The three phases
The methodology involved three overlapping phases.
Phase 1 identified a broad hypothetical learning trajectory (Simon, 1995) which formed the basis of a Draft Learning and Assessment Framework for Multiplicative Thinking (LAF).
Phase 2 involved the design, trial and subsequent use of a range of rich assessment tasks developed to evaluate various aspects of multiplicative thinking. The tasks, and their associated scoring rubrics, were variously used at the beginning and end of the project to inform the development of the LAF using Rasch modelling and other forms of analysis.
Phase 3 involved research school teachers and members of the research team in an eighteen month action research study that progressively explored a range of targeted teaching interventions (Learning Plans) aimed at scaffolding student learning in terms of the LAF.
School clusters
The study was conducted in six school clusters, 4 in Victoria (2 metropolitan and 2 regional) and 2 in Tasmania (both metropolitan). Each school cluster involved a secondary school and at least three primary schools.
Just over 1500 Year 4 to 8 students and their teachers from the three research clusters were involved in Phases 2 and 3 of the project. A similar group of Year 4 to 8 students from the three reference clusters was involved in Phase 2 only. In all, 40 schools were involved in the SNMY Project.
Teacher involvement
During the course of each phase, research team members met with project teachers to facilitate the implementation of the project, provide professional development, and support the development of learning plans and school-based authentic tasks.
For example, a detailed description of the project was prepared and distributed at the Cluster Leaders Meetings in December 2003 and February 2004 (see the Initial Cluster Leaders Meetings documents in the Resource Library).
This was supported by a PowerPoint presentation to research school teachers in February/March 2004, an abridged version of which was presented to reference school teachers in April/May 2004 (see the SNMY Research and Reference Cluster Meetings documents in the Resource Library).
To support the use of the Draft Learning and Assessment Framework, a summary of the key ideas and strategies that underpin multiplicative thinking was made available to research school teachers in March 2004 (see the SNMY Key Ideas and Strategies Mar 04 document in the resource library).
More information
Please visit the resource library for a more detailed description of the development and use of the assessment tasks, the use of Rasch modelling to evaluate both the tasks and to map student learning over time, and a summary of project findings.
In particular, the Research Approach and Rationale document describes how the methodology was developed to address research questions relating to:
- accurately identification of key points in the development of multiplicative thinking and rational number beyond the early years
- gathering evidence about each student’s achievements
- development of authentic (rich) assessment tasks
- assessing student performance against the framework
- assistance for teachers to improve student numeracy performance
- effective strategies and/or teaching approaches
- development of the instruments
- rationale for the analyses
- evaluation of student progress.