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.
2. My current projects:
a. 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).
b. I’m running training courses in prisons to support prisoners to act as Maths
Mentors to other prisoners whose skills are around Entry Level.
c. I’m supporting vocational (Construction and the Built Environment) teachers
in FE to run action-research projects to improve their teaching of
mathematics.
d. My most recent “classroom” teaching included Entry level work with exprisoners and GCSE level work with Access students.
3. I want to make three related points.
a. 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)
b. We should offer adults opportunities to learn to use general mathematical
thinking and questioning skills, not just number-crunching (or even “problemsolving”) skills. We should not stop teaching “number-crunching” or “problemsolving” but we should also offer adults the chance to become critical
mathematical readers, interpreters and interrogators of the world. (Para 5
below)
c. 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)
4. 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.
5. 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 complex situations 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?”
6. 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-making
offers 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, and can 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.