The nature of mathematics.

There is a joke about mathematicians. It involves boiling a beaker of water. A physicist and mathematician are applying for a job and the interviewer has prepared a test to see how good they are. In the first test they are to be presented with a Bunsen burner underneath a tripod, to the left of the Bunsen burner is a box of matches and to the right of the Bunsen is a beaker of water. The physicist goes first. The interviewer asks the physicist to boil the water. He thinks for 5 minutes and then picks up the beaker and stands it on top of the tripod, picks up the matches and lights the Bunsen. The interviewer thanks him and he leaves the room. Then the apparatus is replaced in its original positions and the mathematician is called in. He also thinks for 5 minutes and then picks up the beaker, places it on top of the tripod, picks up the matches and lights the Bunsen. The interviewer thanks him and he leaves the room. The second test is then set up. It uses the same equipment as before but this time the beaker is placed to the left of the Bunsen, and the matches to the right. Again the Physicist goes first. Again he is asked to boil the water. Again he thinks for a full 5 minutes then he lifts the beaker and places it on top of the tripod, picks up the matches and lights the Bunsen. The interviewer thanks him and he leaves the room. The apparatus is returned to its original positions and the mathematician is then invited into the test room. He is also asked to boil the water. Once more he looks at the apparatus for a few minutes. Then he lifts the beaker of water and moves it to the right of the Bunsen, and lifts the box of matches and moves them to the left of the Bunsen. Then he turns to the interviewer and says “hence a problem that’s already been solved”.
And here is a central principal of mathematics. Mathematicians strive to reduce a problem to one which has already been solved. So given a maths problem, the mathematician will use logic to modify it and home in on one that has been solved before. This why so much time is spent learning about geometry and trigonometry, because anything mechanical can often be resolved by applying the rules of geometry and trigonometry. It’s why we learn algebra, because if a problem can be resolved into a formula, then we can stop doing all the hard work of thinking logically and just apply the rules of algebra (which have already been worked out) to arrive at a solution. Many pupils do not understand why they are expected to learn obscure mathematical routines because they see no practical use for them. This makes maths boring. At Puppet Maths we put mathematics into context, so that children understand what it can be used for. Our puppets recreate the circumstances where the maths is needed, so that our pupils can understand why they are learning the mathematical routines that we teach them.