Experiencing a mathematical problem-solving teaching approach: Opportunities to identify ambitious teaching practices


  • Judy Bailey The University of Waikato
  • Merilyn Taylor The University of Waikato


practice-based pre-service teacher education, ambitious teaching, core high-leverage practices, problem-solving


Learning to teach is a complex matter, and many different models of pre-service teacher education have been used to support novice teachers in preparation for the classroom. More recently there have been calls for embedding practice at the centre of teachers’ professional preparation. Preparing novice teachers for ambitious teaching is demanding. A focus on core high-leverage practices such as teaching through problem-solving are suggested. In this study novice teachers engaged in practice-based teacher education to explore the learning and teaching of mathematics using a problem-solving approach. Findings suggest experiencing this approach is an important first step towards novice teachers learning about practices congruent with current reform expectations such as justifying mathematical reasoning, emphasising conceptual understanding, and catering for all learners.  Novice teachers also began to envisage how ambitious mathematics pedagogies could be enacted in their future practice.

Author Biographies

Judy Bailey, The University of Waikato

Senior Lecturer, School of Curriculum and Pedagogy, Faculty of Education

Merilyn Taylor, The University of Waikato

Lecturer, School of Curriculum and Pedagogy, Faculty of Education


Anthony, G., & Hunter, R. (2013). Learning the work of ambitious mathematics teaching. In V. Steinle, L. Ball & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow. Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia (pp. 699-702). Melbourne, Australia: MERGA.

Anthony, G., Hunter, R., Hunter, J., Rawlins, P. Averill, R., Drake, M., & Anderson, D. (2015). Learning the work of ambitious mathematics teaching. Teaching and Learning Research Initiative. Retrieved June 15, 2015, from http://www.tlri.org.nz/sites/default/files/projects/TLRI_Anthony_Final%20Summary%20Report%20%28v3%29.pdf.

Ball, D. L., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497-511.

Ball, D. L., Sleep, L., Boerst, T. A., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. The Elementary School Journal, 109(5), 458-474.

Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Mahwah, New Jersey: Lawrence Erlbaum.

Boaler, J. (2008). What’s math got to do with it?: helping children learn to love their least favourite subject – and why it’s important for America. New York: Viking.

Beswick, K. (2007/8). Influencing teachers’ beliefs about teaching mathematics for numeracy to students with mathematics learning difficulties. Mathematics Teacher Education and Development, 9, 3-20.

Borko, H., Liston, D., & Whitcomb, J. (2007). Genres of empirical research in teacher education. Journal of Teacher Education, 58(1), 3-11.

Breyfogle, L., Williams, L. (2008). Designing and implementing worthwhile tasks. Teaching Children Mathematics, 15(5), 276-280.

Clandinin, D.J., & Rosiek, J. (2007). Mapping a landscape of narrative inquiry: Borderland spaces and tensions. In D. J. Clandinin (Ed.), Handbook of narrative inquiry: Mapping a methodology (pp. 35-75). Thousand Oaks, CA: Sage.

Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3–4), 175–190.

Coburn, C. E. (2005). The role of nonsystem actors in the relationship between policy and practice: The case of reading instruction in California. Educational Evaluation and Policy Analysis, 27(1), 23-52.

Cohen, L., Manion, L. & Morrison, K. (2007). Research Methods in Education. New York: Routledge.

Frankcom, G. (2009). Investigative mathematics: Discovering the teacher mathematician inside. In R. Averill & R. Harvey (Eds.), Teaching Secondary School Mathematics and Statistics: Evidence-based Practice (pp. 23-36). Wellington: NZCER Press.

Forzani, F. M. (2014). Understanding “core practices” and “practice-based” teacher education: Learning from the past. Journal of Teacher Education, 65(4), 357-368.

Grootenboer, P. (2008). Mathematical belief change in prospective primary teachers. Journal of Mathematics Teacher Education, 11(6) 479-497.

Grootenboer, P., & Jorgensen, R. (2009). Towards a theory of identity and agency in coming to learn mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 5(3), 255-266.

Grossman, P., Compton, C., Igra, D., Ronfeldt,M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9). Retrieved February 26, 2015 from http://www.tcrecord.org/content.asp?contentid=15018

Guillaume, A. M., & Kirtman, L. (2005). Learning lessons about lessons: Memories of mathematics instruction. Teaching Children Mathematics, 11(6), 302-309.

Hlas, C. H., & Hlas, C. S. (2012). A review of high-leverage teaching practices: Making connections between mathematics and foreign languages. Foreign Language Annals, 45(S1), S76-S97.

Holton, D. (2009). Problem-solving in the secondary school. In R. Averill & R. Harvey (Eds.), Teaching Secondary School Mathematics and Statistics: Evidence-based Practice (pp. 37-52). Wellington: NZCER Press.

Hunter, R. & Anthony, G. (2010). Developing mathematical inquiry and argumentation. In R. Averill and R. Harvey (Eds.). Teaching Primary School Mathematics and Statistics: Evidence-based practice. Wellington: NZCER.

Jorgensen, R., & Dole, S. (2011). Teaching mathematics in primary schools (2nd ed.). Crows Nest, NSW: Allen & Unwin.

Kane, R. (2007). From naïve practitioner to teacher educator and researcher: constructing a personal pedagogy of teacher education. In T. Russell & J. Loughran (Eds.), Enacting a pedagogy of teacher education: Values, relationships and practices (pp. 60-76). London: Routledge.

Korthagen, F. (2004). In search of the essence of a good teacher: towards a more holistic approach in teacher education. Teaching and Teacher Education, 20, 77-97.

Labaree, D. (2000). On the nature of teaching and teacher education. Journal of Teacher Education 51(3), 228-233.

Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In M. K. Stein & L. Kucah (Eds.), Instructional Explanations in the Disciplines (pp. 129-141). New York: Springer.

Lampert, M., & Graziani, F. (2009). Instructional activities as a tool for teachers’ and teacher educators’ learning. The Elementary School Journal, 109(5), 491-509.

Lomas, G., Grootenboer, P., Attard, C. (2012). The affective domain and mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, & J. Greenlees (Eds.), Research in Mathematics Education in Australasia 2008-2011 (pp. 23-37). Melbourne: MERGA.

Ministry of Education. (1992). Mathematics in the New Zealand Curriculum. Wellington: Learning Media.

Ministry of Education. (1999). Teaching problem-solving in mathematics: Years 1-8. Wellington: Learning Media.

Ministry of Education. (2007). The New Zealand Curriculum. Wellington: Learning Media.

Quinnell, L. Why are mathematical investigations important? Australian Mathematics Teacher, 66(3), 35-40.

Rigelman, N. (2007). Fostering mathematical thinking and problem solving: the teacher’s role. Teaching Children Mathematics, 13(6), 308-314.

Rogers, G. (2007). Learning-to-learn and learning-to-teach: Experiencing history in teacher education. Paper presented at the BERA Annual Conference, Institute of Education, University of London, Sept 5-8, 2007.

Russell, T. (2007). How experience changed my values as a teacher educator? In T. Russell & J. Loughran (Eds.), Enacting a pedagogy of teacher education (pp. 182-191). London: Routledge.

St. Pierre, E. A. (2011). Post qualitative research: the critique and the coming after. In N. K. Denzin & Y. S. Lincoln. (Eds.), The Sage handbook of qualitative research (pp. 611-625). Thousand Oaks: Sage.

Strauss, A., & Corbin, J. (1994). Grounded theory methodology: an overview. In N. Denzin and Y. Lincoln (Eds.), Handbook of Qualitative Research (pp. 273-285). Thousand Oaks, CA: Sage.

Wieman, R. (2011). Students’ beliefs about mathematics: Lessons learned from teaching note-taking. Mathematics Teacher, 104(6), 406-407.

Young-Loveridge, J. (2010). A decade of reform in mathematics education: Results for 2009 and earlier years. Findings from the New Zealand Numeracy Development Projects. Wellington: Learning Media.