Let your mind roam when solving maths puzzles

My personal approach to solving maths problems/puzzles is to use logical reasoning. By habit I use this in preference to mathematical routines. Only once I have reduced the situation to one which I recognise as having solved previously do I resort to using a tried and tested maths routine (algorithm). This suits me, as I can imagine situations and apply logic to them. People vary in their ability to do this. When I taught at a top Public School [for non English readers who use different terminology, that’s one that charges the parents a small fortune each year for the privilege of giving their offspring an education] I asked my class to design a three dimensional chess board. They had difficulty in doing so. When subsequently teaching at a state school [that is one that is funded from taxation] I thought that this would make a challenging task for my pupils. However, they produced a wide variety of suitable solutions with facility, almost with contempt. They found the problem trivial. The difference was in the imaginative ability of the pupils. The state school pupils could imagine the possibilities, whereas those destined to be the leaders of English society lacked the capability to do so. (What does this tell us about the way the country is run, and how it might be run in years to come?). Only if you can imagine the problem/puzzle in your mind’s eye can you apply logic to it to arrive at a solution. This is why we at Puppet Maths encourage the imagination of our pupils. We want them to allow their minds to roam widely so that they can visualise the problem in their own terms before using logic to home in on a solution.