I want to explain in one post the rationale and requested format for the mandatory quiz problem revisions in physics.
I view these revisions not merely as a second chance to obtain the correct answer to a given problem. If that were the chief goal, I wouldn’t ask every student to submit a revision, since many students had the right answer the first time! Instead, I hope you gain two main things from the revisions:
- A deeper understanding of the logic behind your solution; in particular, the revision opportunity asks you to take time to think about why particular mathematical or physical principles apply in a given problem, and how you know that it does.
- Practice in clearly communicating physics to others in writing. On a quiz, few of us can take the time to present our work as clearly as we would like. The revisions will come closer to how one might present work in a real-world setting, such as a technical meeting on a science or engineering project or in a research notebook or publication.
To give a brief sense of how I see the difference between quiz work and revision work, this example from a mathematics instructor at Berkeley may be informative:
You’ll notice that while both are examples of correct answers to some mathematics problem, in the first version it is hard to discern what the problem was, or what the problem-solving logic was. In the second version, the meaning and context of the problem emerge. We know why the writer of the solution took the steps that they did. Some manipulations occur without commentary, but even they are presented in a step-by-step fashion that one can readily follow.
The Physics Quiz Revision Assignment
Your quiz revision should be started on a fresh sheet of paper. I will ask that you use the IDEA problem-solving strategy (see Problem Solving Strategy 1.1 in the first chapter of Wolfson (p. 10 in the 3rd Edition). This entails including, in order, and explicitly labeling four steps:
- Interpretation of the problem – clearly identifying what information is known, what is asked for, and assumptions, laws and principles will likely be employed.
- Developing a solution. Usually this means drawing one or more diagrams, writing algebraic equations that embody the assumptions, laws and principles that apply (along with brief justifications)
- Evaluating the solution. Here you will draw on the equations you have identified (and possibly supplemented along the way by well-known math results like trigonometric identities, the quadratic formula, etc.). I will ask that you refrain from plugging in numerical quantities until you have fully solved the algebra for a given variable – in other words, if you’re finding x you should try to get to an equation that looks like “x=(some stuff)” before you start substituting values for variables, if the problem calls for a numerical value. (This is usually – but not always! – mathematically possible in a physics problem.)
- Assessment of the results – does the solution make sense (magnitudes reasonable, units correct, etc.)? Suppose one considered special cases where a variable gets very large, or very small (perhaps going to zero) – does the symbolic answer you found behave in the way you would expect? Your assessment should be a critical examination of your previous work – actively look for flaws! In particular, you should demonstrate by showing any cancellations explicitly that your units are correct (rather than simply asserting that they are).
More details
Intermediate steps should be logical consequences of previous steps. If you are going to divide by two and/or move a term from on side of the equation to the other it is sufficient to write the new expression on the line below the previous expression without comment. Nontrivial steps require an explanation. If two adjacent expressions are equal, they should be connected by an equal sign (=). If two adjacent expressions are NOT equal do NOT connect them with an equal sign (=).
If you use an equation from the text, your notes, or another reference, you must document it. Equations should not materialize out of nowhere! In addition to giving the reference for an equation, state why the equation is relevant to the situation at hand.
When you use equations from mathematical tables, show any steps necessary to get the equation in your homework to look like the equation in the table.
All quantities should have units! Keep track of your units and show your conversion factors. Answers without units are usually meaningless (occasionally a dimensionless quantity may be asked for, such as a ratio of quantities with the same units, but this is an exceptional case).
Finish each problem with a concluding statement or paragraph (Assessment). What is the final result? How does it relate to the original question asked? What did you learn from this problem – an application of a theory, a sense of the magnitude of a quantity, a math trick, etc.? Put numerical answers in context (Is this a big number? A small number? Relative to what?). You should also mention useful problem solving details that were illustrated. Use the conclusion to bring yourself to a new level of understanding about physics, its application to real world questions and/or the problem. It is your job to use the language of physics and mathematics in a clear and precise manner to demonstrate your mastery of a problem. Remember – the most important reader may be you reviewing for an exam!
Scoring: Each problem will be scored on a 10-point scale. Each of the four steps in the problem-solving strategy receives a separate score on the following scales:
- Interpret 2 points
- Develop 4 points
- Evaluate 2 points
- Assess 2 points
Note that an otherwise perfect answer with no evaluation would receive only 8/10; be sure to comment intelligently on your answers! Notice the heavy weight on the early steps. That’s where the physics lies. So for instance, if you only make algebra mistakes, come up with an incorrect answer but notice that something is awry and tell me how you know there must be an error, you would earn either 8/10 or 9/10.
Example problem: