Comment by jimhefferon
Comment by jimhefferon 3 days ago
In its impact on teaching, I'll say that based on teaching since 1979, students take feeling stupid as convincing evidence that their instructor is doing a bad job. No amount of assuring them that it is the gateway to enlightenment or however you put it will save you.
I've become convinced that, in the end, no one really teaches you anything, you end up teaching yourself. That phrasing is a bit hyperbolic. It's more accurate to say a good teacher only gets you 50%, 60%, maybe 70% of the way there, and it's up to you to get you to 100%.
To be able to truly learn any given concept means being capable of answering a practically infinite number of different questions about that topic. The process of teaching is essentially trying to uncover which questions the student can't answer. The challenge, of course, is that the student doesn't know what questions they can't answer, because the questions haven't occurred to them. That is, until they start testing themselves, to see if they really do understand the concept.
Problem sets in textbooks are the canonical way of addressing this teaching challenge, but there are only so many pages in a textbook, and there are other concepts that need to be taught, so the scope of the problem sets are necessarily finite.
How many times have you nailed all the problems in a book, only to discover that there was some aspect of the topic you didn't understand, despite getting all the right answers?