Times tables made easy by the clock
Every so often an idea comes along which can change everything. Take the times tables. For Wendy Fortescue-Hubbard, who left her happy village school in Scotland for boarding school in Somerset when she was up to her sixes, the sevens, eights and nines were never right. Even when she grew up, went to Rolle teacher training college in Exeter, had two of her four children and began teaching maths in a secondary school, she was still never quite sure, she says. "I used to listen to the tables with a crib sheet, I was so horrified at testing tables. Seven eights - I hated that one."
It was only when she went on to do a maths degree through the Open University that she really became sure of these basic number facts. The whole numerical web of fractions, multiplication and factors, "the beautiful patterns and relationships" fascinated and attracted her. But she also began to see how children who entered secondary school without either sound knowledge of the tables or a standardised way of learning them were at a profound disadvantage.
Sadly, traditional rote learning and individual testing seemed only to reinforce fear of the multiplication tables for all except the fluent few. Even worse, some know the tables song but not the tables.
During the next few years she progressed from sharing her exuberant enthusiasm with her class - "I used to show the bored ones, do you realise how mathematics actually models the tomato ketchup coming out of the bottle" - to setting up maths clubs, a maths centre and an intensive revision centre in Barnstaple. "I really loved teaching and I really loved mathematics," she says, face and eyes glowing.
When personal circumstances forced her to move to Plymouth and the business hit difficulties, she applied to do a PhD at the University there. Supply teaching in a Plymouth comprehensive reminded her of earlier painful experiences. So many children were at a loss when it came to their times tables.
"Not knowing times tables erodes their confidence," she says. As they were Year 7 children, they were ashamed of their ignorance. So Ms Fortescue-Hubbard went home and worked out how to incorporate statistics and data handling processes into the learning of the multiplication tables. She came up with a card game later called Perfect Times (now patented).
The children had to play a kind of patience at home and record their results on a time sheet. Although, as Wendy says briskly, all children cheat, it was hard to cheat at this, because the children would say to themselves, "If I don't do this, when I play it in class, they'll see I haven't done it". The game, of course, was fun. Like patience and snap, it's almost addictive.
It consists of a pack of cards for each table - 2,3,4,5 and 10 for key stage 1 children and 6,7,8,9 for key stage 2. Sets of cards in each pack are colour-coded for the factors (1 to 12) and the multiples. When commercially produced, which should be by Christmas, the cards will also include 11s and 12s, "because most parents teach them and 12 is such a lovely number to chop up". Additional packs for 13-17 are available. "Did you know that Indians used to learn the 16s because their money depended on it?" she says.
With these packs, simple stopwatches and printed timesheets, a class is ready to have a "perfect time". One wet September day in Enfield, north London, at Hazelwood infants and junior schools, the children gathered round in eager anticipation. Explaining the game is the hardest part. Even a teacher as magnetic as Wendy Fortescue-Hubbard found children at the edge of her circle fidgeting as she explained the penalty system. (Extra time is added for mistakes and for reading the information off the back of the pack. But this is not cheating. After all, the idea is for the children to learn their tables. ) But as soon as the games began, heads went down and bottoms were squirming on the edge of seats.
These children were playing the simplest version of the game, where one child places the factor cards face up (in a rectangle of four cards by three) and then times the other child with the stopwatch while he or she places the correct multiple card on top.
For example, for the three times table, the child has to place 9 on top of 3, 12 on top of 4 and so on. Or for the nine times table, the 9 would go on top of 1, the 81 on top of 9. Extraordinarily quickly, usually between the third and fifth go, one or both of the children would get the hang of it and the time they took to do the game would halve - say from one minute to 30 seconds. The time then continued to drop slowly.
As they tasted success, the children became absorbed and confident: "Oh no," they wailed as the whistle went for lunch, "I must just finish this." "Where can we get the cards, Miss?" And - "How did I do, miss? I got 34 seconds. "
"That's very good," Wendy said seriously to each one.
She says that she is sure the number fact has passed from short-term to long-term memory when a child can consistently do a table in 20 seconds or less. This recording system allows the teacher to assess the children at the same time as it teaches them to remember. It frees the teacher to walk around and see where problems are.
Craig was having problems with his twos. His face was contorted with effort. Wendy spent a few minutes showing him that it was "allowed " to count on in pairs on his fingers. Once he understood with his body the principle of multiplication, he quickly progressed to mastering the memorisation and flipping down the cards. He went out singing and bouncing.
Reina is Bengali and seemed not to understand what was going on. But when Wendy said she could count in Bengali, she started to match her (English) partner's times. Ryan kept getting all his cards wrong. So Wendy took away all but four of the pairs of numbers and played only with those. Soon he was starting to build up the table.
"If a child still gets more than four (of the 12 pairs of cards on the table) wrong, we just use the ones they're getting wrong," says Wendy. "If four are still wrong, we use three or two. If that is no good, we draw them out on paper. You can use all the methods, it doesn't matter. Some children are maths poor. They have to be made to make their heads work. But it is suitable for special needs children."
Simple rules - when a card is up it must be played, 10 rounds must be played before a child leaves the table - cut down on the desire to cheat but also make the game practical for slower learners.
And the games are variable. For the quickest, there are head-to-head challenges - my 13 times against your 17s. For the slower ones, there are games played, like patience, privately, and home research. For everyone, there is the possibility of division as well as multiplication.
There are graphs at the maths department at Plymouth University showing recorded times for children like Mark - "Don't understand, don't understand. Oooh, now I understand!" There is work with maths phobic children, cutting response times to below 20 seconds.
The national curriculum, requiring "mental recall" for the multiplication tables, can only fully be implemented if children have automatic recall. If you have to think about it, you're too slow.
After a day watching the light go on in 10-year-old head after head I can't see why the packs are not already in the shops and sold out. Forget oral questioning: it's too time-consuming and can even be humiliating. Forget written tests: children can and do cheat but also they have too much time for recall. Forget, above all, the kind of teaching which says things like "My daughter hates having a shower so I keep her under it until she's learned all her tables". Perfect Times will be available in a few months: get playing as soon as you can.
o For details, tel: 01752 233845