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Durham University

School of Education

Staff Profile

Publication details for Dr David Bolden

Barmby, P., Bolden, D., Raine, S. & Thompson, L. (2013). Developing the use of diagrammatic representations in primary mathematics through professional development. Educational Research 55(3): 263-290.

Author(s) from Durham


Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking.

Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in primary classrooms, through introducing primary teachers to the research literature in this area, and researching the subsequent impact on children and teachers. A professional development programme was designed, involving three one-day training sessions for mathematics co-ordinators. They were asked to implement the ideas from the training back in their schools.

Sample: Mathematics co-ordinators from eight primary schools attended the professional development programme. The study focussed on Year 3 pupils (aged seven–eight) and Year 5 pupils (aged nine–10).

Design and methods: In this paper, we report the qualitative findings from the larger project looking at the overall impact of the professional development programme. The paper focuses on semi-structured interviews carried out with the mathematics co-ordinators attending the professional development sessions, and the Year 3 and Year 5 class teachers who subsequently worked with the co-ordinators on their use of diagrammatic representations in their teaching of mathematics. Lesson observations involving the class teachers were also carried out in order to explore further the possible impact of the project on classroom practice.

Results: The qualitative results identified the impact of the project on mathematics co-ordinators and class teachers’ knowledge and practice. However, the nature of this impact was complex, with a variety of facilitating and hindering factors identified for the transfer of the professional development ideas on the use of diagrammatic representations. In addition, different levels of sophistication of class teachers’ use of diagrammatic representations were identified.

Conclusions: Implications for the development of professional development programmes to facilitate the transfer of research into practice were identified. Recommendations for the use of diagrammatic representations are also put forward.