GROWING enthusiasm in the United States for a return to a more traditional education in schools and colleges has taken university mathematics by storm.
Reforms in the teaching of calculus to make it more user-friendly have borne the brunt of attacks via email, the American Mathematical Society newsletter, and in departments themselves.
"Reform calculus", as it is known, was developed with the blessing of government agencies, in response to figures showing that 40 per cent of undergraduates were failing introductory calculus.
Relying on research about how mathematics is actually learnt, reform calculus encourages professors to talk about concepts with their students to engage their interest and stresses calculus's role in the real world. Students learn the basics with pencil and paper, but use computers and calculators to solve more complex problems.
Critics claim the changes have been forced on mathematics professors in part by politically correct activists and administrators concerned only with getting undergraduates a passing grade.
With its heavy reliance on technology, reform calculus teaches students to plug equations into computers and skirt the thinking process, they claim. Richard Askey, a mathematician at the University of Wisconsin, said the reformers were "a bunch of romantics who felt students were having too much trouble with calculus and we could let technology do the work.
"We do that and the students don't learn anything. They keep talking about making mathematics more accessible to women and minorities, and they want to do that by cutting down on the technical skills."
There are about ten textbooks in reform calculus available and about a third of all students are using them. Typically they feature questions applying calculus to everyday subjects, like cooking or the weather. Some top-ranking institutions, like the University of Michigan, have embraced change. Others, like the University of California at Berkeley, have stuck to traditional approaches.
But it is at colleges, where admissions standards are lower, that reform calculus has been embraced with enthusiasm.
Reformers claim grades have improved. Detractors cite anecdotal evidence of widespread complaints by scholars in other disciplines, from economics to chemistry, that students now come to them with gaping holes in their knowledge.
Berkeley mathematics professor Hung Hsi-Wu said the controversy has its roots in the huge expansion of calculus requirements in other fields, from molecular biology to computer science. "Mathematics in the old days was done without real regard for popularity.
"Those who fell by the wayside, what of it. Unfortunately now, in the high-tech world, something like calculus becomes a meal ticket."
Calculus reformers were trying to reach these new students, he said, but made the mistake of applying their theories across the board, to groups like future engineers and mathematicians. Berkeley is now considering the use of its first reform textbook for these "soft track" students, but not for regular students, he said.