Read the book.
Back in my automata class, the professor would follow the textbook pretty closely. The book had nice example DFAs (chapter 1) where you were asked what they recognised and expected to get it slightly wrong .Then you'd be corrected and get closer until eventually getting the answer. The professor did this just the same, and led us through this very nice progression quite well. But there was a problem: me.
I would read the book before class and so I would know exactly what the DFA actually did as soon as he drew it on the board. After a few minutes, I realised I was completely screwing up his lectures by answering his questions with the correct answers rather than the intended answers. I stopped reading the book, and I learned to recognise when he wanted an incorrect answers and not answer in such cases. He taught in a similar manner in other courses as well, so I've had many occasions where I didn't know the correct answer, having not read the book and only being marginally super-brilliant.
Anyhoo, today he asked us when a matrix will have an inverse, and we all sat around in silence. (We consisting primarily of graduate students). I gave the Gaussian elimination answer of reducibility to Row Echelon form, but what he wanted was of course that the determinant was non-zero. Even after throwing out the word 'determinant' for us, we couldn't provide him with an answer. So he told us the answer, and then pointed out that this was not the right answer (we were under modullo 26) and gave us the correct answer (the determinant is not an invertible element).
Then he asked us, 'and we know that an element is invertible iff...?' Again, silence. 'This is the only major theorem we've proved so far'. Someone got it after a moment, but I think because they looked through their notes.
I think I may start reading the book. This way I'll at know the desired answers (and the correct ones). This way, we won't have awkward silences during class. And if I ever need a letter of recommendation, being an undergrad and still seemingly the smartest person in a graduate course may help elicit one. Gopal's the professor I most respect, so he's the one I'd actually care about a letter of recommendation from (though employers may prefer Dr. Tabrizi [software engineering guy] or Dr. Collins [formerly the co-op person who dealt with students getting jobs].)