Linking practice and theory: A case study of mathematical discourse between a mathematics teacher educator and a primary classroom teacher
Keywords:
preservice teachers . co-teaching . mathematical discourse . primary . theory and practiceAbstract
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.
References
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 http://dx.doi.org/10.14221/ajte.2012v37n12.4
Cobb, P. (2006). Supporting productive whole class discussions. Presentation at the National Numeracy Facilitators’ conference. Retrieved from https://nzmaths.co.nz/search/node/Paul%20Cobb
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. Doi.org/10.1016/j.jmathb.2017.11.004
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 http://docs.education.gov.au/system/files/doc/other/action_now_classroom_ready_teachers_print.pdf.
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.
