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It frequently happens that there's some material I have to cover which is, frankly, boring. The subject itself may be boring, or it may be the particular exercises, but in any case I have to get through it. When this happens I try to adopt a positive attitude in the hopes that at least I will not be as boring as whatever it is I'm teaching. This only helps so much, though, especially in front of a class of students that don't particularly care about math a lot.

I know from personal experience that when you get bored you stop paying attention. What are some ways of not losing your class during the more tedious bits? Something I've thought about is telling them about the applications of the material, or even replacing the exercise I'm doing by something more "real world"; right now my students are in engineering, so they might appreciate a practical example. This doesn't always work, though, because usually applications of the material are more advanced than the basic stuff I want to do.

I've also considered straight up telling the class that this stuff is boring but we just have to get through it, i.e., take the "accomplice" route. Whether this would work is debatable, and also as a teacher I feel I should try to find the fun in everything I teach instead of "taking sides" with the students.

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    $\begingroup$ If you think it is boring, it may be that you have not thought about it enough. You need to be able to find what makes it interesting for you. $\endgroup$ – mweiss Sep 12 '16 at 20:22
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    $\begingroup$ If it's not useful for some next thing, then consider not teaching it? As a fulltime faculty, I feel perfectly secure leaving things out if they don't feel useful. $\endgroup$ – Sue VanHattum Sep 12 '16 at 21:20
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    $\begingroup$ usually applications of the material are more advanced than the basic stuff I want to do Then maybe put more effort into finding basic applications. If there are no applications that your students can possibly do, then they simply shouldn't be learning this material. $\endgroup$ – Ben Crowell Sep 12 '16 at 21:28
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    $\begingroup$ Example of what you or your students find boring might help... $\endgroup$ – Joseph O'Rourke Sep 13 '16 at 1:37
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    $\begingroup$ Sometimes I tell the students something like "I hope that you are getting bored. Boredom in mathematics is a sign that there is a theorem or formula waiting to be born -- something that will handle this boring part once and for all." This doesn't work for all boring things of course, but sometimes it does. For example, completing the square becomes boring after half a dozen examples -- at which stage the students are ready for the quadratic formula. $\endgroup$ – John Coleman Sep 13 '16 at 3:29
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I will concur with and collect several comments and suggest that one consider not teaching it, or at least cutting or refining the presentation. I'll say that in my own teaching, I have come to be sensitive to this as a sign that something is off with my lecture. If some part of the class actually seems to be boring me, then I take that as a signal to inspect and revise that part of my presentation.

Maybe that involves mostly cutting the item, and leaving it for student reading outside of class (example: I used to go over the syllabus in detail on the first day; that's been cut). Or it may be reducing or refining the item (ex.: reducing the number of exercises; cutting basic exercises and going straight to moderate-level ones where multiple points of interest are at play). Or it might be totally re-writing the presentation in a totally different structure (ex.: inheriting some presentation from a book that seems cluttered, and finding a much more straightforward and elegant path of my own).

I would recommend against calling out an item as "boring" in class. If your life is dedicated to the classroom, then do yourself a spiritual favor and find some way to make it not-boring. Hopefully this will have a secondary effect of making it not-boring for students, and infecting them with your interest.

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I'm going to restate and elaborate on something I said briefly in the comments:

If you think something is boring, you need to figure out what is interesting about it.

"Boring" is in the eye of the beholder; everything is interesting to someone, and everything is potentially interesting to you and your students. Part of the teacher's job is to make the content seem interesting to students, and that is not possible for teachers who do not themselves find the content interesting. So if you don't see what is interesting about a specific topic then it is your professional obligation to stop and think about it more and find an angle on it that makes it interesting to you.

You have not provided us with any context or specifics (except for the undergraduate-education tag) so it will be difficult for us to help you with this, but I assure you: nothing is intrinsically, universally boring. Whatever you are teaching, someone, somewhere thinks it is interesting. You need to figure out why.

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I want to depart from the stance that boring parts may simply be put aside, and that one should not acknowledge them as boring. I claim that there are some boring and tedious tasks that are needed to learn mathematics. One needs to compute a few integrals, a few Taylor series, a few derivatives to really get what it is all about. One needs to work some proof in tedious details before having the background enabling one to see the big picture.

Claiming there is no boring part is somewhat misleading and might even be considered rude by the students, who could be bored even by what the teacher finds exciting. Some acknowledgement of boredom is simply honesty.

I usually compare studies (in maths or something else) to high-level sport. You can enjoy tennis. Some train to become good tennis player to enjoy it even more. But training to be a good tennis player needs some boring, tedious (and tiring) stuff: working out, repeating the same gesture again and again to get it right, etc. It does not get right by himself, one needs to put effort in it. I think it very important to stress student that studying needs efforts as much as it can be (in order for it to be) rewarding and enjoyable. No one says to a young person wanting to play tennis: "sure, you can be good at it without running or practicing!"

To be more constructive, a teacher must try to make material non-maximally boring; and one should certainly take the most boring part out of the main lecture by giving it as assignments: the boring parts are usually the ones student need to do by themselves. One can even take a boring proof which one wants to be part of the curriculum, and give it (suitably divided into questions) as mandatory homework. But students need to do some boring stuff, i don't think it is avoidable and it should be explained.

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How to get through the boring stuff?

You could present it in a different way yet still cover the same concepts and procedures. For example, if your topic is multi-digit multiplication of positive integers, instead of providing the factors and asking for the product, you could have them fill in missing digits from the factors and the product, as shown below.

Multi-digit multiplication

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Exactly what the dull topic is matters. The following idea works best for things that are more like prerequisites: Take for example, the domain and range. One option would be to devote a class to them so that you can simply refer to the material later. (In my mind this is fairly dull.) Another option is to fold that material into other lectures in a just-in-time fashion. Say, introduce the domain in a example where there is domain where the formula is valid and a domain where the problem is physically well-defined.

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