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Sometimes a math teacher becomes sick or depressed like any other human and is not able to be prepared for lecture. Sometimes a math teacher spends too much time on a research project and does not prepare the course material appropriately. These are just a few reasons which can make somebody unprepared for a lecture course.

Question: How can a math teacher manage a class when unprepared? What tricks can help an unprepared math teacher teach a nice lecture course in a way that is useful for the students?

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A good math teacher should be prepared. The best pointer I can give is to: – Benjamin Dickman Jun 28 '14 at 0:36
But my real feeling is: 1, if you are asking on Mathematics Educators about best practices -- then you should be ensuring that you are prepared for classes. In fact, you should be over-prepared if anything. 2, Surely the question of How can a math teacher manage a class when unprepared? is too broad. – Benjamin Dickman Jun 28 '14 at 0:42
@BenjaminDickman I really don't understand why this would be closed as too broad. What would a more specific version of the question be? I think it's a good question even though ideally we would never be unprepared for our classes. – Chris Cunningham Jun 28 '14 at 3:53
@ChrisCunningham Who are the students? What is the class? How much is supposed to be covered? Has the teacher taught similar material before? Does it need to be lecture based? And note that being unprepared due to mental illness (e.g. depression) requires a quite different approach as compared to overfocus on research before a single lesson. Etc. – Benjamin Dickman Jun 28 '14 at 9:41
I support Benjamin Dickman's claim. Teaching is like any other job, we should not do it (at least temporarily) if it is not possible to do it correctly. If the teacher is sick, he probably has day off for this. If he was too focused on research and neglicted his teaching duty, I would call it a professional mistake. – Taladris Jun 28 '14 at 12:07

As JoeTaxpayer suggested, my comment is more of an answer than a comment, so I'm copying my comment here. Maybe this will get others to answer, although I realize that appearing to admit that something like this has ever happened can reflect poorly on one's teaching. Personally, this almost never happened to me, if at all. I had more of a problem with having too much that I wanted to cover, and I often resorted to turning the things I didn't get to (or decided I shouldn't try to cover) into supplementary extra credit projects.

You can make it into a "review day" where you ask students to suggest old topics they want you to go over in more detail or you can make it into a "problem day" where you and/or the students present solutions to old homework problems. Or you could simply switch the order of some topics and discuss a later topic you are more comfortable with that doesn't depend on anything new (i.e. do implicit differentiation, which is quite mechanical, if you didn't get a chance to properly prepare for solving some applied max/min problems).

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How about letting students work in groups of 2 or 3 people to understand the next block of theory from their textbooks themselves? I am a huge believer in learning to understand mathematical notation, because this will make almost any new topic easier to learn.

I teach a supplementary statistics course and the professor supplied a set of lecture notes that students will be allowed to use during the exam. Many of them are struggling to understand the theoretical mathematical notation of the content, but for the exam they should understand what all these formulas, assumptions, etc. actually mean. Therefore, I let them help each other read little sections of the lecture notes. Basically, they're supposed to translate the formulas from mathematical notation into actual sentences. Afterwards, I give a brief explanation of what the formulas mean. I think this should work even without a lot of preparation since you know the concepts already (also, the group work phase will give you time to prepare a brief explanation).

(This probably won't work if your students are too young to even have formulas in their textbooks or if the topics are so hard that the session will end in hopeless confusion without your guidance). Good luck!

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+1 for attempting to answer this question, though I might note that you are suggesting group work, whereas the OP writes: a nice lecture course – Benjamin Dickman Jun 28 '14 at 0:39

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