Teaching with Technology

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Teaching with Technology

• Lawrence E. Levine
• Visiting Professor
• Department of Mathematical Sciences

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Levines Technology Theorem

• Everything works either at home or in my office,
  and nothing works when I present it.

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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

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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/m
  a_205.html

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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

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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

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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

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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

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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

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Ma 488 VP Course

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

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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 cadets laptop, monitor, take control,
  attention Go to the Boards
• Homework is submitted via email

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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

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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

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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?

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Discovery Approach I

• Hermites Equation

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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

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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

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Follow-Up Session

• Time 1350
• Date 16 April
• Place MCR
• Format Question and Answer
• Topics Anything you like