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Toward a Lean and Lively Precalculus
In January 1986, Prof. Ron Douglas of Stony Brook assembled a group of 25 individuals for a four-day conference/workshop at Tulane University in New Orleans. This Sloan Foundation–supported event led to the publication of Toward a Lean and Lively Calculus. This conference and the resulting book of written reflections by its participants launched the Calculus Reform Movement in the United States.
The conference called for “a leaner, livelier, more contemporary course, more sharply focused on [its] central ideas.” With the advent of the new Advanced Placement® Precalculus course, the College Board is initiating a Precalculus Reform Movement. This new AP® course is lean, lively, modern, and squarely focused on the central concept of function.
This new course offers other innovations that echo the Calculus Reform Movement. AP® Precalculus extends beyond calculation to include graphical, numerical, algebraic, and verbal representations of functions and an emphasis on student communication and reasoning. The course embraces technology as a tool to explore ideas and deepen understanding. It also dives deeper into applications and mathematical modeling than is typical at the precalculus level. This AP® course centers on properties of functions that students will encounter in Calculus, such as change in tandem, increasing/decreasing, concavity, points of inflection, boundedness, extrema, continuity, holes, asymptotes, and end behavior. It employs limit notation without a formal definition of the concept, which is saved for Calculus.
By scaling back from four required units to three—polynomial and rational functions, exponential and logarithmic functions, trigonometric and polar functions—AP® Precalculus allows teachers and students the opportunity for in-depth coverage of these tested topics while giving them the freedom to explore more advanced functions involving parameters, vectors, and matrices.
All in all, this will be a challenging yet achievable course for college-bound students. And it opens the possibility to offer AP® mathematics within small school districts in towns and rural areas, addressing an often-overlooked equity issue.
Hurray for lean and lively Precalculus!
Greg Foley, Coauthor of the new Demana/Waits AP® Precalculus text and MyMathLab® course
Dr. Greg Foley is the Morton Professor of Mathematics Education at Ohio University. Foley received BA and MA degrees in mathematics and a PhD in mathematics education from the University of Texas at Austin. He has taught arithmetic through graduate-level mathematics and coauthors Advanced Quantitative Reasoning: Mathematics for the World Around Us and Precalculus: Graphical, Numerical, Algebraic.
About the Author
Gregory Foley
Author & Morton Professor of Mathematics Education at Ohio University