Standards Based Grading, Week 2
Most of this entry is just journalling. SBG stuff can be found toward the end.
Day 5 (Tuesday): Clothesline Lab
(Monday was MLK Day)
The short of it: what we did in lab today addresses Standards 15.2, 15.4 and 15.5. Not in entirety, but quite a bit of each.
Lab began with me drawing a picture of a standing wave on a string on the board (y vs. x). I had the students tell me what the measurable quantitites were. Amplitude, wavelength, # of nodes and one student even got at linear density of the string. I was impressed! Replacing one end of the system with a pulley, it became obvious tension in the string was an additional variable that could be measured.
I have to admit, I did some handwaving about how the velocity of a wave on a string is dependent on tension and linear string density. But knowing the derivations is not really an important part of the standards. It’s an example of how really neat derivations can be good exercises, but not critial for understanding the course content as a whole. This SBG approach is really pressing me to trim the extras so we stay on task.
Following a brief introduction of waves on a string, students were introduced to the CENCO string vibrator. They were then tasked with collecting enough data to write out a wave function
y(x, t) = Acos(kx – ωt).
The catch: the frequency of the string vibrator had to be determined from a plot of wave velocity versus wavelength (the slope yields frequency).
Application exercises included writing out y(x, t) for x = 0 (pretty straight-forward) and confirming whether or not the location of the nodes are consistent with their wave function (not so straigth-forward, since x = 0 is problematic). I hope my students recognize that since the system is symmetrical, they can measure x from the node at the pulley rather than estimating it from the tab.
Day 6 (Friday):
Announced that the lab standards (there were 2 of them) were now active. This was after a discussion of lab and average power of a wave on a string. I did not spend much time on the derivation of the equation, but did refer back to the relationship of power in terms of force and velocity. From there,
P = F v
P = F(x, t) v(x, t)
I made loose reference about how there were steps involving calculus lingered in arriving at F(x, t) and v(x, t). I don’t like handwaving explanations, but the steps are outlined pretty clearly in the text. Instead, we used data collected from lab to investigate something I’d noticed “kind of” in the past, but became more clearly defined in Tuesday’s lab.
Students noticed that the amplitude of standing waves on a string varied: the greater the tension, the greater the amplitude. It wasn’t huge, but enough to be noticed. So, we calculated the wave number and periodic wave for four separate standing waves. We then calculated the power associated with each and plotted power as a function of tension (for a stretched wave on a string). I was honest with students and told them I’d never plotted this before, so wasn’t sure what to expect (linear vs. non-linear trend). It turned out to be fairly linear, however a third order polynomial seemed to fit it pretty nicely too. But with only four data points, we decided we’d like to see this done for more data plots. . . maybe one of them will take the initiative (hint, hint!).
The good news is, all of this was directly related to the lab standards. Solving problems involving the normal modes of a string under tension and the wave’s average power. On a side note, I am really looking forward to weeks where there aren’t interruptions in the class week (days off, sickness, etc.)–the next few should be pretty solid weeks.
Students commented that they were excited about SBG. They thought the work load was going to be more at first. However, once they started understanding the material and fully reading the standards, they saw how the standards could be address with a thorough problem. In each of my standards and recommended assignments, I list a “The Point” sentence. In this statement I come clean about why I’m asking them to do that standard. In part this is an open way of being accountable for what I assign and justifies the work (no, it’s not just “busywork”), but it’s also a pretty overt way of being transparent with students. This works well with my calc-based physics students since they are engineers and like to see the applications/worth of things. I don’t know if students in other classes would appreciate it as much.