Tuesday, July 17, 2012

NYC Modeling Workshop: Day 7

"Imagine you couldn't give the test at the end of the unit, but had to wait until a year later. What would you teach, and how would you teach it?" Mark Schober started us out today with that quote from a sponsoring professor from another workshop. I don't know about you, but I don't think I'd teach the way I was taught. Sure, I remember some ideas from my high school physics class, but a) I was really interested and b) I've used those ideas quite a number of times in the decades since.

After whiteboarding worksheets 1a and 1b, with more detail than any high school class would sit still for, we plunged into the weight/mass distinction. Not in so many words, of course, since we're focusing on introducing ideas before names. Instead, Mark (or Craig, I don't remember who did which part of today's festivities) put a pair of seemingly identical boxes in front of a 'student' and asked if he could determine which one had "more stuff in it" without picking it up. After pushing it with a finger, he confidently stated that one box had more stuff in it.
"How do you know?"
"It was harder to move."
"How can you tell?"
At this point, I think frustration and attempts to guess the magic word that would satisfy the teacher began. I'm not sure exactly what a good answer is, since the student in question didn't use "force" or "accelerate." I'm not sure if he said anything about pushing harder to get it to move, but we did establish that his thumb bent further (but didn't change color) when pushing the "more stuff" box than when pushing the other box. After a few rounds of attempted clarification, the student was asked to shake the boxes back and forth rapidly. Everyone agreed that there was a difference in the motion of the boxes and that the "more stuff" box didn't shake as quickly. This idea was reinforced by thinking about (and asking another student to try) shaking a bowling ball back and forth.

We pointed out that we hadn't defined "stuff," and Craig explained a lab or demo (I'm not clear which) in which students use an inertial balance to determine masses. I've actually never used an inertial balance, so I was a little disappointed that we didn't get to do this lab and instead had to make do with a triple beam balance to find out "how much stuff" is in an object. Since the normal method of determining which box contains "more stuff" is to lift it (or open it, but that's cheating), we also used a spring scale to figure out how strong Earth's gravitational force was on each object. My group used a mostly empty water bottle, a full (1L) water bottle, and my cell phone, which gave us a nice range of values. Asking each group to take data on three objects and then using LoggerPro to graph and fit the data, we came up with g=9.799N/kg (which is pretty awesomely close to the standard accepted value).

Mark then asked us to write the equation for the best fit line and to explain the meaning of the slope in words. People came up with a range of statements with varying emphases. While the best fit line had a (tiny) non-zero y-intercept, we were all pretty much convinced (and thought students would be convinced) that the y-intercept ought to be zero by reasoning about the situation in which nothing is sitting on the balance or hanging from the scale.

We then leapt into worksheet 2, defining normal force (a contact force between two objects that would squash a mini-marshmallow placed between the objects) and wrestling with Newton's 3rd Law without appealing to authority. It's hard to explain why the force the monitor exerts on the desk is the same as the force the desk exerts on the monitor without falling back on "Newton said so!" Finally, we decided that the simplest explanation is a combination of reasoning through the question "Can I touch you without you touching me?" and looking at the interaction diagram/system schema and noticing that both forces are represented by a single line, which could be argued has a single magnitude even if it has two directions.

I wasn't very satisfied with that, and I can imagine students being dissatisfied with it, but! Mark then pulled out two bathroom scales and demonstrated how we could test the stacked situation. That was more convincing. Even better was the demo with wireless force probes and graphs projected onto a screen everyone could see as we tested first the constant velocity and then an attempt at the constant acceleration situations. Seeing the messy, but clearly mirror-image, graphs was really satisfying.

Note for the future: 
In the past, I've asked students to translate between different types of graphs, between written descriptions and graphs, and between graphs and force diagrams, but I've only asked them to take written descriptions and create interaction diagrams (formerly known as system schemas). Next year, I think I'm also going to ask students to translate interaction diagrams into plausible stories.

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