We had a little extra time in physics yesterday. Because there was no assigned reading, there was no reading quiz or sample problems to do. All we we had to do was a lab.
So far, lab activities we have done are the following:
- Finding an experimental value for π by plotting measured values of circumference and diameter
- Finding an experimental value for terminal velocity of coffee filter by plotting measured heights and times
- Finding an experimental value for the acceleration due to gravity by plotting measured heights and times²
- Predicting where a projectile will land after experimental determining its muzzle velocity
- Predicting what single force will balance a certain configuration provided for a force table
- Characterizing the relationships between angle and load for a pulley system
Major themes of the labs are:
- Confirming theoretically known values or relationships
- Estimating uncertainties and propagating error (using the weakest link rule)
- Graphing quantities and using slope to extract information about a system
- Linearizing graphs and relationships by making theoretically-informed choices about what variables to graph
- Reporting results using proper uncertainty and significant figures, and comparing with theory or direct measurement
Graphical Analysis in Labs
For the most part, students don’t get why we are graphing quantities in the first place, when we could just plug them into an equation. They don’t seem to get why the slope could possibly tell us something meaningful. They struggle to understand the linearization process, and struggle even more when the slope isn’t directly telling us the value of interest. They are getting better at doing uncertainties, but they still see it as just some hoops to just through. I can’t blame them. We provide them with very little opportunity, scaffolding, and time to make sense of what we are doing. That gets doubled with my lack of experience teaching these skills.
So yesterday, I decided to use our extra time discussing and practicing some of these skills before lab. I went back to linear relationships, where the slope tells us something meaningful, things like
M = ρ V
d = v t
F = k x
W = g m
f = μ N
We talked about each of these in turn, oscillating back and forth between me lecturing for a minute or two, and having them discuss a question for a minute or two. Sometimes I gave them the equation and asked them what the slope should be. Sometimes, I asked them what they would need to plot in order for the slope to give a certain quantity. Etc. Etc.
Then I asked, what if in the π lab, we had plotted radius vs. circumference for all our data. What should we expect our slope to be? As they worked, I heard a range of answers, including π, 2π, -2π, π/2, but we finally converged on an agreement that it should be 1 /(2π).
Then, I returned to the free-fall lab, where had used the equation H = 1/2 g t². I talked about how this equation is different than the others because it’s not a direct relationship, and I pretty much lectured about how the trick of plotting t² on the x-axis, and how that worked. Then, had them practice considering these relationships
A = π r²
V = 4/3 π r³
Then I gave them this one to consider, which would eventually arise in the lab we had to do.
T² = ( 4 π² M / Ft) L
Yesterday, I realized that one hard thing about all of this is simply keeping track of which quantities you are pretending not to know (such as π or g), and which you don’t actually know (yet), but you will know by the time you are in lab (the tension force). This is even harder, because sometimes, like in the π lab, we are pretending not to know π , and other times, like our circular motion lab, we do know the value of π .
I don’t think our class is anywhere close to fully wrapping their heads around all of this, but I think I helped to nudge us along. On Friday, I’m going to give them a quick ungraded individual assessment to see where we are all at.
Teaching with Curriculum Constraints
One benefit of teaching in a common curriculum with many constraints, is that it helps me to understand (even if just a little bit) the situation that public school teachers face. I have a certain amount of material I need to cover in a very strict time frame. I don’t necessarily agree with or value all of things I have to teach. Every so often, my students are assessed by some external exam that I have no control over. I am expected to prepare students to do well on these exams. In a small way, the success of my teaching is reflected in how well my students do on these exams. Amid all of these constraints, I still have to find ways to make sure students are engaged in meaningful learning (not just exam preparation).