In a previous post I wrote some advice on how to read a mathematics (or science) textbook. Having both taught and worked in the publishing world for many years, I have frequently heard (from publishers and other teachers) that students do not read textbooks. My experience working with students one-on-one has provided some details about this, and provided a couple of plausible explanations, which I’d like to discuss in this post.

Average students tend to become overwhelmed with the pace of a typical university mathematics (or science) course, and fall behind within a few weeks of the start of a course. The result is that they are constantly scrambling to catch up, and can’t do a proper job of studying. In the frenzy of deadline after deadline (assignments due, quizzes, tests, labs, lab reports, etc.), it’s all they can do to put out the next fire. As a result, they are very inefficient; they can’t take the time to do a good job of learning the material, which would involve reading the textbook, working through the examples, and doing many practice exercises. Instead, they devote far more time to completing the assignments than would be necessary if they had done many practice exercises, because they attempt the assignments before they really understand the material. But they don’t see an alternative, because the assignments are worth marks, and so they are (unfortunately) a higher priority than actually learning the material. By the end of the course, they understand very little, even if they have managed to score a decent grade.

Top students do tend to read their textbooks, and do all the other good things listed in the previous paragraph. However, when pressed for time, they fall back on just doing the assigned exercises.

For all students, desperation for marks is counterproductive to learning.

So it’s not for lack of desire that students do not read textbooks; it’s because they can’t keep up with our typical university courses that are overloaded with content, and delivered at too fast a pace for many students.

I believe that students would read textbooks, if conditions were different. For example, if courses were designed so that students could work at their own pace, then the pressure would be reduced, and many more students would take the time to read their textbooks.

There is a second reason that dissuades students from reading textbooks. They are unnecessarily difficult to read. There are two reasons for this.

First, there is a misplaced sense that students must be “challenged” by a textbook. But a first-year calculus textbook, for example, might be used by both mathematics majors and by other students; what is appropriate for one group is probably not appropriate for other groups. And I have no problem with challenging students, but do it in the right way. Making prose passages too terse, not explaining the big picture, not explaining the purpose of studying each section, not explaining a worked-out example in full detail, etc., etc.; none of these serves as proper challenges, but rather just works to frustrate readers. If you want to challenge students, then do it by writing challenging activities, not by writing poorly and leaving students to figure it all out, especially when they have been ill-equipped to do so by having vast gaps in their high-school preparation.

The second reason that textbooks are difficult to read is that they try to please too large a market. Publishers produce books because they wish to make a profit, and so they attempt to please as large a market as possible. They do this by including as wide a range of content as is practical, in a way that will please the largest audience, and displease the fewest number of potential adopters. This is the reason for the bloated, dense textbooks that are so common at the first-year university level.

However, publishers are very sensitive to “page count.” Every extra page means more cost, and lower profit. Therefore, they encourage authors to include more topics, but to write in a very compact way, to keep the page count down. They justify this by saying, “students don’t read the prose anyway,” which is another way of saying, “students don’t read textbooks.”

I have had students come to my office saying, “I tried to read through Example 3, but I can’t understand it. Can you help me?” Typically, the problem is that the solution is written in such a compact style, with quite a number of steps of algebra compacted into one, that the* logic* of the solution is not apparent to the readers. If the logic were clearly explained, that would help, but including all the steps in a solution would help more. This type of defect is a feature of virtually all of the major, popular, successful, mainstream first-year mathematics textbooks.

Again, one could argue that students should be required to fill in some details by themselves. Sure, agreed. But then why bother to write textbooks, and why bother have students buy them? We live in an age where the internet is a vast repository of information. Why not assign students to read various web pages (most of which are not of high pedagogical quality, but so what) and then ask them to fill in the gaps? It would be a lot cheaper for students, and it would certainly be very challenging!

To me, the only reason for devoting the enormous amount of time needed to write a good textbook is to actually make it of use to readers. And this means to carefully choose AN audience (just one), and then write in a way that will serve that group of people.

If we do this, and if we change the structure of undergraduate education so that students have the time to learn properly, then students *will* read our books.

(This post first appeared at my other (now deleted) blog, and was transferred to this blog on 22 January 2021.)