The World Wide Web in Mathematical Instruction
Report on sessions held at the AMS/MAA Annual Meeting,
January 7 and 9, 1998, Baltimore, Maryland.
Organizers: Earl D. Fife, Larry Husch, Gene Klotz

This session contained timely and interesting material on how people are using the Web as an aid in classroom teaching. Most presentations contained interactive Web pages for students, and essentially all should be of interest to school as well as college teachers and students. In addition, there were a variety of ideas illustrated as to how to use the Web for communicating with students and doing a lot of the paper work which goes along with teaching.

This is presented as a joint Math Archives - Math Forum project, and can be found on both the sites.

• Robert L. Devaney, Boston University, "Dynamical Systems on the Web."
http://math.bu.edu/DYSYS
This is from a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. Devaney focused on JAVA Applets for chaos and fractals , in particular the chaos game.

• Daniel C. Sloughter, Furman Univ, "An applet a day: Simple calculus demonstrations using Java."
http://math.furman.edu/~dcs
These demonstrations included approximating the area of a circle, approximating the tangent line by the secant, the cumulative area under a curve, trigonometric series, and Taylor polynomials. Sloughter is in the process of creating a calculus text--with applets. His site contained pages which discuss calculus concepts with links to definitions, examples of exams, etc.

• Bruce McLean, Georgia Southern, "Teaching Mathematics using Java and the Web."
http://www.cs.gasou.edu/faculty/mac
The examples mostly involved using the Web for teaching calculus, and most were non-Java. Much of the related material seems to require a password. Unfortunately, this restriction will bar readers of this page from viewing the course. McLean discussed the problems with Java.

• Mary Ann Connors, West Point, "The World Wide Web in Discrete Dynamical Systems and Calculus at West Point."
http://www.dean.usma.edu/math/core/ma103/index.htm
The subject was a discrete dynamical systems (2/3 semester) and calculus (1/3 semester) course at West Point. The Web is used for communication between students and instructors, as a resource for instructors (a section not accessible to students), and for administrative work (also not accessible). Students use the Web as a laboratory tool in their rooms (all have computers). The Web provides the structure for the course, with detailed course information, lessons, drill problems (done before class), technology, tutorials (such as handouts on calculators), Mathcad files. Students use the prof's home page (see Connors' home page), especially after an exam. They provide grade output information (summary, histogram, etc.) Sometimes they have quiz solutions and feedback forms.

• Larry Copes, Augsburg Coll, "MATtours: Web-based calculus curricula using others' Web pages."
http://www.augsburg.edu/math/MATtours/description.html
This is a project to develop "tours" of Web pages to teach calculus from different approaches. They envision a FORMAL TOUR for those who prefer a definition/theorem format, and (having attended to the empty set) a MODELLING TOUR for those who learn best in a context of trying to solve problems, an INVESTIGATOR'S TOUR which would derive equations, etc. They figure that to develop tours for a one-semester calculus course for business majors would require the equivalent of two full-time faculty for one year. They're looking for persons interested in helping develop or teach such courses.

• Mark R. Woodard, Furman, "Calculus I with the Web."
http://www.furman.edu/~mwoodward/math11/index.html
What works and what doesn't in using the Web as a supplement to a traditional course with computer labs? Woodard provides the students with DEMOS: (Often begged and borrowed) Java applets (some from Dan Sloughter, see below), Mathematica notebook files (some from Michigan Tech). DOCUMENTS: syllabi, handouts, information such as practice tests. He has students submit answers to demos by Web forms. DISCUSSIONS: Woodard has an anonymous mailer form and answers questions thus submitted the first thing in class. He also has a message board for student questions, assignments, etc. The students who used email to ask questions (average 10/week) really liked it. DOH !?!: (Those of us in our declining years are not expected to get it, or it's pronunciation). Frequently Asked Questions. DESTINATIONS: Links to other mathematical Web pages.

• Chris Rorres & Robert C. Busby, Drexel, "The Use of the Web in Teaching Freshman Engineering Mathematics."
http://www.mcs.drexel.edu/classes/MFE
This is for 20 sections of students (about 500), so using the Web to do humble things like provide handouts can be very helpful. Basis information for the courses is provided. Copies of exams already given and solutions are made available. They mainly work in Maple, and there are also lots of downloadable Acrobat files. Students have both Macs and PCs, so the Web is attractive for dealing with compatibility problems. Mac users can download some hypercard stacks. Lecture notes are put on the Web. The engineering faculty is convinced of the Web's important and consequently the math department had developed Web-based projects for students. They also use TechTalk chat room software for collaborating. This permits the users to send Maple or MatLab material and have it executed.

• Dan Kalman, American Univ, "Interactive Computer Activities from the Mathwright Library."
http://isaac.engr.washington.edu:80/mathwright/ (Mathwright source)
There one can find information on the software (approximately \$500 for an author copy, \$40 for a student copy), archive of models, and author software which can be used to modify library modules. Kalman gave a brief demonstration on the ease of using the authorware by changing a module for drawing a tangent line into a module for drawing Taylor polynomials.

• Susan Addington, CSU-SB, "Good News! You don't have to learn Java. Configurable Java applets for math."
http://www.math.csusb.edu/faculty/susan/

• Alexander Bogomolny, CTK Software, "Help students make their own math discoveries."
http://www.cut-the-knot.org
A number of examples of applets were provided. Bogomolny displayed several of these showing how interactive experimentation can be used to assist students (regardless of age) in making their own mathematical discoveries. The author's wit comes through in some of them, making the applet that much more enjoyable. (Watch the smiley face change to a sad face as it is included for execution in Josepheus' problem.)

• Susan M. Loveland, James H. Jacobs, ACM, "Java Applets For Introductory Discrete Mathematics."