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Sometimes a teacher prefers to use several textbooks in his/her courses because he/she thinks the arguments of each book is better in a part of course material or there is no comprehensive textbook in the subject.

Question. What are possible advantages/disadvantages of using several textbooks in a course? Based on the different approaches and preliminaries of different textbooks, could it be confusing for students? How should a teacher choose his/her set of textbooks to avoid this confusion?

The question is intended for both graduate and undergraduate levels. But the problem is more complicated in undergraduate case; sometimes it is a real problem for me.

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    $\begingroup$ It can also be sensible to check whether your institution has a policy on assigned textbooks, such as requiring a minimum percentage of the book(s) to be covered during the course. $\endgroup$
    – J W
    Apr 1, 2014 at 16:07

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Based on extensive (if anecdotal) experience, undergrads really cannot cope with more than a single reference, which must be traversed in order, possibly omitting some sections. Having any other source is somehow beyond imagination. Subject=course=textbook.

Grad students can do somewhat better, but are not happy about having to operate at a higher level. Perhaps understandably. Obviously habits from undergrad have inertia.

The most bizarre negative side effect of not "just following a standard textbook" is the occasional suspicion from the students that the instructor doesn't know what they're doing (no matter that they might be a respected expert among their peers, etc). I recall being taken off guard when an undergrad couldn't believe that, in fact, I was the author of the text being used for the course. The idea of author as authority looms very, very large in peoples' minds. (Some etymological connection there, too.)

That is, at lower levels, using several sources (in a math class as opposed to literature, etc) seems to so violate expectations that the instructor's credibility is lost in the minds of a substantial fraction of the student population. Somewhat less so with grad students, but still non-trivial non-sequitur problems. E.g., especially before I had the advantage of a gray beard and bald head, divergence from the students' preferred reference was viewed as lack of preparation, or negligence, on my part, even if/when I explained to them that we can do better than the usual sources.

At the graduate level, especially beyond first-year things, I've tried to change the perspective... by writing my own notes (yes, a bit of work), with historical references, explaining chronology, and so on, the idea being to get students thinking in terms of the subject rather than secondary or tertiary sources.

Unclear to me how successful this is, but I feel professionally obligated to give a push in the right direction.

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    $\begingroup$ I'm afraid I'm having trouble following the logic here. All other things being equal, I would think that a less competent instructor would be more likely to use the same book as everyone else, because the less competent instructor isn't competent to notice the possible problems with the book. I realize that you're recounting student perceptions that are themselves possibly illogical, but ... I really don't get it. $\endgroup$
    – user507
    Apr 1, 2014 at 5:20
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    $\begingroup$ @BenCrowell You are absolutly right! I think, I can explain the "logic" behind that. I had several discussions with students (also when I was one with my co-students). The logic is (to my knowledge) as follows: If there is a standard textbook, then it must be the best textbook because otherwise not almost everyone would use it. So if you don't use to best textbook but something uncommon or even mixed, you must be a bad instructor because you don't see the obvious best book (of which the students even took note!) and you are straying in the topic. $\endgroup$
    – Markus Klein
    Apr 1, 2014 at 6:39
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    $\begingroup$ @BenCrowell, as Markus Klein speculated, many students do have extreme confidence in their own perceptions and expectations, in particular that what is widely chosen must be best. Majority vote rather than expert opinion. $\endgroup$
    – paul garrett
    Apr 1, 2014 at 13:44
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It sounds like you're talking about requiring the students to use one book AND another book AND ..., rather than giving them a list of books and saying they can use this book OR this book OR ...

One problem is cost. For many lower-division courses the cost of a single textbook is already completely exploitative.

In (physics) grad school, I remember really, really hating a couple of courses where the instructor did this. The reason was that the instructor basically wanted to give lectures on the blackboard, which were supposed to present all the material -- but this left us with no organized source of information, just a bunch of hand-written lecture notes without a table of context, index, etc. The multiple books were assigned as an afterthought, and they didn't cover the material appropriately. I felt completely lost in these courses.

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    $\begingroup$ Cost can indeed be prohibitive. Sometimes a workaround can be to compile a reader and/or ensure that the library contains the books in question. The latter can work well if there aren't too many students in the course and the books are more recommended reading than a vital component. $\endgroup$
    – J W
    Apr 1, 2014 at 16:01
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    $\begingroup$ "The latter can work well if there aren't too many students in the course and the books are more recommended reading than a vital component." The disadvantage of such a course is the student has to rely on lectures for his training and loses the support of a book. I am a belt and suspenders guy. Learning math is tough enough. Have a good, helpful book AND have good, helpful lectures. Don't disdain with having a text. It is poor pedagogy. $\endgroup$
    – guest
    Apr 2, 2018 at 2:24
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Disadvantages include cost and efficiency, gaps in explanations, differences in notation, differences in quality of pedagogy, "switching cost" of being used to one way of doing things in a text versus another.

Some of the answers poo-poo the student dislike of this jumping around as irrational. But I would not be quick to condemn the students' hesitation. Students may sense that perfect is the enemy of better. Picking one thing and immersing and doing it well may be better than a smorgasbord that is not well learned. Also, I suspect the teacher desire for this sort of jumping around is strongly motivated by a desire to have perfect rigor or very particular coverage rather than good learning.

I basically agree with the students. The hard part of math class is not finding the perfect proof or ideal coverage but doing the hard slog and learning something. Why not set yourself up for success and pick one best text and use it? There will ALWAYS be alternate choices that could be made, enrichments, or follow-on classes that go deeper. But leave that for later.

In particular, would never do this jumping around for any service class (diffyQ, calc, LA, prob/stat, and probably not for any required math major course). I just honestly think the hurdles to learning are MORE around doing the homework and learning complicated material, rather than bestest ever set of ODE chapters from 4 different books.

We evolved to kill things and make love, not to do math. Think more about what is involved in training well rather than training the most perfect things.

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