I am an early adopter. In terms of teaching this generally means trying new technologies or methods that I believe will increase student learning and/or engagement.
This year I stumbled upon Modeling.
I have been using data as a significant part of my Physics class for years now, which is probably why Modeling appealed so much to me. However, I lacked the interconnectedness that the specific Modeling Instruction program brings to physics curricula. This year I have been learning through blogs (mostly Kelly O’Shea, Frank Noschese, and Scott Thomas), but I have applied for the official training this summer (very excited!).
Not that lack of training will stop me from trying things out.
I teach a class called College in the Schools (CIS) physics, which really is University of Minnesota Physics 1101 taught at the high school level (they get a U of M transcript and everything). I currently have 3 sections with 15-19 students in each section.
We are currently starting Momentum after having already covered Energy. After reading a recent post by Kelly O’Shea, I decided I could ditch 1-2 days of lecture in favor of 3-4 days of modeling to introduce momentum. I modified what Kelly did to meet my needs; 1) my students have not had the strict background in modeling, 2) I don’t have computers available in my room, but do have Labquests with a variety of probes as well as access to a computer lab for video analysis as long as I reserve it around a month in advance (really). Kelly left this wide open, but I told students that graphs and linearizing is less useful here, guiding them to look for a pattern in the numbers themselves.
I started by showing students a collision where a moving cart collides with and and sticks to a stationary cart with the same mass. The goal is to ‘figure it out.’ I gave a bit of guidance on what may need to be measured through questioning the students; they identified initial and final velocities, I generally pointed out mass as well. Then I set them loose.
From there most groups figured out quickly that the final velocity was 1/2 the initial velocity. I liked starting this way because it forced them to think about the final velocity in terms of a ratio (which was a by-product I had not originally intended, but clearly it worked out well).
I then prompted them to think about what happens when the masses are not equal by first adding mass to the moving cart, then to the stationary one. Ooos and Ahhhs were heard when they see the effect is very different depending on which cart has mass. As I walked around observing and asking questions I overheard some great thinking; “The final velocity seems to be about 1/3 the initial. I bet if we switch the mass bar to the other cart it will be 2/3.” “I figured the masses had to form some sort of ratio, so when the 1/3 part worked I just ran with it.”
Many of the groups needed to be prompted to turn their ideas into a mathematical model, but we have done enough modeling where it wasn’t difficult. By the end of the class most groups had figured out something along the lines of
This is mathematically equivalent to the first equation, though I didn’t know that for sure at the time. The group had dropped the negative (as they simply were looking at the pattern of how the (absolute value of the) velocity changed), and the pattern was working strangely well. I had them converse with another group who had quickly come up with the first equation to ‘duke it out.’ They ended up showing algebraically that the representations are equivalent, which was pretty sweet, and they were excited about it. I will be pointing out the not-really-correct use of delta v tomorrow.
Some of the groups got to the point above with around 10 minutes left in the 48 minute period; if so I showed them a simple collision where the carts bounce with magnets and simply stated ‘go.’ This is what we attack tomorrow, but they now have no choice but to think about it tonight.
Data summaries were put up along with any models, thoughts, or other relavent information.