Fordham University            The Jesuit University of New York


Instructor: Mark Howell

Calculus Institutes

Calculus AB Review

July 7-10 & July 14-18
This four day session provides a review of the major content in an AP* Calculus AB course. It is intended for teachers who are preparing to teach the course for the first or second time.

All of 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 the important theorems in AP* Calculus will all be covered.

Calculus AB

July 14-18
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 2014 AP* Reading are all included.
  • 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 derivativeas 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 2013 AP* Calculus AB Free Response Examination, including student samples

Calculus BC

  • 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 2014 AP* Calculus BC Free Response Examination, including student samples

About the Instructor

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, 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.

He 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.

He 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.

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