Transcript Using Technology to Enhance the Teaching/Learning of

Using Technology as a Teaching
and Learning Tool in
Mathematics Education
Lawrence E. Levine
Stevens Institute of Technology and USMA
[email protected]
Alternative Title
My Course Has Been Scheduled in
a High Tech Classroom.
Now What Do I Do With All of This
Equipment?
Words of Caution
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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
Some Uses of Technology as a
Learning/Teaching Tool
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Course Web Sites
Scientific Notebook
Teaching with computers
Teaching in a laptop classroom
Mathematical slide shows
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://attila.stevens-tech.edu/~llevine
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
Scientific Notebook
• Word processing package with Maple
kernel
• Very user friendly front end
• Type no code
• Clicks
• Interfaces with Web
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 to 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
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Prepare math using SNB
Capture portions of file as graphics files
Import these graphics files into Power Point
Add narration, convert to real format
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
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
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/mor
e_stuff/Applets/ProjectileMotion/applet.html
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
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!
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
Teaching Linear Algebra in a
Laptop Classroom III
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NetOp School, synchroneyes
Monitor what students are doing
Take control of a student’s machine
Project screens of students for all to see
Have students make presentations from
where they sit
Teaching Linear Algebra in a
Laptop Classroom IV
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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!!!
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
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