AUSTRALIAN CURRICULUM: MATHEMATICS (and state curricula)
The word ‘multiplicative’ is mentioned only once in the Australian Curriculum: Mathematics (AC: M). However, upon investigation, the AC: M is highly supportive of the development of multiplicative concepts. We identified 71% of the curriculum content descriptors (CCDs)for Years K to 6 that directly support or underpin one or more aspects of multiplicative thinking. Further, we have developed a Curriculum Links document that give details of specific CCDs and their elaborations, what each CCD ‘looks like’ in practice, and how each CCD underpins multiplicative thinking. We are currently working on compiling a similar document for Years 7 to 9. The Years K to 6 document is available through the Maths Store. To learn more about it, and to see an example, click here.
GROWING MATHEMATICALLY – based on the work of Di Siemon
Growing Mathematically is a project funded by the Australian Federal Government. It builds on materials that were developed as part of the RMIT Reframing Mathematical Futures II (Siemon, Callingham, Day, Horne, Seah, Stephens, & Watson, 2018) and the Scaffolding Numeracy in the Middle Years (SNMY) (Siemon, Breed, Dole, Izard, & Virgona, 2006) projects. SNMY content is currently hosted by the Victorian Department of Education.
As a result of the SNMY Project (Siemon et al.,2006), a Learning and Assessment Framework for Multiplicative Thinking (LAF) was developed. It consists of an eight-level learning progression for multiplicative thinking describing its development from pre-multiplicative strategies (Zone 1) to the use of proportional reasoning (Zone 8). Although multiplicative thinking is not consistently evident until Zone 4, strategies that underpin it certainly can be identified.
We decided to investigate the alignment between our model for multiplicative thinking based on four sets of multiplicative connections, and Siemon’s Learning Assessment Framework. The reasoning behind this investigation was that numerous schools are using the LAF as the basis for their teaching of multiplicative thinking and we thought it would be beneficial to see how closely the two models/frameworks align. To download a summary showing the extent of the alignment, click here.
Siemon, D., Breed, M., Dole, S., Izard, J., & Virgona J. (2006). Scaffolding Numeracy in the Middle Years – Project findings, materials and resources, Final report. Retrieved from https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/scaffoldnum.aspx
Siemon, D., Callingham, R., Day, L., Horne, M., Seah, R., Stephens, M., & Watson, J. (2018). From research to practice: The case of mathematical reasoning. In J. Hunter, L. Darragh & P. Perger (Eds.), Making waves, opening spaces, Proceedings of the 41st annual conference of the Mathematics Education Research Group of Australasia (pp. 40-49). Auckland, NZ: MERGA.