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.