Linking practice and theory: A case study of mathematical discourse between a mathematics teacher educator and a primary classroom teacher


  • Ann Downton
  • Tracey Muir
  • Sharyn Livy


preservice teachers . co-teaching . mathematical discourse . primary . theory and practice


In recent years there has been growing concern as to how to bridge the gap between the theory pre-service teachers engage with as part of their learning in their tertiary classrooms and the profession. To enable pre-service teachers to make stronger connections with the profession, a mathematics teacher educator worked collaboratively with a practicing teacher by co-teaching two cohorts of pre-service teachers studying primary mathematics education. As well as providing benefits to the pre-service teachers, the project allowed the mathematics teacher educator to reflect upon her own practice and the impact of the co-teaching experiences and learning. In this paper we present two snapshots of this experience and a framework that was used to identify how the co-teachers helped the pre-service teachers to make connections between theory and practice, when engaged in mathematical discourse.


Allen, J. M., Ambrosetti, A., & Turner, D. (2013). How school and university supervising staff perceive the pre-service teacher education practicum: A Comparative Study. Australian Journal of Teacher Education, 38(4), 108-128.

Anthony, G., Cooke, A., & Muir, T. (2016). Challenges, reforms, and learning in initial teacher education. In K. Makar, S. Dole, J. Visnovska, M. Goos, A. Bennison, & K. Fry (Eds.), Research in Mathematics Education in Australasia 2012-2015 (pp. 305-328). Singapore: Springer.

Anthony, G., Hunter, R., Anderson, D., Averill, R., Drake, M., Hunter, J., & Rawlins, P. (2015). Learning the work of ambitious mathematics teaching: TLRI research report. Wellington, NZ: New Zealand Council of Educational Research.

Anthony, G., Hunter, J., & Hunter, R. (2015). Supporting prospective teachers to notice students’ mathematical thinking through rehearsal activities. Mathematics Teacher Education and Development, 17(2), 7-24.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407.

Beswick, K., & Muir, T. (2013). Making connections: Lessons on the use of video in pre-service teacher education. Mathematics Teacher Education and Development, 15(2), 27-51.

Cavanagh, M. S., & Garvey, T. (2012). A professional experience learning community for pre-service secondary mathematics teachers. Australian Journal of Teacher Education, 37(12). Retrieved from

Cobb, P. (2006). Supporting productive whole class discussions. Presentation at the National Numeracy Facilitators’ conference. Retrieved from

Downton, A., Knight, R., Clarke, D., & Lewis, G. (2006). Mathematics assessment for learning: Rich tasks and work samples. Melbourne: Mathematics Teaching and Learning Centre, Australian Catholic University.

Enfield, M., & Stasz, B. (2011). Presence without Being Present: Reflection and Action in a Community of Practice. Journal of the Scholarship of Teaching and Learning, 11(1), 108-118.

Friend, M. (2008). Co-teaching: A simple solution that isn't simple after all. Journal of Curriculum and Instruction, 2(2), 9-19.

Goos, M., & Geiger, V. (2006). In search of practical wisdom: A conversation between researcher and teacher. For the Learning of Mathematics, 26(2), 33-35.

Geiger, V. S, Muir, T. & Lamb, J. (2016). Video-stimulated recall as a catalyst for teacher professional learning. Journal of Mathematics Teacher Education, 19(5), 457-475.

Graziano, K. J. & Navarrete, L. A. (2012). Co-teaching in a teacher education classroom: Collaboration, compromise and creativity. Issues in Teacher Education, 21(1), 109-126.

Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273-289.

Hong, L. T. (1993). Two of everything. Illinois: Albert Whitman & Company.

Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Stenhouse Publishers.

Kulm, G. (Ed.). (2008). Teacher knowledge and practice in middle grades mathematics. Rotterdam, The Netherlands: Sense Publishers.

Livy, S., & Downton, A. (2017). Exploring experiences for assisting primary pre-service teachers to extend their knowledge of student strategies and reasoning. The Journal of Mathematical Behavior.

Livy, S., Downton, A., & Muir, T. (2017). Developing Pre-Service Teachers' Knowledge for Teaching in the Early Years: Selecting and Sequencing. Mathematics Teacher Education and Development, 19(3), 17-35.

Ma, L. (1999). Knowing and teaching elementary mathematics. Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, New Jersey: Lawrence Erlbaum Associates, Inc.

Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass.

Muir, T., Allen, J. M., Rayner, C. S., & Cleland, B. (2013). Preparing pre-service teachers for classroom practice in a virtual world: A pilot study using Second Life. Journal of Interactive Media in Education, 2013(1), 1-17.

Muir, T. & Beswick, K. (2007). Stimulating reflection on practice: Using the supportive classroom reflection process. Mathematics Teacher Education and Development, 8 (special issue), 74-93.

National Council of Teachers of Mathematics (NCTM), (2014). Principals to actions: Ensuring mathematical success for all. Reston, VA: NCTM.

Novotná J. (2009) The Preparation of Teachers. In: Even R., Ball D.L. (Eds.), The Professional Education and Development of Teachers of Mathematics. New ICMI Study Series, Vol 11. (pp.13-14). Springer, Boston, MA

Perkins, T. (2015). Mentoring to alleviate anxiety in pre-service primary mathematics teachers: An orientation towards improvement rather than evaluation. In M. Marshman, V. Geiger, & A. Bennison (Eds.), Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia (pp. 501-507). Sunshine Coast, QLD: MERGA.

Rowland, T., Turner, F., Thwaites, A., & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the knowledge quartet. London: SAGE Publications Ltd.

Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.

Staples, M., & King, S. (2017). Eliciting, supporting and guiding the math: Three key functions of the teacher’s role in facilitating meaningful mathematical discourse. In D. A. Spangler & J. J. Wanko (Eds.), Enhancing Classroom Practice with Research behind Principles to Actions (pp. 25-36). Reston, VA: National Council of Teachers of Mathematics.

Sullivan, P. (2017). Challenging mathematical tasks: Unlocking the potential of all students. South Melbourne: Oxford.

Wenger, E. (1998). Communities of practice: Learning, meaning and identify. Cambridge UK: Cambridge University Press,.

Teacher Education Ministerial Advisory Group (TEMAG). (2015). Action now: Classroom ready teachers. Retrieved from

Turner, F., & Rowland, T. (2011). The knowledge quartet as an organising framework for developing and deepening teachers’ mathematics knowledge. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 195-212). Springer, Dordrecht.

Yin, R. K. (2009). Case study research: Designs and methods (4th ed.). Thousand Oaks, CA: Sage.

Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge, UK: Cambridge University Press.

Zeichner, K. (2010). Rethinking the connections between campus courses and field experiences in college-and university-based teacher education. Journal of Teacher Education, 61(1-2), 89-99.