Grades are in. So, let me just say a couple of trends that I saw on the physical science final exam.
Gravity on the moon
I asked the question: "why is the gravitational force on an astronaut less on the moon than on Earth?"
The simplest answer is that the gravitational field on the moon is smaller than on Earth (I would accept that answer). Why is this? It is because the moon as a much smaller mass even though it also has a smaller radius (that idea is rather complicated for this class - that gravitational force depends on both mass and radius). I would also take "the mass is smaller" as a correct answer.
The most common incorrect answer for this question was that the gravitational force was smaller because the astronauts are farther from the Earth. As you get farther from the Earth, the gravitational force gets smaller. I see where this is coming from. In a sense, they are correct - especially if they answer only regards to the Earth. I think the big problem here (other than my question which could have been worded better) is that students think of gravity as something that has to do only with the Earth.
Energy is a buzz word
This isn't just on one question, it was all over the place. Students love them some "energy" words. To them, "energy" is the duck tape of words. You can use it for anything. For scientists, energy is just energy. For students, it can be used for any of the following:
- electric charge
- electric current
Sure, you could argue some of those are forms of energy, but you would still have to use it correctly.
Density, mass, volume
I tried to pick some objects that would be clear. Here is the question:
Consider a small marble and a large styrofoam cooler. Which has a greater mass? Which has a greater volume? Which has a greater density?
The correct answer is that the cooler has a greater mass and volume, but the marble has a greater density. I think the biggest problem here is that students think that if something has a greater density (which is a ratio), it must also have a greater something else (mass or volume - you pick). Really, every possible combination of answers was seen on the tests. I think some really think the marble is more massive than a styrofoam cooler, I guess that might be an understandable mistake if didn't actually pick both of them up. Maybe I should have picked better objects. I thought those would be clear.
My cooler is so light I could not guess its mass, so I checked. (Moving it quickly, I am more aware of its drag than its mass.)
Cooler (with lid), 396 g. Marble, 6 g.
Re: Gravity on the moon
Would it be too leading to pair "why is the gravitational force on an astronaut less on the moon than on Earth?" with "why is the gravitational force on an astronaut more on the surface of the sun than on Earth?"? That might wake up some of the folks who gave the most common incorrect answer.
Let's see.... If we set M = (4/3)pR^3 (where p is a poor-man's rho for density), we get F = (4GmpR^3)/(3R^2) = ma, so using k=(4/3)G, we get surface gravity g = kpR.
I asked what I thought was a gimme question once, "Which is a longer wavelength? 380nm or 450nm?" 80% converted it to frequency and missed it. I had ask it 7 more times, to get it up to 80% getting it right. The remaining 20% never reviewed old tests or homeworks. This applied at 2 different universities.
Since p(moon) < p(Earth) and R(moon) < R(Earth), g(moon) < g(Earth).
OK, I can't type less-than symbols, and I can't use the HTML entity notation for them, and the preview button lies, so in English this time....
The surface gravity of a uniform sphere (which I'm using as an approximation of both the Earth and Moon) is proportional to the density of the sphere and to it's radius.
Since the moon is less dense and smaller than the Earth both of these factors would lead to a lower surface gravity for the Moon.
I don't teach energy but I do teach gravity and density to my 8th graders. The hard part for my kids is that they're relational. I teach about density in the context of floating/sinking. It takes me a long time to get them to think of the object in relation to the fluid rather than just absolutes (denser things sink vs. it's got to be denser than the fluid).
Gravity suffers from the same problem. Getting them to think in terms of interactions is....tough.
I enjoy your reflections on teaching. Thank you for the updates.
Thanks for the quick measurements. I guess I was right though that it is not obvious without holding them.
The problem is that it might be difficult to find things that are obvious for volume, mass and density. If I picked a wooden toy chest that holds the marble, I think they would be ok with mass and volume, but not density.
I'm startled by some of the responses. How old are these students?
i am not startled at all by the responses.
students start a physics course with many incorrect preconceptions. even when you lecture, assign homework, do labs and recitations, the incorrect physics ideas are sutbborn.
when faced with tough questions some students will still fall back on their incorrect preconceptions and not use their recently acquired physics knowledge.