Exploring the relationship between mathematics teachers’ implicit associations and their enacted practices

  • Brent DavisEmail author
  • Jo Towers
  • Olive Chapman
  • Michelle Drefs
  • Sharon Friesen


We examine the relationship between how teachers talk about teaching and their actual teaching practices. Analyses of their talk were based on extensive transcripts and writings and focused on metaphors and images invoked when discussing knowledge, learning, and teaching. Three distinct and coherent webs of association were identified, which we describe as “traditional,” “reform,” and “middling.” For both traditional and reform teachers, preferred webs of association proved to be highly consistent with classroom practices. For teachers who tended to draw on the “middling” web, practices tended to vary dramatically, and habits of speaking appeared to be linked to frustrations with teaching. Implications for professional learning are discussed.


Teacher knowledge Teacher beliefs Teaching practices Educational change 



Funding was provided by Social Sciences and Humanities Research Council of Canada.


  1. Alger, C. L. (2008). Secondary teachers’ conceptual metaphors of teaching and learning: Changes over the career span. Teaching and Teacher Education, 25, 743–751.CrossRefGoogle Scholar
  2. August, D., & Hakuta, K. (Eds.). (1997). Improving schooling for language-minority children: A research agenda. Washington: National Academies Press.Google Scholar
  3. Bateson, G. (1972). Steps of an ecology of mind. San Francisco, CA: Chandler.Google Scholar
  4. Bullough, R. V. (2015). Methods for studying beliefs: Teacher writing, scenarios, and metaphor analysis. In H. Fives & M. G. Gill (Eds.), International handbook on teachers’ beliefs (pp. 150–169). New York: Routledge.Google Scholar
  5. Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.CrossRefGoogle Scholar
  6. Cooney, T. J. (1985). A beginning teacher’s view of problem solving. Journal for Research in Mathematics Education, 16(5), 324–336.CrossRefGoogle Scholar
  7. Cummins, J. (2000). Language, power and pedagogy: Bilingual children in the crossfire. Clevedon: Multilingual Matters.CrossRefGoogle Scholar
  8. Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.CrossRefGoogle Scholar
  9. Felbrich, A., Kaiser, G., & Schmotz, C. (2012). The cultural dimension of beliefs: An investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries. ZDM Mathematics Education, 44(3), 355–366.CrossRefGoogle Scholar
  10. Fives, H., & Buehl, M. M. (2012). Spring cleaning for the “messy” construct of teachers’ beliefs: What are they: Which have been examined? What can they tell us? In K. R. Harris, S. Graham, & T. Urdan (Eds.), APA educational psychology handbook, Vol. 2: Individual differences and cultural and contextual factors (pp. 471–499). Washington, DC: American Psychological Association.CrossRefGoogle Scholar
  11. Fives, H., & Gill, M. G. (Eds.). (2015). International handbook on teachers’ beliefs. New York: Routledge.Google Scholar
  12. Handal, B., & Herrington, A. (2003). Mathematics teachers’ beliefs and curriculum reform. Mathematics Education Research Journal, 15(1), 59–69.CrossRefGoogle Scholar
  13. Hoadley, C. M. (2004). Methodological alignment in design-based research. Educational Psychologist, 39(4), 203–212.CrossRefGoogle Scholar
  14. Kahneman, D. (2011). Thinking, fast and slow. New York: Farrar, Straus and Giroux.Google Scholar
  15. Kaplan, R. G. (1991). Teacher beliefs and practices: A square peg in a square hole. In R. G. Underhill (Ed.), Proceedings of PME-NA-13 (pp. 119–125). Blacksburg, VA: Virginia Tech.Google Scholar
  16. Kelly, K. (2010). What technology wants. New York: Penguin.Google Scholar
  17. Kuhn, T. (1962). The structure of scientific revolutions. Chicago: The University of Chicago Press.Google Scholar
  18. Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to western thought. New York: Basic Books.Google Scholar
  19. Leder, G., Pehkonen, E., & Törner, G. (Eds.). (2002). Beliefs: A hidden variable in mathematics education. Boston, MA: Kluwer Academic Publishing.Google Scholar
  20. Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Thousand Oaks, CA: Sage.Google Scholar
  21. Noyes, A. (2006). Using metaphor in mathematics teacher preparation. Teaching and Teacher Education, 22, 898–909.CrossRefGoogle Scholar
  22. Pathchen, T., & Crawford, T. (2011). From gardeners to tour guides: The epistemological struggle revealed in teacher-generated metaphors. Journal of Teacher Education, 62(3), 286–298.CrossRefGoogle Scholar
  23. Pesek, D. D., & Kirshner, D. (2000). Interference of instrumental instruction in subsequent relational learning. Journal for Research in Mathematics Education, 31(5), 524–540.CrossRefGoogle Scholar
  24. Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Charlotte, NC: Information Age.Google Scholar
  25. Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550–576.CrossRefGoogle Scholar
  26. Sawada, D., Piburn, M. D., Judson, E., Turley, J., Falconer, K., Benford, R., et al. (2002). Measuring reform practices in science and mathematics classrooms: The reformed teaching observation protocol. School Science and Mathematics, 102(6), 245–253.CrossRefGoogle Scholar
  27. Sfard, A. (1998). On two metaphors of learning and the dangers of choosing just one. Educational Researcher, 27(2), 4–13.CrossRefGoogle Scholar
  28. Sinatra, G. M., & Pintrich, P. R. (2003). Intentional conceptual change. Mahwah, NJ: Erlbaum.Google Scholar
  29. Skemp, R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26, 29–35.Google Scholar
  30. Skott, J. (2015). The promises, problems, and prospects of research on teachers’ beliefs. In H. Fives & M. G. Gill (Eds.), International handbook on teachers’ beliefs (pp. 13–30). New York: Routledge.Google Scholar
  31. Steier, F., & Jorgenson, J. (Eds.). (2005). Gregory Bateson: Essays for an ecology of ideas. Special issue of Cybernetics and Human Knowing (pp. 1–182). Exeter: Imprint Academic Press.Google Scholar
  32. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17, 213–226.CrossRefGoogle Scholar
  33. Thibodeau, P. H., & Boroditsky, L. (2013). Natural language metaphors covertly influence reasoning. PLoS ONE, 8(1), e0052961. Scholar
  34. Thibodeau, P. H., & Boroditsky, L. (2015). Measuring effects of metaphor in a dynamic opinion landscape. PLoS ONE, 10(7), e0133939. Scholar
  35. Thompson, A. G. (1985). Teachers’ conceptions of mathematics and the teaching of problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 281–294). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  36. 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.Google Scholar
  37. Tran-Davies, N. (n.d.). Knowledge is power: Stop the breakdown of our children’s education. Retrieved January 23, 2018, from
  38. Voss, T., Kleickmann, T., Kunter, M., & Hachfeld, A. (2013). Mathematics teachers’ beliefs. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers—Results from the COACTIV project (pp. 249–272). New York: Springer.CrossRefGoogle Scholar
  39. Windschitl, M. (2002). Framing constructivism in practice as the negotiation of dilemmas: An analysis of the conceptual, pedagogical, cultural, and political challenges facing teachers. Review of Educational Research, 72(2), 131–175.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Brent Davis
    • 1
    Email author
  • Jo Towers
    • 1
  • Olive Chapman
    • 1
  • Michelle Drefs
    • 1
  • Sharon Friesen
    • 1
  1. 1.University of CalgaryCalgaryCanada

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