AP* Institute: Calculus AB District Designed Professional Development Course Syllabus

Transcription

1 Title: AP Calculus AB Summer Institute Dates/Times: July 18, 19, 29 and 21, :00 AM to 4:30 PM (lunch served) * APSI approved for Graduate Credit will require additional out-of-class hours. Location: Montgomery County Intermediate Unit 2 West Lafayette Street Norristown, PA Instructor: Ted Gott Enrollment: Novice and Experienced AP teachers Montgomery County Intermediate Unit Contacts: Kendal Glouner Lois Winton MCIU APSI Director MCIU APSI Secretary Kglouner@mciu.org Lwinton@mciu.org AP* Institute: Calculus AB District Designed Professional Development Course Syllabus *AP, College Board, AP Vertical Teams, Pre-AP, the Advanced Placement Program and the Acorn logo are registered trademarks of the College Board. Used with permission. Course description: This course examines concepts, topics, instructional strategies, and assessments related to the teaching and learning of AP Calculus. The topics outlined in the College Board Course description will be examined at great length. The topics include differential calculus and its applications (maxima/minima, related rates, and optimization), along with integral calculus and its applications (area, volume, definite integrals and Riemann Sums). In addition, the AP Exams will be analyzed, and strategies for preparing students for the AP Exam will be discussed. Prerequisites: None Course Goals: 1. Enhance participant mathematical content knowledge of the AP Calculus curriculum from a graphical, numerical, and analytical point of view. 2. Increase awareness of the subtleties of the curriculum and how it applies to the AP Calculus Exam. 3. Increase participant competency with the graphing calculator as a tool for exploring key concepts in the calculus curriculum. 4. Increase participant capacity to write summative assessments that reflect the AP Calculus

2 curriculum and the AP Calculus Exam. 5. Expose participants to reference materials and texts appropriate for use in AP Calculus. Learning objectives: Learners will: Demonstrate knowledge of the content of the AP Calculus curriculum. Participate in discussions concerning the philosophy of AP Calculus in light of calculus reform. Evaluate, modify, and create curriculum materials and lessons that promote student understanding of essential calculus concepts. Integrate technology into the AP Calculus curriculum and learning activities. Develop strategies and tools for use in preparing students for the national AP Calculus exam. Develop and implement appropriate assessment procedures and tools for use in AP Calculus. Textbook and other required materials: Current calculus textbook used at the participant's school. Workshop handbook (provided). Graphing calculator used at participant s school. The Texas Instruments TI-84 and N-Spire CAS will be used by the instructor for demonstrations. General methodology used in teaching this course: In-class presentations and demonstrations Problem solving activities Group discussion and analysis Use of technology during and outside of class Assigned readings and reflections Exploration of online resources and software Writing, analysis and revision of curriculum materials Individual reflection Evaluation: The course grade will be a letter grade. Minimum for an A is 90%, for a B is 80%, for a C is 70%, for a D is 60%. Below 60% is failing. Evaluation Criteria Percentage AP Type Free Response Problems and Rubrics (3 problems) 25% AP Selected Response Problems % AP Free Response Problems % Unit Plan 25% Evaluation Criteria Rubrics: AP Free Response Problem and Rubric 25% Objectives Exemplary Average Low Each question will feature: the structure of an AP Free Response problem questions questions questions Not acceptable Creation of questions did not meet

3 multiple parts from varied content areas of the AP Calculus AB curriculum. non-routine or creative elements to approaching the content area topics. 15 points possible Each question will be annotated to indicate: content topic(s) covered (Big Idea, Enduring Understandings, Learning Objectives, and Essential Understandings) Mathematical Practices 6 points possible Each question will have a scoring rubric that features: the structure of an AP Free Response scoring rubric nine points that are distributed to the various parts of the problem. points that are assigned based on positive work done or explanations given. wording to reflect the read with the student philosophy of AP grading, where appropriate. for all 3 (13-15) provided for all 3 questions. (5-6) rubrics for all 3 for 2 (8-12) provided for 2 questions. (3-4) rubrics for 2 for 1 problem. (5-7) provided for 1 question. (1-2) rubrics for 1 problem. course expectations. (0-4 points) not provided for question. (0 points) Rubrics did not meet course expectations. 15 points possible (13-15) (8-12) (5-7) (0-4 points) Rubric for AP Selected Response Problems 25% Objectives Exemplary Average Low AB 2015 Selected Response problems Section I Part A points points 0 10 points 28 points possible AB 2015 Selected Response problems Section I Part B points 6 9 points 0 5 points 17 points possible Rubric for AP Free Response Problems 25% Objectives Exemplary Average Low is

4 problem #1 problem #2 problem #3 problem #4 5 points possible problem #5 problem #6 is is is is is and and and and and and

5 Rubric for Unit Plan 25% Objectives Exemplary Performance Average Low Unit plan addresses a topic from the AP Calculus Curriculum Framework that can be approached from a graphical, numerical, and analytical point of view. Unit plan incorporates graphing calculator technology where appropriate. 5 points possible Unit plan involves questioning strategies and activities that promote student involvement. 5 points possible Uses graphical, numerical, and analytical representations of functions and fully illustrates connections in order to enhance student understanding of the topic. Uses graphing calculator both to demonstrate concepts and to allow students to explore the concepts. (4 Includes - 5 points) questioning strategies and activities as an integral part of the lesson. Uses graphical, numerical, and analytical representations of functions and partially illustrates connections in order to enhance student understanding of the topic. Uses graphing calculator to either demonstrate or to allow students to explore the concepts. (2-3 points) Includes questioning strategies and activities as an integral part of the lesson. (2-3 points) Does not use graphical, numerical, and analytical representations of functions or uses but in a way that does not enhance student understanding of the topic. (0-1 Does point) not use graphing calculator or uses in a limited or non-essential way. Does not include questioning strategies or activities. Syllabus prepared by: Ted Gott College Board Consultant December 2015 Graduate Credit Option Requirements Participants must attend all sessions. Three assignments due by July 28, (8 hours) Complete the Selected Response Problems and Free Response Problems on the 2015 Released AP AB Calculus Exam. Identify the Big Idea(s), Essential Understanding(s), Learning Outcome(s) and Essential Knowledge as well as Mathematical Practices associated with each question. Create a spreadsheet of the analysis of the 2015 Released AP Calculus AB. Case studies & problem solving scenarios (Section I Part A 3 hours, Section I Part B 3 hours, Section II 2 hours) 2 (3 hours) Construct three Free Response Calculus AB questions, and writes a scoring rubric for the three items. Modeling (1 hour per problem) 3 (3 hours) Develop a unit plan based on a Big Idea and Essential Understandings from the AP Calculus Framework including of how the Mathematical Practices for AP Calculus will be incorporated and examples for assessment. Guided project

6 Topics AP* Institute: Calculus AB District Designed Professional Development Course Outline Session 1: Welcome Goals for the workshop Resources for the week Discussion AP Calculus Philosophy and Changes Discussion Equity and Access The Exam Technology Building an AP Program: Student Selection & Preparation Conceptual Development of main concepts Local Linearity and Linearization Session 2: Computing Derivatives Applications of Derivatives Implicit Differentiation and Related Rates Extrema (Local and Global) Optimization Mean Value Theorem Integration Riemann Sums Session 3: The Fundamental Theorem of Calculus Applications of Integration Area and Volume The integral as an accumulator Calculus Online: Support & Resources for AP Instructors Techniques of Integration Transcendental Functions Particle Motion Session 4: Differential Equations and Slope Fields The Fundamental Theorem of Calculus with a twist Other AP topics (upon request) Preparing students for the AP Exam Scoring the AP Exam Institute Evaluation Contact Information Contact Name: Contact Address: Ted Gott tedg20776@comcast.net

7 Title: AP Calculus AB Summer Institute Dates/Times: July 18 July 21, :00 AM to 4:30 PM (lunch served) * APSI approved for Graduate Credit will require additional out-of-class hours. Location: Montgomery County Intermediate Unit 2 West Lafayette Street Norristown, PA Instructor: Ted Gott Enrollment: Novice and Experienced AP teachers Montgomery County Intermediate Unit Contacts: Kendal Glouner MCIU APSI Director Lois Winton MCIU APSI Secretary Kglouner@mciu.org Lwinton@mciu.org Participants must attend all sessions. Three assignments due by July 21, Graduate Credit Requirements 1 Complete the Selected Response Problems and Free Response Problems on the 2015 Released AP Exam. 2 Construct three Free Response Calculus AB questions, and write a scoring rubric for the three items. 3 Develop a unit plan based on a Big Idea from the AP Calculus Framework including of how the Mathematical Practices for AP Calculus will be incorporated and examples for assessment.