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
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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
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Syllabus
Office Hours
Homework assignments
Lecture notes
Old Exams with solutions
Grades
http://golem.math.stevens-tech.edu/ma115/
http://golem.math.stevenstech.edu/llevine/ma205/ma_205.html
Mathematical Slide Shows I
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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/graphicsg.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
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Cadets have laptops
Wireless connections
Scientific Notebook
Net OP School
Smart Board
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
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
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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
Follow-Up Session
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Time: 1350
Date: 16 April
Place: MCR
Format: Question and Answer
Topics – Anything you like