Parents across the world are on the lookout for a secret formula to unlock their children's mathematical skills. For some, Kumon is the answer. More than four million children in 43 countries are signed up to the method developed by the Japanese educator Toru Kumon, who believed that repetition and speed are the basis of making a good mathematics student.

Others think that the solution lies elsewhere. As reported in the education pages of The Times last week, parents in France have been flocking to Stella Baruk - the “J.K. Rowling of figures” - in the hope that she can perform the same magic for mathematics that the Harry Potter stories did for children's literacy.

Kumon's philosophy is in tune with that of the music teacher who insists that a pupil must master scales and arpeggios before moving on to anything more interesting. Yet although it is essential to have the technical skills at your fingertips, if pupils are left with the impression that this is what maths is about, I fear that Kumon will only accentuate a student's boredom with mathematics and antagonism to the subject. Many have criticised Kumon as “drill and kill”.

Baruk believes instead that language and understanding are the magic ingredients. Born in Iran, home of the great poet and mathematician Omar Khayyám, Baruk focuses on teaching maths as a living language with meaning. She bemoans the response that eight and nine-year-olds in France gave to this question: “On a boat there are 26 sheep and ten goats. How old is the captain?”

Of the 97 children who were asked, 76 responded by using the numbers contained in the statement - giving the captain's age as 26 or 10 or maybe 36.

Maybe it's all those posters pinned on young children's bedroom doors that cause the problem. Seeing pictures of two apples and three dogs followed by five medicine bottles can be confusing for a child trying to make sense of how you manage to get cough mixture by combining fruit with pets.

Baruk is keen to get children looking beyond the objects, to understand the abstract nature of numbers. But she is not adverse to using a little sorcery in the shape of such mathematical curiosities as magic squares - and it is bringing alive the magic and playfulness of mathematics that, for me, is key for anyone hoping to spark a child's interest in the subject.

I witnessed the power of a simple bit of algebra to capture people's imagination last year at the Barbican in Complicité's hit play A Disappearing Number. At the start of the show, an actor asks members of the audience to think of a number. “Now double your number. Add 14 to the new number. Divide this number by 2. Finally, subtract the first number you thought of.” I was staggered at the gasp of surprise as the actor revealed that everyone was thinking of the number seven.

Although the maths behind this trick is trivial, at its heart is the essence of what makes the subject so magical. It is the power of algebra that reveals why this trick works whatever the numbers.

There are similar tricks which are far more surprising - and which produced a gasp from me when I first encountered them. For example, the French mathematician Fermat discovered this bit of magic:

Think of a number and take a prime number bigger than the number you first thought of. Now raise your first number to the power of that prime number, then divide the resulting number by the prime. The remainder is the number you started with. For example, if you were thinking of 2 and you raise it to the power of the prime number 5, the answer is 2⁵=32. Divide by the prime 5 and the remainder is 2. This is far from just a mathematical curiosity. It is actually the basis of the mathematics at the heart of internet cryptography.

If I were asked to teach arithmancy at Hogwarts, I'd be keen to impress the likes of Hermione Granger with maths spells: “Primenumeros incantato!”

When you see a magician do a trick, the magic often vanishes if he tells you how he did it. For me, this is where maths and magic differ. Understanding why Fermat's trick always works only enhances the magic - and it's such magic that will capture children's imagination.

Conundrum

Think of a three-digit number where the first and last digit differ by 2 or more. Reverse the digits to make a new number, then subtract the smaller of the two numbers from the larger one. Take this new number. Reverse the digits of this new number and add these two new numbers together. Using my magic mathematical power, I can reveal that your answer is 1,089.

Why is the answer 1089? Well, your 3-digit number is ABC=Ax100+Bx10+C. Reverse the digits and you get CBA=Cx100+Bx10 +A. Let's assume that A is bigger than C. So ABC-CBA= (A-C)x100+ (C-A)= (A-C) x100- A-C)=(A-C)x99. So you will be left with a number that is a multiple of 99: 198, 297, 396, 495, 594, 693, 792 or 891. Notice that the first and last numbers of each three-digit number add up to 9.

Take one of these three-digit numbers, add to it the reverse of the number and you always get 1089. Eg, 297+792=1,089.

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