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Growing Mathematically: Multiplicative Thinking

Supporting a targeted teaching approach to multiplicative thinking in the middle years based on an evidenced-based learning progression

This resource has been produced by the  Australian Association of Mathematics Teachers (AAMT), in collaboration with Emeritus Professor Dianne Siemon of RMIT and her colleagues with funding provided by the Australian Government Department of Education.

The views expressed are those of the author and do not necessarily represent the views of the Australian Government Department of Education.

The aim of the Mathematics Teacher Practice Guide is to add value to the existing formative assessment materials for multiplicative thinking developed by the Scaffolding Numeracy in the Middle Years Project (SNMY) (Siemon, Breed, Dole, Izard, & Virgona, 2006)[1].

The update has been made possible by the results of the Reframing Mathematical Futures (2013-2018) projects that explored the efficacy of using the SNMY materials in secondary schools alongside the development of similar formative assessment materials for algebraic, geometrical, and statistical reasoning (Siemon, Callingham, Day, Horne, Seah, Stevens, & Watson, 2018).

[1] https://www.education.vic.gov.au/school/
teachers/teachingresources/discipline/maths
/assessment/Pages/scaffoldnum.aspx

teaching students

Teacher's Manual

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Contents

» What is MT? Definition of Multiplicative Thinking


» Why is MT important? Brief description of the SNMY and RMFII projects, data to show MT the issue in the middle years and targeted teaching works


» Supporting the development of multiplicative thinking The SNMY formative assessment materials


» Targeted teaching Description and evidence to show that TT work


» Instructions How to administer and mark assessment options

» Student work samples To help interpret scoring rubrics


» Links to the Learning Assessment Framework for Multiplicative Thinking 2021 Revised learning progression, teaching advice, and related resources


» Case Studies Examples to show how schools have implemented a TT approach


» References/Further Reading Links to relevant research papers, wider reading


» Research Basis  Appendices

Diagram

Figure 1: A conceptual map of the Growing Mathematically: Multiplicative Thinking Resource

Acknowledgements

We would like to acknowledge funding from the Australian Federal Government, Department of Education, for the Growing Mathematically: Multiplicative Thinking project.

The Mathematics Teacher Practice Guide is supported through funding provided by the Australian Government Department of Education.

The current work builds on previous projects: Scaffolding Numeracy in the Middle Years (now hosted on the Victorian Department of Education and Training) and Reframing Mathematical Future II (RMIT).

The work is led by Emerita Professor Di Siemon, Associate Professor Rosemary Callingham and Lorraine Day. The project has been supported by Will Morony (former CEO AAMT) and Rachael Whitney-Smith (ACARA).

Disclaimer: The views expressed here are those of the author and do not necessarily represent the views of the Australian Government Department of Education.