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Pre-AP: Strategies in Mathematics -- Functions
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The concept of function is present at almost all levels of school mathematics, from pattern recognition to formal representation and analysis. Function is a key concept that prepares students for success in challenging courses, such as AP Calculus, later in high school and in college.
This one-day workshop illustrates a guided-exploration approach as a pedagogical model that emphasizes student thinking as the key to learning and communication as the key to assessing understanding. In addition, teachers learn how to use diagnostic and embedded, formative assessment to monitor and foster mathematical thinking. Teams will work on problems and instructional strategies in small groups and develop cross-grade lessons. Teacher collaboration in curriculum development, across grades, is an essential component in preparing more students to enroll in challenging courses such as AP Calculus later in high school.
General Themes
- Dependency of input and output variables
- Linkages between ratio and rate with variables and the concept of function
- Use of graphs to investigate
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
Introduction to the Concept of Functions
Function as a Model
Break
An Example of Function as a Model
Linear Functions
Lunch
Quadratic Functions
Break
Nonlinear Functions and Functions as Models
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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