Tag Archives: modelling

modphys 29/180: Practicing

I tried a few different approaches to student practice today. First, I had my grade 11 math students create problems with a given answer. They whiteboarded their problems and solution, including a deliberate mistake, and we shared in a group. The deliberate error is useful because it helps to normalize mistakes. By going through the motions of fixing each others’ errors, we accept this process as normal and move pass the emotional charge usually attached to making mistakes.

Next, I had the same class log in to Khan Academy, which I’ve written about before. The website is getting more useful for teachers: I can now recommend exercises for my students, there is a good view to see how students do on individual questions, and the exercises are becoming polished. Today I had the students work on two exercises related to exponent manipulation. Fortunately, the software now runs on mobile devices: it was delightful and strange to see my students pecking away at their cell phones, working through appropriately-challenging problems.

My grade 11 students need a way to pursue individual practice. I have been looking at WebAssign (at least until Stephen lets me use Socratic Brain!), but I’m not particularly impressed. The technology seems quite rudimentary, with limited analytics and a rather poorly categorized set of questions. It is clearly geared toward those big undergraduate physics classes. At USD 10.50 per student, I need to be rather sure of the benefits before paying for student accounts.

What we did during class, however, was to use Kelly O’Shea’s Speed Dating approach to whiteboard problem solving. The students (generally) picked it up easily. It was a pretty good way to get everyone to become familiar with, and more-or-less figure out, a few problems in a short amount of time. The buy-in during our board meeting afterward, when we shared the results, was better than normal.

A common link between these four approaches to practice is instantaneous feedback. There has been some debate about the pedagogical value of instant feedback, especially since the sort of instant feedback that is so trumpeted by Khan Academy and WebAssign is of very little value — being nothing more than “incorrect/correct”. Work during class time, of course, allows for abundant peer and teacher feedback, but this does not obviously extend to homework.

Water Tower Geometry

This year my school obtained a lease on an overgrown orchard adjacent to our back yard. The new land has offered a number of great opportunities for instruction. A disused water tower, located a couple meters past the new rear gate, has piqued my attention this week.

20140923_094622Today, I took my grade 12 math class down to the tower and asked them to determine the height of the small platform you can see near the top. We brought along a meter stick and a white board.


The students decided to think of the challenge in terms of coordinate geometry. They were able to define the problem, draw the indicated line, and outline a solution: determine the equation of a line-of-sight between someone on the ground and the platform. Unfortunately they got stuck at this point, and I needed to remind them that they could use two points to define a line — that was enough for them to establish a procedure whereby one sighted the platform while sitting, and another moved about until the top of her head was in the line of sight of the sitting student.


The students took characteristically incautious measurements, so I went back and re-did the experiment myself. Here is a photo from my attempt.


I found a height of about 20 meters, which jives with my expectations. I’m looking forward to returning to the tower after a forthcoming unit on trigonometry to see if the students can do a better job using angular measure. I might even get them to use my sextant…