Anton's Research Ramblings

A Textbook Review Template

Textbooks are a minefield. Especially technical textbooks. Especially mathematics textbooks. It's hard to build a good set of recommendations for students on different subjects. If you're teaching computer graphics you cross a lot of different disciplines and it's nice to have something good prepared for each. In my mind a lot of textbooks are unsuitable or poorly written because they miss the mark. The authors may be experts, but they often don't understand what their job is as an educator. Especially mathematicians - they are the absolute worst. Finding a good mathematics guide for students on linear algebra or the calculus is a near-impossible task. Part of the reason I wrote a book for students is because I just find the way that these things are done to be dreadful.

So, I'm thinking of doing some book reviews. And to explain my position - why I have a bee in my bonnet, so to speak, I think it would be helpful to have an evaluation table, or rubric, as some countries prefer to call it.

Principles of a Master Teacher

The best educators and teachers really shine. They don't just convey information by reading bullets off slides or dumping fully enumerated points. They don't waste their students' time. They know how to make use of the psychology of the audience, and they know that they must be leaders. They do these three things:

  1. convince their audience of the importance or point of an idea
  2. use their own experience to demonstrate a concept
  3. inspire their audience to learn more

The audience or students must be convinced in the competence and expertise of the teacher or author. This absolutely applies to books as it does to live lectures or talks. The teacher must convey their passion in the subject. This is what motivates. They do not feed the students every last detail - they give enough to demonstrate a concept, and let the student do the tedious work themselves. They do not force the students to mindlessly repeat exercises or other rote-learning work. Fully-defined exercises are the stuff of mediocre teachers, and those who only superficially understand the learning process. If you give the student a task it must be open-ended. This is how the brain is fed, not through tedium but through exploration! That is how we build the hard links in the brain, rather than the weak links of rote learning, the bored links that fade away at the end of semester, to be learned from scratch the next time that they are needed! Exploration is how we get that "buzz" from success - not from knowing we got 67/70 exercises pedantically correct. It is a complete lie of education to say that "first we must learn the tools, then we can apply them". False! First we apply ourselves to a problem, then we learn the tools to suit, and when we do we damned well learn them properly and forever!

I believe these three principles - convince, demonstrate, inspire - apply to any short talk, any book, any chapter within a book, and any full course. And it follows that we can judge any book, talk, or course, based on these three principles.

The Textbook Evaluation Table

This may seem simple, but most textbooks fail at almost all of these points.

convince is sufficient background given first? are we aware of the history?
convince is the point or practical utility explained first? do we know where we might use this?
demonstrate expertise is an author-made example demonstrated?
demonstrate expertise is the principle conveyed clearly?
demonstrate expertise are we shown how this is applied more broadly in the field?
demonstrate expertise are we given practical tips/shortcuts/advice?
demonstrate expertise are we shown how to recover from common problems?
inspire is the author's passion for the subject clear?
inspire do we know where to start looking for more information?
inspire are we motivated to try the topic for ourselves?
cost is the book affordable considering it may be one of several we need for the course?
coverage is the book too small or large considering what we want from it?

It is possible for all of these things to be true, and an author's personality does not appeal to you, or for the information to simply not be that new or interesting to what we want to do. It's hard to be objective about these things as much so we have to be prepared for this too, and just have a good range of sources to choose from.

Certainly, even books that are not good at many of these more framing and motivational tasks can have good value as reference material - if you know what you are looking for first. We must evaluate the good with the bad. I don't mean to only look for failings. But, where a small work really hits a lot of those objectives it should rise to the top!