Roller-skating or tidying? Which is mathematics to be?

Roller-skating or tidying? Which is mathematics to be?

Helen J Williams 

“Mathematics could be like roller-skating, but usually it’s like being told to stop roller-skating and come in and tidy your room.”

Richard Winter, 1992

This has long been one of my favourite quotations in relation to learning mathematics. Winter follows on by saying:

“This is not a superficial matter.”

I dug out Richard Winter’s article this week and was reminded that it has a lot to say about play, work, young children’s strengths as well as cultural domination; which he accuses mathematicians of being complacent about.

What is it about maths that makes many of us feel inadequate and quick to admit we could never “do it”?

The difficulty isn’t something within the mathematics itself, it is in how mathematics is taught, how it is perpetuated culturally as a seat of mystery, power and (yes, still) intimidation; and, critically in classrooms, how much space we provide for learners to think and make sense of what is offered. 

I know this is true. I was maths-phobic at secondary school, it took me two attempts to achieve my GCE (remember them?) and yet I have enjoyed teaching mathematics for (well) over 30 years, I have attended maths conferences for 30 years and now love the puzzles and problems that are posed. 

Winter tells of observing his daughter engaged in philosophical and metaphorical conundrums from infancy. One wonderful story is at 10.5 months where she enjoys ‘mis-taking’ a feeding bottle for a plastic cone. I have a similar experience of my 11-month-old relishing the use of a diving flipper for a “Bag! Bag!” Referring to some eleven-year-olds quoted in an APU document on mathematical development, who abandon their theories in the face of contradictory data, Winter poses the question:

“If infants can take their pleasure in such philosophical ways, one wonders indeed what can have happened to (these) eleven-year-olds.”

What changed for me mathematically was that I became interested in the sense my Reception learners were making of what I was offering them mathematically. I started asking questions “I wonder what they would do with this”, and observing more closely, sharing what I was noticing with colleagues (those who would listen!). I started to try things out that were more in-tune with them as individuals:

How many of those do you think you can hold in your hand? What about both hands? Why do you think that? How far will all those stretch, do you think? Why? What if we tried that game with a different dice? How shall we record that? What do you think?

And I tried hard to be more silent. I started to listen toas well as listening for. 

At the ATM mathematics conferences I attendedhttps://www.atm.org.uk/Association-of-Teachers-of-MathematicsI was able to choose what I took part in, to try things out in a safe and non-judgemental space, to work with others, to think alone.

Early years in particular allows the space and freedom for young children to explore theirs and others’ ideas, to predict, to reason, to explain, to wonder. But often these opportunities are missed where there is a tendency to overcorrect, to steer children closely through a series of small, pre-determined (by whom?) steps, to carefully avoid the making of mistakes, the challenging, the pure, wild enjoyment. In fact to apply what we know works in other curriculum areas to mathematics. Winter argues for a reversal of the following common teaching sequence (largely unquestioned since the Cockcroft Report of 1985): 

Teacher exposition, Discussion, Practical work, Routine practice, Problem solving, Investigation. He argues, and I would agree with him, that children arrive at school very able to apply knowledge to solve problems; in short, to do mathematics; and we often as teachers make mathematics difficult for children by over-complicating what we ask them to do, by undermining their natural perceptions (by treating their thought processes as inferior), and by whilst startingwith games and play, for example, quickly turning these experiences into those that resemble tidying your room.

My ‘to do’ list for early years mathematics begins:

·     go outdoors, to run, do big and noisy, build, climb, collect, 

·     do lots of Cuisenaire play; there really is nothing else like it for exploring relationships between numbers,

·     play with dice; many different types to invent games, 

·     provide lots of different collections, all of large amounts, of both natural and manufactured items to endlessly count, sort out, line up, use for making mini-collections, 

·     collect purses, wallets and small containers to fill, shake, empty, count in and out of, compare,

·     provide paper of all sizes and shapes, tape and scissors to cut, fold, unfold and re-shape,

·     collect large (and tiny) containers and bags to fill and lift, with sand, water, stones, beads…

·     make some balances, including huge outdoor ones,

·     find a great variety of measuring items to use, discuss and compare,

·     collect blocks, boxes and beautiful geometric shape collections to create patterns, constructions, cityscapes and enclosures,

·     put out the calculators and large sheets of paper and pens for ‘free writing and drawing’. 

Enjoyment excitement and motivation are not dirty words. 

Neither is play (“Play - where a grasp of the basic situation is the beginning ofcreative individual improvisation” Winter, 1992)

As Winter says:

“All successful education, I would argue, aspires to the conditions of play.”

References

Cockcroft W.H., (1982) Mathematics Counts: Report of the committee of inquiry into the teaching of mathematics in schools (The Cockcroft Report). London: HMSO

Winter, R., (1992) ‘ ‘Mathophobia’, Pythagoras and roller-skating’ in N. Nickson and S. Lerman (eds.) The Social Context of Mathematics Education: Theory and practice. London: Southbank Pres