Followup: Three years later, what do conceptual students remember about circuits?

In 9th grade conceptual physics, we teach circuits without calculators.  Rather than asking "determine the voltage across each of these series resistors", we ask "estimate the voltage across each" and "rank the resistors by the voltage across each."  We don't allow direct calculation to answer these questions.

Rather, we expect a semiquantitative use of ohm's law, combined with instincts developed in laboratory.  I describe my class's Zen methods in this post.  

Those students who learned circuits conceptually now make up half my AP Physics 1 class.  Can the former conceptual students handle circuits problems in which actual computation is necessary?  Can they deal with more complex circuits than straight-up parallel and series resistors?  Can they describe their conceptual understanding in language appropriate to a college-level examination?  Yes and yes and yes.

In the freshman class, I hand students a page with circuits facts written on it.  (Scroll down on the linkned page to see the facts appropriate to circuits.)  By the second day of the unit, students are using the facts to predict voltages and currents for series circuits.  We do no lecture, no "going over" the facts.  Why not?  Because freshmen wouldn't pay attention anyway.  The class gets in the habit of reasoning based on facts, not of mimicking a teacher's steps.

Freshmen do very well with open-ended "here are some new facts, now figure out how to make predictions with them."  However, I learned the hard way that seniors generally do not.  They expect you to show them what to do, and get pissy if you expect them to use information you didn't "go over" -- even if that information is the first bold line on a sheet you handed them. 

Nevertheless, since half of my seniors had seen circuits in 9th grade conceptual physics, I thought I'd try the open-ended approach.  I was taking a twofold leap of faith:  (1) I hoped that the conceptual veterans would have enough familiarity that they weren't flummoxed by more complex circuit problems, or circuit problems requiring calculation; and (2) I hoped that there was enough comfort with the concepts and with the equipment that the conceptual veterans could provide leadership and advice to those who were completely new to circuits.  

This time -- thank goodness -- my faith was rewarded.  

I handed out the AP version of my circuits exercises, the version that includes series-parallel combinations.    Everyone worked in a relaxed manner and at a similar pace.  Information passed smoothly throughout the class -- when I gave advice to one student, I found that I rarely had to give the same advice to others.  

The conceptual veterans recalled rather quickly the subtleties of straightforward series and parallel resistors.  They easily helped the others make their predictions and set up their circuits.  The team atmosphere we built in the freshman class paid its dividends, as the conceptual veterans assumed -- without suggestion from me -- the roles of tutors and facilitators.  Even the students who had never seen circuits at all moved along at the same pace as most of the class.  Even the student who was new to circuits and was absent the first class picked up the process quickly.

Did anyone struggle now that we included calculation, now that we included combination circuits?  Not at all.  Sure, I had to show two of twenty students how to deal with the combination circuit.  The rest either figured it out for themselves, or were taught by one of the folks I helped directly.  

I'm on my fourth attempt at teaching AP Physics 1-level circuits.  And this is by far the smoothest introduction I've had.  I'm ready now, after a week of class, to discuss the deeper language and tougher situations that AP Physics 1 requires.  Most everyone can already accurately fill out a VIR chart for a simple circuit.  I can focus on the whys and hows.

In other words, teach eighth, ninth, or tenth graders about circuits, but conceptually.  The very basic three-week unit we created has paid off tremendously in my AP Physics 1 class, even though the unit was three years ago, even though we never used a calculator. 

And I remind myself how important the work I do with freshmen is.  I'm planting seeds with them... seeds that I usually don't get to see germinate.  But germinate they do.