Solving Math and Physics Problems You Don't Know How to Solve
Solving Math and Physics Problems You Don't Know How to Solve
Years ago, while tutoring a student in physics, I wrote some notes<br>for her about solving class exercises when you don't know how to<br>proceed: how you can start with what you know, and use the exercise as a<br>stepping stone to expand your skill set, to be the kind of person<br>who can solve that problem easily.
After writing it down, I realized that the notes contained a<br>general approach for learning to solve theoretical problems of nearly<br>any technical topic - math, hard science, or engineering. It's not<br>for problems you already understand; those aren't really problems<br>except in an academic sense. It is for situations in which you<br>currently lack some of the skills or knowledge needed, and must find a<br>way to proceed.
Recently while clearing out some old papers, I found a photocopy of<br>those notes the student made for me. I've edited and<br>reproduced them here for anyone who might benefit.
How To Do It
When encountering a problem you don't immediately know how to<br>solve, make a list of the things you know that might be relevant -<br>either from your own experience, or information that is given that you<br>trust to be true.
Make another list of what it is that you don't know, and want to<br>figure out. Usually it will be a shorter list than the first.<br>Include not only the ultimate goal, but everything else that might be<br>relevant that you don't know yet.
Remember (or look up, or write down) some formulas and concepts that you<br>feel might be relevant. You may want to copy them into another list.
With your skills and insight, attempt to build a bridge - some kind<br>of direct relationship - between what you know and what you want to<br>know. Find several relationships between different pieces if you<br>can. Write equations describing them if you can. Draw diagrams or<br>pictures representing these relationships if you can.
If you get stuck, or encounter a new unknown quantity, identify the<br>things you need to know to get unstuck, and repeat this process.
When you have challenges:
Review the list of things you know, making sure you understand what they mean.
Think about groups of similar concepts, and how they might<br>relate. Examples: power, current, voltage; speed, velocity,<br>acceleration.
Think about ways you can test some of your assumptions. For<br>example, you can use an equation to make a prediction that is easy<br>to check. Or you may be able to use units.
Once you do have the understanding needed, the solution becomes<br>easy to see and grasp, and you won't need anyone to tell you how to<br>solve it. This procedure can help you get to that level of<br>understanding.
Thanks to Sunny Lee, the aforementioned student, for digging up<br>the notes and giving them to me.