By Kevin Cheung, Associate Professor, School of Mathematics and Statistics
Some people regard math as a black-and-white subject. Such a sentiment has a certain degree of truth. Calculus two centuries ago is still calculus today. Theorems that have been rigorously established will not become untrue in the future unless our logical foundations crumble. Yet there are currently dozens of calculus titles in circulation, some of which have gone through more than half a dozen editions and are sold at jaw-dropping prices. What’s going on?
Even though mathematical truths transcend time and culture, how they are explained or taught can vary tremendously. As a result, unless one is writing a reference work, one must settle on no more than one or two approaches and present the material in a certain order. The choices made by textbook authors are often based on their training, teaching experience, and teaching philosophy.
It is therefore not uncommon for instructors to have difficulty finding textbooks that work well for them. Sometimes, what ends up happening is that some instructors will just pick a popular textbook and then teach from their own notes. If these instructors happen to have the habit of typing up their notes, then after a few offerings of a course, they might end up with lecture notes that can be published as a book. In fact, a great many textbooks on my bookshelf began their existence as lecture notes, especially for subject areas for which standard textbooks do not yet exist.
So if you have created a polished set of lecture notes specifically for your course, would you use it as the main course text? I would. And I have. (Though one needs to keep in mind that using one’s own writings as course textbooks could be problematic. See this previous blog post for a discussion.). Unfortunately, having a textbook that I really like is no guarantee that students will like it as well. Perhaps the problem of choosing the right textbook will always be challenging.