*** 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.