For each mathematical subject on the undergraduate level there are many textbooks, often with quite different approaches to the subject. Some are just concise and rigorous, some focus on examples, some on the historical development of the subject, some on intuitive pictures, and so on. When designing a course, one of course wants to find the most illuminating explanations, examples, and pictures that help students to learn the subject. But how does one go about browsing through this vast literature to find them?

Of course one can't read each text book, the time just isn't there. How much should one focus on exploring the literature for better explanations? Or should one focus on coming up with explanations and examples by oneself? (Maybe if one comes up with the explanations oneself rather than taking them from a text book one can convey them to the students more easily?)

I admit this question is very much opion-based, but I would be interested if there's something like a 'consensus' among math educators.

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    $\begingroup$ It would help to give more context. Often, at a specified college/university, at most two or three texts have been used for the course in the past decade (if you even have a choice), so one simply picks one of those that best fits your teaching style. Also, having been an undergraduate, you've presumably taken the course (or something similar), so besides your own textbook, you are likely familiar with other books from your own supplementary library reading, and you likely know about still other books from what your friends/acquaintances (continued) $\endgroup$ – Dave L Renfro Sep 6 '20 at 16:34
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    $\begingroup$ said about alternate books when you were a student. Discussing the merits of certain books was a fairly common activity among students when I was an undergraduate (and even more so when I was a graduate student), especially those who were planning to attend graduate school. In general, my advice would be to use the standard text (or one such, when as is often the case, there are several) until you've taught the course two or three times, after which you will have an idea of what things in a text fit well with your teaching style. $\endgroup$ – Dave L Renfro Sep 6 '20 at 16:36
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    $\begingroup$ That there are so many textbooks is a clue to the difficulty of this problem. Different teachers teach differently. Different students learn differently. The ideal would be computer aided instruction run by an A.I. that adjusted the approach and the problems sets according to the needs of the student. $\endgroup$ – Sherwood Botsford Sep 8 '20 at 2:05
  1. You should know the assigned text perfectly. Read it. Drilled it. Four dot oh. Don't ignore it. After all, it was designed to mesh with the drill problems in it. And if you have the choice, assign a structured text with good explanations, and drill problems. NOT the approach of some liberal arts topic where you just opine on things and assign a bunch of articles or don't have a strong text as a backbone. This will get you to the 80% level. (Note: I'm not saying to recite the book, but you can compose examples that are different numerically or decide what to emphasize/not. Based mostly on the flow of the text.)

  2. Know at least one other text reasonably well (probably the one you had as a student). Use it as your cheat comparison. Really, at that point, having two things to compare, you can see differences and similarities and are at the 90%.

  3. If you have one or two more, checked out from the library, that's enough. Don't feel you need to consult them often at all. Just where you have a real question or if dissatisfied with 1&2. (An example might be repeated roots in linear constant coefficient homo diffyQs.) And if still dissatisfied, I would argue to move on. Remember teaching and learning are processes, not Euclidean proofs. You have to prioritize your time and effort. Think industrial engineering, not Andrew Wiles in an attic for 7 years.


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