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References
- 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
- 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. https://hdl.handle.net/10520/EJC-1579679fa7
- 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
- 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
- Creswell, J. W., Plano Clark, V. L., Gutmann, M. L., & Hanson, W. E. (2003). Advanced mixed methods research designs. In A. Tashakkori, & C. Teddlie (Eds.), Handbook of mixed methods in social and behavioral research (pp. 209–240). Sage. http://rszarf.ips.uw.edu.pl/ewalps/teksty/creswell.pdf
- 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
- 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].
- 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). https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=5784e0b84b51230d72e1e0b6dd4f71e0e5de7e53
- 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.
- Harel, G., & Confrey, J. (1994). Development of multiplicative reasoning in the learning of mathematics. The Suny Press.
- 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
- Hinton, P., McMurray, I., & Brownlow, C. (2014). SPSS explained. Routledge.
- Hurst, C., & Hurrell, D. (2016). Investigating children’s multiplicative thinking: Implications for teaching. European Journal of STEM Education, 1(3), 1-11. https://dx.doi.org/10.20897/lectito.201656
- 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
- 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
- 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
- Mills, G. E., & Gay, L. R. (2016). Educational research: Competencies for analysis and applications (11th ed.). Pearson.
- Muijs, D. (2011). Leadership and organisational performance: from research to prescription?. International Journal of Educational Management, 25(1), 45-60. https://doi.org/10.1108/09513541111100116
- 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
- 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. http://hdl.handle.net/10072/2510
- Siemon, D. (2013). Launching mathematical futures: The key role of multiplicative thinking. Mathematics: Launching Futures, 36–52. https://albert.aamt.edu.au/content/download/38258/547092/file/maths_launching_futures.pdf#page=42
- 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. https://doi.org/10.1163/9789004391413_006
- Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching Mathematics: Foundations to the middle years. Oxford University Press.
- 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.
- 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.
- 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.
- Singh, P. (2012). Multiplicative thinking and learning. Encyclopedia of the Sciences of Learning, 2389–2392.
- 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
- van Dooren, W. (2020). The wonderful world of marginal means. https://jasp-stats.org/2020/04/14/the-wonderful-world-of-marginal-means/
- 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
- 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
References
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
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. https://hdl.handle.net/10520/EJC-1579679fa7
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
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
Creswell, J. W., Plano Clark, V. L., Gutmann, M. L., & Hanson, W. E. (2003). Advanced mixed methods research designs. In A. Tashakkori, & C. Teddlie (Eds.), Handbook of mixed methods in social and behavioral research (pp. 209–240). Sage. http://rszarf.ips.uw.edu.pl/ewalps/teksty/creswell.pdf
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
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].
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). https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=5784e0b84b51230d72e1e0b6dd4f71e0e5de7e53
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.
Harel, G., & Confrey, J. (1994). Development of multiplicative reasoning in the learning of mathematics. The Suny Press.
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
Hinton, P., McMurray, I., & Brownlow, C. (2014). SPSS explained. Routledge.
Hurst, C., & Hurrell, D. (2016). Investigating children’s multiplicative thinking: Implications for teaching. European Journal of STEM Education, 1(3), 1-11. https://dx.doi.org/10.20897/lectito.201656
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
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
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
Mills, G. E., & Gay, L. R. (2016). Educational research: Competencies for analysis and applications (11th ed.). Pearson.
Muijs, D. (2011). Leadership and organisational performance: from research to prescription?. International Journal of Educational Management, 25(1), 45-60. https://doi.org/10.1108/09513541111100116
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
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. http://hdl.handle.net/10072/2510
Siemon, D. (2013). Launching mathematical futures: The key role of multiplicative thinking. Mathematics: Launching Futures, 36–52. https://albert.aamt.edu.au/content/download/38258/547092/file/maths_launching_futures.pdf#page=42
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. https://doi.org/10.1163/9789004391413_006
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching Mathematics: Foundations to the middle years. Oxford University Press.
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.
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.
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.
Singh, P. (2012). Multiplicative thinking and learning. Encyclopedia of the Sciences of Learning, 2389–2392.
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
van Dooren, W. (2020). The wonderful world of marginal means. https://jasp-stats.org/2020/04/14/the-wonderful-world-of-marginal-means/
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
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