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
(mastering measuring feet in the 'shoe shop')
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 wrote this blog in 2018 after digging out Richard Winter’s article 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, as much as how mathematics is taught, how it is perpetuated culturally as a seat of mystery, power and (yes, still - it happened to me last week on Twitter) intimidation; as well as how much space we provide for learners to think and make sense of what is offered. To roller-skate. This 'making sense' space is critical in all settings and classrooms. And it is rapidly being filled with (relentless) 'direct teaching', even in early years settings.
(If.. white = 1, what faces can yon make worth 100 with Cuisenaire?)
Winter tells of observing his daughter engaged in philosophical and metaphorical conundrums from infancy. One story is at 10.5 months where she enjoys deliberately ‘mis-taking’ a plastic cone for a feeding bottle. I remember a similar experience with my 19-month-old relishing the use of a diving flipper for “A bag! A bag!”
Reflecting on some eleven-year-olds quoted in an APU document on mathematical development, who became confused, when faced with contradictory data, often clinging to what they believed must be the mathematically correct answer, despite contrary results, 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.”
My own school experience was of the room-tidying sort. What changed for me was becoming 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. We roller-skated together:
How many of those do you think you can hold in your hand? What about both hands? What will you try now? 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 to as well as listening for.
At the ATM mathematics conferences I attended https://www.atm.org.uk/Association-of-Teachers-of-Mathematics I was able to choose what I took part in, to try some mathematics out in a safe and non-judgemental space, to work with others, to think alone. Are we willing to provide a similar space for our children?
Good early years practice, in particular, does allow the space and freedom for young children to explore their's and others’ ideas, to predict, to reason, to explain, to wonder. But often these opportunities are missed in mathematics, where there is a tendency to overcorrect, to steer children closely through a series of small, pre-determined steps, to carefully avoid the making of mistakes, the challenging, the pure, wild enjoyment. In fact, to apply what we know is critical in other curriculum areas to mathematics. To roller-skate.
Winter argues for a reversal of the following common teaching sequence which he sees as 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 solve problems; in short, to think mathematically. It is experience that they lack. Problems are very powerful ways into learning some mathematics: "Can we share these gold coins equally between these 3 pirates"? "Is that paper sheet large enough to cover this box?" "How many of these will that bag hold compared to this one?"
We can make mathematics more difficult by undermining children's natural perceptions, by treating their thought processes as inferior; and by whilst starting with games and play, for example, quickly turning these experiences into those that resemble tidying your room.
(Collecting natural items to make patterns)
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 numerical and spatial relationships,
· 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, pattern, 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 tools 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’.
- enjoy many mathematical picture books.
and in the main - be playful.
(Measuring how much water we can move from one place to another)
Enjoyment, excitement and motivation are not dirty words.
Neither is play: “Play - where a grasp of the basic situation is the beginning of creative 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
Lerman (eds.) The Social Context of Mathematics Education: Theory and practice. London: Southbank Press
Winter, R., (1992) ‘ ‘Mathophobia’, Pythagoras and roller-skating’ in N. Nickson and S.