There have been several benefits to changing the order, though:
- the oscillation graph analysis seems to come just after they cover it in Pre-Calculus, so that saves me a lot of headache
- I can add motion analysis (where's the acceleration the highest?, find the max v from the position graph, etc.) that I couldn't do before
- the reasoning goes down better after they've done a lot of it in CVPM and CAPM, even though it should've been better to start with the easier reasoning here. It probably has something to do with their familiarity with speed vs. their unfamiliarity with period
Another benefit is that I can put together a robust practicum that uses both CAPM and OPM:
- On the day, I will set up a ramp of unknown length. There will be a pendulum at the end, oscillating perpendicular to the track.
- I will let them observe the pendulum in motion.
- I will demonstrate for them, three times, the cart starting at rest at the top and traveling freely to the bottom. I will tell them the length of the track.
- I will assign each group a number of oscillations - the pendulum must complete this number of oscillations between the time the cart is released and the time that the cart gets to the end, and the pendulum must collide with the cart as it reaches the end
- They need to have a procedure ready to determine how far up the track the cart needs to be released in order for these things to happen.
I let them work for a couple of days in groups, with a pendulum and a 1.2 m cart track. They need to develop and test their method so that it can work in any situation that I give them.
I give them a packet with several pages: one for outlining a plan of attack (which they need to revise, if that plan changes), and several pages for completing each sub-task. Identifying that they need to determine how long the cart will have to travel, and that they need to measure the period of the pendulum and use the given number of cycles to find that time, is one example of a sub-task here.
Students tend to be bad at laying out an abstract 'path' through a problem, especially if there's unknown information there. It's a tricky issue to tackle, but requiring these kinds of tasks of the students is certainly part of the equation. It's basically the same thing that I'm trying to address with the chains of reasoning exercises.
I laid out that structure on the first day, and students jumped into the problem at different spots, and most figured out a couple of sub-tasks at least. There was a lot of average velocity vs. final velocity confusion, as is typical for these students. On the second day, I had them start by writing out a list of the sub-tasks that they had identified - this is the "flow" of problem-solving that I'm trying to help them with. Most were good at this point, even though most groups hadn't figured out how to accomplish all of the sub-tasks yet. Here are the summary boards: interestingly, the first section was able to parse the task very well, but the second section had a great deal of difficulty understanding what the task was, which numbers were measurements and which were calculations, which variables explicitly affect their calculations (and should be measured, like the amount of time for the cart to go down the track) and which implicitly affected it (like the angle of the ramp, which affects the acceleration, but which doesn't appear in their calculations).
For the practicum itself, I'm using my 5 meter (!) air track :)