When I was a Project NExT Fellow back in 1999, one of the hottest discussion topics was calculus reform. In a session on the topic at one of our conference gatherings, I listened to a talk by Len Van Wyk titled something like “To Reform or Not To Reform: and why it doesn’t matter.” His thesis was that when we teach a course, each of us brings to bear resources far beyond the text. If I pick a traditional text whose primary focus is rigor and detail, I’m almost certain to supplement it with intuition and perspective; if I pick a reform text whose emphasis is on intuition, I’ll likely complement the text’s exposition with some additional discussion of rigor or formality.
Regardless of one’s take on calculus reform or how the landscape of teaching has changed since 1999, I take the following broad lesson from Len’s talk: for most courses I teach, the textbook plays a secondary role in what I plan to accomplish in the course. From that point of view, I have come to feel that $150 is way, way too much for a student to pay for a calculus text, particularly if it is being used largely as a source of problems. That observation applies not just to calculus: much of mathematics fits this description. Further, I assert that calculus is well-understood and largely agreed upon as a body of knowledge by the mathematical community, and has been for a long time. Viewing calculus as the property of the mathematical community – and indeed, humankind – collectively leads me to want to find ways to share the subject with others at the lowest cost possible.
Today, an electronic text is the obvious medium for freely sharing with humanity, and the internet is the natural vehicle. Moreover, an e-text is great for a projector in class, students on laptops (searchable, always with them), live links to java applets, and markup on iPads and tablet PCs. The combination of the internet and modern computing technology have prompted new questions for the communication of ideas, and new possibilities for those of us interested in sharing them. Are traditional print textbooks even really necessary?
Having now written a free, open-source, primarily electronic textbook, I’d like to encourage others to do so. Here are some key questions that merit asking before undertaking such a large project:
- Why do I want to write a textbook?
- Writing a book is a big endeavor. Is your book needed? Will it be worthwhile to you? to others?
- What are the features of your proposed text that no other (for-profit) text has?
- How do you want students to use your text? How will what you write shape students' experience?
- Will writing a free, open text be something you can take satisfaction from, independent of (or in the absence of) royalties?
- Will the project be something you can be committed to for many years to come?
Of course, if you do join this movement, be sure to seek counsel from others with experience. Reading this blog is a great way to begin; I know from my own experience that other contributors here are happy to correspond by email and at conferences and to share insights and offer support.
Early in my career at Grand Valley, I had an annual performance review meeting with my then-chair, Phil Pratt. Phil was the author of a series of widely-used computer science texts, and in the meeting, I alluded to my desire to write a textbook someday. Phil encouraged me, and said he had one piece of advice: “Don’t have zero days.” When I looked a bit quizzically at him, he clarified: “Be sure that you do something for the book every single day.” Since that time, I’ve heard another highly successful textbook author say something similar: “I try to write 2 pages a day, 5 days a week, 50 weeks a year.” Remarkably, a person who achieves that writes 500 pages a year.
From my experience in now writing two texts, here are a few thoughts on things to strive for:
- Have a written overall plan: outline, timetable, attainable goals.
- Think about your audience. Write for students, not your peers.
- Appearance matters. Research and develop a visual style that is professional but not unnecessarily flashy or complicated.
- Use standard LaTeX. Make it easy for others to use and edit. You want to be able to give the source code away. Be sure to read David Farmer’s post on this site and Rob Beezer’s, too: if you do your .tex right, your book will have an incredible number of potential outlets in terms of electronic format.
- Think about how to use LaTeX’s href package in a meaningful way.
- Have a plan for high quality figures. They contribute in major ways to your text’s visual appearance and to the effectiveness of your communication.
- Organize your files carefully and intentionally. Investigate how you'll share your source with others. See some good counsel elsewhere on this blog.
- Make key decisions about licensing, such as the Creative Commons. Think about how you'll allow and encourage others to contribute.
My impression is that most textbooks grow out of a base set of notes/activities/ideas that the author(s) have personnally class-tested with success. If you aspire to write a book, but don’t have such a foundational set of materials, consider starting there. Student feedback matters. Your peers’ feedback matters, too, even (perhaps especially) if you’re planning to make your work freely available. When you have a 2-3 dozen pages written on your project, seek some serious editorial feedback. Not just your friends; see what your professional critics think. Think about what a professional editor would say. Being conversational and informal is different from being sarcastic or trying to tell jokes within your text.
Early on edit, edit, edit. It will be good preparation for what is to come. And it will make your work much better: hard writing makes for good reading. In every way, work to have consistent style. Line up some alpha testers, as having multiple users and reviewers will significantly improve your work. Perhaps you have some colleagues who want to join you in the writing itself; one of the great things about a free, open project is that you can take on collaborators easily, and integrate the contributions of others. Throughout, the more you can communicate with others with experience and interest, the more opportunities you’ll have to improve, publicize, and promote your text.
Writing Active Calculus has proved to be the most rewarding writing experience of my professional career. I hope that others will continue to join in this movement and to make contributions to the betterment of mathematics textbooks, teaching, and learning through the marvelous resources being promoted on this site and elsewhere.
Grand Valley State University
Grand Valley State University