This is a followup to an article I wrote about
Teaching and Learning. As I mentioned in a previous post, I find the style of hard to deal with, even as I generally agree with what's said.
I read a followup comment that was intriguing, that I agree with as well. Many teachers just feel they must "cover" the material. They would cover this the same way regardless of audience. To effectively teach, you need a feedback loop. You need to know whether what you're teaching is making sense to enough students or not.
If not, you need to adjust what you do to be more effective. In all likelihood, you have to talk to students and see what's going on. Instead, what usually happens, at least with old school profs is that they blame students for essentially not being good enough.
On the one hand, students are what they are, and you have to work with what you have. If they aren't as experienced or talented or driven as you would like, you have to do more work (and many teachers are not looking for more work). On the other, students do need to improve their skills as students.
This means, as a teacher, you need to figure out what skills students have to have. You need to learn how students learn. Then, you need to adjust your teaching to maximize this learning.
Teachers often think of themselves (and I'm mostly referring to college profs, since high school teachers and below often have education degrees) as fountains of knowledge, and all they do is pass this knowledge on. They don't think about the student as being someone who learns and that the teacher bears some responsibility in helping students to learn, not just to learn the material.
Teaching is harder than people think. It's not simply a one-way transmission of information.
Three opinions on theorems
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1. Think of theorem statements like an API. Some people feel intimidated by
the prospect of putting a “theorem” into their papers. They feel that their
res...
5 years ago
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