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Other departments, whose own teaching often relies on pupils having certain basic mathematical skills, are worried. University mathematics departments, and any other department whose courses have some mathematics content, are complaining of lower standards among each first-year intake.The debate is a complex one. I am certain that those pupils who do not consider themselves to be “mathematicians” – and they are the majority – will be leaving school with a better education.Many heads of mathematics in schools will, like myself, have been used to hearing concerns about maths standards within their own schools similar to those expressed nationally, perhaps over a longer period.The concerns do not just come from within mathematics departments. In particular, we will be introducing an arithmetic course into Form 1, to be done without calculators, with the aim of consolidating basic understanding at that stage.In the rest of the school we will have more frequent revision of basic techniques, again without calculators. We will place more emphasis in our teaching on estimation, and judging the reasonableness of an answer, and we will demand a larger number of repetitions from our pupils by setting a larger number of examples on a particular topic.The modern emphasis of “always provide a context, do a few examples, move on to something new in case they get bored” does not lend itself to the learning of what are fairly mechanical skills – and musicians accept the need to practise scales.In short, we are going to devote a significant amount of time to teaching material that will not be directly examined. What it does show is that pupils in the school now are generally weak at basic arithmetic, when they do not have the use of a calculator. This point is worth stressing: I am quite confident that results would have been much better, had calculators been allowed.

Every pupil would have got at least five of the questions correct.But would that mean that they had a better understanding of arithmetic when they used a calculator? Obviously not, and it is the lack of understanding that is important.The fact that this lack of understanding has not led to poorer external exam results than before says more about the nature of what is being examined, than about pupils’ abilities.The mathematics curriculum has changed significantly in the past 15 years, and pupils are simply not tested on the basic arithmetical skills, which are so important to other subjects as well as to mathematics.As a consequence of the arithmetic test, and subsequent discussion throughout the school, we will be changing our mathematics curriculum next year.We will continue to teach pupils to have a good knowledge of how to use a calculator, but will aim to make them less dependent on it. But they also showed that, in general, averages for a particular set, say set C, decreased as children got older from Forms 1 to 4. It was only in Form 5, where pupils have chosen to take an intensive mathematics course leading to the Scottish Higher examination at the end of the year, that averages went back up to Form 1 levels, which were themselves not that impressive.Clearly, a one-off test such as this cannot compare ability in arithmetic with that of pupils from 15 years ago. This is from a school in which, typically, 99 per cent pass Scottish Certificate of Education standard grade mathematics at age 16, and 80 per cent pass higher grade at 17.The results by individual class showed that our setting structure is good: class averages decreased from set A to set F in each year, with few exceptions. The only questions where more than 50 per cent of the school got the correct answer were the easiest ones of subtraction and long multiplication, and perhaps surprisingly, adding fractions.Fewer than 20 per cent could divide decimals, do inverse proportion, or find the percentage increase. The test had questions on subtraction, long multiplication, long division, addition and multiplication of fractions, division of decimals, inverse proportion, finding a percentage of, and finding the percentage increase.
It thus required a mixture of skills necessary as a foundation for good mathematical understanding, but could also be seen as a test of basic numeracy.The test results were poor In many respects they confirmed worst fears.

Sir Geoffrey would like it to be more like 40 to 50 per cent – and he would like some of them to study in Cornwall.. In February of this year I arranged for around 600 pupils in this school – namely, all those in the Senior School who take mathematics – to sit a 30-minute arithmetic test, without use of a calculator. Sir Geoffrey is pinning his hopes on recent comments made by the council’s chief executive, Professor Brian Fender, that universities should be able to bid for extra students on social, economic and geographical grounds. “They’re clearly beginning to think very seriously about those parts of the country which don’t have a resident core university campus,” Sir Geoffrey says.He is also hoping that the review of higher education by Sir Ron Dearing will help his project along.Sir Geoffrey, a former permanent secretary at the Department for Education and Employment, is a member of the Dearing committee, so he is in a good position to promote his own ideas, one of which is that access to higher education needs to be expanded further.At present around a third of the age-group goes into higher education. The OU is the biggest single provider of higher education in Cornwall and will be given a base on the new campus.But the crucial question is whether the Higher Education Funding Council will cough up recurrent funding of pounds 6m a year to pay for new students.

Potential subjects include business studies, maritime history, heritage, Celtic studies, European languages, information technology, biological and environmental studies and food science.If the approach sounds like the Open University, it is meant to. They will take part-time courses on computer terminals in secondary schools and community centres. The emphasis is on students of all ages being able to study for degrees as well for qualifications that promote their professional development. In other words, schools, colleges and workplaces around the county will hooked up through cyberspace with the core campus Students will study through distance learning. The aim is to have 5,000 students and 300 staff and to emphasise “lifetime learning” rather than simply the education of a group of 18-year-olds. Much needs to be done, however, before it gets off the drawing board.Two weeks ago, officials from the Millennium Commission went to visit the site at Trereife, Penzance, to consider a bid for pounds 22m.

They looked at the impressive estate, the 250-year-old listed house and the view over Mount’s Bay and studied plans drawn up by architects.The steering group hopes that another pounds 22m will come from the EU, and that further sums will come from banks, the National Lottery and the private sector to pay for student residences, business start-up units, a conference centre and arts and sports facilities. It will start small and could eventually expand until it is able to stand on its own feet as the University of Cornwall. The county has one of the highest unemployment rates in Britain. “We believe we have a responsibility to the economy and region of the South-west,” Sir Geoffrey says.The plan is that an pounds 80m Penzance campus should be part of Exeter University, just as Exeter was founded as a college of London University. Mining, fishing and agriculture are declining, and tourism is subject to the cold wind of foreign competition. There are no research establishments to support industry and commerce, and no chance of attracting students into the county.At the same time, Cornwall’s young population is growing as more and more families move to the South-west for the air and scenery Yet its economy is disadvantaged, according to Sir Geoffrey.