It's more difficult than 1, 2, 3

On the day the newspapers were telling us we were a country of mathematical duffers, the lower sixth at Redborne Upper School in Ampthill, Bedfordshire, was looking at trigonometry functions and doing computer graphs with them.

Their teacher, Steve Robinson, head of maths at the school, says: "I didn't do that until I was teaching and the syllabus required it."

Reports that standards have fallen so far in maths that students are turning up at university to take a maths degree unaware the subject requires precision seem out of place in this school where nearly two in three get top GCSE maths grades.

But according to a joint report from the London Mathematical Society, the Institute of Mathematics and the Royal Statistical Society, most new maths undergraduates have little notion of what maths is all about.

Trendy teaching methods are diverting attention from fractions, decimals, ratios and algebra, the report says. As a result, students are incapable of solving problems requiring more than one step, and do not understand the meaning of proof.

They obviously never asked students at Redborne what they thought. Robert Berger, 16, a student in one of the middle GCSE maths sets, is having nothing of it. "It seems to be nothing but algebra and proving what you are doing."

At Redborne, more than 60 per cent of the pupils obtain A to C grades at maths GCSE. Last summer, nearly 16 per cent achieved As or starred As in maths, way above the national average and the best maths results in the county. Maths takes 10 per cent of teaching time, less than the county average.

The school is unremarkable. A popular, modern comprehensive serving two small rural towns in an area heavily populated with London commuters, it has nearly 1,000 pupils, 250 in the sixth form, and is well supported by the middle class. Eighty per cent of the sixth form go on to higher education. The school was, however, recently praised by Ofsted for its very strong maths department.

Nigel Croft, the school's headteacher, says: "As far as this school is concerned, we are turning out better and better mathematicians. The results speak for themselves."

Steve Robinson, a maths teacher for 24 years, says: "Standards haven't slipped. But there is a difference. Students now are being taught a much wider range of maths and, for the student, that has to be right.

"We may not go into the same depth always. A- and O-levels were set up for the universities - they used to write them. It is the universities that have not adjusted."

Mr Robinson says that the advent of calculators means school maths students now do less repetitive basic arithmetic and there is less rote practice of algebra because it is not required by the national curriculum.

"Quadratic equations used to be on CSE papers; now we only do them on higher- level GCSE papers. But then some things we do at GCSE or A-level I didn't do until I was at university or until I was teaching.

"Overall, I would say that our top-ability sets are better all-round mathematicians than they used to be."

Pupils arrive at Redborne generally more confident in maths than they would have a generation ago. Students of differing abilities talk of the sheer enjoyment of maths in a way that would have been inconceivable to most of their parents.

They think they work hard, are good at maths and are well taught yet they encounter prejudice from the older generation in the form of granddads or colleagues in their weekend jobs who believe, because they use calculators and computers, they are not up to scratch in maths.

These students, however, think calculators take away the grind and leave time for more exciting maths. Why wash by hand, they seem to be saying, when you can use a washing machine and have time to go out to the pictures?

Few, though, have any direct evidence, to say they are any better or worse prepared in maths than previous generations. Mark Sheehan, 17, who is in the second year of maths, further maths and English A-levels at Redborne, is on his own in thinking the GCSE maths syllabus has contracted.

His evidence comes from his father's GCE mathematics O-level paper, kept for more than 30 years. "Some of things on my dad's paper, like integration and some of the algebra, I'm only doing now," he says.

Claire Sweetman, 17, who is doing maths, psychology and communications studies at A-level, is the only pupil with a student brother doing a maths degree. "He's at Cambridge and he's not having any problems," she says.

As for students abroad who are supposed to be better at maths than British ones, Mellissa Bellerby, 17, who is taking maths, further maths, French and Spanish at A-level, thinks French students of the same age are behind.

"I've just been on an exchange to France and the maths was easier," she says. "I could do it even though I hadn't been to any of the lessons where it had been explained. They are not allowed to use calculators, though," she says.

Alexandra Cadman, 16, who got a starred A in GCSE maths, is taking maths, economics, English and biology at A-level. None the less, she thinks her mum is probably better at mental arithmetic than she is. "I can work things out in my head rather than using a calculator, but not as efficiently. I couldn't walk round Tesco like she does working out what the percentage savings on things are as quickly as she can.

"But I wouldn't enjoy maths if we had to do loads of arithmetic. I'd just lose interest."

James Dean, 16, is taking maths, further maths, physics and chemistry at A-level. He got a starred A at GCSE. He thinks older people look down on his generation for using calculators. "I think we could do all those complicated computations if we had to but we tend not to because there are alternatives to doing it."

Louise Wilson, 15, is taking 11 GCSEs next year. She is not in the top maths set but hopes to get a B. "I've enjoyed maths more since I came to Redborne because I'm beginning to understand it. Because I didn't understand it before, I didn't like it. It's more interesting now. I can relate it to situations. The statistics have come in very handy in geography and I'm using it in other subjects, too.

"Some of my relations who've seen my maths work books say how much more organised it all is now, how you have to put down all these explanations of what you've done. My mum says it's much harder than when she did O- level."