Catch-24 starts to add up
They turn over another card and are engrossed in the next set of circles. On the next table, Junior tests Rajbinder, Adele and Rebecca to see whether they can get 8 from two circles, one with 9 and 2, one with 5 and 3. Rebecca is confident: "9 take 2 is 8," she proclaims. "Do you agree with that?" asks Sharon Lee, who is class teacher and maths co-ordinator at Slater Street Primary School, Leicester. Junior shakes his head. He is calm and confident, holding the cards and marking results on a sheet. "I know," calls Rajbinder. "5 add 3 is 8." Junior smiles gravely and nods. "You've run out of time. Let's do it again."
The pupils at Slater Street are part of a pilot study on the 24 Game. The 24 Game has in the past two years taken the US by storm, with national and regional 24 Game championships regularly showing up children from highly disadvantaged backgrounds as bursting with mathematical talent. Brainchild of Bob Sun, who moved there from China and himself began as a class "geek" but went on to become an inventor, the 24 Game in its simplest form asks players to make the number 24 out of four numbers on a card, using any of the four operations. It can be as simple or as complex as the player's mind allows, as addictive as Patience, as liberating as learning to swim.
As currently marketed, the game comes in different levels: an initial single digit one which uses the basic factors of 24; two Primers which grade sums using only addition and subtraction and those also using multiplication and division; and the basic 24 Game which first uses addition and subtraction and then adds multiplication and division. All these levels are sub-divided into operations using 2, 3, or 4 numbers. For more advanced students, the Platinum range includes similar tasks for decimals, fractions and a Puzzle Sleeve which hides numbers to be deduced for algebraic functions.
The game can be used in developing number skills right up to the beginnings of A-level, according to Andrew Blow, himself an ex-head of maths and ex- headteacher and now marketing and education director of Summus, which sells the game in the UK.
Ronis Sun, wife of Bob Sun, tells a story of a student who sat on the subway getting more and more agitated over one of the cards until he finally rushed out of his journey and rang her to tell her the firm had made a stupid mistake and that there was no way that 7,7,7,4 could make 25. When she told him the solution (7 divided by 7 = 1, 7 take away 1 = 6, 6 times 4 = 24) he hung up. It is that quality of insistence which makes the 24 Game such a good game Q "I've had parents coming up to me," says Sharon Lee, " and saying I couldn't work that one out, how do you do it?" Q but it is the deep satisfaction of getting a right answer which makes it so educational. "The powerful thing," says Andrew Blow, "is that there are no expectations."
Even the really young Year 1 children at Slater Street enjoy the game. "They are just moving off from the concrete to the abstract," explains headteacher Karen Cane. "And the cards themselves are attractive, bright and durable; they love taking shiny small ones home." Sean, Aliya, Zamina and Adele are sitting eagerly round the table doing single digit sums. Is 4 take away 1, 4? No! But is 8 take away 4, 4? Yes! "I know which wheel it might be," pipes up Sean. He is right. He nods cheerfully. "I think it's really good. When I get the answer it's good."
In Sharon Lee's vertically grouped Year 3, 4, 5 class, Nafisa and her cohorts are testing the others to see if they can jump levels. "These are my little mathematical wizards," says Sharon Lee, "and they fill in these record sheets for me, which are very useful and very accurate. They do that at dinner time. During class they move on through the levels themselves." The game is loved by statemented children and high achievers alike. And as the classroom fills with a happy but loud buzz of voices, Sharon Lee adds the rider that "the teacher needs to keep checking that the game is still meaningful. But the game does involve communication". That oral element is one of its great strengths.
At Beaumont Leys secondary school, Ian Robinson, head of maths, sees this need to talk about maths as most fruitful for his pupils. "A lot of our students find it hard to explain what they've done, but this develops good communication. When we introduced it we worked as a whole group, talking together about how we got the answer." He adds enthusiastically: "even the low-ability students, when they get the answer right, feel good about it. And the beauty of it is you can see them thinking, see how they are working it out." At Beaumont Leys, the pupils have not yet progressed to jumping levels, as pressure of tests confines play to "lesson-ending" activities of 10 minutes or so, but within that time it has made a definite impact.
The game has been tried in Years 7, 8, 9 and 10. According to maths teacher Michael Munday it was the greatest shock to the Year 10s. "They are too used to getting out a calculator. With the game they are forced to realise that they have to use the concepts instead of just get the answers." Mr Munday sees the game as a useful introduction to algebra: "I told them it'll be no good relying on the calculator when you come to algebra. You need concepts, not just number-crunching." Number-structure itself is helped but also, Munday and Robinson believe, playing seems to make the children's minds "more agile, less rigid". Tests on mental maths seem to show a quicker, more inventive approach after a few game sessions.
In one Year 7 class the pupils are dealing out the cards. Matched by friendship, they are also largely paired by ability, except for Zak and Adam, whose neighbours are away. Both claiming to like maths, they are yet at quite different levels, Adam trying addition and subtraction with three numbers on factors of 24, Zak on to four operations with three numbers ending at 24.
While Zak and I puzzle over how 9, 3, 2 or 5, 6, 4 can make 24, Adam rapidly gives up on several permutations of 4, 4, 6 to give 6 or 9, 3, 2 to give 8 . But when we get the answer (9 add 3 = 12 multiply by 2 = 24) Adam rejoices with us, just as Geeta and Rena behind us let out shrieks and giggles as both of them solve three puzzles in 60 seconds. "We've got to level 7, level 7!" they cheer.
Will 24 Game catch on and bring the benefits of calmer, more numerate children, confident in their problem-solving abilities and able to co-operate and harness competitiveness to achieve personal excellence without conflict? A tall order, perhaps, but looking around the classrooms in Leicester, it certainly seems an inspiring method to lure children into realising the fascination of maths. As Nafisa explains, "if you didn't have the game then you wouldn't be as good as you can be".
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