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I am teaching a course in calculus. Things are generally going quite well, but since this is the first course I've ever taught I'm certainly not doing a perfect job. As a result, I sometimes come across lecture topics that don't go so well, either because:

  1. I didn't do a good job of explaining in lecture, typically because I made a mistake or glossed over something or
  2. The concept itself is just difficult, and requires a lot more time to understand than I can devote in lecture.

In these situations, I make sure that I communicate to the class that there was an issue, and I often look for or create resources like video lectures or supplementary documents that clarify things.

If I want to be 100% sure that the message I deliver is in agreement with how I'm teaching the course, I make the material myself. For instance, if there are multiple, conflicting definitions of the same term, I tend to make my own material and post it for the class in order to ensure that my definitions are consistent throughout my entire course. I've done this several times and my resources are well received.

However, there are resources out there that are just clearly better than anything I can whip up, at least in the time I have. Khan Academy is particularly fantastic and has great videos, activities, etc. Rather than re-invent the wheel, I will provide links to these resources when the topic is either not critical or where the resource aligns very well with how I've taught the concept in class. I always make sure to properly give credit and do not take credit myself for things I did not create.

I'm not sure why, but somehow this feels like "cheating". I'm also concerned that it will be perceived as laziness on my part by the students. So the questions:

  1. Is this cheating? Should I be making my own material, in order to 100% guarantee that what my students see is consistent with how I'm teaching it?
  2. If not, is there anything I should be doing to ensure that students understand that these resources are just one part of the course, and shouldn't be exclusively relied on?
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    Do you write all your own textbooks for the courses you give? Why should using a good video from YouTube be any different from using a good textbook? – alephzero Jun 23 '17 at 3:13
  • It's a good question. I've learned this semester that having a textbook is good, but not great, and honestly I'd rather write my own course notes. However, a significant lack of time (and, to some extent, expertise) prevents me from doing so. As a result, I've used the textbook as a guide. I feel that if I were to make my own, it would align much better with how I want to teach the course. Obviously, making my own book for every course is an immense, probably not possible, task. But making supplementary material for every class isn't that unreasonable – Michael Stachowsky Jun 23 '17 at 12:36
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    When I took Linear Algebra, in preparation for the final exam, I went to the library to get a book to do some more preparation with. It got me completely confused, because it assumed and proved opposite sets of things from the course. I would have appreciated it if the instructor had given a short list of compatible enrichment resources. That was before the internet. // Please keep in mind that some students do better with print enrichment resources and some do better with video resources. The ideal is to offer multiple modes so students can find what works for them. // Don't neglect... – aparente001 Jun 25 '17 at 16:15
  • ...to ask students for feedback after trying something. However, I wouldn't just ask for verbal feedback during class. A short questionnaire, either paper or web based, would probably be more useful. Also, you can encourage students to send ongoing feedback through email and office hours visits. // Your questions: (1) no; (2) just tell them (verbally and in writing. – aparente001 Jun 25 '17 at 16:18
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Giving an extra resource from another properly referenced and acknowledged source gives an explanation with a different flavour - I do this and so do my colleagues - do all students use or appreciate - no but some do, so it's worth it. Best of luck you have a good attitude.

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If you are new to teaching, then I give my highest recommendation that you read Steven Krantz, How to Teach Mathematics, published by the American Mathematical Society. From the 3rd Edition, Section 2.7, "Handouts":

It is tempting to write up a lot of handouts for your course. If you give a class hour on Stoke's theorem and feel that you have not made matters clear, then you might be inclined to draw up a handout to help students along. You also might suspect that this extra effort on your part will improve your teaching evaluations and, in particular, that students will appreciate all this additional work that you have put in. Well, it won't and they don't. Only prepare a handout when it will really make a difference. Students feel that they already have enough to read. Inundating them with handouts will only confuse them...

What I can do is examine my own conscience and tell you what I see. If I give a lesson that is not up to snuff, or if I do a poor job of explaining what curvature is, or if I goof up a proof in class, then I can salve my conscience by writing up a handout. It takes about an hour, it is a way of doing penance, and it is a way of working past the guilt of having screwed up in class. In my heart of hearts, however, I know that what I should do is strive to give better classes.

Just speaking for myself, I find it more comfortable and convenient to put ancillary material for the course on the Web. This seems to be less "in your face," and the students think of it as a resource that they can consult if and when convenient. Class emails are also a useful device for supplying extra information or small corrections.

For myself, I would say you certainly don't have to feel guilty about directing students to outside resources. Possibly we don't do that enough in our discipline. It is definitely not "cheating"; it is simply being a professional and knowledgeable scholar. On the other hand, I might also argue that real-deal mathematics does involve reading, and to wean students away from crutches like videos that will only get them so far.

  • Hmm, interesting to see this advice being given to math instructors. In college math courses, I always felt like the lectures were rushed, with way too much material trying to be covered, and always thought it would be nice if the professor would put together a handout that elegantly presented and summarized the main points. I also felt like this would help me in my note-taking, because I could focus on example problems, rather than having to transcribe the main ideas. I was always disappointed that this never happened. I guess everyone's been told not to do it. – Cody Gray Jun 23 '17 at 3:40
  • Maybe it's just me, and I'm just weird in that I can learn effectively from reading printed material. But I still disagree with the blanket statement that "it won't and they don't." There are certainly students who will disregard a handout, but there are students who'll disregard anything; you can't cater to them, and no single style fits everyone. (Granted, it would be less necessary if undergrad textbooks were better. But most of them are, frankly, awful. Plus, in a large university, textbooks are often dictated by department and don't necessarily follow the professor's chosen syllabus.) – Cody Gray Jun 23 '17 at 3:43
  • I would have to agree with @CodyGray. I think what the author is trying to get at is: if you did a bad job teaching it, you'll probably do a bad job writing about it. This is a fair point, but not one that I totally agree with. I've made some blunders during my lectures due to, for example, a rushed set up of a problem. When I wrote the supplementary material, I made sure to take as much time as I could to ensure the setup was correct, and students appreciated it. However, I can see that if I had rushed the handout, too, it would have been poorly received. – Michael Stachowsky Jun 23 '17 at 12:31

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