








THE DECLINE in British people's ability to do simple calculations is a
depressingly rich source of anecdotes. There is the carpet salesman who gave
a price for one metre of carpet but couldn't say how much 10 metres would
cost. And the shop assistant who, when handed two items, refused to sell
them because the battery on her calculator was flat; without it she could
work out neither their combined price nor the correct change. These salespeople
had not learnt basic arithmetical operations thoroughly enough to have the
confidence to apply them.
Now there is evidence that similar problems affect even those who want to
study mathematics at university. A report from three learned societies (see
This Week) reveals that 95 per cent of a group of incoming university students
could not work out the area within a chord of a circle (shown red in diagram).
The failure is interesting because the same group of students were very
successful at solving related problems concerning the areas of triangles
and circles. What they could not do, the report notes, was "draw together
knowledge from different areas and undertake, without instruction, the extra
steps required".
Failings like this come on top of Britain's poor showing in international
comparisons of mathematical skills and a chorus of complaints from university
teachers and employers about the innumeracy of
school leavers. Clearly something is wrong.
The report blames the National Curriculum, which has tried to make children's
lives easy by teaching mathematics in familiar
situations. Questions about fractions, for example, end up being
automatically translated into "problems about dividing pizzas". This leaves
students without the fluency in basic techniques that they will need to advance
to higher mathematicsor, at a lower level, to
have the confidence to add up the cost of a couple of items. As the report
puts it: "Progress in mastering mathematics depends on reducing familiar
laborious processes to automatic mental routines, which no longer require
conscious thought, this then creates mental space to allow the learner to
concentrate on new, unfamiliar ideas."
It is strange that this needs to be spelt out. Every sports teacher knows
that you cannot master tennis, for example, without being able to perform
the individual strokes unconsciously and at speed. And to master them takes
long hours of hard, repetitive training. Of course, the sports teacher can
drive pupils hard because they are hungry for success and the universal acclaim
that brings. Mathematics teachers are not so lucky.
Respect for mathematical skills has also been undermined by the widespread
use of calculators in schools. One of the mathematicians who drafted the
report remembers visiting Japan with the National Curriculum working party
and finding no calculators in schools there. They took this merely as evidence
that Japan was behind the times. But Japanese students are now far ahead
of their British counterparts in mathematical skills. Delaying introducing
calculators and computers until the foundations of mathematics are laid has
paid off.
The use of calculators in schools is soon to be reexamined by the School
Curriculum and Assessment Authority. The many other issues raised by the
reportfrom the devaluation of examination grades to the lack of clear agreement
on which skills are essentialcertainly need urgent attention from the Department
for Education and Employment.
Low marks for 'woolly' maths curriculum
SCHOOLCHILDREN in England and Wales are rapidly sliding to the bottom of
the international class in mathematics, warns a group of university
mathematicians. They blame the woolly wording of the National Curriculum,
which fails to spell out the best ways for teachers to drill their pupils
in the basics of arithmetic, trigonometry, fractions and algebra.
Only when these skills become second nature can pupils reach the level of
mathematical fluency typical of children in other European countries and
Asia, say the London Mathematical Society, the Royal Statistical Society
and the Institute of Mathematics and its Applications in a joint report issued
last week. The report avoids blaming the crisis on teachers, who have borne
the brunt of recent criticism about standards of maths (see This Week, 20
August 1994).
Instead, it points the finger at the National Curriculum. "The advice to
teachers in the National Curriculum is very vague," says Tony Gardner, a
mathematics lecturer at the University of Birmingham, who helped to draft
the report. "It fails to say which methods should be used to teach pupils
the basics," he says.
For example, even after four redrafts, the curriculum still does not insist
that children are taught multiplication tables from 2 times to 12 times.
'As a clear instruction to teachers, that's a very, very simple bottomline
statement, but it's not in the curriculum," says Gardner. Teachers are told
that children should learn the 2, 5 and 10 times tables, but are otherwise
instructed that children "should have opportunities to consolidate number
facts", he says.
The same vagueness plagues basic algebra, trigonometry and fractions. "On
every topic, it says that children should 'experience a range of methods
appropriate to the problem, including trial and improvement'," says Gardner.
"What does that mean?"
He blames the woolly wording on educationalists and bureaucrats who favour
teaching centred on what the child wants to learn, not what a child should
learn. "They don't want thecold, austere precision of mathematics," he says.
"They like things to be woolly, waffly and warm, but that's selfdefeating
in the long run because eventually pupils hit a brick
wall."
Teaching maths is not easy, says Gardner. "But you can't escape
the boredom by dressing problems up with
cartoon characters. Worse still, the jargon can obscure the mathematics."
The societies want a committee of experts to clarify the advice to teachers
in the curriculum. It also calls for the creation of a permanent standing
committee to monitor all maths education.
Andy Coghlan 
Alevel maths will not be easy as
p

EXAM watchdogs denied yesterday denied that changes to
maths Alevels would make the subject easier.
The move to make maths more 'manageable' follows complaints by students two
years ago that the exams were too hard.
Since then, the number taking the subject has fallen by a fifth which, in
turn, has hit universities where a quarter of maths departments face cuts.
From next year, sixthformers will be able to do less pure and more applied
maths, such as statistcs and mechanics.
But that did uot mean the subject was being 'dumbed down', the Qualifications
and Curriculum Authority insisted. Students would still have to cover the
same core content and the
'intellectual rigour' of Alevel
maths was being maintained, chief executive Ken Boston said.
He added: 'We believe that maths is vital to the national interest and it
is worrying that there could soon be a generation of young adults who an
missing out on maths beyond GCSE. 'The high standards that we have always
expected of Alevel students will continue.'
The Mathematical Association and teachers backed the reforms,saying they
were a pragmatic response to the unpopularity of the subject among
sixthformers.










