Thoughts on Better Textbooks

This post is directed at anyone who might think to write a textbook one day and contains tips that might the book easier to learn/teach from. As I’ll hopefully succeed in illustrating, self-studying from a textbook is a deeply ineffective experience. Since textbooks remain the dominant form of information transfer in the undergraduate and high school experience, it’s worth trying to wring out every inch of efficiency we can get from them. This post comes from a place of reflection as I look back on the past 20+n years of my life and think about how much more I could have learned. Heads up, I’m not an educator nor an expert, this is pure anecdata. However, I am pretty obsessive about learning so I’ve spent a fair bit of time being frustrated about the state of textbooks.

Before diving deeper we need to ask: what is the primary function of a textbook? I think its purpose is threefold:

To summarize these into shorter points, textbooks provide information, practice, and context. It’s certainly possible that textbooks can serve other functions besides these three but I think this forms a necessary minimal set without which a textbook should actively be avoided. The first speaks for itself and the second should be familiar to anyone who has tried to read a textbook for leisure or self-improvement and discovered they didn’t understand core concepts at the end. This latter appeal is a bit….niche, but if it applies to you, you’re my intended audience!

Finally, the third item requires a bit more justification. As an absurd reduction, consider a book that’s just a series of bullet-pointed facts interspersed with occasional examples. This would barely satisfy any sane definition of a textbook. Helping readers to chain the pieces into a coherent narrative, showing how they fit and work together, allows the reader to create a hierarchy or knowledge graph that lets them to see which bit is used where. As for the latter clause, placing the information in the context of external knowledge, imagine a book that doesn’t make clear what learning should proceed it nor what learning might follow it. Such a book is orphaned from the rest of knowledge, leaving the student with neither the ability to identify prerequisites (unless implicitly) nor the ability to continue on in their studies.

Do most textbooks tend to satisfy these criteria? Sometimes they’ll satisfy the first two, but almost invariably they miss the third. Even when the first two are satisfied, the books tend to hit several failure modes that prevent them from truly fulfilling their purpose. To me, the essential sins that textbooks tend to commit are

Failing to distinguish essential knowledge<

Your average textbook is a mass of knowledge, put into linear order by a presumed expert, and broken up by chapter titles and sub-headings. If I had to guess, any textbook contains several 1000 facts, and a thousand example problems (in particular, my nightmares often feature a particular physics text that had a one to one ratio between the two). Of those facts, how many is it likely that the expert knows deeply or has memorized? My guess would be no more than a few hundred and possibly much less than that! It’s sometimes suggested that in the case of STEM, what distinguishes an expert is a small set of base knowledge from which they can either re-derive needed results or use to identify what additional knowledge they need from a reference. In particular, when I was going about my graduate school visits, one of the theoretical physics professors gave us a short lecture where he outlined the set of facts/theorems/concepts he expected every decent theoretical physicist to have on lockdown. It would have been useful to have seen such a list beforehand! I’m sure most researchers have a sense of the 100 or so concepts/theorems that constitute the basis of their field.

Thing is, not being an expert, the reader has no idea which of the facts in the book are worthy of careful attention or memorization! If you study the topic in a course, the instructor can help with this, but it’s certainly possible that even the instructor doesn’t know! Unable to distinguish between essential and inessential facts, the reader is left with three choices: memorizing everything, memorizing nothing, or committing many inessential facts to memory. Given that the author is presumably a leading expert, why not provide their readers with a peek into how they represent their knowledge by clearly outlining essential material? It wouldn’t be burdensome, a simple summary section indicating key concepts and base concepts to memorize would suffice. When I’ve been fortunate enough to have a textbook do this, it’s been a giant boon. Key takeaway: Provide a summary section illustrating key concepts and facts worth memorizing at the end of each section/chapter.

Failing to provide a guided path through problems

It’s inarguable that practice problems, exercises, and worked examples are essential for acquiring mastery. However, once you get to the end of a chapter, you’re greeted with a disorganized sprawl of problems and exercises. If you’re lucky the problems are broken down by subsection so that readers can at least identify the concepts that are being tested on each problem. However, they’re still left with the difficulty of identifying which questions are exercises, meaning relatively simple tasks, which are problems, meaning hard tasks, and which of these exercises and problems are in fact necessary to ascertain understanding or mastery. In the context of a course, this is fine! The lecturer, presumed expert in distinguishing the wheat from the chaff, assign only the minimal set of tasks needed for learning, and the student completes them.

There’s no reason to duplicate effort in this way! Presumably, the author is even more expert in the art of learning the field than the lecturer and is perfectly competent to distinguish which questions are essential to answer for base competence, which are essential for mastery, and which are mere curiosities. It would be incredibly helpful, both for autodidact and lecturer, for the author to indicate which questions constitute a good homework assignment. It’s such a simple thing, but it would make the experience of learning out of a textbook so much better.

To be clearer, here’s what my dream problem section of a textbook would look like. First is a homework assignment, a set of problems that the author believes are necessary to solve to achieve any degree of competence. This homework assignment is in turn broken down by which set of concepts it is testing. This makes it easy for the reader to drill down on parts that they found less clear.

In the textbook that appears unbidden in my dreams, brought down gently from the heavens by angels, half of these problems have solutions in the back of the book. Absent solutions, it’s impossible for someone performing self-study to understand whether they’ve grasped the concepts while the half compromise makes it possible for lecturers to still present a homework whose solutions aren’t available (whether homework should have accessible solutions in courses is a whole other topic that I don’t want to touch here). A nice touch would be for this section to have a time estimate of how long the author thinks each problem should take. This lets the reader get a sense of when they should keep pressing on and when they should give up and look for a hint.

Following this section are a set of problems with clearly indicated difficulties and time-estimates as well as an indicator as to whether these are problems for testing basic concepts or that require the types of conceptual leaps that constitute mastery. As before, some of these problems should have solutions!

Since what I’m suggesting is mostly a matter of labelling and including solutions that have already been written, I don’t think this is an onerous burden to put on a textbook author! However, having a textbook written like this would havee been a boon to me as a younger student, back when I was trying to self-study math but would have endless trouble checking if I’d understood anything.

Failure to provide a narrative

Textbooks come with a skeleton of a narrative, namely, the linear arrangement of the material. You know that the material in chapter seven is essential for chapter eight, chapter eight for chapter nine, and so on and so forth. What’s often missing is a sense of coherence, answers to questions like:

Unlike the previous two sections, there isn’t an easy post-fix that introduces a sense of narrative to a text. Yet its absence is sorely felt, often evident in a sense of boredom or a desire to skip chapters. Often times, authors try to alleviate the absence of narrative by providing a host of examples, seeking to motivate by showing all sorts of use-cases. While wonderful in its own right, it doesn’t alleviate the absence of narrative. An example, no matter how exciting, can only implicitly connect the ideas of chapters 4 to chapters 7. There are two suggestions I have that might help. One is incorporating a knowledge graph; taking each core topic as a node of the graph and connecting it to the others by arrows. One can even include topics outside the text, as a way of motivating by showing how many new ideas are opened up by mastering the contents. Additionally, by skipping ahead in the graph, the reader can see the value of the current topic as it might motivate something that they quite want to understand. The second suggestion, pointed out to me in a comment, was to explicitly write up a 2-3 page narrative that either precedes or follows the book. The narrative can serve to motivate the value of the ideas contained within, connect them, and provide a global perspective that the chapter summaries cannot.

Addendums

One point against the arguments here that was brought up in conversation; perhaps my frustrations stem from using textbooks incorrectly in self-study! I tend to use textbooks like so: I identify a field or a topic that I am unfamiliar with and suspect will be useful and then attempt to work through as much some textbook as I can. An alternative to reading and working through textbooks is using the textbooks as reference material. In this perspective, textbooks are reached for not preemptively, but only when motivated by a project or problem that requires the material. As a consequence, structure is provided by the issues arising from working on the project, and it becomes somewhat more obvious which problems to work on, which sections to read, and what is worth knowing. The counter to this would be that even in this case, the previously mentioned structural improvements would still be helpful. Additionally, this argument presumes a level of expertise needed to identify missing knowledge and figuring which sections of the text correspond to it. Still, this is a valid perspective and switching to it might immediately make the process of self-study easier.

A few points of caution. I’m certainly not an educator, the suggestions are primarily an amalgamation of my own experiences trying to self-study as well as some insights I’ve gleaned by asking other students about their experience with textbooks. This experience is also heavily influenced by STEM texts; while I’ve read the odd humanities text here or there I can’t really claim too much knowledge. I’m motivated to write this because I rarely see either of these tools used in textbooks but I’m certain that they would help me immensely. One thing I’m quite curious about is whether other people feel the same way, or whether they have alternate suggestions for what would improve the average textbook. Let me know your thoughts!

Acknowledgements: this is the second draft of this post. Some interesting thoughts and comments on the first article that made me really want to rewrite it were provided by Spandan Madan, Adam Jermyn, Ellora Sarkar, and Prastuti Singh. Props.