Using Technology to Enhance the Teaching/Learning of

Mathematics

Lawrence E. Levine

Stevens Institute of Technology

llevine@stevens-tech.edu

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

• 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

• 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– 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

• 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– 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

• 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

• 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

• 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