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

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

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

Course Web Sites All the important information about the course Syllabus Office Hours Homework assignments Lecture notes Old Exams with solutions Grades http://attila.stevens-tech.edu/~llevine/ http://golem.math.stevens-tech.edu/llevine/ma205/ma_205.html

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

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

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

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

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

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

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 email

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

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

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?

Discovery Approach I Hermite’s Equation

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

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