Tuesday, July 10, 2012

NYC Modeling Workshop: Day 2

I confess I was late to class today. In my defense, I'm not in charge of NYC buses or traffic on the George Washington Bridge (just in case there was any confusion on that point). So I missed the lead in to the whiteboard meeting discussing the Measurement & Graphing station lab. Fortunately, I didn't miss the discussion itself.

We talked about questions to ask students:
  • What are possible sources of error (one of my lab partners tells his students that "human error" is a bad word, and writes it as "h***n e***r")?
  • What physical interpretation(s) of parts of the graph (axes, slope, zeroes [we skipped area underneath, which doesn't have a physical interpretation yet]) make sense?
  • What units apply to anything and everything?
  • Could they predict something based on their results? (require it if time permits, or use it as a challenge for students faster than the majority)
We discussed the payoff in having students plot the final equation on the original axes, and Joe Kremer sent out instructions on how to get LoggerPro to do that. We also discussed how to handle groups that get garbage as data: either have 'spare' data (say from our own trials or another class) or have them analyze classmates' data.

We then whiteboarded and discussed worksheet 3 (and a little of worksheet 2, because we have 8 groups and worksheet 3 only has 7 problems). The emphasis was on discussing the reasoning behind the answers given, rather than giving them a stamp of approval. (Mark Schober has a spherical cow stamp, but it's for homework completion, not correctness.) There was also some discussion of sentence frames/stems for interpreting aspects of graphs and writing graph titles/lab purposes:
  • With zero independent variable, description of physical situation at y-intercept. ("With zero mass, the water needs 3.4s to travel 1.5m.")
  • With each additional independent variable unit, physical interpretation of slope. ("With each additional kilogram, the water needs an additional 2.6s to push the rock 1.5m.")
  • Effect of independent variable on dependent variable in context ("Effect of mass on time needed to travel 1.5m")
  • To study the relationship between independent variable and dependent variable in context ("To study the relationship between length and period for a rubber stopper pendulum.")
The discussion got tangled around the question of whether the equation of the linear test plot describes the original graph as well, with a disagreement about what "describes" should mean in this context. Mark's explanation that the "test plots move the 'curviness' from the points to the axes" really stuck with me. I think I will use that when I talk to students about the equations and the graphs.

We wrapped up the morning with a reflection on the McDermott article about matching our teaching to how students learn. We all agreed that we want to change science teaching to emphasize thinking skills (to protect our students from anti-reality hysteria like the 2012 nonsense), as well as the awesome coolness of physics.

After lunch, we dove into the first actual physics content unit with the Buggy Paradigm Lab. We generated a bunch of suggestions for what we could measure about the system. There was some confusion (and I, at least, dropped temporarily into trying to guess what the 'teacher' wanted) when cellphone timers were vetoed as timing devices, but we got over that and tackled the task of gathering enough data to "predict where a buggy will be at a later time or predict how long it will take for a buggy to travel a given distance."

My group elected to use a metronome as a timer and to mark position along a piece of masking tape stretched across our table by tapping a whiteboard marker behind the buggy at each 'tik' of the metronome. We then made a ruler by trimming a piece of paper to buggy length and folding it into eight parts and measured distance from the start to each of the marks. Other groups used different procedures, including one group who measured from one mark to the next mark (rather than from the start each time) and two groups who measured the time to reach each of several marks on the floor. This made for a great discussion afterwards, as we tried to start hashing out how to lead students into differentiating between position and distance, as well as to notice which graphs were most useful for answering the original task (all but the change-in-distance vs. time graph).

We then started our "Consensus Meeting" in which we tried to start writing general equations and defining vocabulary. Following Arons, we're trying to be very careful about the difference between instantaneous time (clock reading) and time interval (Δt). I'm still trying to wrap my head around it. In my head, y=mx+b is a function that describes what y is for every value of x. Converting that into x=vt+x0 makes sense if t is the instantaneous time and x0 is the position when the clock was started/instantaneous time was zero. Which makes the equation x=vΔt+x0 a bit off, since Δt is a time interval that doesn't necessarily start when the clock starts, but x0 is still the position when the clock started. I think I'm much happier using either Δx=vΔt or xf=vΔt+xi, with the explicit understanding that xi is the position at the start of the time interval chosen, not the position at the beginning of the motion. All of which may make much more sense in my head than on paper...

For homework tonight, we're supposed to read Arons chapter 1 and write up the paradigm lab in lab report format. I've done most of the reading, but I have no idea what lab report format I'm going to use this year. Plus, it's after bedtime and 6am comes way too early...


Brian said...

Where are the rest of the updates? ;)

jsb16 said...

My brain died on the commute last week. :)