University of York

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Subject Knowledge in Mathematics

Researcher: Maria Goulding

Research questions
Investigating primary teachers’ subject knowledge in a formal way may induce feelings of anxiety which may depress performance and/or reinforce an instrumental view of mathematics. The self audit, specimen answers and commentary, given to students early in their training, were designed to dispel some of these feelings, encourage self assessment and clarify the expectations of the later audit. This element of the research set out

  • to find out what weaknesses and gaps the trainees identified in their subject knowledge through doing the self audit and using the support materials
  • what trainees revealed about their beliefs and feelings about mathematics
  • what strategies the trainees intended to adopt to address weaknesses and gaps before the audit

After completing the self audit, the students rated themselves on a four point scale from ‘my response was completely secure on this item’ to ‘I couldn’t begin this question without help’, and to write general comments about their mathematical subject knowledge. The ratings gave information about the relative difficulty and/or familiarity of the sixteen self assessment items across the sample of about 400 students in the three institutions. The free written comments gave data on levels of confidence, beliefs and feelings about mathematics, and the ways in which students intended to address their weaknesses in preparation for the final audit. The weaknesses identified by the students’ self-assessment were compared with weaknesses and strengths on the later formal audit.

In the self assessment the most commonly identified specific difficulties were in shape and space and graphs and the most commonly identified generic difficulties were with terminology and with explaining their thinking. Most students were confident that they could address these weaknesses in time for the audit although a small number expressed anxiety and panic.
On the audit, reasoning and proof emerged as a common difficulty, and difficulties with space and shape remained whilst problems with graphs were much less common. Some differences may be explained by a change in students’ understanding over the period, by differences in the audit or by differences between perceived and actual difficulties.


  • A better understanding of the needs of students with particular concerns about their subject knowledge, and ways of supporting them on training courses.
  • Knowledge which will enable links between self assessment and actual performance on mathematical items and in practical teaching to be investigated further.

This research was supported by the University of York Department of Educational Studies Research Fund