Maths 100, run by Cheryl Maiden in Buckinghamshire, is one such scheme. It has been running for three years and now serves 3,000 children. This term it has added new materials catering for A-level and junior-school children.
With low fees, about Pounds 130 per year per family, and a reasonable work commitment - a recommended maximum of three sessions of 30 minutes each per week - Maths 100 runs somewhat like a homework club.
Parents and children first establish in an interview with the organisation how the child and family feel about maths, how keen they are to commit themselves to work, and how extra work will fit in with school work.
"It's not for every child, no question of that," says Ms Maiden. Once they have signed on, the pupils receive weekly assignments from their book with guidance on how to follow the work on an accompanying cassette. A student liaison officer, always a maths undergraduate, visits to sort out any problems and a tutor is available on the phone four nights a week. The tutor will help not only with maths from the course, but also with any school maths problems.
The materials may seem at first sight quite dull, according to their originator. But research has shown that children like and are reassured by "that textbook look". Old-fashioned virtues, like practice, sit comfortably with more modern notions of investigative problems; "a lot of this is about the psychology of the child," according to Cheryl Maiden.
Children are encouraged to progress at a rate they can manage, while their interest is held by diversifying examples in the written materials and on the tapes. New students are always started at a level lower than their current attainments, so that they can build on the skills they feel certain of. "You cannot enjoy maths fully unless you have mastered basic skills," she says.
Customers' interests are stimulated by the thrice-yearly newsletter, which contains curriculum material (answers at the back as "teenagers need fairly prompt gratification") with puzzles, jokes, artwork from students, historical snippets and optical illusion illustrations.
Maths 100 also runs a yearly conference for heads of maths departments, attended this year by 270 delegates and with speakers like David Burghes of the Centre for Mathematics Education at Exeter Uniiversity on whole-class teaching and Guy Claxton, visiting professor at the school of education at Bristol University on the importance of looking at the whole child.
A Maths 100 Odyssey for six to nine-year-olds features a magazine-format publication which links maths with mythology; while workshops can be arranged in individual schools on any subject from maths and music to developing algebraic skills. It's a burgeoning business, spreading largely by word of mouth from satisfied customers and, says Ms Maiden, there is no question but that it can improve grades.
Daniel Soltanifar from Weybridge was "very average" and drowning in the maths class at his independent school. Now the proud possessor of an A grade at GCSE maths, he has also grown, according to his mother, in confidence, self esteem and motivation. Daniel and his parents put much of his success down to learning how to revise, with practice in past papers particularly useful.
Fourteen-year-old Anne Marie Evans from Bolton has found that practice from the Maths 100 kit has had great effect. Her mother adds that her science subjects have benefited from her increasing confidence in maths.
Confidence-building, though important, is not the only benefit. The courses themselves, initially developed by the husband-and-wife team of Pam Buxton, ex-head of a London comprehensive, and Laurie Buxton, former staff inspector for maths at the Inner London Education Authority, are now scanned by a fairly hefty voluntary advisory team of 15 maths authorities, and combine careful and imaginative exposition of concepts with sound and sufficient repetition. Some questions (following Piagetian principles) are useful for tutors monitoring the course because common errors in answering will show up misunderstandings.
Rachel Bently from Leicester - predicted an E along with the rest of her class - had, she said, been finding it "a bit of a struggle". With the "personal touch" of Maths 100, she got a B at GCSE. She is now studying maths A-level at FE college.
Her father puts her success down to the scheme and suggests teachers may not have the patience and understanding that personal tutors can offer. "With Maths 100, if she hadn't got it right, she could just ask and ask again until she did. On your own in the class, it can be more difficult."
* Maths 100. Tel:01491 411686