Calculus AB and BC
DATES: July 3-7, 2023 (Monday, Wednesday, Thursday and Friday; off on Tuesday, July 4)
Instructor: Mark Howell
This virtual 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 most recent AP® Reading are all included. Changes in the course related to the new Curriculum Framework will also be discussed.
- Day One: limits, continuity, and introducing the derivative; the Course and Exam Description, and AP® Classroom and AP® Central resources overviews.
- Day Two: Mean Value Theorem, applications of the derivative, introducing the integral; using AP® Classroom.
- Day Three: Riemann Sums, trapezoidal sums, the Fundamental Theorem of Calculus, applications of the integral, introduction to differential equations; using the Instructional Planning Report.
- Day Four: Slope fields, separation of variables, additional topics to suit the needs of the participants, planning the course, textbook selection, the grading of the AP® exams, and tips for preparing for the exam.
Dates: July 10 - July 13, 2023 (Monday-Thursday)
Instructor: Mark Howell
This virtual 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. Strategies for teaching in a virtual classroom setting 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; Infinite series, Taylor polynomials.
- Day 4: Taylor's Theorem and the Lagrange form of the remainder and error bound; tests for convergence, reviewing for the AP® Calculus Exam; planning and pacing; the AP® Reading - organization and process; review of the most recent AP® Calculus BC Free Response Examination
About the Instructor (Calculus AB and Calculus BC)
Mark Howell teaches mathematics and computer science at his alma mater, Gonzaga High School in Washington, D.C. He earned a bachelor's degree in mathematics in 1976 and master of arts in teaching in 1981, both from the University of Chicago. Mark 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, he was a member of the AP® Calculus Development Committee from 1997 to 2001. Mark has spoken at professional conferences in the United States and internationally.
Mark 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. Mark 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.
All participants need to agree that you will not make any video or audio recordings of any APSI sessions, for any use, including personal use, without the prior written consent of College Board.
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