Night and day

After all of the smack talk about grading I've laid down in my past few posts, I have to admit that I really enjoyed responding to the students' work on which I was working today.

Today's task was to give feedback to the students on the "application miniprojects" on which we'd worked in class for two days late in the last week of October. I'd made up three handouts, each of which led the students through an application of derivatives involving differential equations. One concerned terminal velocity, another population dynamics, and a third capacitance, current, and charge in a simple circuit. I made only the slightest effort to clean up the computational details, making sure to leave some messiness for the students to deal with as they solved the problems placed before them. (I wanted them to see some at least marginally unprettified problems stemming from realistic applications.)

Working in groups in class, the students were asked to complete one handout apiece and then put together a fairly extemporaneous informal presentation on their solution. Those presentations were solid, especially considering the students hadn't prepared much at all. They were then asked, for this past Friday, to complete two of the three handouts neatly as part of their homework for the week.

With no solutions manual to fall back on (they'd only whatever notes they'd scrawled during their peers' presentations to help them out), the students' completed handouts offered authentic examples of their work. They made mistakes, obviously, but the mistakes were real and understandable ones, not like the odd transcription errors that show up when a student is sloppily copying straight from a manual or from a friend's superior solution. (A tip to those of you who rely too heavily on the manual: when you begin a problem on your own and get stuck, ending your work in a messy pile of erroneous figures...yet somehow in the next line the correct answer magically appears after a logical lacuna the size of Texas, I'm liable to suspect that you didn't do the whole problem yourself.)

When the students failed in these handouts, it was because they honestly miscomputed a derivative, and didn't simply miscopy it. Or it was because the wording of their interpretations were clumsy, and not because the interpretations were offered in the stilted technical language peculiar to textbook authors.

In short, without the solutions manual, they really honestly had to do this homework. It was a refreshing experience to respond to them.

I'm going to ask them how they felt about it. Similar assignments could serve as a stepping stone towards a more outcome-based course, something I could reasonably put together for next Spring's Calc II courses. I envision suggested (but optional) textbook problems for computational practice, coupled with weekly handouts challenging the students to apply the principles discussed in class. These handouts could be the basis for in-class presentations, just as were the handouts from two weeks ago.

We'll see. I'm going to get the students' take on these handouts soon.

Further bulletins as events warrant.