Mathematics subject knowledge is a source of concern to primary teacher trainers and trainees alike. The requirement for newly qualified primary teachers to have an adequate level of mathematical expertise is undeniably sound. Identifying the appropriate level of knowledge, and ensuring the trainees are both competent and confident, is proving more problematic. Mike Askew and his colleagues at King's College, London, expressed the dilemma at the end of their influential research into effective teachers of numeracy: "Government policy appears to be aiming for a cohort of teachers who partially understand a lot of hard maths, whereas this research has shown that what we really need is teachers who really understand a lot of easy maths."
GCSE grade C pass in maths is a minimum entry requirement for teacher training. Even with this, trainees are often insecure in their understanding and very few have the mental ability they need.
Trainees' mental ability can be developed in the same way as mental maths skills are developed in primary schools, through regular practice and sharing of calculation strategies. It is more challenging to bridge the gap between that "partial understanding of hard maths" and the maths of the primary programmes of study.
The Secondary Maths Handbook: Laying the Foundations for Good Mathematics by Lesley Medcalf (The Maths Press pound;14.90. Available from QEDMultimedia, Pentagon Place, 195 Berkhampstead Road, Chesham HP5 3AP. Tel: 01494 772973. All ages from primary to A-level and adults) seems to do this very well. Stages of reasoning and calculation are shown in great detail. Each new topic begins with examples that will be familiar to teachers of the upper primary years, before moving on to a level very close to that required in the initial teacher training national curriculum for maths. his progression is particularly well demonstrated in the section on growing patterns - an introduction to straight line graphs that links primary and secondary algebra seamlessly.
Many of our trainees at Wolverhampton University who were insecure about their subject knowledge found The Secondary Maths Handbook particularly helpful. The cover notes say the book is designed for independent use by pupils at home. Our students found it to be sufficiently clear and self-explanatory for this to be a valid claim. One commented: "I worked through nearly all the examples even though they were done for you. I could check my work with the book. It made me feel I was on the right lines."
For students in initial teacher training who are fairly confident of their maths, the Letts self-assessment guide Mathematics for Primary Teachers: An Audit and Self-Study Guide (Letts pound;9.99) gives helpful advice on what they need to know and why. Trainees who are less secure could turn to standard secondary texts. The pick of these is Oxford Mathematics: Intermediate GCSE (OUP pound;12.50), which is packed with well-organised information and many questions for self-testing.
Bob Davies is senior lecturer, primary maths teaching, at Wolverhampton UniversityA summary of the King's College team's research 'Effective Teachers of Numeracy' can be found at: www.teach-tta.gov.uk
A brief note on the Teacher Training Agency numeracy skills tests - a different requirement altogether. Numeracy skills tests are being introduced this year for all trainee teachers, primary and secondary, whatever their subject. They involve the use of everyday maths, including percentages, decimals and many forms of data. The TTA has circulated to all initial teacher training institutions copies of some very well prepared numeracy support materials, also available on the TTA website at www.teach-tta.gov.uk