Observing textbooks on introductory collegiate mathematics, and instructors who use these textbooks, one notices that there is little consensus on the role or function of a mathematics textbook. Some textbooks attempt to provide a narrative that tries to access concepts through intuition, application, and explanation. Others attempt to provide an exhaustive resource and reference. Yet others function primarily as a repository of worked examples. In addition, there are the ubiquitous tensions between rigor and accessibility, and between conceptual understanding and skill acquisition.

In our experience, many students use mathematics textbooks as little more than large collections of homework problems, templates for the “types” of problem encountered in the homework, and lists of answers (usually to the odd-numbered exercises). In some of the classes that we have taught, students clearly believed that their textbooks were dry, boring, expensive, and not at all to be read!

We both base our philosophies of the role of the textbook in a mathematics course on the assumption that such an expensive investment ought to, in fact, be read. Much more than economic considerations drive our intent to have our students read their textbooks—we feel that the textbook can and should be a vital part of the course that contributes to the learning goals that we have set for our students. Many of these specific goals are mentioned in this meeting.