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Learning about number is central to the development of numeracy and underpins later success in mathematics. A central aim of this evaluation was to determine the impact of the CMIT pilot project on the achievement of the students, as measured by their progress on the five aspects of number in the SENA interview. As explained in chapter three, the use of reference data enabled clarification that the improvement in the students' understanding was due to the impact of the project rather than to gains expected with normal growth. There was clear and positive growth in all aspects of number understanding irrespective of students' age and ethnicity and school region and decile and this growth exceeded that of the reference data. Although similar gains were made by all the students, there are marked differences between the subgroups, when their number profiles, expressed as stages on the Learning Framework for Number, are compared. The decile of the school and the ethnicity of the student are strongly related to the number profiles, with the latter being higher if the students are of European or Asian descent or if the students attend a higher decile school. 

A key focus of the project was the improvement of teachers' pedagogical content knowledge and increased teaching quality and confidence. It was evident from case-study data, and corroborated by findings from the questionnaires, that the teachers generally benefited professionally and personally from their involvement in CMIT. The teachers increased their knowledge and understanding of number strategies, of number knowledge, and of how students learn number. This increase in knowledge was linked to statements about increased confidence and enthusiasm for teaching mathematics. Many of the teachers commented on the usefulness of a framework which clearly sets out the progressions in a student's understanding of number. The teachers changed their mathematics programmes to include a greater focus on number and, in particular, the number strategies that students use to solve addition and subtraction problems. Many of the teachers had higher expectations of students, felt more able to identify learning needs, and grouped their classes more effectively. The teachers indicated that their programmes were now more active, with a greater emphasis on encouraging students to share their thinking, and with a reduction in the time spent on worksheets. 

Central to the success of the project was the adopted model of school-based and classroom-based professional development. The teachers met regularly with each other and the facilitator to share experiences and insights and to discuss appropriate learning activities for the students. The teachers also valued highly the opportunity to observe their students while the facilitator modelled group and whole-class teaching activities. 

Although there were a number of minor modifications suggested, the one that stands out was a strong recommendation for centralised production and distribution of teaching resources related to the project. In particular, the teachers and facilitators identified a lack of teaching and learning activities to support the development of number strategies. 

References 

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Appendices A to I 

Appendix A: The Learning Framework for Number (PDF, 24K)

Appendix B: Schedule for Early Number Assessment (SENA) (PDF, 36K) 

Appendix C: Summary of Questionnaires (PDF, 21K)

Appendix D: Concept Mapping (PDF, 18K) 

Appendix E: Detailed SEAL Results (PDF, 23K) 

Appendix F: Detailed Base Ten Results (PDF, 10K) 

Appendix G: Detailed Forward Number Word Sequence Results (PDF, 20K) 

Appendix H: Detailed Backward Number Word Sequence Results (PDF, 20K) 

Appendix I: Detailed Numeral Identification Results (PDF, 13K)