Main Article Content


Teaching ‘out-of-field’ is a present obstacle in mathematics education in many countries, and developing professional learning programs aimed at upskilling non-specialist teachers is urgent. A teacher study group was established wherein two non-specialist teachers of mathematics (Years 7–10; aged 12–16) engaged with algebra to develop a deeper understanding of the subject and its teaching. The study group lasted one school year, during which the teachers actively participated in the learning. Multiple data sources were collected, including reflection forms, open-ended questionnaires, and a storytelling form. Analysis of the teachers’ solutions to a sample of algebra problems and self-reports suggests that the study group enabled teachers to acquire new knowledge/skills in mathematics pedagogy, gain a new understanding of how student thinking and understanding develop, adapt new classroom instruction strategies, develop ability/confidence in problem-solving, and develop new knowledge/ability in algebra. The study findings contribute to our understanding of supporting non-specialist mathematics teachers’ professional development.


Algebra Professional Development Study Groups Secondary Mathematics Teachers Teacher Learning

Article Details

How to Cite
Hatisaru, V. (2024). Non-specialist secondary mathematics teachers learning in study groups by engaging with activities of algebra. Journal on Mathematics Education, 15(1), 131–150.


  1. Australian Council for Educational Research (ACER). (2014). Staff in Australia’s schools 2013. Retrieved from
  2. Australian Mathematical Science Institute (AMSI). (2020). The state of mathematical sciences 2020. 7th discipline profile of mathematics and statistics in Australia. Retrieved from
  3. Arbaugh, F. (2003). Study groups as a form of professional development for secondary mathematics teachers. Journal of Mathematics Teacher Education, 6(2), 139–163.
  4. Birchak, B., Connor, C., Crawford, K. M., Kahn, L. H., Kaser, S., Turner, S. & Short, K. G. (1998). Teacher study groups: Building community through dialogue and reflection. Urbana, IL: National Council of Teachers of English.
  5. Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students: A review. Journal of Mathematical Behaviour, 32, 613–632.
  6. Borko, H., & Potari, D. (Eds.). (2020). Teachers of mathematics working and learning in collaborative groups. ICMI STUDY 25 Conference Proceeding. National and Kapodistrian University of Athens.
  7. Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers’ learning. The Elementary School Journal, 103(3), 287–311.
  8. Cuoco, A. (2013). High school teaching: standards, practices, and habits of mind. Center for Mathematics Education (CME), Education Development Center, Inc. (EDC).
  9. Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947–967.
  10. Crespo, S. (2006). Elementary teacher talk in mathematics study groups. Educational Studies in Mathematics, 63(1), 29–56.
  11. Darling-Hammond, L., Hyler, M.E., & Gardner, M. (2017). Effective teacher professional development. Learning Policy Institute.
  12. du Plessis, A. E. (2015). Effective education: conceptualising the meaning of out-of-field teaching practices for teachers, teacher quality and school leaders. International Journal of Educational Research, 72, 89-102.
  13. Faulkner, F., Kenny, J., Campbell, C., & Crisan, C. (2019). Teacher learning and continuing professional development. In L. Hobbs & G. Törner (Eds.), Examining the phenomenon of “teaching out-of-field”: International perspectives on teaching as a non-specialist (pp. 269–308). Springer.
  14. Fishman, B. L., Davis, E. A., & Chan, C. K. K. (2014). A learning sciences perspective on teacher learning research. In K. Sawyer (Ed.), The Cambridge Handbook of the Learning Sciences (pp. 707–725). Cambridge.
  15. Gersten, R., Dimino, J., Jayanthi, M., Kim, J. S., & Santoro, L. E. (2010). Teacher study group: Impact of the professional development model on reading instruction and student outcomes in first grade classrooms. American Educational Research Journal, 47(3), 694-739.
  16. Goldsmith, L. T., Doerr, H. M., & Lewis, C. C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17(1), 5–36.
  17. Goos, M. (2013). Knowledge for teaching secondary school mathematics: What counts? International Journal of Mathematical Education in Science and Technology, 44(7), 972–983.
  18. Goos, M., O’Donoghue, J., Ní Ríordáin, M., Faulkner, F., Hall, T., & O’Meara, N. (2020). Designing a national blended learning program for “out-of-field” mathematics teacher professional development. ZDM Mathematics Education, 52, 893–905.
  19. Grandau, L. (2005). Learning from self-study: Gaining knowledge about how fourth graders move from relational description to algebraic generalization. Harvard Educational Review, 75(2), 202–221.
  20. Grossman, P., Wineburg, S., & Woolworth, S. (2001). Toward a theory of teacher community. Teachers College Record, 103(6), 942-1012.
  21. Hatisaru, V. (2021). A reflection on Star and Seifert’s (2006) operationalisation of flexibility in equation solving. For the Learning of Mathematics, 41(2), 37-39.
  22. Hatisaru, V. (2022). How to develop a structural conception of algebra of school students. LUMAT-B: International Journal on Math, Science and Technology Education, 7(1), 56–66.
  23. Hatisaru, V. & Erbaş, A. K. (2017). Mathematical knowledge for teaching and student learning outcomes. International Journal of Science and Mathematics Education, 15(4), 703-722.
  24. Hatisaru, V., Oates, G, & Chick, H. (2022). Developing proficiency with teaching algebra in teacher working groups: understanding the needs. In N. Fitzallen, C. Murphy, V. Hatisaru, & N. Maher (Eds.), Proceedings of the 44th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 250‒257). Launceston: MERGA.
  25. Hill, H. C., & Chin, M. (2018). Connections between teachers’ knowledge of students, instruction, and achievement outcomes. American Educational Research Journal, 55(5), 1076–1112.
  26. Hill, H. C., Lynch, K., Gonzalez, K. E., & Pollard, C. (2020). Professional development that improves STEM outcomes. Phi Delta Kappan, 101(5), 50-56.
  27. Hobbs, L., & Törner, G. (Eds.). (2019). Examining the phenomenon of teaching out-of-field: international perspectives on teaching as a non-specialist. Springer.
  28. Hollingsworth, H., & Clarke, D. (2017). Video as a tool for focusing teacher self-reflection: supporting and provoking teacher learning. Journal of Mathematics Teacher Education, 20, 457–475.
  29. Hu, Q., Son, J. W. & Hodge, L. (2022). Algebra teachers’ interpretation and responses to student errors in solving quadratic equations. International Journal of Science and Mathematics Education, 20, 637–657.
  30. Hsieh, H.-F., & Shannon, S. E. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15, 1277–1288.
  31. Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: using student work to promote collective inquiry. Journal of Mathematics Teacher Education 7, 203‒235.
  32. Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390‒419). Macmillan Publishing.
  33. Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707‒762). Information Age Publishing.
  34. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. The National Academy Press.
  35. Lachance, A., & Confrey, J. (2003). Interconnecting content and community: A qualitative study of secondary mathematics teachers. Journal of Mathematics Teacher Education, 6(2), 107–137.
  36. Lane, C., & Ní Ríordáin, M. (2020). Out-of-field mathematics teachers’ beliefs and practices: An examination of change and tensions using zone theory. International Journal of Science and Mathematics Education, 18, 337–355.
  37. Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33–40) Hillsdale, NJ: Lawrence Erlbaum Associates.
  38. Martin, M. M., Goldberg, F., McKean, M., Edward, P., & Turpen, C. (2022). Understanding how facilitators adapt to needs of STEM faculty in online learning communities: a case study. International Journal of STEM Education, 9, 56.
  39. Muir, T., Deed, C., Thomas, D., & Emery, S. (2021). Achieving teacher professional growth through professional experimentation and changes in pedagogical practices. Australian Journal of Teacher Education, 46(9), 2.
  40. Noble, H., & Heale., R. (2019). Triangulation in research, with examples. Evidence Based Nursing, 22, 67–68.
  41. Perry, E., & Boylan, M. (2018) Developing the developers: Supporting and researching the learning of professional development facilitators. Professional Development in Education, 44(2), 254–271.
  42. Ponte, J. P., Quaresma, M., & Mata-Pereira, J. (2022). Teachers’ learning in lesson study: insights provided by a modified version of the interconnected model of teacher professional growth. ZDM Mathematics Education, 54, 373–386.
  43. Porsch, R., & Whannell, R. (2019). Out-of-field teaching affecting students and learning: what is known and unknown. In L. Hobbs & G. Törner (Eds.), Examining the Phenomenon of “Teaching Out-of-Field”: International Perspectives on Teaching as a Non-Specialist (pp. 179–191). Springer.
  44. Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.
  45. Qi, C., Cao, C. & Huang, R. (2021). Teacher learning through collaboration between teachers and researchers: A Case Study in China. International Journal of Science and Mathematics Education.
  46. Schwarts, G., & Karsenty, R. (2020). “Can this happen only in Japan?”: mathematics teachers reflect on a videotaped lesson in a cross-cultural context. Journal of Mathematics Teacher Education, 23, 527–554.
  47. Stanley, A. M. (2011). Professional development within collaborative teacher study groups: Pitfalls and promises. Arts Education Policy Review, 112(2), 71-78.
  48. Tatto, M. T., Peck, R., Schwille, J., Bankov, K., Senk, S. L., Rodriguez, M., … Rowley, G. (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M). International Association for the Evaluation of Educational Achievement.
  49. Thorne, S. (2000). Data analysis in qualitative research. Evidence Based Nursing, 3(3), 68-70.
  50. Thurlings, M., & den Brok, P. (2018) Student teachers’ and in-service teachers’ peer learning: A realist synthesis. Educational Research and Evaluation, 24(1-2), 13-50.
  51. Wadjaja, W., Vale, C., Groves, S., & Doig, B. (2017). Teachers’ professional growth through engagement with lesson study. Journal of Mathematics Teacher Education, 20, 357–383.
  52. Weldon, P. (2016). Out-of-field teaching in Australian secondary schools. Policy Insights, Issue 6. Australian Council for Educational Research.
  53. Wongsopawiro, D. S., Zwart, R.C., & van Driel, J. H. (2017). Identifying pathways of teachers’ PCK development. Teachers and Teaching: theory and practice, 23(2), 191-210.