Post Number: 35
|Posted on Wednesday, 01 October, 2008 - 09:34 pm: |
Wot! No Polya?
I'm amazed this book has no review so far.
In my opinion this slighted dated book is an absolute gem and tackles the rarely tackled, difficult and extremely important topic of how to approach new maths problems.
We have all experienced (some more than others unfortunately ) that situation of not knowing where to start on a new maths problem - how to get a "grip" or a foothold to at least start. The idea is that once you have started you might get an idea where to go next.
There no magic process that can be applied to every maths problem but there are questions that I try to apply to every quesiton I am stuck on. These quesitons include:
What is the unknown?
What am I trying to prove?
Can I apply anything I know?
Have I solved a similar problem before?
Can I solve a simpler problem?
Can I solve a more general problem?
and others ....
Now these may all seem trivial and obvious questions but their triviality does not diminish their power and usefulness. Their obviousness does not mean that we all apply them all the time to every question we tackle.
Polya shows how the techniques are applied to particular problems.
The techniques do not guarantee success but when they fail they prepare one's mind to understand the solution much more readily because a lot of "exploration" of the problem has been done.
When, it seems to me, much maths tuition is about finding the right answer the much neglected journey to a solution is much more valuable. Stephen Siklos' note on STEP problems makes exactly that point (so I don't claim any originality in what I have written).
My recommendation is you buy the book, work through it, apply it and I feel it will continue to pay dividends beyond school maths.