What is a fundamental, anyway?

So, about a bobzillion years ago, I prepared my class for their first test.  I offered to allow them to use an equation sheet of their own design.  Oops.

These honors students, who were well versed in memorizing but not so well trained in physics reasoning, wrote down every equation in their book.  Including intermediate steps in a derivation; including the solutions to example problems.  No wonder they were confused on the test.

I still sometimes get tripped up in differentiating between what is a fact to memorize, and what is a problem solving process to be learned.  For example, velocity-time graphs are so common that we should simply memorize the physical meaning of the slope and area.  A separate "fundamental" skill is to figure out the meaning of an unfamiliar graph's area.

It's a fool's errand to memorize every possible graph that might be made.  The fact to memorize is "multiply the quantities (not the units) of the axes, then use an equation on the equation sheet to relate the quantities."  So a force vs. time graph has an area that means impulse, because an equation says that impulse is FΔt -- NOT because I can instantly recall "force vs. time graph, area = impulse."

In my senior honors class, I gave a 20 minute, cumulative fundamentals quiz.  You can see the original quiz at this link.  Some folks did quite well... but as you might expect, I had a number of students for whom the questions "just seemed to run all together."

Part of the issue for the lower-level students was the sheer quantity of material.  But another part, one that I too often underestimate, is that some of the questions I'm asking require a step of reasoning in addition to memorization.  When I teach freshmen next year, I'm going to have to differentiate better between fact and process.  For now, though, I need to get all my seniors stone cold solid on these kinds of questions, even if they do require a quick thought.

I've been observing my colleague who does teach freshmen.  He's been making the students write, in their own handwriting, some basic facts of physics.  He gives a fundamentals quiz the next day on which the students can use their notes.  Then he gives ANOTHER quiz the next day with the same material, but with no notes allowed.  He's found that even though it takes several days longer to present material, problem solving skills can be developed far more quickly and correctly.

On this quiz, then, I took a cue from this colleague.  I handed out this document which contains detailed discussion of the answers to this quiz.  I offered another quiz, on which handwritten notes were allowed, but on which students must spit back my detailed discussion WORD FOR WORD on the questions they originally missed.  My hope was that the process of writing the solution in their notebook, and then rewriting on the quiz, would help their memorization issues.

But I also hoped to help differentiate between facts and processes.  On one hand, students can see that "the force of a spring is given by kx, where k is the spring constant, and x is the displacement of the spring from its equilibrium position."  That's a fact.

On the other hand, students can write, "Total power dissipated by a circuit is the sum of the power dissipated by each resistor, no matter how the resistors are connected.  So two resistors in parallel that each dissipate 100 mW will dissipate 200 mW total."  I've started by stating the fact; then I've applied the fact to a specific situation.  Hopefully, next time my students are asked to find the total power dissipated in a circuit, they won't add the power dissipated by parallel resistors inversely.  :-)