1. SCAFFOLDING NUMERACY IN THE MIDDLE YEARS A Linkage Research Project 2003 - 2006

2. TASMANIAN Department of Education Support for this project has been provided by the Australian Research Council, RMIT University, the Victorian Department of Education and Training, and the Tasmanian Department of Education. Research Schools Mid-term Teachers Day February/March, 2005 Project Update Elaborating the Learning Assessment Framework

3. RESEARCH TEAM: Associate Professor Dianne Siemon, Project Director, RMIT University Ms Jo Virgona, Senior Project Officer; RMIT University Ms Margarita Breed, Ph.D student, RMIT University; and Professor Peter Sullivan (Latrobe University), Dr Shelley Dole (University of QLD), and Adjunct Professors John Izard and Max Stephens (RMIT University) – Consultants Ms Denise Neil (Tas DoE) and Mr Maurie Sheehan (DE&T) – Industry Partner Representatives

4. PROJECT AIM: In broad terms, the project will investigate the efficacy of a new assessment-guided approach to improving student numeracy outcomes in Years 4 to 8. In particular, it will identify and refine a Learning & Assessment Framework for the development of multiplicative thinking using authentic assessment tasks.

5. RECAP: Why authentic tasks? Why the middle years/Years 4 to 8? Why multiplicative thinking? Why an assessment-guided approach? What is a Learning Assessment Framework? For more details, see the Project Information handout distributed at the Teacher’s Day in Feb/March 2004 and Project Notes 1 to 5.

6. WHAT WE’VE ACHIEVED TO DATE: Identified research and reference schools: 1 in Tasmania, 2 clusters in Victoria Developed a set of rich tasks and scoring rubrics to evaluate multiplicative thinking in Years 4 to 8 Assessed 3172 students in Term 1, 2004

7. WHAT WE’VE ACHIEVED TO DATE: Analysed the initial and subsequent trial data and identified a draft Learning Assessment Framework for multiplicative thinking Established Learning Plan teams Developed and trialled initial Learning Plans for each Level of the Learning Assessment Framework

8. WHAT WE’VE ACHIEVED TO DATE: Learning Plans revised and distributed for other teachers to use (Round 1) Round 1 Implementation Reports completed and returned to Cluster Coordinators Identified who will develop Authentic Tasks and how this process will be supported

9. WHAT WE’VE LEARNT: Adjusted Mean Scores 2(L+5) Adjusted Means by Year Level and Gender Research Schools 2004

10. WHAT WE’VE LEARNT: Adjusted Mean Scores 2(L+5) Adjusted Means by Year Level and Gender Reference Schools 2004

11. WHAT WE’VE LEARNT: There are little or no gender differences evident at any Year level in either the Research schools or the Reference schools – this may be a function of the form of assessment which privileged explanations over answers alone Multiplicative thinking clearly improves with time, although, consistent with other middle years data, this appears to ‘level off’ in Years 7 and 8, suggesting that school transition is a factor impacting achievement at this level Although the levels of achievement are comparable at Year 8, reference school students appear to be starting from a lower base than the research school students

12. WHAT WE’VE LEARNT: In terms of the Learning and Assessment Framework for Multiplicative Thinking (LAF), the average level of achievement for both research and reference schools ranges from Level 2 or 3 of the Framework in Year 4 to about Level 5 in Year 8, ie, 12345678 This suggests that, for many students, multiplicative thinking may be much more difficult than previously recognised and may take many more years to acquire than is typically assumed in curriculum documents. But this only shows differences across Year levels, what about the differences within Year levels?

13. WHAT WE’VE LEARNT: Proportion of Students at each Level of the LAF by Year Level Research Schools 2004

14. WHAT WE’VE LEARNT: Proportion of Students at each Level of the LAF by Year Level Reference Schools 2004

15. WHAT WE’VE LEARNT: There are students at each level of the Learning and Assessment Framework for Multiplicative Thinking in each Year level – this does not equate to every class but it does illustrate the enormous range of achievement within each Year level LAF12345678 CSF1/222/333/444/55 %49.728.4201.9 N102558741339 A significant number of Year 4 to 8 students appear to rely on additive thinking or naïve notions of multiplication (LAF Levels 1-3) Proportion of Victorian sample at corresponding levels of LAF and CSF for multiplicative thinking in 2004

16. WHAT WE’VE LEARNT: Overall, the vast majority of students appear to have little difficulty using additive thinking strategies to solve problems involving relatively small whole numbers; Students can work with sharing division, simple proportion, and simple Cartesian product problems earlier than expected; While initial ideas for multiplication and division appear relatively early, students may take many years to develop a flexible capacity for multiplicative thinking.

17. WHAT WE’VE LEARNT: Detailed item analysis suggested additional tasks were needed to tease out the upper end of the LAF (Year 7 Trial, October 2004) Classroom observations suggest that students identified at LAF Levels 1 or 2 may need considerably more support than anticipated, eg, Poly Plug Activity with group of Year 4 (LAF 1) students (Tas) and 0-99 Number Chart Activity with Year 4 (LAF 1/2) students (Vic); and that We need to find ways to engage under- performing, older students.

18. WHAT WE’VE LEARNT: School/Cluster visits and discussions have identified a number of useful ideas and resources which will be developed and shared as appropriate, eg, Easy Quezy, a similar game to Multiplication Toss that uses Cuisennaire Rods to reinforce the countability of the group. 6 fives 4 threes 1 one …

19. ELABORATING THE LAF: The Learning and Assessment Framework for Multiplicative Thinking (Feb 05) was developed on the basis of the detailed item analyses conducted on the May and October 2004 data and relevant research. It attempts to bring together, in a loose hierarchy, all the key ideas, strategies and representations of multiplication and division needed to work flexibly and confidently with whole numbers, fractions, decimals, and per cent across a wide range of contexts.

20. THE LEARNING & ASSESSMENT FRAMEWORK (LAF): See the Draft Learning and Assessment Framework for Multiplicative Thinking (February, 2005) The LAF is organised in terms of 8 Levels from initial explorations with concrete materials through to the confident use of a wide variety of multiplicative structures and symbolic forms. It is linked to the rich assessment tasks used to evaluate multiplicative thinking and contains explicit advice on teaching implications. It also reflects the growth of problem-solving skills and higher-order cognitive thinking.

21. WHAT DOES THIS MEAN FOR ME? For more details, see the Calendar of Events in Project Note 5 (22 October, 2004) On-going professional support (Professional Development) Opportunity to work with colleagues to plan focused learning activities (Learning Plans) Experience in developing and using authentic tasks (Task Development) Experience in using rich assessment tasks (Testing)

22. LEARNING PLANS: Teachers to revise, share and implement Learning Plans with identified students Cluster Leaders to collect and distribute Implementation Reports School grants can be used to support teacher release and/or for the purchase of materials, resources, or additional professional development. Classroom/school visits by members of the research team should be used to support the further development of the Learning Plans For further details see Project Note 5 (Oct 2004)

23. TASK DEVELOPMENT: Each cluster is expected to develop a small number of Authentic Tasks that embody key aspects of the Learning and Assessment Framework Guidelines for the preparation of authentic tasks have been provided and research team members will help facilitate the process The authentic tasks will be used to evaluate the Learning Plans and student progress against the Learning Assessment Framework during 2005. See Authentic Task Guidelines (July 2004) and Project Note 5 (Oct 2004)

24. FINAL TESTING: Research schools will be provided with booklets of rich assessment tasks, scoring rubrics, and instructions in October, 2005 Teachers will be expected to implement the tasks over a period of 2-3 weeks in late October/early November 2005 and assess students’ work using the scoring rubrics provided. Coordinators are expected to collect all data and send it to Jo Virgona as required. Further details later in the year

25. AUTHENTIC TASK EXAMPLE : Title: Not Enough Twine School: Blackman’s Bay PS (Tas) Context/prompt: School litter problem Activity: Lunch-box audit (3 times/week for 3 weeks), data recorded, analysed and communicated Resources: Coloured dot stickers, reference material from the NSW Canteen Association 021