Navigating Uneven Lanes
On the road, when you come across this sign you immediately begin assessing your choices: Which lane is the safest to navigate? Should I straddle the two lanes? Will I be able to go back and forth between lanes safely if I have/choose to?
I’m responsible for sections of calculus-based and algebra-based physics in the same semester this year. While these are two different tracks of physics to begin with, a theme I’ve noticed is that there are distinctly different yet analogous levels of preparation in each section. I suppose this is generally the case, but a quick non-official poll of math/physics background at the start of the semester and some early after-class discussions with students really brought it to light.
These are the uneven lanes of the physics classes physics of my current sections:
- Students taking algebra-based physics who are also in calculus or have AP high school physics experience . . . as compared to others who took college algebra years ago with little to no high school level physics.
- Students enrolled in calculus based-physics who completed algebra-based physics and/or calculus I & II the previous year for preparation . . . as compared to those who are just now learning the meaning of a derivative and have not yet taken any physics.
I don’t think this is anything too extraordinary. But it begs the question “How do you make course content accessible, meaningful and challenging across differences in academic demographics?” Maybe more signifiant: “How do learners respond to the varied academic demographics of their peers?”
Should we choose one lane only?
Should we attempt to cater to both?
Can we switch gears every so often without creating problems?
Something I’ve started doing after asking a whiteboard question and following a class discussion is quickly scanning them as I collect them in a pile. I hand pick a few to fuel the discussion a little further. Of the boards I pull aside, I make sure to select one or two that are not as well developed as the others. The purpose: emphasize what worked even among students’ responses that may have been more limited. This alone won’t bridge the gaps. But if students can see the value in their efforts, even if they are only emergent, then they are more likely to want to contribute more–despite the uneven lanes across their colleagues’ levels of preparedness for the class. It can also be eye-opening for students to see
Another thing I do is discuss derivatives in the algebra based physics course. Not at length, but enough to offer intrigue to those who have taken or at least heard of calculus. Care needs to be taken though–some students get awfully nervous when you spend time in class on math that is beyond the scope of the class. I like to think this demonstrates how equations in physics come from someplace; that they didn’t just appear one day as formulas for mortals to memorize. All that said, I don’t get into the calculus very often. Like switching lanes on an uneven road: if you switch lanes too many times, it can get uncomfortable and/or unsafe.
So there you have it. A somewhat scattered post about a couple ideas regarding straddling the lanes of levels of student preparation. To be honest though, I don’t think these are very brave or innovative — I’m more curious how others address uneven lanes in their classrooms . . .