Today, I didn’t have time to revise the sample problem I’m supposed to do in physics. So I worked the sample problem as given. We were doing standing waves. In the particular problem, there was a string with both ends fixed and we were told it was vibrating in the second harmonic. In this case, the wavelength is equal to the length of the string.
After my sample problem, students were given a problem where the string was vibrating in its fifth harmonic. A fourth of the class did it correctly, drawing it out and concluding that the wavelength must be 2/5 the string length. Half the class did it wrong saying that the wavelength was equal to the string length. And a third of the class said the wavelength was 5/2 of the string length. As I was walking around, I asked a student why they thought so many people were making these mistakes.
She responded without hesitation, “The sample problem was poorly designed. You shouldn’t have given us an example in which the wavelength and the string length were equal. That makes it easy for everyone to think that’s what you are supposed to do every time. Plus dividing by 1 or multiplying 1 gives you the same result, so it’s easy for people to mix it up. Next year, you should use a different harmonic to set up the problem.”
I wish my future physics teachers knew had to unpack a sample problem like that, and see how it might lead to over-generalizations and misinterpretations.
Teach. Brian. Teach. 
that’s really cool. I really enjoy interacting with students in cases like this. I’ve especially enjoyed that when teaching teachers in PD situations.
Nice. I’ve been talking with some students lately about how many practice problems should be in each practice sheet in our packets. It was prompted by them scolding me for leaving so much space for a few problems that didn’t take them much space to do at all (though they didn’t notice that some of their classmates did actually need a lot more space, but that’s a different thing). Then they started talking about what math classes used to feel like for them (here’s a type of problem; now do 30 more of the same thing) and how useless that was, what math classes feel like now (in honors precalculus, no book, and they aren’t ever sure what’s going on), and where physics is fitting into that spectrum for them.
I love when the students start to get interested in how the class is being designed (and so when they start to be really aware that the class is, in fact, being designed really specifically and intentionally). More awareness about patterns (etc) in every part of their life is good! 🙂