The following is a summary of professional research into physics problem-solving. Your goal is to move from the “novice” column to the “expert” column. Notice how expert problem-solvers stop to think about the problem, draw pictures to visualize the problem, plan out their strategy, before beginning, etc.—and still manage to solve problems much faster than novices. Short-cuts aren’t always short!
|
Novice problem solver |
Expert problem solver |
|
Studies worked examples rapidly, without bothering to understand the examples |
Studies worked examples until sure examples are understood |
|
Consults worked examples later in hopes of finding a plan |
Consults worked examples later to verify that chosen plan is correct |
|
Collection of knowledge is a random jumble of miscellaneous facts |
Collection of knowledge is well organized in person’s head: centered around physical principles and hierarchies (topic trees) |
|
Separates intuition/“real world” knowledge from theoretical/formal knowledge |
Constantly integrates “real world” with theoretical knowledge |
|
Little or no planning before trying to solve equations |
Develops a definite problem-solving strategy before starting to solve equations |
|
Not able to construct a physical picture of what’s going on, or is unable to recognize when chosen picture is inappropriate |
Constructs a useful physical picture of the problem |
|
Does not stop to think of a qualitative answer before starting to solve the problem |
Uses qualitative physics principles/physical reasoning to have a reasonable answer to the problem in mind before beginning to solve numerically |
|
Focuses on surface structure (physical items involved in problem) |
Focuses on deeper structure (physical laws involved in problem) |
|
Works backward (looks for equation that has the unknown in it) |
Works forward (looks for equations that include the given quantities) |
|
Does not stop to think about the answer that was obtained |
Stops to think if answer makes sense (checks against qualitative answer) |
Here are web pages with tips on studying and solving problems:
www.oberlin.edu/physics/dstyer/StudyTips.html
www.oberlin.edu/physics/dstyer/SolvingProblems.html
A lot of students get good scores on HW, but poor scores on exams because they really didn’t master the HW…they got help enough to turn it in, and that’s about it. The goal is not to memorize the HW (or sample exam), but to master strategy, concepts and skills that you will need to solve new problems…you probably won’t see the identical problem on the exam.
If you get help on homework, you need to
1) ask enough questions until you really understand the step, skill or concept you missed, and how it works in other situations.
2)
write down what your error was, and your new understanding in your
own words (you can use these notes in reviewing for the exam...they
record what you are weak in and errors you will probably repeat).
3)
find another problem that uses the same skills, and try it.
4) practice outlining problem strategies. Look at new problems, and write down steps, drawings and concepts that you would use to solve the problem, without actually solving them. Go over these strategies with other students you study with, or ask a TA if that’s the right approach.