Math Relax: Getting More Comfortable with Taking Tests

I just had the most wonderful experience. I heard a student in the math lab say, "... It's called Math Relax. It really helped me get more comfortable taking math tests." I popped my head out, and saw a student I don't know talking to two other students, who were listening intently. She was telling them about the meditation cd she listened to.

I said, "Did you know I made that?" She looked shocked and said no. I said a bit more about it, and then emailed the link (always available to the right) to the two students she had been talking to. I think she had just convinced them it was the answer to their problems.

So I just revised the blog post that goes with the recording. I realized that I have never posted my edited version of the questions George Polya suggests that we should ask ourselves at every stage of the problem solving process. Here it is:

Problem Solving

Learning how to solve problems is the most important part of math. When a problem stumps you at first, pull out this sheet. It will help you break down the problem-solving process by suggesting things you can ask yourself each step of the way. [Revised from How To Solve It, by George Polya, 1945.]

Step 1: Understanding the Problem

First, you have to clearly understand the problem.

• What are you being asked to find? (It usually helps to write:   “Let x =”  this quantity.)

• What information are you given?  It might help to organize the information, maybe in a table.

• Draw a picture. (Try to show the relationships, don't worry about good artwork.)

Step 2: Devising a Plan

Second, find the connections between the information given and what you're being asked for. You may need to consider other problems you've done in the past that are similar, or that would solve part of the problem. You want to come up with a plan for the solution.

• Can you restate the problem in your own words? (If not, discuss with someone else.)

• Have you seen a problem like this one before?

• If you can't solve this, can you solve an easier problem with the same structure?  (If so, make one up now to solve. That will give you insight that may help you with this one.)

• Can you add information to your picture that will make it easier to solve your problem?

• Are there definitions that might help you?

• Can you solve part of the problem?  (If so, do it and state a new problem from what's left to solve.)

• Can you figure out anything interesting from the given information?

• Can you say: "If I knew _____, then I could solve this" ?  (If so, state a new problem in terms of trying to find _____.)

• Are you sure you've used all the given information?

• Is there information that may be implied but not stated outright?

Step 3: Carrying Out the Plan

Third, carry out your plan.

• While carrying out your plan, check each step.

• Can you see clearly that the step is correct?

• Can you prove that it is correct?

Step 4: Looking Back

Fourth, examine your solution.

• Can you check your answer?

• Can you check the steps and the reasoning?

• Is there another way to figure out the answer?

• Can you see it at a glance now?

• Can you use your answer, or these methods, for some other problem?