Introduction to Calculus AB
Instructor: Gregory Timm
This four-day session provides a review of the major content in a AP® Calculus AB course*. It is intended for teachers who are preparing to teach the course for the first time. The four days for the Introduction to Calculus AB course run from July 8-July 11, 8 a.m.-4 p.m. Participants MUST also attend the Calculus AB Institute led by Mark Howell, which runs from July 15-July 19 from 8 a.m.-4 p.m. (see below). In addition to Introduction to Calculus AB, participants must register for Calculus AB.
In order to attend either course, participants must register through both CVENT and the University.
All the topics from the AP Calculus AB course description will be covered using graphing calculators where appropriate or required by the expectations of the AP® examination. A multiple representational approach will be followed throughout, looking at each main idea graphically, numerically, symbolically and verbally. Limits, continuity, the derivative and its applications, the integral and its applications, differential equations and slope fields will be covered. This course will focus on classroom strategies that encourage teachers not only to enjoy teaching calculus, but also to learn how to creatively engage students in mathematical investigations that enable the students to "discover" the major concepts.
*NOTE: Participants who are not interested in taking the introduction course have the option to register for AP Calculus AB only.
Instructor: Mark Howell
This five-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 2018 AP® Reading are all included. Changes in the course related to the new Curriculum Framework 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
- Day 2: Concept of a derivative; derivative at a point and derivative as a function; 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
- Day 3: Riemann sums and trapezoidal sums; 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
- Day 5: The AP® Reading - organization and process; review of the 2018 AP® Calculus AB Free Response Examination, including student samples; the new Curriculum Framework
Instructor: Mark Howell
This institute will cover all of the topics in the AP® Calculus BC course, with special emphasis on the BC-only topics. A multi-representational approach will be used throughout, looking at concepts symbolically, graphically, numerically, and verbally. A substantial collection of student-ready activities will be distributed, including many that use technology in ways that engage students in the learning of key Calculus concepts. The most recent free response problems will be discussed, as well as insights from the AP® reading. Sharing of ideas for planning the course, pacing, resources, and AP® exam preparation will be part of the institute. Changes in the course related to the new Curriculum Framework will also be discussed.
- Day 1: Limits; continuity and its consequences; the derivative and local linearity; l'Hospital's Rule; applications of the derivative to parametric and polar functions
- Day 2: The integral and Riemann sums; the Fundamental Theorem of Calculus; applications of the integral; applying the integral to polar and parametric functions; improper integrals
- Day 3: Differential equations, slope fields, and Euler's Method; the logistic model; improper integrals; antiderivatives by parts and partial fractions
- Day 4: Infinite series, Taylor polynomials, Taylor's Theorem and the Lagrange form of the remainder and error bound; tests for convergence
- Day 5: Reviewing for the AP® Calculus Exam; planning and pacing; the AP® Reading - organization and process; review of the 2018 AP® Calculus BC Free Response Examination, including student samples; the new Curriculum Framework
About the Instructor
Mark Howell teaches mathematics and computer science at his alma mater, Gonzaga High School in Washington, DC.
Howell 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, and Question Leader. A long-time College Board® consultant conducting workshops and summer institutes, Mark was a member of the AP® Calculus Development Committee from 1998 to 2001.
Howell has spoken at professional conferences in the United States, Australia, China, Taiwan, Thailand, Switzerland, Malaysia, and Colombia. He is co-author of the popular prep book Be Prepared for the AP® Calculus Exam from Skylight Publishing, and author of the current 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.
Howell won the Presidential Award from the District of Columbia in 1993, 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.
*College Board®, AP®, Advanced Placement Program® and Pre-AP® are registered trademarks of the College Board. Used with permission.