This week's acceptance by the Department for Education of the introduction of four-year maths degree courses by many universities, coming close on the heels of acceptance of four-year physics degrees, is an acknowledgement of the difficulties that academics are up against, and of the overwhelming need for change.
The Government accepted a submission from the Joint Mathematical Council, which represents most university departments in England and Wales. As a result the universities of Manchester and Southampton will offer M Math or M Sci courses from October. Sixteen others intend to follow suit in 1994.
The DFE's approval, despite its stated intention that universities should move towards shorter degree courses, comes after forceful argument from academics, who say they need a greater number of stages to prepare even the brightest students for research.
Many three-year courses will also be substantially reshaped. The plan is for all students to undertake a two- year core course which will provide a thorough training in basic mathematics. Those who pass but then wish to leave for jobs or move on to a different subject, will gain a Dip HE.
Those who need to acquire broad mathematical skills for such jobs as accountancy and retail management, which require analytical, problem- solving skills and a high level of numeracy and conceptual thinking, will continue on the course to a third and final year.
A minority of students - about 25 per cent - aiming for research posts and advanced professional work are expected to go on to take a further two years of specialised studies after the core course. This will take them to a more advanced stage than the current three-year degree course and correspond more closely to European maths degrees.
The London Mathematical Society, a national body for mathematicians, has argued for some time that the maths degree needed to be upgraded to compare with those from Continental Europe.
It also argued that university maths departments needed to take account of changes in secondary education. Some would undoubtedly reply that the schools should take greater account of the standards demanded by the universities, rather than vice versa, but the LMS approves of many of the changes already introduced in secondary schools and welcomes further changes that would encourage more students to choose A-level maths followed by a maths degree.
While the number entering university mathematics courses has remained more or less stable at about 4 per cent of the student body, the number taking the subject at A-level is falling. Universities therefore find themselves admitting students of greatly differing abilities, but who are generally less skilled.
Fred Cornish, mathematics professor at York University, which plans to introduce a four-year maths degree course by 1995, sat on the LMS working party. He says few students now arrived at university with a clear idea of what a mathematical proof was. 'In the past,' he says, 'students used to be much more skilled at calculus. They used to have greater manipulative skills, in dealing with equations, for example.
'There is a lot to be said for not expecting students to learn things for the sake of it, but there are things that need to be known.'
At present there is a gap between GCSE - which is arithmetic based and emphasises problem-solving and practical work - and A-level, which is largely a preparation for university. Teachers, who find themselves having to cover a lot of groundwork to close the gap, believe that an overloaded and difficult mathematics A- level course is putting many students off.
Current changes in A-level maths involve a reduction of the common core, increased use of sophisticated calculators and computers, and reduction of expertise in areas such as algebraic manipulation, proof, calculus and geometry.
New courses such as 16-19 Mathematics, an A-level devised by the Schools Maths Project and administered by the Northern Examination and Assessment Board (NEAB), also include changes in the style of teaching so that students are given the opportunity to apply limited maths skills to practical problem-solving. Equipment is used and pupils perform experiments.
Stan Dolan, project director of 16-19 Mathematics, says the intention is to turn out students who are enthusiastic and confident about the subject. The traditional maths A-level tended to sap the confidence of all but the brightest.
Dr Dolan says: 'With a pass mark of 35 per cent a student could gain a 'C' having answered only half of the paper, so even those who fare reasonably well and go on to study maths in some form at university tend to have negative feelings about their maths abilities.'
Like many other courses being piloted, 16-19 Mathematics aims to give those who work hard, as well as those who possess aptitude, the chance of being successful at A-level.
Chris Belsom, chief maths examiner for the NEAB, has been heavily involved in writing the syllabus for the 16-19 Mathematics course. He believes students need a clearer understanding of a more limited range of topics. An overloaded syllabus, he says, was placing unrealistic demands on many A-level students.
Many schools which had introduced this streamlined A-level syllabus had experienced an increase in the number of students wanting to take maths and a lower drop-out rate. At Ampleforth College, where Mr Belsom is head of maths, he says he had seen an 8 per cent increase in pupils at A-level and none dropping out.
The LMS believes that 16-19 Mathematics and similar A-level courses will lead to an increase in the numbers of students wishing to go on to university to study maths, and that universities should match their teaching styles and adjust course content accordingly.
Chris Robson, professor of pure mathematics at Leeds University, favours changes to A-level mathematics and believes they will lead to greater enthusiasm for the subject at degree level. However, he says that universities are having to be more flexible in response.
He believes that the option of a three- or four-year course, alongside the move towards more modular degrees, will allow institutions to
differentiate between students. He says: 'Many institutions are
introducing more elementary courses. No two students are the same and there has to be more flexibility at the beginning.'
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