SCAFFOLDING NUMERACY IN THE MIDDLE YEARS A Linkage Research Project

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 Final Teachers Day April/May, 2006 Project Overview Enhancing Multiplicative Thinking

RESEARCH TEAM: Professor Dianne Siemon, Project Director, RMIT University Jo Virgona, Senior Project Officer; RMIT University Margarita Breed, Ph.D student, RMIT University; Professor Peter Sullivan (Latrobe University), Dr Shelley Dole (University of QLD), and Adjunct Professors John Izard and Max Stephens (RMIT University) – Consultants Denise Neil (Tas DoE), Meg Parker, Ruth Crilly, Maurie Sheehan, Cheryl McCashney & Nadia Walker (DE&T) – Industry Partner Representatives; Marcus Bucher, Nadia Cavallin and Marilyn chambers – Cluster Coordinators and over 50 teachers.

PROJECT AIM: The project was designed to investigate the efficacy of a new assessment- guided approach to improving student numeracy outcomes in Years 4 to 8. In particular, it was aimed at identifying and refining a Learning & Assessment Framework for multiplicative thinking using rich assessment tasks.

RATIONALE: Why rich tasks? Why the middle years/Years 4 to 8? Why multiplicative thinking? Why an assessment-guided approach? What is a Learning Assessment Framework?

APPROACH: 18 month action research study involving three research school clusters: 1 in Tasmania, 2 in Victoria, and a matching set of reference schools; Draft Learning Assessment Framework for Multiplicative Thinking (LAF) derived from the research literature and used to inform task design; Rich tasks and scoring rubrics used to evaluate multiplicative thinking in Years 4 to 8 in March 2004 and November 2005;

APPROACH (cont.): Initial data collected from over 3400 students, LAF revised and elaborated; Over 55 teachers involved in developing, trialling, and refining Learning Plans for a particular level of the LAF; Research schools asked to devise and trial at least one authentic task to evaluate aspects of the LAF; Work in schools supported by visits from research team members and cluster meetings.

WHAT WE’VE ACHIEVED: An evidence-based Learning Assessment Framework for Multiplicative Thinking that can be used to inform teaching; A set of valid and reliable tasks that can be used with confidence to assess multiplicative thinking across Year levels; 8 Learning Plans per cluster, one for each level of the framework; and A number of authentic tasks.

WHAT WE’VE LEARNT: Adjusted Mean Scores 2(L+5) Adjusted Means by Year Level and Gender Research Schools 2005

WHAT WE’VE LEARNT: Adjusted Mean Scores 2(L+5) Adjusted Means by Year Level and Gender Reference Schools 2005

WHAT WE’VE LEARNT: There remains little or no evidence of gender differences 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 irrespective of intervention – however, intervention had little/no impact on the ‘levelling off’ phenomenon in Years 7 and 8 Targeted intervention makes a difference - considered overall, research school students demonstrated more learning in relation to multiplicative thinking than their reference school peers

WHAT WE’VE LEARNT: In terms of the Learning and Assessment Framework for Multiplicative Thinking (LAF), the average level of achievement for research school students ranged from Level 3 of the Framework in Year 4 to Level 6 in Year 8, that is, For reference school students, the average level of achievement remained the same as it did in 2004, that is, from Level 2 of the Framework in Year 4 to Level 5 in Year 8, that is, Range of LAF Levels for Research School Students in November 2005 Range of LAF Levels for Reference School Students in November 2005

WHAT WE’VE LEARNT: Proportion of Students at each Level of the LAF by Year Level Research Schools 2005

WHAT WE’VE LEARNT: Proportion of Students at each Level of the LAF by Year Level Reference Schools 2005

WHAT WE’VE LEARNT: The enormous range of achievement within each Year level remains, although the relative proportion of students at each level of the Learning and Assessment Framework for Multiplicative Thinking (LAF) appears to have shifted more for research schools than for reference schools, even though reference school students started from a lower base. This is evident in the following graph which compares whole cohort data for 2004 and 2005

WHAT WE’VE LEARNT: Research Schools by LAF Level Reference Schools by LAF Level

WHAT WE’VE LEARNT: Targeted intervention works, students in an identified sub-sample of ‘at-risk’ students demonstrated major shifts in achievement as a result of an 18 week teaching program involving 3 sessions per week* * The Intervention Teaching Program for At Risk Students is included in the SNMY CD-ROM: Project findings, Materials and Resources, October 2006 Participants: 9 Year 6 students identified at Level 1 of the LAF in May 2004 Results:All 9 students achieved at Level 4 or 5 in November 2005

WHAT WE’VE LEARNT: Many students continue to rely on additive thinking strategies to solve multiplication problems involving relatively small whole numbers, although this is less evident among research school students than it was; Evidence that students can work with sharing division, simple proportion, and simple Cartesian product problems earlier than expected suggests that these areas may be worthy of greater consideration in curriculum planning; While targeted intervention works, there is no easy route to developing a flexible capacity for multiplicative thinking – it takes time and deliberate, planned effort.

WHAT WE’VE LEARNT: Time is a major issue in schools - competing demands limit the extent to which teachers can participate in/contribute to what is often seen as ‘additional work’; Working in teams to develop targeted interventions is much more difficult than anticipated – we are not quite sure why; Some structure is better than none - the value of hindsight!

ENHANCING MUTLIPLICATIVE THINKING: Professional sharing – learning from others and reflecting on experience Understanding what the data tells us; Intervention strategies – What worked, what didn’t and why?; A review of key ideas; and a Presentation on current system initiatives – Where to from here?.