Skills we can count on
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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 mathematics-or, 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 re-examined by the School
Curriculum and Assessment Authority. The many other issues raised by the
report-from the devaluation of examination grades to the lack of clear agreement
on which skills are essential-certainly 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 bottom-line 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 self-defeating 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 |
A-level maths will not be easy as p |
| EXAM watchdogs denied yesterday denied that changes to
maths A-levels 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, sixth-formers 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 A-level 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 A-level students will continue.' The Mathematical Association and teachers backed the reforms,saying they were a pragmatic response to the unpopularity of the subject among sixth-formers. |