Imagining the puzzle

In maths the ability to imagine the problem is key. A couple of years ago I was studying in the company of a group of postgraduate students the eldest of whom was 14 years my junior. As a result all were too young to remember when the UK currency consisted of pounds, shillings and pence. These were all highly intelligent people. I proposed a pub challenge, in which I would ask the questions and they would compete against the clever clogs [this guy was a Physics PhD, who got 780 (out of 800) on his GMAT exam score] to do sums in pounds shillings and pence, the winner being the one who could furnish the correct answers first. My proposed quiz never took place because the PhD was unwilling to try his brain at calculating in bases 12 and 20 (there being 12 pennies in a shilling and 20 shillings in a pound) in such a public arena, where he might lose face. What he lacked, because he had never been previously required to possess it, was the ability to imagine counting in these bases. If he had tried, he would quickly have been able to imagine piles of copper pennies growing in height until they were 12 high when they turned into a silver shilling, and piles of shillings growing in height until they were 20 coins high, when they turned into a pound. Had he developed this picture in his mind he would have been able to solve any questions that I would ask involving the old UK currency, but until he did, until he could imagine the problem, he was not in a position to attempt the questions I might ask. So often, maths is not related to a real situation. As a result children are unable to imagine the problem. Like the Physics PhD, they just cannot get their heads it. At Puppet Maths we couch the puzzles we give our pupils in terms of familiar situations, so that they feel at home with the puzzle and can imagine what’s being asked of them and apply their minds to finding a solution. We mean to help them develop their ability to visualise in their mind’s eye what needs to be done to arrive at a solution.