Teaching somebody else's class

Question

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?

Answer 1

If you are an invited speaker, do as asked: Talk on your own terms on your area of expertise. What came before or after doesn't matter at all.

Some coleagues here (in some completely different subject matter) teach an upper-level undergraduate course by halves: A teaches the first half, B teaches the remainder. Even two courses simultaneously: at mid-term, they switch groups. Only works for independent material, obviously. Works very well for them, as it makes the most of their respective areas of expertise.

If you are taking over a class, it is important to (try to) keep continuity. I.e., check notation beforehand (or ask the students), etc. If this is scheduled, it is easier as you can coordinate with the coleague; if it is an emergency it's harder. It also depends on the duration. I.e., covering a class or a week is quite different than taking over a class mid-term.

Respect missing intuition/definitions/notation, perhaps ask the class. But many students, when asked, will tell you they never learned anything beyond $2 + 2 = 4$... use your judgement/ask whoever taught them before.

Answer 2

In the "emergency" scenario, many of the problems can be avoided, if you start off with having the class instruct you on "how things are done here". Students will be delighted to reverse the direction of teaching, and get you up to speed on what happened when. Warn them that they have to watch you carefully, as you might slip up now and then ...

For "planned" scenarios, you should have collected the relevant information before entering the classroom so that you have some common ground with the students.

Answer 3

By far the easiest method I have found for this is for the usual teacher to prepare lecture notes containing the entire lecture as they would teach it. Many US professors already have such notes or are in the process of building a collection of them.

Given the other professors notes, one knows, at least, what they would have taught. You can then work within that framework, and only change things if the other professor is comfortable with it and if you feel strongly about it.