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Pre-AP: Strategies in Mathematics -- Accumulation
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Accumulation is a process that has its roots in middle school and early high school mathematics. Calculus students formalize accumulation concepts back to their middle school experiences, refining and extending their knowledge of discrete accumulation to apply to a function over an interval. For example, area and distance are two topics, often compartmentalized, that are actually related to each other by accumulation, and participants create and analyze a speed graph to demonstrate this. When students have an early introduction and continue to develop their understanding of accumulation at each grade level, they are prepared for challenging classes, such as AP Calculus, later in high school and in college.
In this one-day workshop, teachers examine a seamless 6-12 development of accumulation concepts through grade-level-appropriate content, classroom strategies, and technology usage. They experience a guided-exploration approach that they can use in the classroom to build knowledge and create understanding for each student. Teams develop problems, instructional activities, assessment items, and cross-grade lessons for classroom use. Participants also gain embedded diagnostic and formative assessment strategies that can be used to develop students' communication skills and allow teachers to monitor and foster mathematical thinking.
General Themes
- Connections between the presentation of accumulation concepts throughout the curriculum
- Accumulation of rate of change
- Accumulation of area
The workshop conforms to:
The workshop provides:
- Substantial content background for teachers
- Activities for students across grade levels
- Activities meant to illustrate good pedagogy (various instructional approaches including cooperative learning)
- Activities that require communication to support observations and conclusions
- Opportunities for reflection
- Connections between activities
- Optional online follow-up
Agenda
Accumulation and the Concept of Area
Accumulating Distance When Speed Is Constant
Break
Accumulating Distance When Speed Changes
Lunch
Accumulating Distance When Speed Is a Function
Break
Velocity Distinct from Speed
The Big Picture of Accumulation
Author
James R. Choike is a professor of mathematics at Oklahoma State University. He has been involved with the College Board for 20 years as an AP Reader, a workshop presenter, a curriculum developer, and a professional development specialist. Besides AP, he has also been involved with other College Board programs: Equity 2000, Pacesetter, CLEP, SAT, and Springboard. Dr. Choike teaches undergraduate and graduate mathematics courses at OSU and uses his summer months to work with middle and high school teachers and their students.
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