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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
– http://golem.math.stevens-tech.edu/ma115/
– http://golem.math.stevens-tech.edu/llevine/ma205/ma_205.htm

5. Mathematical Slide Shows I
• http://attila.stevens-tech.edu/~llevine/
• 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”
• http://www.math.psu.edu/dna/graphics-g.html
• 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?
• 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 email

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
emailed 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

18. Follow-Up Session
• Time: 1350
• Date: 16 April
• Place: MCR
• Format: Question and Answer
• Topics – Anything you like