Journal of Mathematics Teacher Education

, Volume 15, Issue 3, pp 227–249 | Cite as

Facilitating growth in prospective teachers’ knowledge: teaching geometry in primary schools

  • Rod Nason
  • Chris Chalmers
  • Andy Yeh


This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants’ pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.


Teacher education Pedagogical-content knowledge Computer-supported collaborative learning Mathematics education 


  1. Alsup, J. (2004). A comparison of constructivist and traditional instruction in mathematics. Educational Research Quarterly, 28(4), 3–17.Google Scholar
  2. Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.Google Scholar
  3. Baturo, A., & Nason, R. A. (1996). Student teachers’ subject-matter knowledge within the domain of the measurement of area. Educational Studies in Mathematics, 31(3), 235–268.CrossRefGoogle Scholar
  4. Bereiter, C. (Ed.). (2002). Education and mind in the knowledge age. Mahwah, NJ: Erlbaum.Google Scholar
  5. Berenson, S. (2003 April). Lesson plan study: A viable pedagogy for teacher educators. Paper presented at the annual meeting of the American Education Research Association, Chicago, IL.Google Scholar
  6. Bredekamp, S., & Rosegrant, T. (1992). Reaching potentials through appropriate curriculum: Conceptual frameworks for applying the guidelines. In S. Bredekamp & T. Rosegrant (Eds.), Reaching potentials: Appropriate curriculum and assessment for young children. (Vol. 1, p. 33). Washington, DC: National Association for the Education of Young Children.Google Scholar
  7. Brett, C., & Hewitt, J. (2010). Understanding private discourse in a public online forum. Toronto: IKIT. Accessed September 10, 2010.
  8. Brett, C., Nason, R. A., & Woodruff, E. (2002). Communities of inquiry among pre-service teachers investigating mathematics. THEMES in Education, 3(1), 39–62.Google Scholar
  9. Cavey, L. O., & Berenson, S. (2005). Learning to teach high school mathematics: Patterns of growth in understanding right triangle trigonometry during lesson plan study. The Journal of Mathematical Behavior, 24(2), 171–190.CrossRefGoogle Scholar
  10. Chaney-Cullen, T., & Duffy, T. M. (1999). Strategic teaching framework: Multimedia to support teacher change. Journal of the Learning Sciences, 8(1), 1–40.CrossRefGoogle Scholar
  11. Chinnapan, M., Nason, R., & Lawson, M. (1996). Pre-service teachers’ pedagogical and content knowledge about trigonometry and geometry: An initial investigation. In D. Clarke & S. Groves (Eds.), Proceedings of the 19th annual conference of the mathematics education research group of Australasia (pp. 115–123). Melbourne: MERGA.Google Scholar
  12. Darling-Hammond, L. (2000). Teacher quality and student achievement: A review of state policy evidence. Educational Policy Analysis Archives, 8(1). Accessed August 10, 2006.
  13. Even, D., & Tirosh, R. (2002). Teacher knowledge and the understanding of student knowledge. In L. English (Ed.), Handbook on international research in mathematics education (pp. 219–240). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  14. Ewenstein, B., & Whyte, J. K. (2005–2006). Knowledge practices in design: The role of visual representations as ‘epistemic objects’. EBK working paper 20052006. London: Economic and Social Research Council. Accessed January 12, 2011.
  15. Floden, R. E., & Buchmann, M. (1993). Between routines and anarchy: Preparing teachers for uncertainty. Oxford Review of Education, 19(3), 373–382.CrossRefGoogle Scholar
  16. Goffman, E. (1959). The presentation of self in everyday life. New York, NY: Anchor.Google Scholar
  17. Goodyear, P., & Ellis, R. (2007). The development of epistemic fluency: Learning to think for a living. In A. Brew & J. Sachs (Eds.), Transforming a university: The scholarship of teaching and learning in practice (pp. 57–68). Sydney: Sydney University Press.Google Scholar
  18. Hakkarainen, K., Ritella, G., & Seitamaa- Hakkarainen, P. (2009). Epistemic mediation, chronotype, and expansive knowledge practices. Accessed January 15, 2010.
  19. Jagede, O., & Taplin, M. (2000). Trainee teachers’ perception of their knowledge about expert teaching. Educational Research, 42(3), 287–308.CrossRefGoogle Scholar
  20. Jones, K., Mooney, C., & Harries, T. (2002). Trainee primary teachers’ knowledge of geometry for teaching. Proceedings of the British Society for Research into Learning Mathematics, 22(2), 95–100. Accessed June 25, 2008.
  21. Kimmerle, J., & Cress, U. (2008). Group awareness and self-presentation in computer-supported information exchange. Computer-Supported Collaborative Learning, 3(1), 85–97.CrossRefGoogle Scholar
  22. Kovalainen, M., & Kumpulainen, K. (2005). The discursive practice of participation in an elementary classroom community. Instructional Science, 33, 213–250.CrossRefGoogle Scholar
  23. Lampert, M. (1988). What can research on teacher education tell us about improving quality in mathematics education? Teaching and Teacher Education, 4(2), 157–170.CrossRefGoogle Scholar
  24. Leikin, R., Berman, A., & Zaslavsky, O. (2000). Applications of symmetry to problem solving. International Journal of Mathematical Education in Science and Technology, 31(6), 799–809.CrossRefGoogle Scholar
  25. Leinhardt, G. (1989). Math lessons: A contrast of novice and expert performance. Journal of Research in Mathematics Education, 20(1), 53–75.CrossRefGoogle Scholar
  26. Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for Better Schools.Google Scholar
  27. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Newbury Park, CA: Sage.Google Scholar
  28. Pickering, A. (1995). The mangle of practice. Chicago: The University of Chicago Press.Google Scholar
  29. Pirie, S., & Kieren, T. (1994). Growth of mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165–190.CrossRefGoogle Scholar
  30. Rheinberger, H.-J. (1997). Toward history of epistemic things: Synthesizing proteins in the test tube. Stanford, CA: Stanford University Press.Google Scholar
  31. Robert, L. P., & Dennis, A. R. (2005). Paradox of richness: A cognitive model of media choice. IEEE Transactions on Professional Communication, 48(1), 10–21.CrossRefGoogle Scholar
  32. Scardamalia, M. (2002). Collective cognitive responsibility for the advancement of knowledge. In B. Smith (Ed.), Liberal education in a knowledge society (pp. 67–98). Chicago: Open Court.Google Scholar
  33. Scardamalia, M. (2003). Knowledge building environments: Extending the limits of the possible in education and knowledge work. In A. DiStefano, K. Rudestam, & R. Silverman (Eds.), Encyclopedia of distributed learning (pp. 269–272). Thousand Oaks, CA: Sage Publications.Google Scholar
  34. Scardamalia, M., & Bereiter, C. (2003 April). International design principles for knowledge building: Innovative learning processes in knowledge-rich interactive environments. Paper presented at the Chaired symposium at the annual meeting of the American Educational Research Association, Chicago, IL.Google Scholar
  35. Scardamalia, M., & Bereiter, C. (2006). Knowledge building: Theory, pedagogy, and technology. In K. Sawyer (Ed.), Cambridge handbook of the learning sciences (pp. 97–118). New York: Cambridge University Press.Google Scholar
  36. Scardamalia, M., & Bereiter, C. (2007). Fostering communities of learners and knowledge building: An interrupted dialogue. In J. C. Campione, K. E. Metz, & A. S. Palincsar (Eds.), Children’s learning in the laboratory and in the classroom: Essays in honor of Ann brown (pp. 197–212). Mahwah, NJ: Erlbaum.Google Scholar
  37. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  38. Sims, L., & Walsh, D. (2009). Lesson study with preservice teachers: Lessons from lessons. Teaching and Teacher Education, 25(5), 724–733.CrossRefGoogle Scholar
  39. Sowden, S., & Keeves, J. (1990). Analysis of evidence in humanistic studies. In H. Walberg & G. Haertel (Eds.), International encyclopaedia of educational evaluation (pp. 649–663). London: Pelgamon.Google Scholar
  40. Steffe, L. (1991). The constructivist teaching experiment: Illustrations and implications. In E. VonGlaserfield (Ed.), Radical constructivism in mathematics education (pp. 177–194). Dordrecht: Kluwer.Google Scholar
  41. Sterelny, K. (2004). Externalism, epistemic artefacts and the extended mind. In R. Schantz, (Ed.), The externalist challenge: New studies on cognition and intentionality (pp. 239–254). Berlin: de Gruyter.Google Scholar
  42. Weinberger, A., & Fischer, F. (2006). A framework to analyze argumentative knowledge construction in computer-supported collaborative learning. Computers & Education, 46(1), 71–95.CrossRefGoogle Scholar
  43. Weinberger, A., Fischer, F., & Mandl, H. (2002). Fostering computer supported collaborative learning with cooperation scripts and scaffolds. In G. Stahl (Ed.), Computer support for collaborative learning: Foundations for a CSCL community. Proceedings of the international conference on computer support for collaborative learning (CSCL) 2002 (pp. 573–574). Hillsdale, NJ: Erlbaum.Google Scholar
  44. Wilson, S. M., Floden, R. E., & Ferrini-Mundy, J. (2002). Teacher preparation research: An insider’s view from the outside. Journal of Teacher Education, 53(3), 190–204.CrossRefGoogle Scholar
  45. Yin, R. K. (2003). Case study research: Design and methods (3rd ed. Vol. 5). Thousand Oaks: Sage Publications.Google Scholar
  46. Yoshida, M. (2005). An overview of lesson study. In P. Wang-Iverson & M. Yoshida (Eds.), Building our understanding of lesson study (pp. 3–14). Philadelphia, PA: Research for Better Schools.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Queensland University of TechnologyKelvin GroveAustralia

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