Problem Solving:
Students often feel like there is a unique technique for solving each type of problem they encounter in physics or any other calculational class. This can lead to loads of anxiety when confronting a problem of a kind one doesn't recognize. It's helpful to note that there is a pretty general approach that is used by successful (expert) problem solvers. This version of the process is typical though you can undoubtedly find many variations.
A: Framing:
Visual Representation: a basic sketch of what is happening, the important quantities (forces, velocities, masses, energy, etc) and what you are solving for.
Relevant Concepts: possible physics concepts related to setting
Similar Problems (this is an internal discussion): past problems that may be relevant
Assumptions and Simplifications: Details you are explicitly neglecting
Information Needed: Values stated in the problem and other values you might need to look up or estimate
B: Planning:
Solution Plan: a rough outline of pathway
Rough Estimate: What do you expect the answer to be - reasonable, maximum, minimum - and why?
C: Execution:
Carry out your plan (adjusting as needed): Plug numbers in a very LAST step.
Check Units: Beginning, middle, and end
Clearly Indicate Result(s): Box or underline clearly.
D: Answer Checking:
Compare to Estimate: If different consider where the error may be - result or estimate.
Limits Test: Look at dependencies in your result. When an input value increases does the result increase or decrease? Does that make sense? Are there extreme angles or masses that lead to predictable outcomes?
Units Check: Double check units of result and that they arise from units of calculation.
Getting (Un)stuck: If you didn't reach a solution can you explicitly identify where you got stuck?
Samples of Student Work:
Here are some anonymous example of good student work. There are some aspects which could be clearer but the intention of the students is clear and on track. These are all pdf's.
Engineering Courses: Required Solution Format
For reference the above is linked to the required format for solutions in most engineering courses.
This version of the expert approach to problem solving is very much the same though it uses slightly different language [my thanks to the Physics Dept at WVU for this article which they published without attribution].
Steps in the Expert’s Approach
The order of these steps is purposeful. The earlier the step, the more critical. For example, you cannot “plan a solution” when you do not have a “clear mental image of the problem.”
1. Focus on the Problem. Establish a clear mental image of the problem.
A. Visualize the situation and events by sketching a useful picture.
B. Identify physics concepts and approaches that might be useful to reach a solution.
C. In your own words, precisely state the question to be answered in terms you can calculate.
2. Describe the Physics. Refine and quantify your mental image of the problem.
A. Draw any necessary diagrams with coordinate systems that are consistent with the approaches you have chosen.
B. Name and define consistent and unique symbols for any quantities that are relevant to the situation. Consistency here will avoid problems later.
C. Identify the target quantities that will provide the answer to the question.
3. Plan a Solution. Turn the concepts into math.
A. Construct specific equations to quantify the physics concepts and constraints identified in your approach.
B. Outline a plan either leading backwards from the target quantities to quantities that are known,or leading from known quantities to the target quantities.
4. Execute the Plan. This is the easiest step – it’s just the algebra/calculus/etc.
A. Arrive at a formula for your target quantities by following the solution steps.
B. Check the units of your final formula before putting in numbers.
C. If quantities have numerical values, substitute them in your final equation to calculate a value for the target quantity.
5. Evaluate the Answer. Be skeptical. Ask yourself what a wrong answer would look like.
A. Is the answer properly stated as an answer to the question you identified?
B. Is the result reasonable?
C. Is the answer complete?
We will modify this framework as we go along if needed.
