A chance to ask real questions;Mathematics;Subject of the week
Statistics sits uneasily within the mathematics curriculum. Under the current regulations it occupies a massive 25 per cent weighting in the secondary mathematics curriculum.
Yet it is not at all clear that we are doing statistics itself any favours. The ability to interpret and present data is a vital skill in our information age, but instead of the subject being a lively applied one it is being strangled in the mathematics classroom.
Mathematics teachers have a preoccupation with the minutiae: how to calculate the angles of the pie chart precisely, how to draw the cumulative frequency curve, what to label the axes etc. The data itself is nearly always made-up data, or data from questions in books: nice, reliable and unambiguous data.
When real data is used it is frequently utterly banal: a survey of favourite pop groups or some such. The view presumably is that education should be nice and relevant rather than nourishing the spirit.
Inasmuch as we have seen the new national curriculum proposals, it does look as if statistics will be taught as a properly applied subject. The emphasis is to be on solving a problem. A question is posed to which an answer is of real interest; data is collected from either primary or secondary sources; the data is analysed and an attempt made to answer the question, or to look for clarification with more investigation.
This is a bold move and very much in the right direction. Statistics comes to life when the question is a real one to which an answer is valued; it may well give rise to data that is problematic due to its quantity or its sheer messiness. But the task now has a meaning beyond a class repetition of the difference between the median and the mode.
Where, however, will these real questions come from? After generations of meaningless exercises, where will interesting problems be found?
I do believe that, as mathematics teachers, we have undervalued the amazing resources to be found in the classroom next door.
Our colleagues in geography, history, personal and social education, science, PE, to name but a few, are constantly dealing with data. When these are too bogged down with national curriculum documents to join us, our colleagues in religious education are often keen to co-operate.
Cross-curricular work is hard to organise. Different subjects operate with different views of the nature of knowledge and very different preconceptions. It is, in my experience however, always worth it and those very differences combine very creatively.
In a joint statistics project it is important that the non-mathematical subject chooses the question to be explored and puts some time into framing it exactly. I once undertook a joint piece of coursework with an RE colleague to answer the question: "Does religious up-bringing affect patterns of giving to charity?" Pupils had first to decide how they were going to sample both aspects of the question, framing questions exploring religious background, and deciding what patterns of charity-giving they were interested in. They had to construct a data base to hold and process the data, and produce their conclusions.
It was a most enriching piece of work, throwing ethical questions into the mathematics classroom and statistical ones into RE. It brought out quite unexpected results and, most importantly, made pupils really think. This was a substantial project, and lasted on and off for about six months. Projects do not have to be anything like as long.
In the current national curriculum review I would hope that we set statistics substantially free of mathematics and recognise it as a vibrant cross-curricular subject in its own right, much as we did with computer studies 15 or so years ago.
Indeed, it would be good to see the two linked up in a key skills module whose assessment would be different to but parallel to GCSE. For it is GCSE, with its obvious but restricting assessment requirements, that has led to the strangulation of statistics much as it has to investigative work in mathematics.
In August 1988 the National Curriculum Mathematics Working Group produced proposals which were not accepted and were in some ways potty, but which are worthy of re-examination. Their recommendation for the application and investigating of mathematics was called "Profile Component 3" and contained, among more conventional strands, the need for pupils to work co-operatively, take initiative and show creativity. GCSE is of necessity based on individual and not group achievements. Could a revamped "key skills" be different?
It was employers who were so keen on this idea of team work. Perhaps a key skills module could be assessed in parallel to GCSE and be named the "employers certificate"? Perhaps the CBI could sponsor it? Could it link with the need to be able to write reports and precis? Could it link with other essential skills such as understanding mortgages and pensions?
This would not only be of great benefit to pupils and to statistics. It would help to save mathematics. for the past 10 years key stage 3 has been a wilderness of low expectation and lack of curriculum clarity. I anticipate that the new curriculum Order will address this, but if statistics could be limited to, say, 10 per cent of maths teaching time, then there is more of a chance that the real nature and power of mathematics will begin to shine through again. That prize alone would make the exercise worthwhile.
Robert Barbour is county mathematics inspector for Worcestershire