Self-deluded or what?
The first point to make about research on adult numeracy is that there is too little of it. Whether trying to find out which mathematical skills adults want or need or how to teach them, the British researcher is working in relatively untouched terrain.
"Adult numeracy isI under-researched, under-theorised and underdeveloped," is the conclusion of a review by Diana Coben of the University of Nottingham, published last autumn.
Dr Coben should know. She heads the numeracy programme at the National Research and Development Centre for adult literacy and numeracy (known by the mercifully short abbreviation of the NRDC), established by the Government to underpin its Skills for Life strategy. The centre, led from the London Institute of Education, is overseeing a busy research programme to fill some of the gaps.
Recent national and international surveys show that action is needed. They suggest that most English adults have low levels of numeracy and that this has harmful effects on their family and working lives, on the economy and on society.
But the evidence raises many questions. Have these surveys been measuring the right things? Do adults just need better basic skills, as set out in the adult numeracy core curriculum, to cope with their everyday lives? Or should the Government be aiming higher, to help them solve problems rather than just master skills?
Two studies to be published this summer will discuss how to relate the numeracy in adults' lives to that taught in the classroom and how to teach measurement to adults.
A central finding emerging from both contradicts what might be expected.
Learners do not, on the whole, consider their numeracy studies as having a practical application to either their home or their working lives. Indeed, they feel they are coping quite well, thank you very much.
"Some do come to class and say, "I really need help to check my change," says Dr Coben. "But it's not very common."
Most are motivated by a desire to succeed in a subject that has previously defeated them and which they recognise as essential for many types of further study and training. With few exceptions, they want to understand the mathematical system: its principles and underlying relationships.
Parents also want to be able to help their children with homework.
This echoes the findings of the Government's Skills for Life survey last year. That found that most 16 to 65-year-olds scored poorly on numeracy tests - only one in four reached a level equal to top-grade GCSE - and nearly half were operating at or below the level of the average 11-year-old.
Yet it also found very few - even among the least able - who regarded their maths skills as below average and only a tiny fraction felt their weak skills had hindered their job prospects or led to mistakes at work.
Were these adults just blind to the truth? (International comparisons of teenagers' performance in maths do suggest the British tend to overestimate their skills.) Or had the tests, perhaps, not picked up the skills they had?
Alison Tomlin of King's College, London, certainly thinks such surveys tend to underestimate what most adults can actually do. "We buy mortgages, we sort out family budgets," she points out, "which 11-year-olds don't."
Dr Tomlin has been conducting the NRDC study on teaching and learning measurement in basic numeracy courses. Three teacher-researchers, working in FE colleges and a prison in Greater London, are producing teaching materials on the topic. Learning to measure is a major element of the adult numeracy core curriculum. All project participants agree that measurement is essential for success in exams and for helping their children with homework. But only a few consider measurement skills vital for everyday life - to ensure they are properly informed or to avoid being cheated - and most think they already have the skills needed outside the classroom anyway.
The researchers sympathise with "Bob", one of the participants in the study, who says: "The work on measurement seems quite separate from the rest of the numeracy course. You get bits and pieces which aren't connected to each other."
They feel measurement should be incorporated into a richer, problem-solving approach, where students can work out their own methods (for instance, by pacing out a room) rather than be taught as a discrete skill with the use of rulers and work-sheets.
"If we offer a more demanding approach - perhaps involving algebra - it becomes more interesting to the students and they can feel their brains working," says Dr Tomlin. Yet the adult numeracy core curriculum does not include algebra.
Another call for the Government to be more ambitious about adult numeracy tuition comes from Alison Wolf, also of King's College, London, who conducted a survey published 18 months ago that examined the maths required by people in a range of mid-level jobs. Professor Wolf found that new technology had actually increased rather than reduced the need for maths skills. Employees increasingly need broader problem-solving skills, inter-relating IT with mathematics, she discovered, to work out, for instance, at what price to offer an unbooked block of hotel rooms.
"What do people need to work in a functioning business?" she asks. "They need a great deal more than to add and subtract - they can do that. Adults feel what they really need is GCSE. And they're quite right."
A third study for the NRDC over the next two years will cover effective teaching and learning styles. It is likely to recommend only general approaches, not a detailed blueprint. No single technique could suit tutors in so many diverse situations: from special needs to English as a second language, parents to prisoners, low-achieving 16 to 19-year-olds to 25-year-olds aiming at banking.