NYC Modeling Workshop: Day 6

Commuting rather wrecked my brain last week. I don't know how people who commute over an hour every day stand it: there's no time left for anything else, and attempting to shoe-horn in homework after hanging out with my daughters left me severely sleep-deprived. I'm going to try to do homework on the train this week, which might work better than doing homework on the bus last week. (Not that that's difficult, mind you, since drawing graphs on a bus is practically impossible.)



Today, started out whiteboarding CAPM worksheet 3, skipped Free Fall on Planet Newtonia, and then whiteboarded worksheet 4. Motion maps are still a bit problematic for some of us, so we talked about different ways to construct , check, and read them, including:

• how to represent the instant of zero velocity when an object turns around
• how to handle the last position
• how to relate a motion map to a position-time graph (thinking of the motion map as the shadow/projection of the graph, thinking of stretching the motion map out to make the graph)
• how to relate a motion map to a velocity-time graph (laying velocity arrows from time-axis to velocity-line)

We also talked about extensions, either for differentiation or for AP classes, including goalless problems, Jeopardy problems, and "Tell me a story that matches this graph/motion map." Students, especially "good students," aren't used to being asked for the imagination required to tackle the last two, or the lack of direction provided by all of them. Which just makes them more useful to get students to think deeply about the concepts.

After that, it was time for a new unit, which meant a new seating arrangement. Everyone continued moving in the same direction, giving us entirely new groups again. I'm not sure how practical this method is for high school students, but it works for adults...

Mark pointed out that this is our first "causal model": the first model to deal with "what causes x?" rather than "what is x?"


The paradigm lab for this unit is the bowling ball race/activity/obstacle course. It's less clear-cut than the first two, with no measurable data to be taken. I'm not sure what I think of that, given the pattern established in the first two content units of asking "what can we measure?" to tease out the important factors. Trying to get a fifteen pound bowling ball to change course abruptly is certainly a good way to get a feel for inertia, but it feels less lab-like with no measurements. We discussed using alternate materials for large classes with insufficient space or bowling balls/brooms for every group of three students. One possibility is using whiteboards instead of brooms. Another is making a pair of relay obstacle courses and dividing the class into two teams that get to strategize while waiting for their turn. A third possibility is using some of the classic Newton's First Law demos as stations alongside the broom-ball activities.


Trying to talk about what students found out during this activity leads to the need for a diagram of the forces involved, which lets us introduce FBDs as conventional diagrams. We talked about brainstorming types of forces and the conditions under which they occur (e.g. friction only happens when objects are pressed against each other), as well as the need to have both an object acted on and an object acted by. (I'm not entirely clear on how to get students to grasp that forces always involve an interaction between two objects other than simply stating it, but I'm okay with letting that slide for a little while.) 


We talked about leading students from the broom-ball activity to a first understanding that balanced forces mean no acceleration and unbalanced forces lead to acceleration. Mark jumped straight from the broom-ball discussion to talking about the vertical forces and expecting that there has to be an upwards force. I think that's a bit of a big jump. I think I'll pose it as a question to my students ("Is there an upward force on the bowling ball?") and use the repeated polling and demos described in the Minstrell article on the "at rest" condition to get the class to agree on the need for an upward force, but only after talking about (and demo-ing) the balanced condition of two brooms acting on the same ball, both at rest and in motion.


After that, we talked about system schemas/diagrams. Dan L suggested using dashed lines to represent non-contact forces in system diagrams, which I like because it gives us another check on the correctness of our diagram. Several people pointed out that we can start a system diagram without having decided what's going to be at the center of our FBD(s), which makes them useful for the "I don't know where to start" students.


Most important take-away (again): Nothing is as simple for a novice as it seems to an expert. In this case, motion maps and the forces involved in an object sitting on a level table.


Incidentally, I know these posts are at/near the lowest level of Pappas's Taxonomy of Reflection. I'm hoping practice helps.