I'm referring here to (math or other subjects) textbooks which include an exposition, main text and examples, references and exercises in each of the chapters.

From my experience, in most cases, it isn't feasible to really work through a chapter in a single reading. I keep finding myself getting tired (and confused) with the texts and jumping forward to see more complete examples and to try my hand at the exercises. And I keep wondering, why won't anyone make textbooks with more manageable chapters.

Why not cut the subject matter into small chapters, as in popular fiction, or as in Khan Academy tutorials? Is anyone here familiar with any research measuring the effect of chapter length on comprehension or any other parameters?

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    $\begingroup$ There is a reason why chapters are divided into sections, and sections into subsections. Given the existence of smaller subdivisions, I do not really understand the necessity of "working through a chapter in a single reading". $\endgroup$ – Willie Wong Jun 5 '14 at 14:38
  • $\begingroup$ @WillieWong, one reason being that subsections generally don't have exercises (and I wonder why not). $\endgroup$ – yoniLavi Jun 5 '14 at 14:43
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    $\begingroup$ Hmmm... perhaps you should specify what level of mathematics are you considering the textbooks. Primary, secondary education, or beginning or advanced undergraduates? $\endgroup$ – Willie Wong Jun 5 '14 at 14:47
  • $\begingroup$ I'm mostly considering undergraduate textbooks (and have had similar experience with the beginning and advanced subjects). $\endgroup$ – yoniLavi Jun 5 '14 at 15:02

This phenomenon is actually debatable. The length of the individual "lessons" in a textbook is one of the indications of its quality, because the smallest division in the book is the natural material for a single class: it is hard to teach half a section because the internal organization does not support it. A textbook with sections containing too much material to cover in (say) one hour is poorly designed as a classroom reference. So in that sense, what you describe is answerable with "a better book wouldn't do that".

Often, in the highly polished mega-textbook franchises (e.g. Stewart's Calculus), there is bloat with different contents: examples. They try to give one for every kind of problem, since their goal is not for students to appreciate the theory, but to do the standard exercises fluently. These, again, can't all be done in class, but it doesn't mean the book is poorly designed: rather, it provides insurance against confusion. Though it is somewhat condescending.

Whether this is what you are seeing, or whether you simply need to skip to the exercises without reading the whole section first because of your personal learning style, I can't say.

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    $\begingroup$ has that chapter<->lesson been your actual experience? As far as I recall from my (undergraduate) studies, a single chapter would often span across two or three 90min lessons. In any case, the experience that prompted this question is of reading textbooks chapters for self-study. Do you think, there could be any didactic harm in having a single class contain several chapters? $\endgroup$ – yoniLavi Jun 5 '14 at 15:00
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    $\begingroup$ What's a "chapter"? If it's a thing called an actual "Chapter" with multiple subsections, then of course, it is not one lesson. If it's a single section, then, yes, I do teach one section per lesson most of the time. If the book you're thinking of has chapters with sections but you actually mean the chapters, then I am confused, because surely, the sections themselves have exercises at the end? And if not, and the chapters are actually long, then my answer applies and the book is poorly organized. $\endgroup$ – Ryan Reich Jun 5 '14 at 15:05
  • $\begingroup$ I think I agree with you. It's just that all books I can currently recall lacked exercises following subsections. Could you please point to a book that you consider well built (preferably previewable in Amazon/Google Books)? $\endgroup$ – yoniLavi Jun 5 '14 at 15:12
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    $\begingroup$ I'd have a harder time thinking of one that doesn't have the structure of "sections with exercises". For example, look at Stewart's Calculus; you can search inside on Amazon and see that section 1.1 has exercises at the end. Now, I don't know that there are any calculus books that aren't overwrought (I mean, the same section has 11 examples), but in this aspect, it is well-designed. $\endgroup$ – Ryan Reich Jun 5 '14 at 15:27
  • $\begingroup$ thank you, most other books I looked at now at Amazon also had subsection exercises. I suppose I was just on a roll of bad/old books. One of the examples on my mind was Ross's "A First Course in Probability", which has very long chapters and no subsection exercises (but does have good examples). In any case, I still wonder whether the issue of textbook chapter length has ever been rigorously studied. $\endgroup$ – yoniLavi Jun 5 '14 at 16:47

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