MAGNET CALCULUS I
The Textbook
Most texts treat calculus from a theoretical point of view before they get around to its applications. Most texts talk about a “rule of four” when introducing or discussing ideas and topics in calculus (graphical, verbal, numerical, and symbolic). I believe that these texts, while worthwhile, miss the opportunity to introduce the mighty concepts of calculus from only the numerical, verbal, and graphical points of view.
This textbook attempts to do that. In the first (short) chapter, students are introduced to “rate equations” and they begin to use graphing calculators to use the equivalent of Euler’s method to compute values given by a predictive model---a model stated or developed as a rate (differential) equation. Only after this first chapter is any of the traditional calculus theory presented.
I strongly believe that, although the graphical, verbal, and numerical approach is vital to understanding, I also strongly believe that without theory (definitions, theorems, and proofs), then calculus is just a science, and not mathematics. As this is the first course my students encounter that lends itself to being presented as a cohesive theory, it is important to present theorems and proofs of all relevant results clearly and plainly. But understanding is not sacrificed in favor of mathematical rigor.
"Calculus: Dynamic Mathematics, Volume One"
Second edition, 454 pp., $39.95
The Syllabus
The course includes all AP Calculus AB topics, as well as some AP Calculus BC topics, and other additional topics, such as linear differential equations, surface areas, and hyperbolic functions.
The syllabus corresponds to chapters and section in the textbook.
Although I used large portions of the preliminary edition of the textbook with my AP Calculus BC class in the 09-10 school year, this is the sixth year I have taught the actual Magnet Calculus I course.
Why “Magnet Calculus I” and not just Calculus AB?
When the state of Georgia went to the new integrated curriculum (the Georgia Performance Standards), I decided to take another look at the AP course. Frustrated that everyone at my school is required to take calculus (with only 20% or fewer taking Calculus AB) which resulted in less than ideal AP exam scores, I strove to find a way to alleviate this situation.
With the support of my administration, I designed a calculus curriculum that would, over two years, encompass all of Calculus AB, Calculus BC, an introduction to linear algebra, differential equations, and multivariable calculus. With the restrictions that result in even calling the course “AP” removed, I was free to teach the topics in the order I saw fit, introduce extra topics, and still prepare students for the AB exam the first year and the BC exam the second. It seemed to have worked: every student in the Magnet Calculus I class in 2010-2011 passed the AP Exam.
The textbook is the result of these efforts. Volume two, for Magnet Calculus II, was published in Summer 2011, with the second edition in 2014, and the third edition in 2019.