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 by John D Bransford and Barry S Stein. The IDEAL in the title is an acronym for a five-step process, similar to the 7 steps I listed above.

Next was Wayne A Wickelgren's How to Solve Mathematical Problems, the most complete view of problem solving techniques and heuristics I have seen. Some of the techniques don't work well on less well defined types of problems, but most do.

Polya's How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) had a significant impact when I read it, but that was more than 15 years ago. I strongly recommend this to anyone interested in math or general problem solving, before reading Wickelgren's book.

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 by David Lewis and James Greene and an earlier edition of Problem Solving & Comprehension.

I am currently reading Thinking and Deciding by Jonathan Baron. It is a more difficult read, and more psychologically oriented than the others. The author's claim that effectively all thinking, deciding, problem solving, creativity are a combination of search and selection is interesting and looks very useful.

Great Post, but I have question: Isn't that (exactly) what Pólya 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.