Identify opportunities to improve situation.
Identify opportunities for innovation.
2. Recognize and define problem.
3. Define the goal.
4. Search for and develop alternative solutions.
Explore possible strategies for achieving goals.
Formulate hypotheses.
5. Select alternative solution or strategies. Anticipate the precise outcome. Choose the hypothesis to test.
6. Implement solution or strategy. Act on it. Commit through action. Test the hypothesis (do the experiment).
7. Gain feedback and compare to anticipated outcome. Refine the solution.
Trying too hard to avoid complications often creates them.
When in total ignorance, try anything, at the least you will learn something that doesn't work. And watching how it fails should teach you a lot more than that. Seeing to what extent it looked like it could work before it finally failed should reveal interesting data also.
Edited to Add References: I was in a hurry yesterday when I posted the above and didn't have time to lokk these up in Amazon.
The greatest source for the above is The Ideal Problem Solver: A Guide to Improving Thinking, Learning, and Creativity
Next was Wayne A Wickelgren's How to Solve Mathematical Problems
Polya's How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
Two more books that made a significant impression on me at the time I read them, but that I didn't actually refer to for this are Thinking Better
I am currently reading Thinking and Deciding
Great Post, but I have question: Isn't that (exactly) what PĆ³lya advises in "How to Solve It"?
ReplyDeleteAnd if it's so, what's the point of copying down that method without any contribution or commentary? Are you simply advocating his suggestion? In that case I (by and large) agree with your post!
Cheers,
Steven Ray
Actually, I am planning on adding references, I was just in a hurry. Polya is one, but more came from "The IDEAL Problem Solver" and some from Wickelgren's "How to Solve Mathematical Problems".
ReplyDeleteI wish you a joyful time reading those personal development books. I have always been skeptical about their actual effect on our everyday life, though. I mean (genuinely) I'm not sure that by reading a book about solving problems in math I will gain a greater power and capability in solving more difficult mathematical problems.
ReplyDeleteP.S. BTW, Have you checked out this one: http://www.stevepavlina.com/ It has a section about problem solving.