In-Service Training
Some teachers may not feel confident about their ability to teach mathematics at levels beyond that generally expected of their classes. As a result, they may feel diffident about providing appropriate support for gifted pupils in mathematics.
Schools report a need to enable mathematics teachers working at all key stages to develop both their mathematical skills and their teaching styles and approaches. A major and continuing focus for the National Numeracy Strategy is the provision of ‘5-day courses’ to support schools in addressing this. The Key Stage 3 Strategy provides similar training. Team teaching, with teachers sharing expertise and learning, can help. For example, a specialist mathematics teacher could work with teachers in different classes, disseminating subject knowledge and good practice in the teaching of able pupils by taking lessons with the class teacher or working with particular groups of pupils.
In order to devise a suitable programme for gifted pupils, teachers need a clear sense of:
which content in school mathematics is most important in the long term for developing a firm foundation in mathematical concepts and the ways in which these concepts are used in a wide range of applications — for example fluency with arithmetic, fractions, standard measures (especially compound measures and problems involving different measures with ratio and proportion), algebra, word problems, the geometry of triangles, functions, and the links between algebra and geometry. It is this content that deserves to be given priority when devising an extension programme for gifted mathematicians;
- which non-content aspects of school mathematics embody and develop important mathematical ways of thinking and reasoning — for example, letter sums, cryptic crossnumbers and logic puzzles have little value in their own right, but provide a simple, appealing and highly satisfying vehicle for conveying the idea that mathematics is about deduction rather than guesswork;
- the difference between routine, step-by-step instruction, with its associated one-step routine exercises, and the more serious challenge of real mathematics (embodied in an appropriate form), with its multi-step problems;
- what actually appeals to able young mathematicians and which non-curricular topics provide the richest sources of suitable material.
The points above are rarely covered in pre-service training; nor are they automatically absorbed as part of the day-to-day experience of teaching. Therefore it is important that headteachers and heads of department recognise that teachers who are expected to implement an enrichment and extension programme are likely to need extra support.
Opportunities may arise through LEA organised in-service days, or through local branches of the two national mathematics teachers associations, the Mathematical Association (MA) and the Association of Teachers of Mathematics (ATM).