1. Wade Ellis, Jr. Bowen Kerins William Bauldry Robert Lopez
Teaching and Learning Mathematics in a CAS Enriched Environment: College Algebra to Real Analysis
Wade Ellis, Jr.
Bowen Kerins
William Bauldry
Robert Lopez

2. Presenters Wade Ellis, Jr. Bowen Kerins William Bauldry Robert Lopez
Mathematics Instructor, West Valley College
Bowen Kerins
Research Associate, Center for Mathematics Education of the Educational Development Center
William Bauldry
Professor, Appalachian State University
Robert Lopez
Emeritus Professor, Rose-Hulman Institute of Technology

3. Outline Introduction Secondary School Mathematics Elementary Calculus
Vector Calculus, Differential Equations, and Linear Algebra
Real Analysis

4. Introduction Computer Algebra Systems
1958 LISP (John McCarthy of MIT)
1980s and early 1990s
Personal computers
muMath, Derive, Maple, Mathematica
Labs and projects in courses
Late 1990s
Handheld devices
AP Calculus allows CAS
Current situation in the classroom

5. Bowen Kerins
Secondary School

6. Calculus Polynomial zeros The definition of differentiation
The Riemann definition of the definite integral
Symbolic anti-differentiation
Partial fraction decomposition
The importance of numerical computation in real world situations

7. solve(x^4-2x^3-3x^2-5=0,x)
Derive

8. solve(x^4-2x^3-3x^2-5=0,x)
Derive

9. Definition of the Derivative
TI-Nspire

10. Using the Definition of the Derivative
TI-Nspire

11. Symbolic Anti-Differentiation
Derive

12. Step-by-Step

13. Riemann Definition of the Definite Integral

14. Numerical Definite Integrals
Derive

15. Importance of Numerical Approaches
Symbolic approaches often fail
Using the definition of the definite integral provides a simple way to approximate definite integrals when symbolic methods fail
This idea carries over into differential equations

16. Robert Lopez
Vector Calculus, Differential Equations, Linear Algebra

17. Bill Bauldry
Real Analysis

18. Questions and Comments