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Calculus AB

Mark Howell

Photo of Mark Howell

Mark Howell teaches mathematics and computer science at his alma mater, Gonzaga High School in Washington, DC. He earned a bachelor’s degree in mathematics in 1976 and Master of Arts in Teaching in 1981, both from the University of Chicago. He has served the AP® Calculus community since 1989 in a variety of roles, including AP® Exam Reader, Table Leader, Question Leader, and Exam Leader. A long-time College Board Consultant conducting workshops and summer institutes, Mark was a member of the AP® Calculus Development Committee from 1997 to 2001. He has spoken at professional conferences in the United States and internationally.

He is co-author of the popular prep book Be Prepared for the AP® Calculus Exam from Skylight Publishing, and authored an AP® Teachers Guide for Calculus. He is a contributing author to each of the College Board’s Topic Focus publications in AP® Calculus, including Differential Equation, the Fundamental Theorem of Calculus, Approximation, and Series. He won the Presidential Award from the District of Columbia in 1993, was a national Presidential awardee in 2017, and received the Tandy Technology and Siemens Awards in 1999. He has a special interest in the use of technology to enhance the teaching and learning of mathematics, and has served as a consultant to both the Hewlett-Packard and Texas Instruments calculator operations.

Course Description

This four day institute will focus on instructional materials and methodologies for an AP® Calculus AB course. Hands on student-centered activities and explorations are a prominent component of the institute. Pacing, reviewing for the AP® exam, using old AP Exam problems, assessments, and a discussion of the recent AP® Reading are all included. Recent changes and new points of emphasis in the course will also be discussed.


Day 1

Overview of the AP Calculus program; limits, relative growth rates of functions, and asymptotic behavior; continuity and its consequences; rates of change; tangent lines and local linearity; Concept of a derivative; derivative at a point and derivative as a function;

Day 2

Higher order derivatives; the Mean Value Theorem; the role of sign charts and writing justifications; applications of the derivative, including optimization; implicit differentiation and related rates; Riemann sums and trapezoidal sums;

Day 3

Functions defined by an integral; calculating net change as the accumulation of a rate of change; the Fundamental Theorem of Calculus; average value of a function; applications of the integral, including volumes of solids with known cross-sectional area;

Day 4

Differential equations; slope fields; constructing assessment items for AP Calculus; instructional and supplementary materials; reviewing for the AP Calculus Exam; planning and pacing; The AP Reading – organization and process; review of the most recent AP Calculus AB Free Response Examination; using the Curriculum Framework and AP Classroom.

Note: A TI 84 graphing calculator will be used.