[cabinpark]

Interesting. I used linear algebra with quantum mechanics where eigenvectors represent quantum state of the Hamiltonian which is how I initially understood them.

And as for TAing, have you ever TA'd? You definitely get a feeling but I can count numerous times when I've stood in front of the tutorial class and asked if there are any questions only to get no response back. I think it's a symptom of first years. I've TA'd calculus as well and I get similar responses. It's very frustrating sometimes.

[Jtsummers]

> You definitely get a feeling but I can count numerous times when I've stood in front of the tutorial class and asked if there are any questions only to get no response back.

When I realized I was understanding subjects better than my classmates, I'd take on the task of asking the "dumb" questions for them. It was partly selfishness, I was tired of answering those questions for them outside of class. But it really did prove helpful to my classmates. It really helped that, when I was sitting with the students, I got to hear them mumbling and grumbling about what they didn't get. So I knew exactly what questions to ask to get the professor/TA to help my classmates.

I never TA'd myself so I have no idea if this would actually work, or at least work consistently. But, if you have a couple students that really seem to be getting the material, you could try talking to them one-on-one and ask them to help you out in this manner.

[dalke]

I have TA'ed. Asking for questions in public doesn't help much. Students rarely like to admit they don't know something.

I was thinking more of when you look at their assignments. There are often multiple ways to approach a problem, and the route chosen can reveal something about one's level of comfort.

It doesn't help that university TAs get almost no training in how to be a TA. At least, I didn't.

[cabinpark]

Yeah I know. It's hard to squeeze information out of them. I actively tell them to please, please come to me if they don't understand something and I have office hours for a reason. Yet no one takes advantage. At a certain point, you can only do so much since I'm a grad student and not a lecturer and my time is finite.

The problem I've found with assignments though is that people copy and cheat. Many times someone will do very well on assignments and then do absolutely terrible on midterms and finals. It's very frustrating. I remember one course where everyone did nearly perfect on the assignments and yet the final and midterm followed the standard bell curve.

[cokernel]

It's worth devoting a portion of classroom time (in my opinion, a substantial portion) to discussion of the topic, perhaps focusing on particular problems and generalizing from there. For example, you might select random students each day to present problems from homework. If you've ever noticed that you learn something better once you teach it to someone else -- well, it works for your students, too.

Moreover, if you create a non-judgmental environment in which people are free to talk about their approaches to problems and get feedback not only from you but from other students as well, then just by watching carefully, you will learn some of the more common gaps in understanding. (Note that some students will not talk in these situations unless forced, but that does not mean they do not benefit from following the discussion.)

If you're anything like I was when I was first TAing courses like this, you might think that if you do this, you won't have enough time to "cover the material". But I put it to you that a lecture that is not absorbed doesn't cover anything.