Business, Innovation and Skills' Inquiry on ADULT LITERACY AND NUMERACY.

Written evidence submitted by Joan O’Hagan (personal submission).

  1. I am a self-employed adult numeracy / mathematics professional with roughly 35 years experience in the adult sector. I teach maths to adults and run projects to support the professional development of adult maths teachers throughout England. I have worked on local, regional and national projects for the National Centre for Excellence in Teaching Mathematics and the National Institute of Adult Continuing Education. I have a degree in Physics, an M.Ed (Adult and Continuing Education), a Certificate in On-Line Education, and a Level 5 Diploma in Adult Numeracy.
  1. My current projects:
  2. I’m leading, with two NCETM colleagues, the Further Education Professional Development Leads Support Programme (training 60 people who will in turn train 2000 teachers to deliver GCSE maths courses to 16-19 year olds).
  3. I’m running training courses in prisons to support prisoners to act as Maths Mentors to other prisoners whose skills are around Entry Level.
  4. I’m supporting vocational (Construction and the Built Environment) teachers in FE to run action-research projects to improve their teaching of mathematics.
  5. My most recent “classroom” teaching included Entry level work with ex-prisoners and GCSE level work with Access students.
  1. I want to make three related points.
  2. Our offer to adults should relate directly to what they perceive as their needs (personal, social, economic); we should then negotiate honestly with prospective learners so that we respond in ways which will benefit society as a whole. At the moment we pre-empt this negotiation and make only brief curtseys to their “needs”. (Para 4 below)
  3. We should offer adults opportunities to learn to use general mathematical thinking and questioning skills, not just number-crunching (or even “problem-solving”) skills. We should not stop teaching “number-crunching” or “problem-solving” but we should also offer adults the chance to become critical mathematical readers, interpreters and interrogators of the world. (Para 5 below)
  4. When I say “adults” I’m not just thinking about adults whose skills are measurably weak by our current standards. Most of us probably underestimate how much better and happier our society would be if we were more mathematically active. (Para 6 below)
  1. Curtseying to adults’ needs.

A key underpinning idea, starting with the Skills for Life Initiative, is that “the learner brings the context that will be the ultimate “proving ground” for their improved skills” (DfES, 2001, p. 8). But we act (via the Skills for Life, Key Skills, Functional Skills, and GCSE for all initiatives) as though we – the professionals – know in advance what mathematical ideas and skills adults need. And in fact our specifications are really just slightly modified versions of the school curriculum. We second-guess what adults are interested in and might need, we select (with a sigh of relief) bits from the curriculum, and we offer the learners exercises which purport to help them solve real life problems but all too often only serve as vehicles for the skills we have already decided they need. For example, we often offer them inauthentic exercises on how to calculate the area of carpet needed for a room, ignoring the way most adults negotiate a price for the job with a carpet retailer; our real aim is to “teach them area and perimeter”, and the carpet “context” is a fairly empty curtsey to their real lives. Or we teach them about probability by asking them to toss coins or spin dice, when perhaps the adult we are working with is grappling with decisions about the (probabilistic) risks associated with medical procedures or lifestyle choices.We can’t go on pretending to listen whilst shuffling our curriculum cards so that regardless of what they say, they still “cover the curriculum” sooner or later, en route to a pre-determined qualification. Adult learners see beyond our curtseys - they know that we’re not really negotiating the curriculum with them - and they can see us shuffling the curriculum cards. If there is good-will, they trust that teachers, curriculum developers and qualification-creators are acting with their interests in mind, (Oughton, 2009); but ceding this power to the professionals is surely ultimately infantilising for everybody involved. We urgently need more research about how mathematical thinking might support better decision-making by adults, e.g.(O'Hagan, 2012). In the meantime, if our initial offer to adults were to listen to what real life issues they are currently dealing / grappling / struggling with, and our next step was to help them analyse how mathematical thinking might help address those issues, we might get more people approaching us (via health literacy or financial literacy projects), and we might get more engagement, more learning. Probably fewer traditional maths qualifications, but better skills, better decisions, better health and economic outcomes.

  1. Reading, interpreting and interrogating mathematical text.

In our anxiety to make sure that adults can crunch numbers efficiently and can “solve problems” using mathematical thinking, we risk ignoring the fact that in many of the complexsituations we face in life, we can’t realistically expect to find or process all the available information.(G Gigerenzer, Todd, & Research Group, 1999) Instead we often have to settle for intelligent interrogation of some of that information, and of the credibility of the information-holders. For example, when doctors tell us about our test results, we might find it more useful to be able to discuss statistically intelligent questions like “What’s the false positive rate?” “Given my positive test result, what are the chances that I really do have the disease I’ve been tested for?” than to attempt an ab-initio number-crunching analysis of the data. We might find it vital to engage intelligently in discussions about what is meant by “more than usual deaths” in our local hospital. Or it might be useful for us to have mathematically-informed discussions with IAG or Citizens’ Advice workers about questions like “If I pass this exam, what are the likely economic returns to my learning?”or “Within bike-riding distance, where are the skills shortages and the growth opportunities, what are my chances of competing successfully, and how much better off will my family be?”

  1. Them and Us.

For mathematically literate discussions to happen, it’s not only the potential “learner” – the person whose measured skills are at Entry level - who needs to change. Many doctors struggle to understand test results(G. Gigerenzer & Muir Gray, 2011), and many IAG and Citizens’ Advice workers would struggle to discuss “returns to learning” in mathematically meaningful ways. Many, perhaps most, adult numeracy / mathematics teachers would also struggle to make much headway with these issues using the skill and knowledge set implied by our pre-specified curriculum. But all is not lost. Research about decision-making, and about the role of analytical / mathematical and intuitive or heuristical thinking in decision-makingoffers us some possibilities(G. Gigerenzer, 2003, 2008; G Gigerenzer et al., 1999; Kahneman, 2011; Kahneman & Tversky, 1974). Humans can decide when and whether to use mathematical thinking, andcan learn to use mathematical thinking intelligently to make better decisions, even in situations where we’re not able to do the number-crunching. But, although these ideas and skills are certainly accessible to adults operating “at Entry level”, they are not (yet) being offered to them (us).

DfES. (2001). Adult Numeracy Core Curriculum. London: Department for Education and Skills.

Gigerenzer, G. (2003). Reckoning With Risk - learning to live with uncertainty. London: Penguin.

Gigerenzer, G. (2008). Rationality for Mortals - how people cope with uncertainty. Oxford: Oxford University Press.

Gigerenzer, G., & Muir Gray, J. A. (Eds.). (2011). Better Doctors, Better Patients, Better Decisions - Envisioning Health Care 2020. Cambridge, Massachusetts

London, England: The MIT Press.

Gigerenzer, G., Todd, P., & Research Group, A. (1999). Simple Heuristics That Make us Smart. Oxford: Oxford University Press.

Kahneman, D. (2011). Thinking, fast and slow. London: Penguin Books Ltd.

Kahneman, D., & Tversky, A. (1974). Judgment under Uncertainty. Science, New Series, Volume 185(No 4157), 1124-1131.

O'Hagan, J. (2012). (When) can we trust ourselves to think straight? – and (when) does it really matter? ALM18 Proceedings.

Oughton, H. (2009). A willing suspension of disbelief? ‘Contexts’ and recontextualisation in adult numeracy classrooms. Adults Learning Mathematics - An International Journal, 4(1), 16 - 32.