGraw-Hill.
24. Grossman, P. (1990). 77te making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
25. Guba, E. G., & Lincoln, Y. S. (1989). Fourth generation evaluation. Newbury Park, CA: Sage.
26. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C, Wearne, D., Murray, H., et al. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.
27. Integrating Mathematics and Pedagogy. (n.d.). IMAP Web-Based Beliefs-Survey manual. San Diego, CA: Center for Research in Mathematics and Science Education, San Diego State University. Retrieved October 15, 2007, from http://www.sci.sdsu.edu/CRMSE/IMAP/Beliefs-Survey-Manual.pdf
28. Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. The Elementary School Journal, 702,59-80.
29. Kennedy, M., Ball, D., & McDiarmid, W. (1993). A study package for examining and tracking changes in teachers' knowledge. East Lansing, MI: National Center for Research on Teacher Learning.
30. Knapp, M. S. (1995). Forces inside the classroom linked with teaching for meaning. In M. S. Knapp, N. E. Adelman, C. Marder, H. McCollum, M. C. Needels, C. Padilla, et al., Teaching for meaning in high-poverty classrooms (pp. 145-159). New York: Teachers College Press.
31. Knapp, M. S., Shields, P. M., & Turnbill, B. J. (1995). Conclusion: Teaching for meaning in high-poverty classrooms. In M. S. Knapp, N. E. Adelman, C. Marder, H. McCollum, M. C. Needels, C. Padilla, et al., Teaching for meaning in high-poverty classrooms (pp. 183-204). New York: Teachers College Press.
32. Land, D., & Legters, N. (2002). The extent and consequences of risk in US education. In S. Stringfleld & D. Land (Eds.), Educating at-risk students. One hundred first yearbook of the National Society for the Study of Education: Part II (pp. 1-28). Chicago: The University of Chicago Press.
33. Leatham, K. R. (2006). Viewing mathematics teachers' beliefs as sensible systems. Journal of Mathematics Teacher Education, 9,91-102.
34. Leinhardt, G. (1993). On teaching. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 1-54). Hillsdale, NJ: Erlbaum.
35. Leinhardt, G., & Steele, M. D. (2005). Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction, 23, 87-163.
36. Lerman, S. (1983). Problem solving or knowledge centred: The influence of philosophy on mathematics teaching. International Journal of Mathematical Education in Science and Technology, 14,59-66.
37. Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.
38. Lippman, L., Bums, S., & McArthur, E. (with Burton, R., Smith, T. M., & Kaufman, P.). (1996). Urban schools: The challenge of location and poverty (NCES 96-184). Washington, DC: U.S. Department of Education.
39. Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass Publishers.
40. Merriam, S. B. (1998). Qualitative research and case study applications in education: Revised and expanded from Case study research in education. San Francisco: Jossey-Bass.
41. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
42. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
43. Pajares, M. F. (1992). Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62,307-332.
44. Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21,491-508.
45. Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1-94.
46. Schoenfeld, A. H. (1999). Models of the teaching process. Journal of Mathematical Behavior, 18, 243-261.
47. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
48. Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C, & Strawhun, B. T. F. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287-301.
49. Spillane, J. P. (2001). Challenging instruction for "all students": Policy, practitioners, and practice. In S. H. Fuhrman (Ed.), From the Capitol to the classroom: Standards-based reform in the States. One hundredth yearbook of the National Society for the Study of Education: Part II (pp. 217-241). Chicago: The University of Chicago Press.
50. Stake, R. E. (2000). Case studies. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (2nd ed.). Thousand Oaks, CA: Sage.
51. Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10,313-340.
52. Stigler, J. W., Fernandez, C, & Yoshida, M. (1996). Traditions of school mathematics in Japanese and American classrooms. In L. P. Steffe & P. Nesher (General Eds.) & P. Cobb (Section Ed.), Theories of mathematical learning (pp. 149-175). Mahwah, NJ: Erlbaum.
53. Stipek, D., Salmon, J. M., Giwen, K. B., Kazemi, E" Saxe, G., & MacGyvers, V L. (1998). The value (and convergence) of practices suggested by motivation research and promoted by mathematics education reformers. Journal for Research in Mathematics Education, 29,465-488.
54. Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
55. Thompson, A. G., Philipp, R. A., Thompson, P. W., & Boyd, B. A. (1994). Calculational and conceptual orientations in teaching mathematics. In D. B. Aichele (Series Ed.) & A. F. Coxford (Vol. Ed.), Professional development for teachers of mathematics: 1994 yearbook (pp. 79-92). Reston, VA: National Council of Teachers of Mathematics.
56. von Glasersfeld, E. (1995). A constructivist approach to teaching. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 3-16). Hillsdale, NJ: Erlbaum.
57. von Glasersfeld, E. (1996). Introduction: Aspects of constructivism. In C. T. Fosnot (Ed.), Constructivism: Theory, perspectives, and practice (pp. 3-7). New York: Teachers College Press.
58. Wood, T, Cobb, P., & Yackel, E. (1995). Reflections on learning and teaching mathematics in elementary school. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 401-422). Hillsdale, NJ: Erlbaum.
59. Wood, T., Williams, G., & McNeal, B. (2006). Children's mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37,222-255.
60. Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.