Solving Difficult Problems

Don't Panic!

My students have been brought up in the math tradition of fast is best, and there's only one way to solve problems, using tried and "true" procedures. Their previous physics teacher had selected a college textbook for them (thinking they were all AP-Physics students, which they were not, even though they were all very intelligent in their own ways.) The textbook took great pride in generating formulas for every conceivable situation, so my students had great difficulty accepting my collection of 4 formulas on the board, which I said would cover any situation they could think of that applied to Newton's 3 Laws. Time and again one of the students (usually the ones who had gotten high grades from the previous teacher) would bring that textbook to me and ask if some version of a formula was the right one to use for a particular problem. I always said, "No, use one of the four on the board." This was very difficult for them to accept until I discovered a wonderful video clip, which I show below.

I have been auditing a MOOC with Stanford Professor Keith Devlin, based on his book Introduction to Mathematical Thinking. ("Auditing" means, I'm not taking it in the allotted time, nor submitting assignments, but I'm at least watching all the video lectures.) In the very first week, he offered a video, which I called How to Solve Difficult Problems.

Techniques the Pros Use to Solve Hard Math Problems from Keith Devlin on Vimeo.

I think showing a clip from this (about half) was the turning point in getting students to understand what I was talking about.The course is intended to introduce HS students to what college math (beyond calculus) will be like, and I am auditing it, so I can mentor my students in what they need to know to succeed in college. One important thing is problem solving - not just math and physics, but everyday life away from home. So we talked about his recommendations

• Don't panic
• take your time
• take a break
• draw a picture or diagram
• write down everything you know
• learn from your mistakes, etc. 

in connection with problem solving in everyday life - deciding which college to apply for or accept, whether to buy a car, and which one, whether to date someone, etc. 
And then we applied these concepts when solving physics problems. After the video they had a much better understanding of how to solve problems. Interestingly enough, on the last test I gave them, they were very good at solving problems where they were expected to model the problem in 6 different ways, but they did poorly on multiple-choice, where I figure many rushed through in their usual manner, bringing in all their physics misconceptions.