Using%20Technology%20to%20Enhance%20the%20Teaching/Learning%20of%20Mathematics

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Using Technology to Enhance the Teaching/Learning
of Mathematics

• Lawrence E. Levine
• Stevens Institute of Technology
• llevine_at_stevens-tech.edu

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Alternative Title

• My Course Has Been Scheduled in a High Tech
  Classroom.
• Now What Do I Do With All of This Equipment?

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Words of Caution

• Lecture/teaching model still good
• Technology will not put us out of business
• Use technology only where appropriate
• Can add new dimensions to the classroom
• Can add new dimensions to student learning
• Limitations of Technology
• Do not force its use

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Some Uses of Technology as a Learning/Teaching
Tool

• Course Web Sites
• Scientific Notebook
• Teaching with computers
• Teaching in a laptop classroom
• Mathematical slide shows
• 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//attila.stevens-tech.edu/llevine

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Web Site Cautions

• Time considerations in creating a web site
• Time considerations in maintaining a web site
• Good support a must
• Undergraduates or graduates
• Clever, deal with technical aspects

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Scientific Notebook

• Word processing package with Maple kernel
• Very user friendly front end
• Type no code
• Clicks
• Interfaces with Web

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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 to 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
• Import these graphics files into Power Point
• Add narration, convert to real format

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Teaching with Computers

• Present subject matter easily
• Incorporate demonstrations in the lectures
• Show students how to use software
• Cautions
• Must be easy to use
• Requires a great deal of good support

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Classroom Set-ups

• Basic Set-up PC, Projector, Network Connection
• Better Set-up Laptop connection
• Student is basically passive
• Even Better students have laptops with network
  connections
• Wireless connections best

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Some Things One Can do

• Lecture Notes
• Should also be available as handouts or as
  downloads from web
• Use only when appropriate many formulas
• Software Demonstrations
• How to use certain software
• Demonstrations and Simulations
• http//www.phys.virginia.edu/classes/109N/more_stu
  ff/Applets/ProjectileMotion/applet.html

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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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Teaching Linear Algebra in a Laptop Classroom I

• Linear algebra with computers
• Students with networked laptops
• Two classrooms in one
• Laptop covers down ordinary classroom
• Laptop covers up computer lab
• No written work accepted
• Download SNB notes
• Present some material laptops down!

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Teaching Linear Algebra in a Laptop Classroom II

• At appropriate points have students do exercises
  using SNB
• These were homework problems to be turned in
• Discuss problem under consideration
• Use this alternating format lecture/computer

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Teaching Linear Algebra in a Laptop Classroom III

• NetOp School, synchroneyes
• Monitor what students are doing
• Take control of a students machine
• Project screens of students for all to see
• Have students make presentations from where they
  sit

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Teaching Linear Algebra in a Laptop Classroom IV

• Teach mathematics behind the methods
• Not just a course in clicking
• Reducing matrices to echelon form
• Exams
• Two parts written and computer
• Upload computer part
• Many technical issues!!!

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Discovering Things Using Technology

• Polynomial solutions of DEs
• Which equations have a polynomial solution?
• Nonhomogeneous Hermite equation
• Using SNB to investigate this
• Extrapolate general results form specific cases

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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