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Calculus BC

Chris Lane

Lane, ChrisChris Lane has been an Assistant Professor of Mathematics and Computer Science in Forest Grove, Oregon since 1999. During this time, he has taught a wide range of courses in both mathematics and computer science in addition to graduate courses in statistics, data analytics, and machine learning within the MBA program at Pacific.

He has been involved with the AP Calculus program since 2000, serving in a variety of roles including Reader, Table Leader, Question Team Member, Question Leader for both the operational and alternative exams, and Exam Leader for multiple years for a variety of alternative exams. He has also written multiple-choice questions for the exam and has served as an AP course auditor.

Outside of the AP Calculus program, his professional interests involve using mathematics and computer science for the social good.  He has worked as a lead programmer for a multi-year prostate cancer study using tablets at OHSU in Portland, and also as a technical advisor on an NIH grant involving ethics and philosophy in medicine.  For his 2021-2022 sabbatical, he plans on studying and developing applications of machine learning to medicine and to continue his involvement in the AP Calculus program as part of the leadership team and as a consultant.

Course Description

This course is for AP Calculus BC teachers.  The intent of this course is to reinforce and deepen each participants’ understanding of the topics included in the AP Calculus BC curriculum, to help teachers understand how these topics are tested on the exam, and to explain how the scoring guidelines are developed and applied to scoring student responses.  Common student misconceptions and errors seen in student responses will also be thoroughly discussed throughout the curriculum.

During the course, we will also engage in discussions on classroom techniques and participants will be given the opportunity to share techniques and activities that they have found to be beneficial in their own classrooms.

The online course will run for four days and will be primarily synchronous, although it will include some asynchronous components.

Agenda

This four-day workshop is designed to meet the needs of both beginning and experienced AP Calculus BC teachers.  In the agenda given below, there is flexibility regarding both the ordering and some of the specific material covered as we cater to the collective needs of the group.

General Material:

  • Introductions and Goals for the course: Discussion of the pre-workshop survey
  • Overview of the AP Calculus BC course including key concepts, methods, and applications
  • Examination of the AP Calculus BC Exam including the BC Exam Description Book
  • Review of the use and limitations of graphing calculators
  • Discussion of the most common student errors on pre-2021 BC Free Response questions as well as an In-depth discussion of each question on the 2021 AP Calculus BC Free Response Exam
  • Examination of the resources available to teachers including review materials, worksheets, websites, and classroom activities and participants will also be encouraged to share resources that they have found helpful

Specific Mathematical Content:

  • AB Calculus Topics (briefly)
    • Chain Rule Differentiation
    • Implicit Differentiation and Related Rates
    • Mean Value Theorem
    • Curve Sketching
    • Integration and The Fundamental Theorem of Calculus
    • Differential Equations and Slope Fields
    • L’Hospital’s Rule
  • BC Calculus Topics (in-depth)
    • Euler’s Method
    • Integration by Parts
    • Improper Integrals
    • Sequences
    • Series
    • Taylor Series
    • Convergence Tests
    • Interval of Convergence
    • Taylor Polynomials and Error Bounds
    • Parametric curves
    • Polar coordinates
    • Vectors

Individual and group activities including games will be used throughout the discussion of the topics as time permits.

Note: A TI 84 graphing calculator will be needed throughout this course participants should come prepared with their own devices.