So a problem about three pigs may be changed into one which has any number of pigs. The answer to this problem will contain the answer to the previous three questions.
There we were asked for the number of towers of height one, two and three.
But Problem Solving also contributes to mathematics itself.
It is part of one whole area of the subject that, until fairly recently, has largely passed unnoticed in schools around the world. The skills are things that we are all familiar with.
Pólya’s second stage of finding a strategy tends to suggest that it is a fairly simple matter to think of an appropriate strategy.
However, there are certainly problems where children may find it necessary to play around with the information before they are able to think of a strategy that might produce a solution.
Naturally enough, Problem Solving is about solving problems.
And we’ll restrict ourselves to thinking about mathematical problems here even though Problem Solving in school has a wider goal.
If we have some sort of formula, or expression, for any height, then we can substitute into that formula to get the answer for height three, for instance.
So the "any" height formula is a generalisation of the height three case. Then we get34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1We certainly got to 1 then. Well we can extend this problem, make another problem that’s a bit like it, by just changing the 3 to 5.