Department of Education Scaffolding Numeracy in the Middle Years Project Findings, Materials and Resources An Australian Research Council Linkage Project conducted by a team from RMIT University in collaboration with the Department of Education & Training Victoria and the Tasmanian Department of Education from July 2003 to June 2006. Prepared by the RMIT Research Team led by Professor Dianne Siemon RMIT University, October 2006. TASMANIA Department of Education

About this CD-ROM This CD-ROM contains a brief description of the project, a report on project findings, and copies of the materials and resources used in conjunction with the Scaffolding Numeracy in the Middle Years Linkage Project 2003-2006 (SNMY). The report on project findings includes a rationale for the analyses used, a detailed data report, and a summary of outcomes in relation to the research questions. It also includes the summary data provided to research schools at the Cluster meetings in 2005 and 2006. The materials include two validated Assessment Instruments, the elaborated and final version of the Learning and Assessment Framework for Multiplicative Thinking, an Intervention Program for ‘At-Risk’ Students, a set of targeted interventions in the form of Learning Plans for each level of the framework, and a number of school- developed Authentic Tasks. The resources include copies of the support materials used in professional development sessions and/or school visits, papers and presentations not included elsewhere, and a bibliography. The Research Team believes the information and material contained on the CD-ROM is a valuable and useful resource to help scaffold the development of multiplicative thinking and thereby improve numeracy outcomes in the middle years of schooling. However, as is true of all teaching and learning materials, teachers are advised to carefully read the activities and tasks in relation to the Learning and Assessment Framework for Multiplicative Thinking with a view to modifying or adapting the activities to suit the particular, identified learning needs of their students.

Contents Overview and Project Findings Assessment Materials for Multiplicative Thinking Learning and Assessment Framework for Multiplicative Thinking Intervention Teaching Program for At Risk Students Learning Plans Support Materials Authentic Tasks Papers and Presentations Bibliography

Overview and Project Findings Project Description and Acknowledgements Research Approach and Rationale by Dr John Izard Adjunct Professor RMIT University What We Have Learnt SNMY Research Cluster Meetings 05 (PowerPoint Presentation) SNMY Research Cluster Meetings 06 (PowerPoint Presentation) Technical Data Report by Dr John Izard Adjunct Professor RMIT University Summary of Project Outcomes by Professor Dianne Siemon & Dr John Izard Adjunct Professor RMIT University Return to Contents

Assessment Materials for Multiplicative Thinking Instructions for Teachers Assessment Task Booklet Option 1 Assessment Task Booklet Option 2 Return to Contents

Learning and Assessment Framework for Multiplicative Thinking Introduction Learning Assessment Framework Return to Contents

Intervention Teaching Program for At Risk Students Introduction Intervention Teaching Program for At Risk Students by Margarita Breed 2006 Australian Postgraduate Award Industry scholarship recipient Return to Contents

Learning Plans Introduction Level 4 Introducing Level 1 Consolidating Return to Contents

Support Materials Introduction SNMY Key Ideas and Strategies (PowerPoint) Subitising Materials Additional Assessment Tasks Multiple Patterns Multiplication Toss Place Value Game How Many Wholes Can You Make Supermarket Packer Target Practice Factor Cross Max’s Matchsticks Return to Contents

Subitising Materials Subitisation Dice and Card Set Subitisation Two Collections 1-5 Ten Frame Doubles Set Ten Frame Build on Five Set Subitisation Two Collections 1-7 Ten Frame Random Set Two Ten Frame Set Subitisation Three Collections 1-5 Subitisation Three Collections 1-7 Subitisation Four Collections 1-5 Subitisation Four Collections 1-7 Return to Support Materials Return to Contents

Additional Assessment Tasks Computer Game Fencing the Freeway Filling the Buses How Far Is It Missing Numbers Orange Juice Task Pizza Party School Fair Swimming Sports Return to Support Materials Return to Contents

Authentic Tasks Introduction Paper Audit Water Conservation Authentic Task Guidelines Pizza Day Mini Golf Sports Day Fatty Foods Health Survey Healthy Lunches Paper Audit Water Conservation A Useful Grid Pocket Money Interruptions Galore Mud Bricks Food Festival Return to Contents

Papers and Presentations From Additive to Multiplicative Thinking – The Big Challenge of the Middle Years by Professor Dianne Siemon, Margarita Breed and Jo Virgona A New Use for an Old Tool – Cuisenaire by Professor Dianne Siemon and Margarita Breed Multiplicative Thinking by Professor Dianne Siemon Partitioning - The Missing Link in building Fraction Knowledge and Confidence by Professor Dianne Siemon Teaching and Learning For about and Through Problem Solving by Professor Dianne Siemon and George Booker Return to Contents

Papers and Presentations cont… There’s More to Counting than Meets the Eye by Professor Dianne Siemon From Their Point of View – Middle Years’ Students Perceptions of School Mathematics by Professor Dianne Siemon and Jo Virgona The Derivation Of A Learning Assessment Framework For Multiplicative Thinking by Professor Dianne Siemon, Dr John Izard, Margarita Breed & Jo Virgona Return to Papers and Presentations Return to Contents

Bibliography References and Further Readings Return to Contents