Thursday, May 1, 2014


I am very pleased to announce that I will be joining the team of authors for the AP Calculus text Calculus: Graphical, Numerical, Algebraic by Finney, Demana, Waits, and Kennedy (commonly known as FDWK). Ross Finney has not been an active member of the team for some years (he died in 2000), and Frank Demana and Bert Waits are easing out of their roles, but their names reflect the incredible pedigree of this text. It began with George Thomas in 1951 and has variously been known as Thomas; Thomas & Finney; Finney & Thomas; Finney, Thomas, Demana, Waits; and Finney, Demana, Waits, Kennedy.

I was fortunate to be able to get to know George Thomas after he retired from MIT and moved to State College, Pennsylvania. I knew him as an extremely modest and gentle person with a continuing fascination with mathematics. I have long admired Frank Demana and Bert Waits for their pioneering work in the Calculus Reform efforts. Dan Kennedy and I have known each other for many years through the AP Program, and it is a particular delight for me now to be collaborating with him.

I also am very happy to be joining an effort aimed at high school calculus. Roughly one million U.S. students begin the study of calculus each year, and close to 700,000 of them, at least two-thirds of the total, start this journey in high school. This is the place where one can have the greatest impact in shaping students’ understanding of calculus.

There are limitations that I, as an author of “niche textbooks” for which I can take whatever approach I wish, find constraining. First of all, the text has to be closely tied to the AP Calculus syllabus and exams, which, in their turn, are closely tied to the curricula as enacted at the major universities, the big consumers of AP Calculus results. The emphasis on limits is one of those limitations. I would love to ignore them until we get to infinite series, but that really is not an option.

Second, the books I write for my own pleasure can assume whatever level of sophistication on the part of the reader I choose to impose. I recognize that this text will be used by teachers and students for whom digressions and elaborations may be more confusing than helpful. That said, I do hope to push both teachers and students a little and to open more perspectives, especially historical perspectives, on this subject.

Third, I am now working for the behemoth that is Pearson. I’ve worked with Pearson people on several projects and have always found them to be intelligent, conscientious, and seriously concerned with producing quality products. Nevertheless, this is a mass-market endeavor that travels with its own peculiar baggage of demands and constraints. I am pleased that in the face of so much pressure to bulk up with every tidbit relevant to Calculus, FDWK has managed to maintain a lean profile of only 717 pages (16 fewer than the first edition of Thomas).

Also on the plus side is the large and talented staff that will be working with us to produce the next edition of this text. As I observed in my contribution to “Musing on MOOCS,” which appeared in the Notices of the AMS this past January, the real revolution in education created by the online world is not the disappearance of the live instructor but the richness of supporting resources that instructors can now draw upon. Robert Ghrist argued that the ease with which individuals can produce their own online materials will eliminate the need for big publishers. I argued that the situation is exactly the opposite: “The problem is that few of us will have the time to develop our own materials, and anyone who searches for such resources online is quickly inundated with options. In an era of overwhelming choices, it is the reputable bundlers who will dominate.” MAA is one reputable supplier, as evidenced by WeBWorK (see my column from April, 2009). Pearson is well aware of this need and is actively building these supports.

By an opportune coincidence, I also am working with Karen Marrongelle and Karen Graham on the calculus chapter for the next version of the NCTM Handbook of Research on Learning and Teaching Mathematics.  This means that I am currently steeped in the accumulated research on how students understand and misunderstand the key concepts of calculus. I expect to translate some of this knowledge into the shaping of future editions of FDWK, and I also hope to share some of what I’m learning in future Launchings columns.


  1. "I would love to ignore [limits] until we get to infinite series, but that really is not an option."

    I'd be interested to hear you elaborate on this comment. Do you discuss infinite series prior to differentiation in your ideal curriculum, or do you motivate the definition of the derivative without focusing so heavily on limits?

    1. At Macalester, we strongly downplay the use of the term "limit" in the first semester of Calculus. For differentiation we rely on numerical observations that as the change in the input variable is taken progressively, the average rate of change is getting closer to a value that we call the derivative. The same idea is used in integration, observing what happens to \sum f(x_i) \Delta x_i as the Delta x_i are taken progressively smaller. Limit terminology does appear in the second semester, when we worry more about precise definitions and justifications.