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For questions on general considerations and problems of teaching mathematics, such as issues specific to teaching mathematics that are relevant in various contexts or courses.

4 votes
1 answer
241 views

Elementary examples for non-reversible logical steps

While listening to recordings of Calculus $I$ lectures, I noticed that some students get confused between showing that "some object $x$ is a solution", and showing that "every (possible) solution mus …
Asaf Shachar's user avatar
10 votes
1 answer
374 views

How to explain the concept "Without loss of generality" (through examples)?

This is not a precise question. I am curious to know how do you present to your students the (imprecise) concept of "without loss of generality", and how to use it correctly/incorrectly. I got curious …
Asaf Shachar's user avatar
3 votes
6 answers
1k views

Is this motivation for the concept of a limit a good one?

tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my …
Asaf Shachar's user avatar
12 votes
7 answers
4k views

Does induction really avoid proving an infinite number of claims?

I am teaching calculus $1$ this semester, and I saw the following motivation for using induction by another teacher: Since we can't go over "manually proving" all claims $1,2,\ldots$ and actually get …
Asaf Shachar's user avatar