A head for numbers;Primary;Reviews;Mathematics;Books
Ask 20 teachers to add 16 and 17 in their heads and then get them to tell you how they did the calculation. Unless you've tried this exercise before, you're likely to be surprised by the range of different strategies that are employed.
The national numeracy strategy places a timely emphasis on the development of pupils' mental calculating skills and reinforces the idea that pupils should have a range of flexible methods at their disposal. It recognises that these depend on, and grow from, a familiarity and confidence with numbers and our number systems.
Many commercial primary maths schemes have paid scant regard to the building of mental models or a repertoire of mental strategies. Heinemann has launched this comprehensive range of resources to address these needs and suggests they are used for regular short sessions with other materials. This approach fits with the guidance for the daily maths lesson from September 1999.
The Teaching Mental Maths Strategies books provide three types of activities: those which attempt to generate new approaches to particular types of calculation, those which practise using strategies in various situations and linking units "looking back and looking forward". The introduction reminds teachers of the value of pupils discussing their methods with each other and with the class.
However, rather than helping teachers draw out, celebrate and build on pupils' own ideas they sometimes encourage teachers to impose predetermined strategies - those identified in the particular unit. Similarly, the instructions ask the teacher to represent pupils' ideas on the board. In my experience, it is far more revealing and powerful to get children to explain and record their own approaches for the class. None the less, these books will prove useful to teachers prepared to use them judiciously.
Similarly, the Mental Arithmetic audio tapes provide useful practice in working under time pressures and preparing for the national tests. Many will find the standards challenging - reflecting the demands of the new framework. Each tape offers 10 tests and is accompanied by transcripts of the questions, answers and record sheets.
The Mental Maths Practice books are, to my mind, the least useful elements. They contain pages of short exercises of mixed, closed questions. They do not exploit or explore the range of strategies pupils might use, and the range of topics in each exercise makes them difficult to use in a diagnostic manner. On the positive side, there is some gradation of difficulty and each page has a more open-ended question to absorb those who finish ahead of their classmates. But I suspect most schools already have many similar sets of revision and practice exercises.
Linton Waters is mathematics adviser for Shropshire