By David Bressoud @dbressoud
As of 2024, new Launchings columns appear on the third Tuesday of the month.
FDWK refers to Ross Finney, Frank Demana, Bert Waits, and Dan Kennedy, the team of authors who for many years and multiple editions updated Calculus: Graphical, Numerical, Algebraic, one of the most popular textbooks for the College Board’s Advanced Placement Calculus. In 2013, after Finney’s death and with Demana and Waits in failing health, I was asked to join the authorship team to help prepare the fifth edition. This was not an immediate “yes”. While I had written several textbooks, these were all books that I wished I had had available as a student, books written to read with lots of historical context. Students in large calculus classes do not expect to read the textbook. I knew that mass market textbooks rely on exercises and examples. I also was leery of how much freedom I would have to shape this text. It clearly had to hew closely to the AP Calculus syllabus which itself is constrained to follow the structure and emphases of the large calculus classes at major universities.
I am very glad that I agreed to come on board. I have long known Dan Kennedy as a friend and colleague, and it has been a delight to work with him. He has allowed me a certain amount of freedom to push the text in directions that are important for me. I also have been impressed by the pedigree of FDWK as well as its rich and extensive collection of examples and exercises. The book’s lineage goes all the way back to George Thomas’s Calculus and Analytic Geometry, the first edition of which was published in 1951 and which, in ensuing years, would serve as the model for virtually all calculus texts used in the United States. Eventually, Finney joined Thomas as co-author, then took over as George Thomas embraced retirement.
Frank Demana and Bert Waits, both professors at Ohio State, were early adopters of graphing calculator technology. In 1989 they published Precalculus Mathematics: A Graphing Approach. In the early 1990’s as the College Board began preparing to require graphing calculators for the AP Calculus exam, Demana and Waits teamed up with Finney to write a calculus textbook that drew on the abilities of these calculators. The subtitle, Graphical, Numerical, Algebraic, was a mantra of the Calculus Reform movement of the late ’80’s and early ’90’s. The intent was to broaden student understanding of calculus beyond a set of procedures for turning one algebraic expression built from polynomials, trigonometric functions, exponentials, and logarithms into a different one. Those engaged in Calculus Reform wanted to enrich conceptions of function beyond these algebraic expressions and to enable students to see how the principles of calculus applied to a broader range of functions, functions only described graphically or through data.
The first edition of Calculus: Graphical, Numerical, Algebraic appeared in 1994, listing Finney, Thomas, Demana, and Waits as authors. While George Thomas was no longer a participating author, this served as an acknowledgement of his work on the earlier editions on which this book was founded. In the same spirit, the current sixth edition lists Frank Demana and Bert Waits as authors even though they did not participate in this revision.
In 1995, graphing calculators became a requirement for the AP Calculus exam. The authoring team realized they needed someone with direct experience using these calculators in the high school classroom. They brought in Dan Kennedy who taught at the Baylor School, a private boarding and day school in Chattanooga, Tennessee. They could not have done better. In addition to his nationally acknowledged expertise in the classroom use of graphing calculators, Dan had served as a member of the AP Calculus Development Committee from 1986 to 1990 and as its Chair from 1990 to 1994. This is the committee that sets the syllabus and writes the exams. In his role as Chair, Dan oversaw the transition to the use of graphing calculators. He became a co-author for the 1999 edition.
For the fifth edition that appeared in 2015 the updating was mostly done by Dan and me. Ross Finney had died in 2000 and Frank Demana was not well enough to participate. Initially, Bert Waits worked with us, but he died as we were preparing that edition. There were a few minor changes that I brought to the fifth edition. One was to talk about the derivative as a measure of sensitivity to small changes in the independent variable. Another was to beef up the historical references.
As we approached the time when a sixth edition was needed, it was clear we also needed to bring someone new on board. The choice was obvious: Mike Boardman. He was a former Chief Reader for AP Calculus (the person who oversees the “Reading”, the grading of the exam), and as such participated in the Development Committee. He and Roger Nelson had also co-authored their own calculus textbook.
I am very proud of the sixth edition. I was able to move into the text some of the ways of understanding calculus that I consider to be essential while also continuing to build the marginal notes on the historical context of its development. I know that most students do not read the text, but I hope that most teachers do. I want my additions to enrich teacher understanding of calculus while not diverging from the prescribed curriculum. This column is getting long enough that I am going to wait until next month to describe those insertions that I consider important for how anyone teaches calculus.
New editions continue to roll out, driven by changes in the AP Calculus program. The most important current innovation is that the College Board is in the process of transitioning from graphing calculators to the graphing technology provided by Desmos. The exam is now given on computers with a version of Desmos embedded in the appropriate questions. Students can still use their calculators on the exam, but I think the days of graphing calculators as we have known them are now numbered.
Dan is no longer the young man he was in the ’90’s and has announced that this is the last revision on which he will work. Recognizing the importance of a team member with relevant high school experience, we again went with an obvious choice: Mark Kiraly, a teacher at Ryan High School in Denton, Texas who has impeccable credentials and is young enough to help see this series through for the next few decades. He has served as Reader, Table Leader, Questions Leader, and most recently Exam Leader for AP Calculus. As a Lead Consultant for the College Board, he conducts national workshops for AP teachers and moderates the popular Facebook group serving over 10,000 AP Calculus teachers.
This 75 year-old lineage still has a lot of life in it.
David Bressoud is DeWitt Wallace Professor Emeritus at Macalester College and former Director of the Conference Board of the Mathematical Sciences. Information about him and his publications can be found at davidbressoud.org