Scaffolding Numeracy in the Middle Years: Project Outcomes

To what extent can we accurately identify key points in the development of multiplicative thinking and rational number beyond the early years?

Key points were identified.

1. Points were described and elaborated in the Learning and Assessment Framework (LAF)

To what extent can authentic assessment tasks be developed and used to assess student performance against the framework?

Relevant assessment tasks were developed with associated scoring rubrics.

The relative positions of key points fitted a Rasch item response model.

Thresholds of components of tasks were consistent with postulated levels of thinking in most cases.

All but a small number of tasks proved to be reliable indicators of a student performance in relation to the LAF.

Rich assessment tasks provided evidence of increasing sophistication of student learning.

2. Teachers were able to use the scoring rubrics consistently with most tasks

3. Tasks that could not be used in a valid way were rejected

4. Item difficulty within and between tasks was generally consistent with the levels of thinking

5. The LAF was validated by administering relevant rich assessment tasks

6. Rasch Item Response Modelling showed that the postulated continuum for multiplicative thinking and rational number was able to be modelled

7. A Raw Score Translator enabled teachers to interpret test scores in terms of the levels achieved

To what extent can we gather evidence about each student’s achievements with respect to these key points to inform the development of a coherent learning and assessment framework?

Valid and consistent information was obtained about each student’s status on the LAF with respect to the continuum

For students in the Research Schools changes in status over a two-year period were identified

8. Achievement levels on the continuum could be used to generate targeted teaching responses

9. Development of an alternate test with its own Raw Score Translator made it possible to interpret changes in achievement (learning)

To what extent does working with the tasks and the knowledge they provide about student understanding assist teachers to improve student numeracy performance at this level?

Learning by students in Research Schools was demonstrated. On average:

• changes from Year 4 to Year 5 were large
• changes from Year 5 to Year 6 were large or medium
• changes from Year 6 to Year 7 ranged from large to small changes
• changes from Year 7 to Year 8 ranged from medium to large.

For Reference Schools, assuming no changes within classes, on average:

• differences between Year 4 and Year 5 ranged from small to large
• differences between Year 5 and Year 6 were medium
• differences between Year 6 and Year 7 ranged from very small to medium
• changes from Year 7 to Year 8 ranged from small to medium.

10. Some teaching at some levels in Research Schools is more effective than in other Research Schools

11. Some teaching at some levels in Reference Schools appears to be more effective than in other Reference Schools

12. Final Research School Data supports the efficacy of the assessment-guided approach (assuming Reference Schools were comparable)

What strategies and/or teaching approaches are effective in scaffolding multiplicative thinking and rational number understanding in the middle years?

Targeted teaching activities that revisit core concepts and strategies explicitly, assist the scaffolding of new learning, and provide opportunities for meaningful practice.

13. Advice provided in Learning and Assessment Framework (LAF) Learning Plans to support each level of the LAF

14. Support Materials (games, activities, handouts provided to Research School Teachers)

15. Intervention Program developed by APAI to support identified group of ‘at risk’ learners

What are the key features of classroom culture and discourse needed to scaffold students’ numeracy-related learning at this level?

Teacher knowledge

Teacher flexibility

16. Case Study Reports

17. APAI Thesis

18. Authentic Tasks advice