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Journal of Mathematics Teacher Education

, Volume 12, Issue 5, pp 325–346 | Cite as

Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices

  • Dionne I. CrossEmail author
Article

Abstract

This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of teacher education.

Keywords

Mathematics teachers’ beliefs Teacher beliefs Belief systems Teacher practice Belief models 

References

  1. Ambrose, R. (2004). Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building on beliefs. Journal of Mathematics Teacher Education, 7, 91–119.CrossRefGoogle Scholar
  2. Anderson, D., & Piazza, J. (1996). Changing beliefs: Teaching and learning mathematics in constructivist preservice classrooms. Action in Teacher Education, 18, 51–62.Google Scholar
  3. Aquire, J., & Speer, N. (2000). Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behavior, 18(3), 327–356.CrossRefGoogle Scholar
  4. Ashton, P., & Gregoire, M. (2003). At the heart of teaching: The role of emotion in changing teachers’ beliefs. In J. Raths & A. McAninch (Eds.), Teacher beliefs and classroom performance: The impact of teacher education (Vol. 6, pp. 99–122). Norwood, NJ: Ablex.Google Scholar
  5. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.Google Scholar
  6. Belenky, M., Clinchy, B., Goldberger, N., & Tarule, J. (1986). Women’s ways of knowing: The development of self, voice and mind. New York: Basic Books.Google Scholar
  7. Beuhl, M., Alexander, P., & Murphy, K. (2002). Beliefs about schooled knowledge: Domain general or domain specific? Contemporary Educational Psychology, 27, 415–449.CrossRefGoogle Scholar
  8. Bishop, A. (1988). Mathematical enculturation. Dordrecht: Kluwer.Google Scholar
  9. Chapman, O. (2002). Belief structure and inservice high school mathematics teacher growth. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 177–193). Dordrecht: Kluwer Academic Publishers.Google Scholar
  10. Charmaz, K. (2000). Grounded theory: Objectivist and constructivist methods. In N. Denzin & Y. Lincoln (Eds.), Handbook of qualitative research (Vol. 2, pp. 509–535). Thousand Oaks, CA: Sage Publications.Google Scholar
  11. Cobb, P., & Steffe, L. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83–94.CrossRefGoogle Scholar
  12. Cobb, P., Yackel, E., Wood, T., Nicholls, J., Wheatley, G., Trigatti, B., et al. (1991). Assessment of a problem-centered second-grade mathematics project. Journal of Research in Mathematics Education, 22(1), 3–29.CrossRefGoogle Scholar
  13. Cochran-Smith, M. (1991). Reinventing student teaching. Journal of Teacher Education, 42(2), 104–118.CrossRefGoogle Scholar
  14. Cooney, T. (2003). Mathematics teacher education in rural communities: Developing a foundation for action. Paper presented at the ACCLAIM Research Symposium, McArthur, OH.Google Scholar
  15. Cooney, T., Shealy, B., & Arvold, B. (1998). Conceptualizing belief structures preservice teachers secondary mathematics teachers. Journal of Research in Mathematics Education, 29(3), 306–333.CrossRefGoogle Scholar
  16. Cross, D. (2008). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education. doi:  10.1007/s10763-008-9144-9.
  17. Dionne, J. J. (1984). The perception of mathematics among elementary school teachers. Paper presented at the Sixth Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, University of Wisconsin, Madison.Google Scholar
  18. Dweck, C., & Leggett, E. (1988). A social-cognitive approach to motivation and personality. Psychological Review, 95, 256–273.CrossRefGoogle Scholar
  19. Ernest, P. (1988). The impact of beliefs on the teaching of mathematics. Paper presented at the ICME IV, Budapest, Hungary.Google Scholar
  20. Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics: A model. Journal of Education for Teaching, 15, 13–33.CrossRefGoogle Scholar
  21. Ezzy, D. (2002). Qualitative analysis: Practice and innovation. Victoria, Australia: Routledge.Google Scholar
  22. Fives, H., & Beuhl, M. (2008). What do teachers believe? Developing a framework for examining beliefs about teachers’ knowledge and ability. Contemporary Educational Psychology, 33, 134–176.CrossRefGoogle Scholar
  23. Frank, M. (1988). Problem solving and mathematical beliefs. Arithmetic Teacher, 35, 32–34.Google Scholar
  24. Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Karns, K. (1998). High-achieving students’ interactions and performance on complex mathematical tasks as a function of homogeneous and heterogenous pairings. American Educational Research Journal, 35, 227–268.Google Scholar
  25. Green, T. (1971). The activities of teaching. New York: McGraw-Hill.Google Scholar
  26. Hart, L. (2002). A four year follow-up study of teachers’ beliefs after participating in a teacher enhancement project. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 161–176). Dordrecht: Kluwer Academic Publishers.Google Scholar
  27. Hofer, B., & Pintrich, P. (2002). Personal Epistemology: The psychology of beliefs about knowledge and knowing. Mahwah, NJ: Erlbaum.Google Scholar
  28. Kuhs, T., & Ball, D. (1986). Approaches to teaching mathematics: Mapping the domains of knowledge, skills and dispositions. East Lansing: Michigan State University, Center of Teacher Education.Google Scholar
  29. Lerman, S. (1983). Problem-solving and knowledge-centred: The influence of philosophy on mathematics teaching. International Journal of Mathematical Education in Science and Technology, 14(1), 59–66.CrossRefGoogle Scholar
  30. Lindblom-Ylanne, S., Trigwell, K., Nevgi, A., & Ashwin, P. (2006). How approaches to teaching are affected by discipline and teaching context. Studies in Higher Education, 31(3), 285–298.CrossRefGoogle Scholar
  31. Muis, K. (2004). Personal epistemology ad mathematics: A critical review and synthesis of research. Review of Educational Research, 74(3), 317–377.CrossRefGoogle Scholar
  32. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  33. Nespor, J. (1987). The role of beliefs in the practice of teaching. Journal of Curriculum Studies, 19, 317–328.CrossRefGoogle Scholar
  34. Pajares, F. (1992). Teachers’ beliefs and educational Research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307–332.Google Scholar
  35. Perry, W. (1970). Forms of intellectual and ethical development in the college years A scheme. New York: Holt, Rinehart & Winston.Google Scholar
  36. Philipp, R. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Charlotte, NC: Information Age Publishing.Google Scholar
  37. Philipp, R., Ambrose, R., Lamb, L., Sowder, J., Schappelle, B., Sowder, L., et al. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438–476.CrossRefGoogle Scholar
  38. Raymond, A. (1997). Inconsistencies between a beginning elementary teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550–576.CrossRefGoogle Scholar
  39. Rimm-Kaufman, S., & Sawyer, B. (2004). Primary-grade teachers’ self efficacy beliefs, attitudes toward teaching, and discipline and teaching practice priorities in relation to the responsive classroom approach. The Elementary School Journal, 104(2), 321–341.CrossRefGoogle Scholar
  40. Rokeach, M. (1968). Beliefs, attitudes & values: A theory of organization & change. San Francisco: Jossey-Bass.Google Scholar
  41. Schommer, M. (1990). Effects of beliefs about the nature of knowledge on comprehension. Journal of Educational Psychology, 82, 498–504.CrossRefGoogle Scholar
  42. Schraw, G., & Olafson, L. (2002). Teachers’ epistemological world views and educational practices. Issues in Education: Contributions from Educational Psychology, 8(2), 99–148.Google Scholar
  43. Schutz, P., Hong, J., Cross, D., & Osbon, J. (2006). Reflections on investigating emotions among educational contexts. Educational Psychology Review, 18(4), 343–360.CrossRefGoogle Scholar
  44. Stake, R. (2000). Case studies. In N. Denzin & Y. Lincoln (Eds.), Handbook of qualitative research (pp. 435–454). Thousand Oaks, CA: Sage.Google Scholar
  45. Stipek, D., Givvin, K., Salmon, J., & MacGyvers, V. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226.CrossRefGoogle Scholar
  46. Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures & techniques. Newbury Park, CA: SAGE Publishing.Google Scholar
  47. Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Education Studies in Mathematics, 15, 105–127.CrossRefGoogle Scholar
  48. Thompson, A. (1992). Teachers’ beliefs and conceptions: A synthesis of research. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). New York: Macmillan.Google Scholar
  49. Torff, B. (2005). Developmental changes in teachers’ beliefs about critical thinking activities. Journal of Educational Psychology, 97(1), 13–22.CrossRefGoogle Scholar
  50. Torff, B., & Warburton, E. C. (2005). Assessment of teachers’ beliefs about classroom use for critical thinking activities. Educational and Psychological Measurement, 65, 155–179.CrossRefGoogle Scholar
  51. Valderrama-Aguelo, C., Clarke, B., & Bishop, A. (2007). Explanations of attitudes to change: Colombian mathematics teachers’ conceptions of the crucial determinants of their teaching practices of beginning algebra. Journal of Mathematics Teacher Education, 10(2), 69–93.CrossRefGoogle Scholar
  52. Wilder, R. (1981). Mathematics as a cultural system. Oxford: Pergamon.Google Scholar
  53. Williams, M., Cross, D., Hong, J., Aultman, L., Osbon, J., & Schutz, P. (2008). “There is no emotion in math”: How teachers approach emotions in the classroom. Teachers College Record, 110(8), 1574–1612.Google Scholar
  54. Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development. The role of beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–147). Dordrecht: Kluwer Academic Publishers.Google Scholar
  55. Woolfolk-Hoy, A., Davis, H., & Pape, S. (2006). Teacher knowledge and beliefs. In P. Alexander & P. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 715–738). Mahwah, NJ: Erlbaum.Google Scholar
  56. Yerrick, R., Parke, H., & Nugent, F. (1997). Struggling to promote deeply rooted change: The ‘filtering effect’ of teacher’s beliefs on understanding transformational views of teaching science. Science Education, 81(2), 137–160.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Indiana UniversityBloomingtonUSA

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