Investigative work in maths develops pupils’ competence and confidence. You may not have coursework, but you do have plenty of opportunities to improve their understanding, says Paul Metcalf

I may be a lone voice in mourning the passing of maths coursework. But it has done much to support pupils’ performance on the GCSE examination paper making pupils much better at algebraic manipulation and statistical representations, for instance.

Now, after the initial euphoria, teachers need to prepare themselves to achieve the same benefits by other means. After all, 20 per cent of the marks for the written paper will now be given for “using and applying mathematics within the contexts of the questions”, with more open-ended questions.

Teachers can use the time to undertake more investigative and statistical work with pupils. And, now that such work will no longer count towards the assessment, they can treat it as a shared enterprise, rather than worrying whether they might be inadvertently giving their pupils too much help.

Investigative work can develop pupils’ competence, consolidation and enjoyment of maths. Two of my favourites, which produce surprising answers, are: * You are paid 1p on the first day, 2p on the second day, 4p on the third day, 8p on the fourth day. How much will you be paid on the 30th day?* (number and algebra). ** Secondly, imagine a length of string around the equator at ground level. How much extra string would you need to circle it one metre above the ground?** (shape, space and measures).

Useful sites such as the NRICH website, www.nrich. maths.org have many more. Statistical tasks can introduce and develop ideas such as planning, collecting, representing and interpreting data. The Census at School website (www.censusat school.ntu.ac.uk) provides us with real data and some excellent resources, such as the statistics of da Vinci’s Vetruvian Man. For example, the length of the hand is one 10th of the height.

For the future, we should remind ourselves that “using and applying mathematics” is an integral part of the revised national curriculum and assessment objective 1 for GCSE. The new functional maths standards are underpinned by process skills listed under the headings of representing, analysing and interpreting. Now where have I heard all that before*

*more than pound;5m

**about 6.3 metres

Paul Metcalf is an educational consultant in mathematics, principal moderator of an exam board and a council member of The Mathematical Association. The views expressed are his own.