1. Teaching with Technology
Lawrence E. Levine
Visiting Professor
Department of Mathematical Sciences

2. Levine’s Technology Theorem
Everything works either at home or in my office, and nothing works when I present it.

3. Some Uses of Technology as a Learning/Teaching Tool
Course Web Sites
Teaching with computers
Locating Web resources
Mathematical slide shows
Computer homework assignments and projects
Discovering things using technology

4. Course Web Sites All the important information about the course
Syllabus
Office Hours
Homework assignments
Lecture notes
Old Exams with solutions
Grades

5. Mathematical Slide Shows I
These use stream technology
How created
Power Point good for creating slides
Then can easily add narration
Real media add-on to convert real format
Power Point not good for writing math

6. Mathematical Slide Shows II
SNB is good for writing math
Power Point does not read tex files
Solution
Prepare math using SNB
Capture portions of file as graphics files
Important these graphics files into Power Point
Add narration, convert to real format

7. Computer Projects and Simulations
Add new dimension to learning
Make things come “alive”
Projects that reinforce and extend
Harmonic Oscillator Project
Combination of analytic and simulation

8. The Case for Laptops I Faculty must have laptops
PCs in classrooms not adequate
Prepare everything before on laptop
Should be able to come in, plug in laptop and teach
Ideally just a little more difficult than using chalk and a board

9. Case for Laptops II Computer labs expensive
Students bring lab to classroom
Incoming student has state of the art equipment
Really use technology while teaching
Opportunity for interaction with and engagement of students

10. Ma 488 VP Course TH 120 Advanced Technology Classroom Classroom set-up
Cadets have laptops
Wireless connections
Scientific Notebook
Net OP School
Smart Board

11. How is Course Taught? Homework is submitted via email
Prepare notes in SNB for presentation of material
Discuss this material: laptop covers down
Have cadets work specific examples using SNB
Monitor work using Net OP School
Project cadet’s laptop, monitor, take control, attention – “Go to the Boards”
Homework is submitted via

12. Some Cautions Technology must work easily – need good support
Must come earlier to set things up
Tendency for class to go in unexpected directions – instructor must be fluid in approach
When something new comes up, file is ed on the spot

13. Course Content and Goals I
Differential Equations
Solution of constant coefficient homogeneous and nonhomogeneous equations
Infinite series
Series solution of DEs near an ordinary point
Cauchy-Euler Equations
Method of Frobenius

14. Course Content and Goals II
Use technology to discover new results
Nonhomogeneous Hermite, Legendre, Chebyshev equations
Assume one has a polynomial on the RHS
Under what conditions will one of these DEs have a polynomial solution?

15. Discovery Approach I
Hermite’s Equation

16. Discovery Approach II
SNB will solve the equation for specific values of n
It will not solve the IVP in general
By looking at specific examples one tries to extrapolate a general result.
SNB illustrations

17. Conclusions The world is changing
Technology will become more prevalent
Students must be fluent with technology
Technology opens new horizons
Many approaches
Some good, some not so good
Try new approaches, identify good ones, develop them
No small challenge