Thinking Like a Physicist: Super Mario and Problem Solving

My two-week orientation with the physics department began this week.  This program entails some getting acclimated to the program, the department, and the university at large, as well as our first free shot at the qualifying exam (more on that after I finish failing it tomorrow).  However, the bulk of the time will be devoted to learning how to be an effective TA for labs and discussion sessions.  The first part of the TA training has been to think about what the phrases “thinking like a physicist” and “problem solving” mean to us.  In order to help me crystallize some of these thoughts, I have decided to blog about them.

Thinking Like a Physicist

We were told to ask our advisers their opinion on these topics when we met with them to discuss course selections for the upcoming semester.  My adviser had some interesting ideas about “thinking like a physicist.”  The main thing that he said is that he finds learning physics to be more personal than learning math.  By this, he means that physics is done more by feel and concept than symbol manipulation, which he thinks is more emphasized in math.  Because of this personal basis for physics, the instructor is very important, as the students try to emulate him when they set out to solve problems for themselves.  The students must also work to go beyond simply solving the problem and make sure that they can extend the conceptual reach of the problem.

I agree with this idea to a certain extent.  I do believe that a conceptual understanding of the system is the key in understanding a system.  Simple “plugging and chugging” may get you the right answer, but this is useless if you don’t have an idea what this answer means.  This is why physicists often employ the “limiting case” concept: if you can understand how the system behaves as certain parameters get very large or very small, then you go a long way to understanding how the system really works.  I disagree, however, that math is very different in this regard.  My best undergrad math teachers repeatedly emphasized the importance of understanding what was going on by visualization and drawing pictures of the situation, rather than depending on some formulaic “recipe” to spit out the right answer.

How Super Mario Saved the Princess

An important distinction made in our Instructor’s Handbook is the distinction between completing exercises and solving problems.  I think that for my generation, a handy analogy can be drawn to video games.

Let’s take Super Mario 64 as our example.  To win the game, Mario, our favorite Italian plumber, must travel through different worlds, completing different challenges to obtain stars.  As Mario moved through the worlds, the challenges got harder, and, in the early levels, you had to acquire the ability to perform certain skills that Mario could do.  These skills formed your basic toolbag: different types of jumps, things to pick up and throw, ways to attack or avoid enemies.  These are like the equations and mathematical techniques that you must learn in order to answer questions about physics.

Exercises: Making Use of Your Skills

Some of the challenges were very straightforward: climb to the top of the wall to collect the star, for example.  Now, just because the challenge is straightforward does not mean that it is easy.  Perhaps Mario must use his entire repertoire of jumps to move from ledge to ledge, where the slightest misstep would send him to the ground to start over again.  In fact, some of these challenges were the most difficult, at least for me.  Being able to see the exact steps I needed to get to the star made it all the more frustrating when I repeatedly fell off of the same ledge.

These straightforward problems are like exercises in physics.  When the question is posed, you immediately see the route to the solution, as well as which tools you will need to solve it.  But even if you know that you must calculate the curl of the electric field in order to find the time derivative of the electric field, the actual calculation of this may be difficult if the expression is very complicated or you have not had much practice with calculating the curl of a field.

In summary, exercises are simply a check of how well you have practiced your skills.  Can Mario perform the running long jump?  Do you know Gauss’ Law and can you evaluate the necessary integrals?  The skills needed are clear, all that is left is to execute them.

Problems: Deciding which Skills to Use

But the more rewarding challenges, the ones that made Super Mario such a fun game to play, were the ones where the route to the star was not obvious.  These challenges forced Mario to attempt ridiculous things: trying to jump across an uncrossable chasm, trying to pick up huge boulders, running around in circles… it could be enough to make you bash your head into a brick wall (sometimes literally — you never know when the wall might break!)  In the end, the skills that were needed were often trivially easy to perform: all you do is stomp three times on the post and the dog breaks down the gate and you can get to the star.  But it wasn’t the execution of the skill that was the important part, it was determining which skill to use.  Now, of course, sometimes you would discover that the skills you needed to use were still quite tricky, but the problem has now been reduced to the level of an exercise.  If you were to play the level again, you would go immediately to the right place and start performing the necessary skills.

The Role of Problem Solving in Physics Education

My department believes that problem solving plays the central role in physics education, at least on the undergraduate level, and I tend to agree.  (I think a conceptual understanding of the phenomena is right up there with it, though.)  Of course, you need to learn to use The Handy Bag O’ Tricks, but this is secondary to problem-solving skills.  You can program the formulae into a computer (or write them on a notecard) and the computer can do a cross product for you, but it can’t solve problems the way humans can.

I know find myself asking whether I was really taught how to solve problems in my undergraduate physics education.  I did learn problem solving skills as an undergrad, but much of this was learned on my own as I tackled the homework sets.  I don’t know that any of my professors systematically taught me to solve problems.

I’m sure we’ve all heard and used this phrase before: “It’s not hard if you see the trick to it.  Otherwise, it’s pretty much impossible.”  Well, duh.  It’s the trick that makes the problem worth doing.  If someone tells you the trick, and then you crank out the equations and the mathematical operations, what have you really done?  But in tutoring and homework help sections with professors, it is often the case that the prof will share the trick and ask you to finish the problem on your own.  What are we doing here?

I will find it very interesting to see how they teach us to help coach the students in the sections we TA without resorting to telling them the “trick” that reduces their problem to a mere exercise.


35 Responses to “Thinking Like a Physicist: Super Mario and Problem Solving”

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    Problem solving has the added advantage that yo uend up thinking about the problem in a lot of different ways, which is a great way to get a ‘feel’ for it. My experience is that developing that sort of intuition for physics is massively important for doing research on a day-to-day basis.

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