In the following I will describe what problem solving skills are and list some books.
Many students have difficulties understanding a problem but they don’t recognize why exactly they can’t solve it. They sit in front of it and have absolutely no clue on how to proceed. The famous mathematician George Polya asked himself if it is possible to teach something like “problem solving skills”. And the result is his little book entitled “How to Solve It”.
He describes four steps on how to approach a problem:
1. Understanding the problem:
First. You have to understand the problem.
What is the unknown? What are the data? What is the condition?
2. Devising a plan:
Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
3. Carrying out the plan:
Third. Carry out your plan.
Carrying out your plan of the solution, check each step
4. Looking Back
Fourth. Examine the solution obtained.
Can you check the result? Can you check the argument?
Can you derive the solution differently? Can you see it at a glance?
The steps don’t sound impressive but I can assure you they are a mighty tool. Read the rest of this entry »