AP Calculus (AB and BC)



AP Calculus ABSyllabusDrew UniversityMadison, NJChristinia M. Frazier- InstructorCollege Board AP Calculus and Pre-AP Mathematics Consultantghsfraz@ – emailCourse DescriptionThis course will provide a complete overview of the AP Calculus course and is appropriate for teachers who are both new to the course or have limited teaching experience seeking new strategies and methods to improve their calculus programs. The course will focus on instructional strategies for helping students learn calculus concepts and techniques. Participants will get a deeper understanding of the concepts and techniques of calculus. We will focus on the College Board outline for Calculus, with special emphasis on those topics that have changed most recently due to calculus reform and the introduction of technology. You should definitely download the Course Description effective Fall 2012.We will emphasize a multi-representational approach to the concepts in the topical outline including concepts of the derivative, linear approximations, related rates, optimization, techniques and concepts of the integral, the Fundamental Theorem of Calculus, areas, volumes, accumulating rates of change, approximation techniques for the definite integral, working with functions defined as integrals, slope fields, differential equations, and series approximations of functions where possible. There will be time built into the week for the group to share, discuss and explore problems together. Participants will examine the reading and scoring process including scoring sample exams. Participants should bring the calculator they will be using in their classes. The TI- 83/84 & 89 will be used for demonstration purposes as well as additional online websites. Participants should also be able to indicate the textbook they either use or plan to use for their AP Calculus course.It is requested that participants bring with them a copy of a Pre-Calculus or Calculus lesson that they have already done with students, to share with participants. These lessons and strategies will become good resources for each participant.Course ObjectivesParticipants will be able to work with functions represented in a variety of ways, graphically, numerically, analytically and verballyParticipants learn the meaning of the derivative in terms of a rate of change and local linear approximations and will be able to use the derivative to solve a variety of problemsParticipants will gain increased understanding of the meaning of the definite integral both as a limit of Riemann Sums and as the net accumulation of a rate of change. They will be able to use integrals as expressed in both parts of the Fundamental Theorem of Calculus.Participants will be able to use technology to help solve problems, experiment, interpret results and verify conclusionsParticipants will learn how the AP exam in calculus is graded and will use this information to prepare assessments for their own students that are holistic and rubric-based.Instructional MethodsLecturesGroup discussionsCooperative learning projects AssessmentsDaily homework problems- from selected texts where availableParticipation and completion of in-class activities and group workAttend EACH session of the institutePossible Text/ Readings:Calculus for AP*(Second Edition) Jon Rogawski, Ray Cannon Calculus (3rd edition) AP* Edition- Finney, Demana, Waits, Kennedy MAA Notes. Resources for Calculus Collection. Washington D.C.: MAA, 1993Other Resources Available – Check Online or with PublisherBe Prepared for the AP Calculus Exam, Mark Howell and Martha Montgomery, 2006-Present, Skylight PublishingAdditional resources may be availableAgenda Outline: AP Calculus Summer InstituteDrew University, APSI: July 21, 2014 through July 25, 2014 IContent for AP Calculus ABFunctions, Graphs and LimitsAll About SLOPEGraph analysisLimits of functions- L’Hopital’s RuleAsymptotic behaviorContinuityDerivativesConcepts and DefinitionDerivative at a pointDerivative as a functionHigher order derivativesApplications of the derivativeComputation of the derivative – especially the Chain RuleParticle Motion ProblemsGeometric interpretation of differential equations using slope fieldsIntegralsRiemann SumsInterpretations of the Definite IntegralApplications of IntegrationFundamental Theorems of CalculusNumerical approximations to the integral Improper Integrals- uses LIMITS- an after the test topic of interestIIGrading of Free Response QuestionsLook at the most recent released exam( 2008)- news about future releasesLook at the 2014 Exam with student samplesWrite your own questions on selected topics- Discuss special ActivitiesIIITechnology in the AP Calculus CurriculumKnow your calculator and when to use itSharing information, programs, hand-outs that work for you!! ................
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