Peter Reynolds played quite a rôle in my career. He invited me to join the Mathematical Association’s Diploma Board, he gave me my first speaking engagement outside my own county, and he was the first to suggest I might have something to offer schools in general rather than just my own. One day a letter arrived: “Dear Alan – have you ever thought of becoming an advisory teacher? I think you’d be excellent in that rôle. Come along for interview ….”
(I turned up, clutching my hand-written letter – and found seven others all with their individual letters! So in fact I never got to work in Peter’s team, but it was this experience that started me thinking and a couple of years later I did make the AT step in my own authority.)
Peter never sought a high profile, but he contributed enormously to mathematical education. Much of his work was done for the Mathematical Association ( http://www.m-a.org.uk ); he was the first editor of Mathematics In School, and the Diploma Board was a leading influence in the development of maths teachers. He also served on the Cockcroft committee which resulted in the hugely influential report “Mathematics Counts”.
I suspect that his image was responsible for much of Peter’s effectiveness. He was always well turned-out, and quietly well-spoken. He looked in fact like the typical grammar school teacher of my own schooldays, and was comfortable with officials and committee members. They looked at Peter and saw someone they could work with and who wouldn’t rock the boat. What they didn’t realise until it was too late is just how deceptive that image was.
Peter was in fact a deeply subversive individual and it was his influence that saw Suffolk as a hot-bed of curriculum development in mathematics. He assembled a team (sadly not including myself) of iconoclasts. Not all of them shared his impeccable dress sense, but they were all committed to innovation, most particularly in the contribution the electronic calculator could play in the development of children’s understanding on numbers. Peter’s team played a large part in Hilary Shuard’s pioneering CAN Project that we in nearby Hertfordshire followed with interest.
Peter was another who died much too early, in 2000 aged 68. Not long before, we’d worked together again on an MA group, and on the last occasion we found we were both planning to look in at Mole Jazz. Mole Jazz was at Kings Cross and even in that somewhat dilapidated area was a bit of an eyesore. I bet not one of those committee members who imagined Peter was one of themselves had ever heard of it.
Hilary Shuard was a giant of mathematical education. To generations of teachers “Williams and Shuard” was mandatory reading, she was a member of the committee that created the Cockcroft Report of 1982 and an important part of the working group that created the National Curriculum in 1989 – as an obituary said “Indeed, it would be unthinkable to have had a national committee concerned with mathematics education on which she did not sit.”
I’d never claim to have known Hilary well, but we served together on a number of working groups and we did meet on dozens of occasions. I was proud to claim after one meeting that it was the only time in my life when a member of the opposite sex plied me with strong drink, pinned me against the wall, and refused to take no for an answer. The result of this meeting was that in Hertfordshire we introduced a project built on one of Hilary’s most dramatic innovations, the Calculator Aware Number curriculum.
As the 1980s progressed and the electronic calculator became widely available and easily affordable Hilary saw earlier than anyone its potential for helping children learn. “For the first time we have a toy that contains the whole number system”, she said. One 6-year-old told me he “Did experiments with my calculator, like see what happens when I multiply numbers by 99”.
Before Paul – whose teacher felt he was not of exceptional ability – no child in history had the opportunity to play with numbers in this way. Hilary maintained passionately that if children were allowed to use calculators they would understand numbers better. For many people this was controversial, even though the CAN results, and indeed the findings of our own Hertfordshire project, gave dramatic support to her view. A group of our own teachers gave a presentation at a national conference and people flatly refused to believe their findings, and of course even today our new National Curriculum refuses to see the calculator as having anything to offer other than as a short-cut to getting sums right.
Tragically, Hilary was prevented from bringing CAN to full fruition. A horrific road accident, where a dislodged cats-eye hit her in the head, caused her to spend many months in hospital. Amazingly she returned to work, but died in 1992 aged just 64.
I can’t believe we’ve ever had someone with such a breadth of expert knowledge as Hilary Shuard. She was as at home in an Early Years class as she was working with A level students; what she wrote for teachers of both groups was recognised as being the state of the art; she also wrote authoritatively on the use of Logo at a time when computers were just being introduced to classrooms.
When I went to her memorial service at Cambridge I learned she’d been just as prominent in a totally different walk of life, and she’d been active in women’s sport at a high level. I’ve a feeling she played top-class hockey, and I know for sure she played cricket at county level and was good enough to be selected to play against touring teams from Australia and New Zealand.
Like many of the great people, Hilary would be happy to treat you as an equal even when it was patently obvious that this wasn’t remotely true. I remember with great pride the evening the phone went; Hilary said she’d more engagements than she could handle and would I mind deputising for her to speak at the National Association of Head Teachers conference? No of course I didn’t mind, though I doubt the NAHT were half as thrilled as I was. A few years later my wife and I were on holiday in Italy and we shared a table one night with a couple. During our conversation we learned that the woman was a teacher and Hilary’s name came up. I mentioned the NAHT story and she couldn’t have been more impressed if I’d told her it was the Prime Minister himself I’d been asked to deputise for. It seems a pretty good reflection of the love that teachers had for Hilary that ten years after she died our new friend couldn’t wait to get back to school to tell her colleagues she’d met someone who just once was the next best thing to Hilary Shuard.
*** In a Y4 classroom I asked children to put 8 into their calculator and add on the number which would make it display 20. I then asked them to work in pairs and use their own numbers. Every pair was able to choose the target that suited them – within 15 minutes one pair was playing to 1000, with the rule that their numbers must have at least three places of decimals!
*** If all the number keys except the 3 and 4 have fallen off your calculator how can you make it display numbers like 10?
*** Paul, aged 6, and not of exceptional ability, told me “I do experiments with my calculator; I see what happens when I multiply numbers by 99”. I set him the challenge of finding two two-digit numbers whose product is 7326, and he refused to go out to break until he’d found them.
*** I have a special calculator that the manufacturers call the “Wrongulator”. If you ask it the answer to 4×4 it shows 11. For 22-8 it shows 9. What do you think it displays for 27+19?
The obvious thing that calculators do is give the answer to sums. From there it’s a very short step to say that they impede mental and written arithmetic. But in each of the cases above, ask yourself where the arithmetic is actually being done, and then you get a different perspective. All the arithmetic is being done by the children, and being done mentally; the calculator’s rôle is providing feedback on the work already done in the head. In the Y4 classroom no teacher can possibly give instant feedback to fifteen pairs of children each working at a different problem (and what teacher has ever dared ask children to do six- or seven-digit mental arithmetic?). Similarly, without the stimulus of the calculator could I ever have expected a 6-yearold to be able to handle multiplication by 99? The “Broken Calculator” activity is so well-established that a Google search locates more than 47 000 000 hits. And my Wrongulator turns the conventional situation around so that you have to think what the answer should be, rather than what answer it actually displays.
Each of these activities makes it clear that the calculator has the potential to stimulate and enhance children’s mental arithmetic rather than stunt it. It’s now approaching thirty years since since Hilary Shuard’s CAN project demonstrated that when primary children had unrestricted use of a calculator their arithmetical understanding and fluency were not handicapped but greatly improved. In an allied project in Hertfordshire we found this was true not just for junior school children, but for all ages from Early Years through secondary.
Policy-makers are happy to encourage schools to spend thousands and thousands on computers and allied equipment, but ignore the proven benefits of the simplest piece of IT, which every child has in their pocket on their mobile phone. We have a quasi-religious attachment to traditional algorithms for long division, etc. Why stop there? After all, at school I had to learn an algorithm for extracting square roots, and even once encountered the corresponding method for cube roots!
I often read superficial arguments that calculators necessarily reduce mental exercise (not true – see the examples above) and that mental exercise is analogous to physical exercise. Maybe it is, but anyone who advances that view to me is liable to be asked whether they do their washing by taking it down to the river bank. Everybody knows that the traditional way of washing is by banging it with stones, but having a washing machine makes it possible to wash more things more efficiently, and make more time to do other things.