University of Cambridge, Faculty of Education

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Subject Knowledge in Mathematics

Researchers: Anne Thwaites, Peter Huckstep and Tim Rowland (left to right below)


Research Officers: Fay Turner and Jane Webster

Research question
In what ways is primary trainees’ teaching of mathematics (planning, reflection and classroom interaction) informed by their subject knowledge during the final school-based placement?


Earlier in their PGCE course, all trainees completed a written audit of their mathematics subject knowledge. The scores from this audit were used to divide the trainees into three groups, reflecting strong, adequate and weak levels of subject knowledge (as assessed by the audit). Within these three groups, two ‘lower primary’ (broadly, Key Stage 1) and two ‘upper primary’ trainees were selected as a sample for observation. Video recordings were made of two whole lessons given by these 12 trainees during the 8-week placement – once during week 4 or 5 and again during week 7 or 8. In addition the whole cohort was graded on two aspects of their teaching – preactive and interactive – towards the end of the placement.


Using grounded methodology, the videotaped lessons were scritinised to identify moments and episodes when a trainee’s subject knowledge, or lack of it, was evident in their teaching of mathematics. Critical incidents in these lessons were isolated to illustrate different aspects of the knowledge and understanding of subject matter that enable effective teaching.

The grades for teaching will be analysed in relation to the audit data and a number of other variables (such as chosen age phase) for the trainees.


The main finding from the video study has been the identification of four broad categories of ways in which trainees’ knowledge of subject matter and mathematics-specific pedagogy comes into play in their teaching. We have named these categories:

· Foundation
· Transformation
· Connection
· Contingency


  • further knowledge of the role of subject knowledge in effective mathematics teaching
  • identification of ways in which this subject knowledge is manifested in trainees’ teaching
  • examples which may be helpful to school and HEI staff to help to focus on aspects of subject knowledge in initial teacher education.
This research was supported by the University of Cambridge Faculty of Education Research and Development Fund