Introduction

This paper presents findings on a study into the factors that influence student primary teachers to improve their mathematics subject knowledge.  The complex relationship between cognition and affect within mathematics is explored with a view to finding out how to encourage developing professionals within initial teacher education to take responsibility for their own subject knowledge.

Policy Context
The European Commission key competences for lifelong learning include Mathematical Competence and Learning to Learn (European Commission, 2007).  The former promotes the ability to develop mathematical thinking and the latter the ability to pursue and persist in learning.  In Scotland the new national curriculum (Scottish Executive, 2004) recognises the importance of both abilities in learners yet interestingly in the documentation no reference is made to the importance of the teacher’s development of these, either through their own subject knowledge or how this can be developed throughout their teaching careers.  This aspect is now being addressed (HMIE, 2010; Donaldson, 2010).  The latter, a major review on teacher education, noted that issues with teachers’ understanding of basic mathematics need to be addressed at entry to and during initial teacher education by means of an online assessment.  Such a tool has been used extensively with student primary teachers at the University of Dundee and is central to this study. 

Theoretical Context
This paper draws on evidence from literature about the importance of mathematics knowledge for teaching.  It would seem obvious to state that in order to be able to teach a subject effectively knowledge of the content to be taught, or subject matter knowledge (SMK), as it was famously dubbed by Shulman (1987), is essential.  He also identified pedagogical content knowledge (PCK) as being of special interest.  It takes the content knowledge that a teacher possesses and combines it with professional understanding of how children learn; it is a blending of subject knowledge and pedagogy which transforms topics from mere content to a form that appeals to the different abilities and interests of learners.  Hill et al. (2008) broke PCK down further into Knowledge of Content and Students (KCS) and Knowledge of Content and Teaching (KCT).  The main consideration in these models, however, is content knowledge.  Effective teachers of mathematics must be able to move back and forth between the mathematics and the pedagogy (Steele, 2005), drawing on both to meet the needs of the learner.  If subject knowledge is deficient, however, this can have serious implications for the learners’ understanding.  Yet often student teachers are in a state of unconscious incompetence (Luft and Ingham, 1955 cited in Perkin, 1999) about their own subject knowledge.  In order to address deficiencies and move them to a state of conscious incompetence and hence conscious competence an Online Maths Assessment (OMA) and questionnaire were created and used to answer the following research questions:

1.      Why do some students stop at a tutor-determined, pre-set threshold and others improve on it?

2.      What factors appear to be associated with differences in how students engage with the OMA?

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