Does every student need to do the same number of practice problems?
Early in the year, yes. Even the best students need practice. Even Allen Iverson needs practice. And the top students gain confidence not just by doing their practice problems well, but also by helping their classmates. The not-top students gain confidence by occasionally being right when the top students are wrong.
But as the year wanes? Especially now, in Pandemic Times? Awarding exemptions from practice problems can be a powerful incentive to students to take their work more seriously.
It's not the doing of the practice problems that develops physics skills - it's doing the practice problems carefully. Even, especially, incorrect practice problems can help students learn physics. But only if the student's incorrectness was born of a misconception, not of laziness or fatalism. And only if the student cares about being correct.
When my students are all living together on dorm, when they can come to my classroom to work together the night before a problem is due, then it's easy to convince students to put forth serious effort on each problem. The incentive isn't the grade - the incentive is, no one wants to see their name on the board. The name on the board means to come in during an assigned free period to redo the problem. It's not a punishment, but nevertheless... students work carefully the first time so that they're not likely to have to visit me for a second bite of the apple.
I can't use the name-on-board incentive method when we're online. And since the students don't have in-person contact with any of their classmates, they don't work together; they don't incentivize each other through their presence.
So, I've taken to exempting students from the next assignment if they do well on today's assignment.
Aren't these exempt students missing out on important practice? Maybe. Perhaps they are. But is it really *important* practice for someone who's shown they can do the previous problem perfectly or near-perfectly? I think a lot of teachers, parents, and students take it on faith that more practice is always better. I disagree. It's okay to let a student earn a break.
It's early March. I already know which students care about grades and which don't, which students tend to get problems done for the sake of being done rather than for the sake of understanding the material. These folks have already shown that the incentive of a job well done, the incentive of a high grade, isn't important to them. So I need a different incentive.
I've seen students suddenly, for the first time all year, show tremendous effort, skill, and willingness to collaborate when they know that good performance will get them out of future work. It's not a good idea to shame these folks with "you know, if you worked that carefully on every assignment, maybe you'd be doing better in this course." They know. Rubbing their noses in it is condescending and counterproductive. I just congratulate such students on their exemption, and move along.
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