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Abstract

Multiplicative thinking is important for students’ learning of key topics in mathematics such as algebra, geometry, measurement, fractions, statistics, and probability. This study employed an embedded mixed-method approach to investigate primary school teachers’ pedagogical content knowledge for developing multiplicative thinking in students. The study participants (n = 62) were primary school teachers in Australia at different levels of teaching experience, from preservice teachers to novice, experienced, and expert teachers. Teachers completed a carefully designed questionnaire, and a model of Teacher Capacity was the framework for instrument design and data analysis. The investigation in this research focused on three key teaching stages for developing multiplicative thinking: transitional, multiplicative, and proportional reasoning. Estimated marginal means, pairwise comparison, and regression analysis statistical tests were conducted using SPSS 2.0. The results highlight specific areas requiring attention in teacher professional development and preparation programs to enhance teachers’ capacity to effectively support students’ learning and development around multiplicative thinking. For example, there is a need to enhance teachers’ capacity for multiplicative thinking during transitional teaching and the need to emphasize the development of teachers’ knowledge of students and the design of instruction.

Keywords

Multiplicative Thinking Pedagogical Content Knowledge Teacher Capacity Teaching Experience

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How to Cite
Malola, M., & Seah, W. T. (2024). Primary school teachers’ knowledge for teaching multiplicative thinking. Journal on Mathematics Education, 15(4), 1175–1196. https://doi.org/10.22342/jme.v15i4.pp1175-1196
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References

  1. Askew, M. (2018). Multiplicative reasoning: Teaching primary pupils in ways that focus on functional relations. The Curriculum Journal, 29(3), 406–423. https://doi.org/10.1080/09585176.2018.1433545
  2. Askew, M., Mathews, C., Takane, T., Venkat, H., Ramsingh, V., & Roberts, N. (2019). Multiplicative reasoning: An intervention’s impact on Foundation Phase learners’ understanding. South African Journal of Childhood Education, 9(1), 1–10.
  3. Clark, F. B., & Kamii, C. (1996). Identification of multiplicative thinking in children in Grades 1–5. Journal for Research in Mathematics Education, 27(1), 41–51. https://doi.org/10.5951/jresematheduc.27.1.0041
  4. Coxe, S., West, S. G., & Aiken, L. S. (2009). The analysis of count data: A gentle introduction to Poisson regression and its alternatives. Journal of Personality Assessment, 91(2), 121–136. https://doi.org/10.1080/00223890802634175
  5. Creswell, J. W., Plano Clark, V. L., Gutmann, M. L., & Hanson, W. E. (2003). Advanced mixed methods research designs. Handbook of Mixed Methods in Social and Behavioral Research, 209(240), 209–240.
  6. Day, L., & Hurrell, D. (2015). An explanation for the use of arrays to promote the understanding of mental strategies for multiplication. Australian Primary Mathematics Classroom, 20(1), 20–23. https://search.informit.org/doi/abs/10.3316/informit.059089282275483
  7. Downton, A., Giumelli, K., McHugh, B., Roosen, T., Meredith, N., Caleta, G., King, M., Salkeld, K., & Stenning, P. (2019, June 30–July 4). The impact of whole school professional learning on students’ multiplicative thinking [Paper presentation].
  8. Ell, F., Irwin, K., McNaughton, S. (2004). Two pathways to multiplicative thinking. In I. Put, R. Faragher, & M. McLean (Eds.), Mathematics education for the third millennium, towards 2010. Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia (pp. 199–206).
  9. Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 147–164). Macmillan.
  10. Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434. https://doi.org/10.5951/jresematheduc.27.4.0403
  11. Harel, G., & Confrey, J. (1994). Development of multiplicative reasoning in the learning of mathematics. The Suny Press.
  12. Hill, H. C., & Chin, M. (2018). Connections between teachers’ knowledge of students, instruction, and achievement outcomes. American Educational Research Journal, 55(5), 1076-1112. https://doi.org/10.3102/000283121876961
  13. Hinton, P., McMurray, I., & Brownlow, C. (2014). SPSS explained. Routledge.
  14. Hurst, C., & Hurrell, D. (2016). Investigating children’s multiplicative thinking: Implications for teaching. European Journal of STEM Education, 1(3). 10.20897/lectito.201656
  15. Malola, M., Stephens, M., & Symons, D. (2021). Key teaching stages for developing multiplicative thinking in students. Australian Mathematics Education Journal, 3(1), 9–15. https://search.informit.org/doi/abs/10.3316/informit.759368128817474
  16. Malola, M., Symons, D., & Stephens, M. (2020). Supporting students’ transition from additive to multiplicative thinking: A complex pedagogical challenge. Australian Primary Mathematics Classroom, 25(2), 31–36. https://search.informit.org/doi/abs/10.3316/INFORMIT.284655920537973
  17. Matitaputty. C., Nusantara, T., Hidayanto, E., & Sukoriyanto. (2024). How mathematics teachers' special knowledge changing: A case study in the Professional Teacher Education program. Journal on Mathematics Education, 15(2), 545-574. http://doi.org/10.22342/jme.v15i2.pp545-574
  18. Mills, G. E., & Gay, L. R. (2016). Educational research: Competencies for analysis and applications (11th ed.). Pearson.
  19. Pincheira, N., & Alsina, Á. (2024). Assessing knowledge to teach early algebra from the Mathematical Knowledge for Teaching (MKT) perspective: A support tool for primary school teachers. Journal on Mathematics Education, 15(2), 639-660. http://doi.org/10.22342/jme.v15i2.pp639-660
  20. Seah, R., & Booker, G. (2005). Lack of numeration and multiplication conceptual knowledge in middle school students: A barrier to the development of high school mathematics. Stimulating the ‘Action’ as Participants in Participatory Research, 3, 86–98.
  21. Siemon, D. (2013). Launching mathematical futures: The key role of multiplicative thinking. Mathematics: Launching Futures, 36–52.
  22. Siemon, D., Banks, N., & Prasad, S. (2018). Multiplicative thinking a STEM foundation. In T. Barkatsas, N. Carr, & G. Cooper (Eds.), STEM education: An emerging field of inquiry (pp. 74–100). Sense Publications
  23. Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching Mathematics: Foundations to the middle years. Melbourne: Oxford University Press.
  24. Siemon, D., Breed, M., & Virgona, J. (2005). From additive to multiplicative thinking: The big challenge of the middle years. Proceedings of the 42nd Conference of the Mathematical Association of Victoria, Bundoora, Australia.
  25. Siemon, D., Breed, M., Dole, S., Izard, J., & Virgona, J. (2006). Scaffolding numeracy in the middle years: Project findings, materials and resources: Final report. RMIT University.
  26. Siemon, D., Virgona, J., & Corneille, K. (2001). The middle years numeracy research project: 5–9. Final report. Department of Education, Employment and Training, Victoria, Catholic Education Commission of Victoria and Association of Independent Schools of Victoria. RMIT University
  27. Singh, P. (2012). Multiplicative thinking and learning. Encyclopedia of the Sciences of Learning, 2389–2392.
  28. Sowder, J., Armstrong, B., Lamon, S., Simon, M., Sowder, L., & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1(2), 127–155. https://doi.org/10.1023/A:1009980419975
  29. van Dooren, W. (2020). The wonderful world of marginal means. https://jasp-stats.org/2020/04/14/the-wonderful-world-of-marginal-means/
  30. Venkat, H., & Mathews, C. (2019). Improving multiplicative reasoning in a context of low performance. ZDM, 51(1), 95–108. https://link.springer.com/article/10.1007/s11858-018-0969-6
  31. Zhang, Q., & Stephens, M. (2013). Utilising a construct of teacher capacity to examine national curriculum reform in mathematics. Mathematics Education Research Journal, 25(4), 481–502. 10.1007/s13394-013-0072-9