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2012 March 25

Physics problem-solving

Filed under: home school — gasstationwithoutpumps @ 16:57
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Brian Frank, on his blog Teach. Brian. Teach., had a short post (Learning to Value Systematized Ways of Thinking), in which he expressed distaste for the rather formal descriptions of physics problem solving found on several web pages:

I’m not quite sure what his objection was.  Were the web pages too dry and formal? Were the methods presented not good for solving physics problems? Or were they only good for solving textbook problems, and not for thinking about physics in general?

All the web pages seem to present very similar methods (drawing pictures, using symbolic manipulation before plugging in numbers, keeping track of units, using mnemonic names for variables, …).  The advice tends to be specialized for physics problems, but is not very different from more generic problem-solving advice.

I’m not sure how one teaches problem solving.  It is a mental skill that is extremely useful in fields like mathematics and computer science, but it seems to me that coursework usually selects for those who have learned it on their own rather than actually teaching it.  I’ve seen books and articles (like the web pages above) that try to summarize what skilled problem-solvers do, but I’m not convinced that they are effective in getting novice problem-solvers up to even rudimentary skill levels.  (My favorite of such books is Pólya’s How To Solve It, which has been selling well since about 1945—I got my copy in 1970, I believe.)

I’m convinced that the only way people learn how to solve physics problems or debug computer programs is by doing it.  Some guidance and scaffolding when they are first starting may be necessary for them to build the belief that they can solve problems, but they need to have the guidance removed fairly soon, or they’ll never learn to solve problems—just to follow the guiding instructions.

I’ve seen the results of too much scaffolding sometimes in my senior/grad-level class where students were expected to design, code, and debug short programs.  Several of the students who had passed prior programming classes were helpless at designing data structures or short programs, because all their previous classes had given them very clear designs to implement.  They had learned how to code (and to a limited extent how to debug), but had never learned how to take an application problem and figure out how to design a program to solve that problem.

Though many of us who do a lot of problem solving (whether in physics, math, computer science, or some other field) like to believe that problem-solving skills are fairly generic, so a good physics problem solver should also be a good computer program debugger, I think that “problem-solving” is actually a bundle of skills and knowledge, some of which is generic and some of which is quite domain-specific.

For physics problem solving, some of the diagramming techniques are quite domain-specific, as is knowing which complexities can be safely stripped away to make a problem tractable.  Some of the other techniques are quite generic (comparing what you do know to what you need to know, for example).

Doing routine textbook exercises may help learn how to turn the crank on problems that have already been solved, but it does little for learning how to approach new problems.  A good physics problem for homework gives students a question and requires them to come up with an appropriate model (not just using whatever model the current section is teaching) in order to answer the question.  One risk in designing such questions is providing precisely the necessary information—giving the students too strong a hint about what model to use.

I like the Art of Problem Solving math classes for my son, because they provide doable problems (though sometimes only barely doable) that really require students to synthesize their knowledge, pulling together ideas from seemingly unrelated previous work. They usually use some of the most recent material, but not always.

I’ve not seen a similar approach in physics (not even in the Matter and Interactions book we’re using).  Although some problems build on a base built up over several chapters, they almost always are keyed to the current chapter and even specific sections within a chapter, so that the models needed are the ones just learned.  Occasionally an extraneous number is included in the problem statement, but for the most part they provide exactly the information needed in the most convenient form.  (Sometimes there is deliberately missing information, which can be quite hard to figure out, such as in problem 8.P.35, where students have to guess at the spring constant for an H-Cl bond.  I think that they are supposed to guess that it is about as stiff as Cu-Cu bond in metallic copper, which was estimated 4 chapters earlier, though I know no a priori reason that the bonds should be of similar lengths or stiffness.)


  1. I agree with what you have said here. As a science teacher, I always get frustrated when students start memorizing formulas instead of understanding what happens. Sure, the best way to solve is by practice, but a lot of people do without understanding. It’s just like reading a book for the sake of it, without getting the real story behind it or techniques in the writing.

    That is why I wrote a very short how-to series on solving physics problems, but with the idea that these techniques are also for any problem, even in real life. I hope you find these links useful.

    feel free to browse through the content if you wish. :)

    Comment by dennisseda — 2012 March 25 @ 21:17 | Reply

    • I read your example of solving physics problems. The example chosen does not really lend itself to “problem solving” since the data is presented in precisely the correct order for grinding through on a calculator with almost no thought. In fact, it is such a stereotypical textbook problem, that students could likely just change the numbers on an example in their text, without understanding any of the physics.

      I think that this is part of the difficulty in teaching problem solving: students are not often asked to solve problems, but are given routine exercises that are almost identical to the examples that they are given. This leads to simple template-matching behavior, and does not help them when they encounter problems that are not exact matches to their limited number of templates.

      I can’t claim that I can come up with anything better—designing problems (rather than exercises) is hard. Dan Meyer has gotten a lot of mileage out of a handful of good problems for math classes on his blog (so far about the only physics problems were a basketball shot and somewhat challenging one about when a fan would stop.)
      He has been trying to get others to put up picture or video prompts that lead to interesting problems—crowd-sourcing may be a fruitful approach here.

      Comment by gasstationwithoutpumps — 2012 March 26 @ 17:20 | Reply

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