Concepts of Calculus for Middle Level Teachers

Concepts of Calculus for Middle Level Teachers

Summer 2007

COURSE OVERVIEW

Graduate Credit Hours: 3

Usual Delivery Format: On-site summer course. Designed to be completed in one week, meeting M – F from 8:00 – 5:00 (with one hour break for lunch).

Instructors: Michelle Reeb Homp and Kristin Pfabe

Course Description: Students in this course will develop conceptual knowledge of the processes of differentiation and integration, an understanding of their applications and an understanding of the relationship between the two processes. Topics will include average and instantaneous rates of change, slopes of tangent lines, limits, derivatives, extrema, derivatives of polynomials and exponential functions, anti-derivatives, areas, integrals and the Fundamental Theorem of Calculus. Emphasis is placed on conceptual understanding and connections to the middle level curriculum.

Course Goals: This course serves to introduce the basic concepts of calculus to middle level teachers. The primary goal is to help teachers develop a fundamental understanding of the key mathematical ideas in calculus in order to broaden their mathematical perspective and gain insight into the topics in middle level curriculum which are related and foundational to its development. Participants will develop conceptual knowledge of the processes of differentiation and integration, an understanding of their applications and an understanding of the relationship between the two processes. Problems sets which guide participants throughconcrete examples conveying the fundamental concepts of calculus will form the basis of the course.

Instructional Style: The course is designed around a series of explorations (worksheets) through which students are led to “discover” the main ideas of calculus. Instructors’ roles are primarily to answer individuals’ questions that arise in completing the worksheets, facilitate class discussions as the explorations are completed, and summarize the main ideas developed in the course.

Course Schedule:

Day / Section / Topic
1 / 0 / Linear Functions and Polynomials Revisited.
1 / Limits
2 / Average Rates of Change.
3 / The Slope Function
4 / Instantaneous Rate of Change and the Derivative
2 / 5 / Derivatives of Polynomials
6 / Understanding Derivatives
7 / Derivatives of the Exponential Function
8 / Roots of Polynomials
3 / 9 / Increasing and Decreasing
10 / Maxima and Minima
11 / Velocity Graphs
12 / Area Under a Curve
4 / 13 / Definite Integrals
14 / Distance and Velocity
15 / Anti-derivatives of Polynomials
16 / Area Functions
5 / 17 / The Fundamental Theorem of Calculus
18 / Using Calculators to Integrate
19 / Applications of Integrals

Required Texts:

Harcharras, A & Mitrea, D, Calculus Connections,Prentice Hall Series in Mathematics for

Middle School Teachers, 2007.

Dunham, William W, The Mathematical Universe, Wiley & Sons, 1994. Chapters K and L are

assigned as readings.

Course notebook containing Problem Sets 0 – 19 and additional handouts.

Acknowledgements:

Materials for this course were adapted from worksheets first developed by Kristin Umland and Matt Bardoe of the University of New Mexico for the La Meta (Mathematics Educators Targeting Achievement) Summer Institute. They are printed by permission. For more information visit the La Meta website:

Other Materials:

Graphing calculators
NOVA Video: Newton’s Dark Secrets. Movie can be ordered at (search by Program).