June 29 - July 3
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 2017 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.
July 13 - 17
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.