At one minute to midnight every September 30, the decrepit, cluttered schoolroom of Tetsuya Miyamoto stands frozen in time. Breaking the sepulchral silence of the Yokohama side street, the clock ticks over into the first day of October and a fax machine in the corner shudders to life.

Throughout the rest of the night, page after page spews out of the machine, each one representing a different seven-year-old child, each one an application form pregnant with parental hopes and fears.

The huge majority of parents will be bitterly disappointed: only the children in the first 20 applications received are allowed to attend Mr Miyamoto’s classes from next March to be introduced to the radical methods of the man who has vowed “not to teach children”.

What he does instead is to set them a puzzle which, he says, transforms the brain into a vigorous problem-solving engine. The puzzle, of Mr Miyamoto’s own devising, is called KenKe*, which translates as “cleverness squared”.

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KenKen is perfect for improving numeracy in children and brain-training for adults

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Mr Miyamoto’s theory is that the brain – of a child or adult – is failed by conventional teaching. By concentrating on a “third way” of problem-solving, he believes that the mind becomes a more potent tool for dealing with the rest of life, from main-stream education to the challenges of the workplace.

Mr Miyamoto, 49, offers his students no instruction. KenKen’s power to train the brain lies in the fact that in his “lessons” – and from Monday on the back page of times2 – the puzzle is there to be solved alone. There are important keys to be found but no fixed starting place and no method of progression that can be learnt as a strategy. For both children and adults, runs Mr Miyamoto’s theory, the brain feeds on what it has worked out for itself rather than what it has been told to focus on.

By combining the four main mathematical functions of addition, subtraction, multiplication and division, the brain is forced to dart between competing theories. The puzzle, he says, is impossible to solve without the scientific process of trial and error. One reason why his class is so heavily oversubscribed is that parents believe it will propel their children towards science.

The puzzle, Mr Miyamoto says, draws out the primal, self-starting learning instinct of human beings – an instinct that is notoriously suppressed by the fact-cramming teaching methods of the Japanese education system, but which he says needs to be encouraged in people of all backgrounds.

As well as for its brain-stimulating qualities, KenKen has been constructed to be addictive. Every puzzle, says Mr Miyamoto, contains a “trick, a discovery – a story”. The puzzle works in his classroom, he says, only because the children want to root out the clues and persevere with the discovery process. “As the feeling of achievement increases, so too does the level of concentration,” he says.

He admits that he was not academically gifted as a child. He had to go to an extra examination school to bring himself up to scratch for the university entrance examinations. He went to the private University of Waseda, Tokyo, where he studied a mainly arts-based course. On graduation he became a teacher at a juku (cramming school) in Yokohama, two floors below where he holds his classes. It was then that he formed his theories of how better to train young brains for the real world.

Mr Miyamoto is unapologetic that KenKen has more mathematical demands than puzzles such as Su Doku. KenKen, he explains, is all about numeracy. Su Doku may look like a number game but the numbers are in reality convenient symbols in what he sees as a fairly straightforward logic puzzle. “The numbers in Su Doku could be replaced with melons and you would still be able to play. In KenKen the value of the numbers is absolutely central to the solution. There is no such thing as a child who dislikes maths from the start. The secret lies in the material you use.”

Mr Miyamoto’s classes, which take place every weekend, are a scene of astonishing concentration. The children file in and take their seats. The poky room is plunged into pin-drop silence and the puzzle master hands each child a handcrafted KenKen. At the start of the year’s course, puzzles are not too taxing and start with a 4x4 grid. Children are told to begin and a 40-minute timer begins a countdown.

When each child thinks he has correctly finished the puzzle, he raises a hand. Mr Miyamoto takes the puzzle and checks it. If it is correct he hands out a more difficult puzzle in a 5x5 grid. The best children manage three puzzles in 40 minutes but most do not make it to the end of the second grid.

In the session’s second half, a large KenKen grid is drawn on the blackboard. Mr Miyamoto offers two words – maru, correct, or botsu, rejected – as the children are called to say which numbers should fill the boxes.

Because of Mr Miyamoto’s rigid beliefs about the importance of the “personal pattern and style of learning”, he is careful not to offer any advice to readers of The Times. Successful solvers often seem to start with the higher-value number clues and to focus on the numbers, particularly the primes, where possible solutions are naturally limited. Beyond that, he says, it is up to you. “Nobody can tell you how you should do it.”

*KenKen ™ Puzzles are used with permission of Gakken Co., Ltd and Nextoy, LLC. Puzzle content © 2008 Gakken Co. Ltd.

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