Our next set of recommendations is for Web sites which have proven valuable sources for enrichment material for students or teachers on specific topics, or for classroom activities.
MegaMath (Los Alamos National Laboratory)
http://www.c3.lanl.gov/mega-math/
The MegaMath site brings important mathematical ideas to
elementary school classrooms with unique activities. The
site was developed
by Nancy Casey and Michael Fellows [5,6].
It includes many discrete math activities including the following:
The Most Colorful Math of All (map and graph coloring);
Games on Graphs;
Untangling the Mathematics of Knots;
Algorithms and Ice Cream for All (an interesting problem
on graphs); and
A Usual Day at Unusual School (logic and paradoxes).
This site offers
teachers the opportunity to bring discrete
mathematics into their classroom with engaging stories.
MacTutor for Math History Information
http://www-groups.dcs.st-and.ac.uk:80/~history/
Mathematical_MacTutor.html
MacTutor offers the history of mathematics on the Web. The Welcome Page for the site includes a Famous Curves Index, a Biographical Index, Chronologies, a History Topics Index, a Birthplace Map, the Mathematicians of the Day, Anniversaries for the Year, a Search Form, and Search Suggestions. I (Kowalczyk) used MacTutor to find a wealth of information about Fibonacci and the Fibonacci numbers (see also the article [20], which I wrote before I found this site).
Dynamical Systems (Boston University)
http://math.bu.edu/DYSYS/dysys.html
This site is designed to help teachers bring contemporary mathematics topics--chaos, fractals, and dynamics--into the classroom and to illustrate how to use technology effectively in the process. The interactive activities at this site can also help teachers understand the mathematics behind these topics. This site is well worth exploring--especially for high school teachers. This site was developed by Robert Devaney, who has used these activities in teaching calculus [10] and differential equations.
After exploring the site, Judy Brown LP `92 sent a note which is excerpted below.
I spent a lot of time with the ``chaos for the classroom'' section. This is in such an easy-to-read digestible format that I really can't wait to go back and investigate the Mandelbrot and Julia set information. I don't know exactly how to express my feelings, except that some of the ``neat stuff'' that I've done before now has taken on a more mathematical tinge. There are also a few fractal ``movies'' that you have got to see [under the heading Rotations and Animation]. My favorite is the dancing Sierpinski triangle. I'll never be able to look at a Sierpinski triangle again without imagining it dancing.
Fractal Frequently Asked Questions and Answers
(Ohio State)
http://www.cis.ohio-state.edu/hypertext/faq/usenet/
fractal-faq/faq.html.
This is another good source for those interested in fractals, with hyperlinks to many other interesting and useful fractal sites on the Web. A sample of questions addressed are as follows. ``I want to learn about fractals. What should I read first?'' ``What is a fractal?'' ``What are some examples of fractals?'' ``What is chaos?'' This site is recommended for both teachers and students who want to begin learning about fractals.
AIMS Puzzle Page
http://204.161.33.100/puzzle/puzzlelist.html
Here is a delightful site with excellent classroom-ready activities, which are based primarily on discrete mathematics. Each month a new and challenging puzzle is posted, complete with student worksheets, which can be downloaded. As I (Kowalczyk) viewed the puzzles for the first four months of 1996, I could hardly wait to print them so I could get started.
The World of MC Escher
http://www.texas.net/users/escher
At this site you will come to know this fascinating artist (and mathematician) through stories, his tessellations and other art works, as well as his insights into these works. The site also offers high-quality (commercial) products featuring Escher's designs. If you are already familiar with Escher you'll have a great time just looking around, otherwise, it's time to explore and be captivated by his work. (See also the books Teaching Tessellating Art and Visions of Symmetry, described in Section 5.)