I spent a large fraction of last week marking assignments. I’m currently teaching three different papers, and, due to a major lack of concentration on my part, I managed to set each class an assignment that was due on the same day. To be useful for students, assignments need to be marked rapidly, which meant I suddenly had a hundred scripts to race through.
When I set an assignment, I often throw in a not-very-obvious-at-all situation for students to think about. The idea is to get them to think through what they have learned and how it applies in a real situation. In that way they can get to grips with how a piece of theory actually works and I can see whether their understanding is along the right tracks.
I good example of this came out of the second year quantum physics class. We had been talking about Heisenberg’s uncertainty principle, (also see the nice movie here) and rather than set them a straightforward question along the lines of "if I measure the position of something to an uncertainty of xxx, what is the minimum uncertainty to which I can know the momentum?", which basically tests their ability to stuff numbers into a formula and use a calculator, I set this curlier problem:
"I’m driving along a straight road, and go from a 100 km/h speed zone into a 50 km/h zone. I don’t slow down quickly enough and, unfortunately for me, there’s a revenue-gathering traffic cop hiding behind a bush 20 metres into the 50 km/h zone. He clocks me doing 61 km/h. Being a physicist, I try to wriggle my way out with the following: ‘By Heisenberg’s uncertainty principle, it is impossible for you to know exactly where I am and my momentum at the same time. If you’ve clocked me at exactly 61 km/h, that means you have specified my momentum exactly, and therefore cannot say anything about where I was. So, I might still have been in the 100 km/h zone, in which case I wasn’t speeding.’ Is my argument valid?"
This got some interesting answers – nearly all said my argument had to be invalid, though some had difficulty in pinning down why. From my point of view, as the teacher, this question worked really well in flushing out exactly what the students made of the uncertainty principle, and identifying misconceptions. For example, several students incorrectly believed this was to do with relativity -that the principle only applies when things are moving close to the speed of light. Another popular thought was that the principle only applied to elementary particles, such as electrons. By seeing this incorrect thinking, I was able to talk about it in a subsequent lecture.
So this question, in fact, worked really well – helping not just the students but also me. Next time I teach this stuff I’ll be wiser to what the students might make of it.