Wednesday, November 29, 2006
Physics Problem Solving
The following is a summary I wrote of professional research into how experts go about solving physics problems, contrasted with how novices solve the same problems. I can dig out the reference for the original (quite lengthy) review paper, but don't have it handy. I thought the findings were quite interesting.
I gave this to my Intro Physics students, with a note saying, "Your goal as a student should be 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!"
1. Novice: Studies worked examples rapidly, without bothering to understand the examples.
Expert: Studies worked examples until sure examples are understood.
2. Novice: Consults worked examples later in hopes of finding a plan.
Expert: Consults worked examples later to verify that chosen plan is correct.
3. Novice: Subject knowledge is lacking.
Expert: Has a thorough knowledge of subject matter.
4. Novice: Collection of knowledge is a random jumble of miscellaneous facts.
Expert: Collection of knowledge is well organized in person's head: centered around physical principles and hierarchical (topic trees).
5. Novice: Separates intuition/"real world" knowledge from theoretical/formal knowledge.
Expert: Has integrated real world with theoretical knowledge.
6. Novice: Not able to "translate" problem statements.
Expert: Able to correctly infer situation from the given information.
7. Novice: Little or no planning before trying to solve equations.
Expert: Develops a definite problem-solving strategy before starting to solve equations.
8. Novice: Not able to construct a physical picture of what's going on, or is unable to recognize when chosen picture is inappropriate.
Expert: Constructs a useful physical picture of the problem.
9. Novice: Does not stop to think of a qualitative answer before starting to solve the problem.
Expert: Uses qualitative physics principles/physical reasoning to have a reasonable answer to the problem in mind before beginning to solve numerically
10. Novice: Focuses on surface structure (physical items involved in problem).
Expert: Focuses on deeper structure (physical laws involved in problem).
11. Novice: Generates several physical models at start, and sometimes shifts models midstream because not certain of correct way to look at problem.
Expert: Develops one model at a time; additional models only are used to check solution of first model, or if first model doesn't seem to be working
12. Novice: Works backward (looks for equation that has the unknown in it).
Expert: Works forward (looks for equations that include the given quantities).
13. Novice: Does not stop to think about the answer that was obtained.
Expert: Stops to think if answer makes sense (checks against qualitative answer)
14. Novice: Spends a lot of time working on problem.
Expert: Solves problem quickly.
15. Novice: Unaware of understanding gaps.
Expert: Recognize when something is not understood.
I gave this to my Intro Physics students, with a note saying, "Your goal as a student should be 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!"
1. Novice: Studies worked examples rapidly, without bothering to understand the examples.
Expert: Studies worked examples until sure examples are understood.
2. Novice: Consults worked examples later in hopes of finding a plan.
Expert: Consults worked examples later to verify that chosen plan is correct.
3. Novice: Subject knowledge is lacking.
Expert: Has a thorough knowledge of subject matter.
4. Novice: Collection of knowledge is a random jumble of miscellaneous facts.
Expert: Collection of knowledge is well organized in person's head: centered around physical principles and hierarchical (topic trees).
5. Novice: Separates intuition/"real world" knowledge from theoretical/formal knowledge.
Expert: Has integrated real world with theoretical knowledge.
6. Novice: Not able to "translate" problem statements.
Expert: Able to correctly infer situation from the given information.
7. Novice: Little or no planning before trying to solve equations.
Expert: Develops a definite problem-solving strategy before starting to solve equations.
8. Novice: Not able to construct a physical picture of what's going on, or is unable to recognize when chosen picture is inappropriate.
Expert: Constructs a useful physical picture of the problem.
9. Novice: Does not stop to think of a qualitative answer before starting to solve the problem.
Expert: Uses qualitative physics principles/physical reasoning to have a reasonable answer to the problem in mind before beginning to solve numerically
10. Novice: Focuses on surface structure (physical items involved in problem).
Expert: Focuses on deeper structure (physical laws involved in problem).
11. Novice: Generates several physical models at start, and sometimes shifts models midstream because not certain of correct way to look at problem.
Expert: Develops one model at a time; additional models only are used to check solution of first model, or if first model doesn't seem to be working
12. Novice: Works backward (looks for equation that has the unknown in it).
Expert: Works forward (looks for equations that include the given quantities).
13. Novice: Does not stop to think about the answer that was obtained.
Expert: Stops to think if answer makes sense (checks against qualitative answer)
14. Novice: Spends a lot of time working on problem.
Expert: Solves problem quickly.
15. Novice: Unaware of understanding gaps.
Expert: Recognize when something is not understood.
# posted by John Colton @ 12:16 PM 
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I really enjoyed this. I've read similar research in problem solving in general--not specific to physics. I use those same principles in my math classes (especially calculus) as well. Do you have a link to the research article you're summarizing?
# posted by 
: 12/03/2006 12:49 PM
: 12/03/2006 12:49 PM
Not a link, but here's the reference: It's from chapter 12 of _Handbook of Research on Science Teaching and Learning_, edited by Dorothy L. Gabel, publised by MacMillan Reference Books, 1994. Hopefully you can find it in a library, because it's apparently not available from amazon.com.
Chapter 12 was written by David P. Maloney of Indiana University and Purdue University-Fort Wayne, is 28 pages long (small print!), and summarizes 79 research papers in the field. These 15 points were my summary of his summary, so to speak--although he had other things in his review article unrelated to the novice/expert issue.
I'd bet some other chapters would interest you as well, but that's the chapter I've read in the most depth.
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Chapter 12 was written by David P. Maloney of Indiana University and Purdue University-Fort Wayne, is 28 pages long (small print!), and summarizes 79 research papers in the field. These 15 points were my summary of his summary, so to speak--although he had other things in his review article unrelated to the novice/expert issue.
I'd bet some other chapters would interest you as well, but that's the chapter I've read in the most depth.
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