GCSE Mathematics: the 'new' curriculum

I have been trying and failing to get The Guardian interested in issues around mathematics. Following Jennie Golding's wonderful presentation at the IMA Festival of Mathematics in Manchester last month the plight of teachers and pupils seemed worth highlighting. Given that I have failed to attract national interest, let me at least post my first draft here.

 

GCSE Mathematics Exam Madness

The last overhaul of the school mathematics curriculum had a catastrophic effect: the number of students taking A level maths plummeted by 20% and it took ten years to bring the numbers back to historic levels. A subject that had always been seen as ‘hard’ was up-graded to ‘well-nigh impossible’ in the eyes of pupils. Given the centrality of mathematics to a wide range of disciplines and careers, the long-term effects of Curriculum 2000s introduction have yet to be understood.

Teachers returning to schools in England this September will be teaching the ‘new’ GCSE curriculum for the first time. This is designed to provide pupils with a deeper understanding of material and to enhance the UKs standing in international education league tables. These are laudable aims, but the experience of Curriculum 2000 shows that great care needs to be taken in a subject where answers require precision, and where even small changes in the difficulty of examination questions can lead to large differences in performance.  There is very little evidence that such care is being taken.

Last week Ofqual, the examiners’ watchdog, indicated that that there are likely to be significant and unexpected changes in this years’ GCSE results, and that grade boundaries might have to be lowered. This should be yet another warning to those introducing the new curriculum which will be examined for the first time in 2017. This year’s GCSE examinations were made ‘tougher’ on the orders of then Education secretary Michael Gove. But the warnings emanating from Ofqual suggest that toughening has had unpredictable effects and may yet lead to paradoxical outcomes.  For example, if, as Ofqual seems to be suggesting, grade boundaries have to be adjusted, candidates will do as well as previous years by showing less understanding of the material (because they are not being given the opportunity to show what they know, but rather what they do not know). In these circumstances, it is not at all clear what, if anything, will have been achieved by ‘toughening’ up.

The new GCSE curriculum presents schools with even greater challenges. Not only are teachers expected to provide pupils with a deeper understanding, but they are to do this based on a syllabus with 30% more material in it. It is important to recognise that the deeper level will be new to many of the teachers as well. They will require training so that they have the knowledge and confidence to deliver the lessons effectively.

Independent schools, with their greater resources, will be more able to negotiate these challenges than state schools, and this will exacerbate the inequalities in the education system. A recent report from the Sutton Trust shows that the proportion of state school educated students going to the country’s top universities is already falling. Therefore the pool of people from which we draw our best mathematicians and scientists is shrinking. Changes which have not been properly though through risk making things even worse. Indeed, one of the criticisms of the Tomlinson Report of the roll-out of Curriculum 2000 was that there had been insufficient work on the effect of the proposals.

In June, Liz Truss, then Education Minister, announced the creation of 32 Maths Hubs nationally to act as ‘centres of excellence’. This seems a woefully inadequate response. How will 32 hubs cover the country as a whole? How will other schools interact with these hubs? How and to whom will they be accountable?

The experience of Curriculum 2000, which was designed to broaden the mathematical experience of pupils and also modularised the examination system, suggests we need to be careful when we tamper with the mathematics curriculum – and perhaps other curricula as well. Even during periods of stability there can be variations of 10 marks (out of 75) in some grade boundaries of A level mathematics papers, so the system is very sensitive. There is still time to act, but it is running out, and my fear is that the consequences of getting the new GCSE curriculum wrong will be a massive fall in the level of mathematical skills for most pupils. This is, of course, the opposite of what the new curriculum was designed to achieve, but it will also have potentially severe consequences far beyond secondary education.

This is because mathematics matters, not just in our schools and universities but across our economy. Last year a report from Deloittes on the economic impact of mathematics estimates that mathematics research is responsible for some 16% of the country’s economy; thus anything that reduces our capacity to produce good mathematicians risks seriously damaging our economy.

At a less advanced but no less important level, people in a range of industries need to be able to use mathematics accurately and with confidence. Nurses need to calculate drug dosages, tellers count change, bank employees and their customers need to understand the effect of changes to the interest rate, and we all need to be able to complete our tax returns. The analysis of risk in making life choices – what foods to eat or avoid, which surgical procedures to consent to – involves understanding basic probability, and much of the information we are given is statistical.

Nearly all technological innovations -- GPS, mobile phones, medical scans, financial markets, computer programmes -- have mathematics at their heart. Whilst the user does not need to know the mathematics in detail, it is hard to appreciate this increasingly digital world without a basic sense of mathematics and what it can do. This extra level of appreciation and understanding will be lost if pupils have a bad experience of mathematics. Fewer pupils will go on to do more mathematics with resulting skills shortages – not least in the teaching of mathematics.

And from a purely intellectual point of view, mathematical ideas can be beautiful, and that beauty should be available to everyone.

So mathematics does matter. It matters for the individual in terms of earnings, confidence of being in the world and intellectual stimulation. It matters for our country in that we need a workforce able to do crucial jobs with confidence. And it is crucial for an economy which is increasingly dependent on the innovations that mathematics supports.

Pre-16 education is the beginning of a process which produces the next generation of mathematicians at all levels. My plea to the new Secretary of State is to fix the obvious problems (educationalists have been pointing them out for months) so that it will not also be the end.    

Paul Glendinning

Paul Glendinning is Professor of Applied Mathematics at the University of Manchester and Vice-President of the Institute for Mathematics and Its Applications. The opinions expressed in this article are his own.

Dave Broomhead

Since Dave died last week a poem I read a while ago but had not then connected with Dave keeps going around my head. Dave inhabits both the magician (able to do spectacular deeds but aware of the limitations of what he can do) and the student (able to ask the simple but searing question). It is by Miroslav Holub, translated by George Theiner.

                    Zito the magician

To amuse His Royal Majesty he will change water into wine.
Frogs into footmen. Beetles into bailiffs. And make a Minister
out of a rat. He bows, and daisies grow from his finger-tips.
And a talking bird sits on his shoulder.

There.

Think up something else, demands His Royal Majesty.
Think up a black star. So he thinks up a black star.
Think up dry water. So he thinks up dry water.
Think up a river bound with straw-bands. So he does.

There.

Then along comes a student and asks: Think up sine alpha
greater than one.

And Zito grows pale and sad: Terribly sorry. Sine is
between plus one and minus one. Nothing you can do about that.
And he leaves the great royal empire, quietly weaves his way
through the throng of courtiers, to his home
                                                                         in a nutshell.


Of course, Dave would have smiled and talked of an imaginary alpha.

And now I think of Dave having retired into his nutshell.

Goodbye Dave.