How do you approach a class taught by somebody else?
There are multiple reasons why one could find him/herself in such a situation:
- an instructor is sick,
- there is a scheduled rotation of teachers,
- you are visiting some other university and want to exchange teaching experiences (never experienced on my own, but seems possible),
- you are a specialist on some topic and came just for this one lecture,
- and so on...
With biology or history you might just continue where your predecessor ended. On the other hand, with math there are additional issues, to name a few:
- You might be used to different notation.
- You might be used to different definitions (e.g. something which is a definition for you, would be a theorem for them).
- They might lack some intuition you think of as essential.
- You might rely on some specific order of topics (e.g. there is this nice explanations for $X$, but it needs $Y$ which has not been covered yet).
- Students might be taught using some analogy which you think is wrong.
There are pros and cons to each of these, e.g. it's best to talk to students in a language they understand (i.e. use their notation), but also there might be additional benefit in letting them see a different perspective (i.e. review some older/already done topics).
So, how do you approach a class taught by somebody else?