Adult learners are a diverse bunch. In the numeracy classroom - whatever form that takes - they bring a wide range of half-remembered, half-understood computational methods from different eras of mathematics teaching and from different cultures. The situation may be further complicated where learners who are parents are trying to reconcile their own previous learning with the way they see their children being taught at school. In this respect, adult learners present a more complex challenge for the tutor than a group of primary school children who are making their first foray into mathematics.
Much mathematical thinking - whether this is to do with calculating change in a shop or working out how to adjust a knitting pattern - involves envisaging things in the mind's eye. Given the history and diversity of adult learners, it is absolutely crucial that we find out what they are seeing on this mental screen. Yet, we seem to spend relatively little time doing this. Today's emphasis on diagnosis focuses on where the learner's logic breaks down, rather than on how it breaks down; where the transition between devising a mathematical intention and implementing it becomes fuzzy. But if someone has reached adulthood and is still struggling numerically, this may be exactly where the problem lies. And for those learners, or tutors, who are dyspraxic or dyslexic, the issue may be particularly acute. The point is: how can you help learners adjust the aerial if you don't know what's on the screen?
What's more, adults have evolved a wide range of problem-solving strategies that we need to recognise. There's nothing wrong with being different if what you do works. When tutors undertook an exercise to find out how many times people in a group would have to shake hands for everybody to meet, some actually shook hands, others devised tallies and others drew diagrams to arrive at the solution.
Yet, in this society, mathematics is a field where a rigid orthodoxy prevails. People - and this includes many tutors - perceive that mathematics is a discipline about universal truths, but that you can only have access to them if you employ the authorised strategems. On this basis, all aspire, but few attain.
It takes an awful lot of practical illustration and even more reassurance to convince tutors that there may be more than one way to skin a cat. If this is how they feel, how much more challenging to persuade learners that they have something valuable to offer? Once the realisation dawns, it can be destabilising: a field that five minutes ago was full of certitudes is now an expanse of shifting sand. Being confident enough to work with the plurality of adult learners' approaches, being able to ask the open-ended question rather than the closed one, is crucial. Forcing learners down tramlines not of their own making is going to be a painful experience which may bring few long-term gains.
Becoming numerate is about developing a good feel for numbers, understanding how they behave - and why - and being able to discern how to use them to assess situations and make decisions about them. Many of us cling to operational rituals we acquired years ago. We may not fully comprehend them, but we feel we would be mathematically adrift without them. The temptation is to drill learners in the rituals we have memorised ourselves. A more confident approach would aim to move learners from the superficial and operational to the understood, experienced and owned.
Another challenge is to flesh out the core curriculum with appropriate content: decisions about health, education, employment; decisions with ethical, environmental and social implications. These are part of everyday life for adults. Problem-solving cannot wait until they've graduated numerically: it's part of their here and now. Yet little attention has been given to numeracy as an aspect of active citizenship.
"In the early 1980s," one newspaper reported recently, "wave power was going to be the bright new future for energy, but in a government evaluation of how much the electricity would cost to produce, someone moved a decimal point - and made it ten times more expensive." Thus, the development of energy from renewable sources was halted while investment in the nuclear industry soared. Whether or not this was a genuine mistake, is debatable. What's more worrying, perhaps, is that no one spotted it. So much for the numerate active citizen, then.
All the issues highlighted here require a significant investment of tutor time and energy. Yet many tutors work in situations where it is unrealistic to expect this of them. Many fell into work as numeracy tutors by chance.
"I went to bed a literacy tutor and woke up a numeracy one," is not an unusual scenario.
Staff working with particularly challenging groups, such as disaffected young men, are set the impossible task of getting them through national tests after 20 hours' tuition, often on appallingly low rates of pay. Many tutors seldom meet anyone else who teaches numeracy. All this has to change if we are to make any significant ground. And, hopefully, it will!
Janet Swinney is a freelance writer and educational consultant, specialising in adult and community education. Many of the insights expressed here arise from workshops for adult numeracy tutors which she co-ordinated recently for Niace. She acknowledges the valuable contributions made by her co-facilitators.