Cosine of the times

June 1, 2007

Today's students need to be made to feel confident in using mathematics and making sense of it in the context of their subject, says Claire Morris

Aquick web search revealed that courses in ecology, marketing and primary education at three different universities all require study of mathematics, statistics or both. This is no surprise. Every September, students who thought they had said goodbye to maths for ever arrive at university only to discover that there is a substantial numerate content in their chosen course, even if it is disguised as "research methods" or "data analysis".

Many are dismayed at having to re-engage with mathematics; they lack confidence and have labelled themselves "bad at maths". Even those with decent GCSE grades often say things such as: "I don't know how I got a B - I never understood what I was doing."

In examining the reasons for this, the first priority is to increase students' confidence in their mathematical skills. One way to achieve this is by encouraging students to reflect on how their understanding of mathematical concepts has developed; the Open University's Open Mathematics course does this successfully by building into the process reflective questions as well as computational ones. Many students dislike this because it cuts across their ideas of what maths questions should involve, but by the end nearly all acknowledge that it has been helpful.

Another confidence booster is to put structure on to the bits of half-remembered maths that float about in students' minds - things such as "change side, change sign" and "two minuses make a plus" learnt as instrumental rules, but the rationale for which has never been understood.

Demystifying these rules helps make students realise that they know more than they thought they did.

Academics need to be more adventurous in constructing curricula. It is better to cover a smaller number of topics in a way that ensures proper student understanding than to gallop through a wide range of material that is not fully grasped. Some topics seem to appear in syllabuses simply because they always have done; sometimes because of the curious requirements of professional bodies. For example, much print, and student angst, is expended on making histograms with unequal classes despite the superiority of the boxplot over the histogram for many practical purposes.

And then there is relevance to consider: mathematical ideas must be related to students' subject interest to make their importance clear. This should not be merely a cosmetic exercise:if you are teaching a class of nurses, you need to know what nurses use mathematics for. This provides a chance to establish a relationship of equality with learners: "You explain the nursing context to me, and I'll explain the required maths to you." The Higher Education Academy's Maths, Stats and OR (operational research) Network is active here. One thorny aspect of the "relevance" debate concerns who should be teaching maths and stats to non-specialists.

Recently, much "service" teaching by professional mathematicians and statisticians has been replaced by the integration of the mathematical material into subject teaching by subject specialists. Students carry out, say, a psychology experiment, then learn about the statistical methods for analysing the results from their psychology lecturer. It is not possible to do justice here to the pros and cons of each approach, although as a professional statistician I am clear where I stand in the debate.

And what about the responsibilities of employers, who are quick to complain about a perceived decline in standards of numeracy? In August 2006, the Confederation of British Industry claimed that "16 per cent (of employers) had concerns about graduates' numeracy skills". But it is not easy to pin down what exactly employers want. The CBI's press release cited "simple mental arithmetic without a calculator, the ability to interpret data, competence in percentages and calculating proportions", but this does not exactly define a coherent university-level curriculum. If the CBI wished to do something constructive on this front and not just carp, it could do worse than to produce some decent case studies illustrating why these skills are needed.

The UK has a poor showing in international league tables of numeracy skills. We reportedly languish mid-table along with the US, New Zealand and Italy, while being consistently defeated by India, China and South Korea.

Critics say that the better performing countries have "traditional" approaches to teaching, involving learning of "times tables", lots of mental arithmetic and so on. They do well in tests; ergo we should be returning to the use of such approaches.

But the true picture is much more complex. It is obvious that those who are highly placed in league tables are good at what is being tested. If the tests examine skills in mental arithmetic, algebraic manipulation and so on, students who have been taught in a system that emphasises those skills will do well. But my experience is that although it is true that students from East and South Asian countries are very capable at carrying out calculations, they are less well prepared to deal with questions such as:

"What does the average you have calculated imply about the data?" or "Do the solutions you have obtained provide realistic answers to the business problem we started with?" And encouragingly, it seems that the UK performs better at tests examining the use of mathematics to solve everyday problems rather than at those examining abstract competences, according to a recent survey by the Organisation for Economic Co-operation and Development.

This brings me to my final point: what is required by many students is best described not as numeracy, with its connotations of mathematical competence, but rather what I call "dataracy" - the ability to look at numerical information intelligently and to link the numbers to the practical situation to which they relate. Developing this skill is more challenging than teaching students to plug numbers into the formula for computing a standard deviation and it is a heck of a lot more useful. So let's get rid of numeracy - too often interpreted by students as "remedial maths" - and start teaching our students to be "data literate" instead.

Claire Morris is dean of quality and standards development at Gloucestershire University, and author of Essential Maths (Palgrave Macmillan).

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