Advanced Placement Summer Institute – Calculus AB
GI623
Sonya Land, AP College Board Consultant
[email protected]
Course Description:
This course will prepare secondary mathematics teachers to be highly effective in teaching AP
Calculus to students as well as give strategies for teachers to share with students to be successful
on the AP Calculus Exam in the spring. Teachers will become familiar with the Curriculum
Framework and the Mathematical Practices that accompany the AP Calculus course. The
College Board has published the following as the key takeaways from an AP Calculus Summer
Institute. These takeaways will be taught through hands-on activities, presentations, and
problem-solving.
1. Incorporating the Mathematical Practices provides opportunities for students to think and act
like mathematicians.
2. Students must demonstrate a deep understanding of the concepts, in addition to a solid
knowledge base and proficiency in the mathematical practices, to receive qualifying scores on
the AP exam.
3. The Understanding by Design model of the updated AP Calculus AB/BC concept outline
supports planning that helps to build students’ conceptual understanding.
4. Revisiting concepts in multiple contexts helps students make stronger mathematical
connections and deepen their understanding of the concepts.
5. Setting up a full-year course plan helps to highlight focus areas and to mitigate instructional
challenges.
6. Building student proficiency in the Mathematical Practices requires a deep understanding of
what each practice means, how it will be assessed, and which teaching strategies can be used to
target the development of those skills.
7. Teachers have choice and flexibility in determining when to embed skills-based instruction
into their courses, and those choices will drive their instructional planning.
8. Students must be explicitly taught to think and act like a mathematician, not just perform
complex mathematical problems.
9. Thoughtful scaffolding of skills allows students to access a skill at an appropriate level of
challenge and to build that skill progressively throughout the year.
10. Teachers must thoughtfully sequence the explicit instruction of skills in order to account for
the inherent levels of challenge within and interdependencies among the Mathematical Practices,
and to help students apply those skills in different contexts.
11. A student who truly understands a mathematical concept should be able to effectively
communicate reasoning and justification. Therefore, students need to be explicitly taught how to
communicate about their solution as much they need to be taught how to find the solution.
12. Targeted instructional strategies help students to master the skills used by mathematicians.
13. In order to be successful on the AP exam, students must be provided with multiple
opportunities to practice independent transfer of understanding, knowledge, and skills to
questions modeled after AP Exam items.
Key Takeaways (continued)
14. Resources that align with the AP Calculus Curriculum Framework and support the needs of
students will have a positive impact on learning outcomes.
15. An instructional plan incorporating targeted support can help to ensure that students who
enter AP Calculus with gaps in their prerequisite understandings are successful in the course.
16. Students are more likely to be successful when learning goals and instructional practices
align with assessment strategies.
17. Formative assessments and meaningful feedback enable both teachers and students to know
what the students understand.
18. The curricular requirements set expectations for teachers and ensure consistency among AP
Calculus courses.
19. Teaching the updated AP Calculus course presents opportunities for professional learning
and collaborative problem solving.
Course Requirements:
Teachers are required to attend all five days of the summer institute and participate in classroom
discussions, activities, presentations, and problem-solving sessions. Teachers should bring a
graphing calculator for use during all days of the summer institute. 75% of the teacher’s grade
will be based upon in-class participation, and 25% of the teacher’s grade will be based upon
completing any requested problems or short reading that is assigned at the end of each day.
Teachers will take both a pre-test and post-test as a tool for the instructor and teachers to reflect
upon. Specific grades on the pre-test and post-test are NOT included in the grade for this course,
but improvement from the pre-test to the post-test should be shown.
AP Calculus AB
Summer Institute
AGENDA
The following agenda may change depending on the needs and concerns of our participants.
Homework Prior to Day 1: Watch all 5 videos (about an hour in length total) at
http://apcentral.collegeboard.com/apc/public/courses/231722.html. These give a ton of great
information from the basics of the exam itself to an overall guide of what materials you will be
receiving during the Summer Institute. Please keep a piece of paper handy during the videos so
that you can come to class with any questions you may have while watching these videos.
Fill out the Survey of Interests at http://goo.gl/forms/YJlvVwe4yitGEHFD3. If not all teachers
are interested in a given topic (from the ranking results), I will offer it in a session from 5 to 5:30
on one of the days.
Day 1
Introduction, Pretest
Questions about Video Homework
Multiple Choice Questions on 2016 Practice Exam
L’Hopital’s Rule & Integration Techniques (new topics for the 2017 Exam)
Use of Technology (Graphing Calculators and Software)
Lesson 1: Goals of AP Calculus (page 7)
Day 2
Free Response Questions on 2016 Practice Exam
Graphing of Derivatives Packet
Free Response Questions on AP 2014 Exam
Discussion of Scoring Statistics & Commentary
Lesson 3: Understanding the Curriculum Framework (page 28)
Lesson 5: Planning Your Course (page 44)
Day 3
Free Response Questions on AP 2012 Exams
AP Central Resources & Useful Websites
Slope Fields and Solving Separable Differential Equations
Lesson 9: Scaffolding the MPACs (page 98)
Day 4
Free Response Questions on AP 2016
Lesson 11: Comparing Student Responses (page 129)
Sharing of Participants’ Resources and Lesson Plans
Lesson 12: Strategies for Teaching AP Calculus (page 134)
Motion Curriculum Module (Curriculum Modules from AP)
Day 5
Free Response Questions on AP 2011 Form B exam
How to Review before the Exam
Lesson 18: Syllabus Development (page 192)
Posttest
Each day will run from 8:00 a.m. to 5:00 p.m. with a morning and afternoon break and lunch
from approximately 12:00 p.m. to 1:00 p.m. each day. From 5:00 p.m. to 5:30 p.m. each day,
teachers may stay to have individual questions answered, or we may have sessions for special
topics that only a group of teachers are interested in learning.