Redefining the Mathematics Teaching and Learning Infrastructure

Redefining the Mathematical Teaching and Learning Infrastructure

by

Fred T. Hofstetter
University of Delaware

It was my pleasure to present a keynote presentation at the Delaware Council of Teachers of Mathematics (DCTM) Project 301 conference in Ocean City on November 21, 1996. At the request of the conference, I promised to write this article summarizing my presentation and providing the Internet resources I recommended for keeping up with advances in educational technology.

As articulated by Brown, Collins, and Duguid (1989), skills and knowledge are too often taught out of context, as ends in and of themselves. To overcome this, teachers are using multimedia to bring into the classroom real-life examples of situations that provide the contextual framework so important for learning. Brown calls this use of multimedia situated learning. Multimedia gives teachers instant access to thousands of slides, videos, sound tracks, and lesson plans. These materials can be called up instantly, either for classroom use, or as a networked resource for student exploration, discovery, reflection, and cooperative learning. Among educational researchers, the capability to demonstrate vividly and convincingly the real-world applicability of knowledge has become known as anchored instruction (The Cognition and Technology Group at Vanderbilt, 1990).

How Can Multimedia Help?

Mathematics is one of the most highly developed multimedia application areas. Due to the computational nature of mathematics, computers can model the content and help students master educational objectives. The National Council of Teachers of Mathematics (NCTM) has issued a set of guidelines that rely heavily on computers as an agent for change in the way mathematics is taught. The NCTM guidelines encourage the teaching of math in real-world contexts in which students investigate problems that have meaning.

For example, Scott Foresman teamed with ABC to produce Wide World of Mathematics, in which video footage from ABC News and ABC Sports broadcasts is used to demonstrate how mathematics is used every day, in virtually every field of endeavor. Pictured below are the Middle School topics, which are available in videotape, videodisc, and CD-ROM versions. Well-known runner Marty Liqouri takes students step-by-step over the New York City marathon course, using mathematics to compute the length of the course, the runners' rate of travel at different checkpoints, and the combined weight of the runners as they cross the Verazzano-Narrows Bridge. The Hubble Space Telescope provides a real world setting for a treatment of very large and very small numbers. The construction of the Chunnel that connects France and England beneath the English Channel introduces dimensions and units. Hurricane Andrew situates prediction techniques with footage from forecasters at the National Hurricane Center.


To get a demonstration copy of the Wide World of Mathematics, phone (800) 554-4411 and ask for the videotape demo (code number 37520-X) or the CD-ROM demo (code number 37521-8). The CD contains the situated learning example I demonstrated showing how an NFL football game provides the context for using the playing field as a number line on which students learn addition and subtraction.

How Can the Internet Help?

Imagine what it would be like if we could make high-quality situated learning materials available to every student, keyed to the NCTM standards, which are available at the Eisenhower National Clearinghouse on the Web at http://www.enc.org. I believe that by combining the multimedia and Internet technologies that are available today, the DCTM could redefine the mathematics education infrastructure and provide a powerful environment for teaching and learning mathematics through a multimedia database of situated learning materials hosted on the World Wide Web.

For example, Microsoft gives away for free the plug-in that makes Microsoft Word capable of turning word-processed documents into Web pages. The plug-in is called the Internet Assistant. You can download it for free from the Microsoft Web site at http://www.microsoft.com/msword/internet/ia/. Using the Internet Assistant, anyone who can word process can create Web pages in just a few minutes. For example, I wrote this article using Microsoft Word with the Internet Assistant plug-in. To prepare this article for publication on the Web, all I had to do was pull down the File menu, choose Save As, and select the document type HTML, which is the hypertext markup language used to encode documents on the World Wide Web. As a result, you can find this article on the Web at http://www.udel.edu/fth/dctmkeynote.html. All of the Web sites mentioned in this article are hotlinked, putting you just a mouse click away from taking advantage of the resources mentioned here.

When learning resources are mounted on the Web, they are available worldwide, to anyone connected to the Internet. As the Internet becomes a mass-market retail commodity, the cost of connecting is becoming affordable by the average household. During the 1996 holiday shopping season, WebTV was introduced. For a few hundred dollars (probably less by the time you read this), you can purchase the equipment needed to connect any television set to the World Wide Web. For a monthly fee comparable to basic cable television rates, the world of interconnected knowledge becomes available to any household-including electronic mail services.

Imagine how such connectivity could be used to deliver situated learning materials to students at home. I believe that meaningful activities such as the Wide World of Mathematics modules discussed earlier could compete for the large amount of time students spend watching commercial television. Factor in the network's ability to track student progress, facilitate cooperative learning among groups of students, and connect parents and teachers via the Internet's communication services, and you have a powerful medium for improving teaching and learning.

I would like to encourage every mathematics teacher to visit the Eisenhower National Clearinghouse Web site at http://www.enc.org. If you do not have Web access, visit your local college or library. When you discover the wealth of mathematics teaching and learning resources available on the Web, I think you will agree that doing this was well worth your time. Some of the things you will find at the Eisenhower site include a resource finder that provides access to more than 7,000 curriculum resources; highlights and tours of each month's most highly rated math sites; online documents containing the full text of curriculum frameworks and reform documents; an index of Web sites containing classroom-ready material for teachers; and a communication tool that can connect you to conversations with other teachers about how the new technology can be used to redefine the mathematical teaching and learning infrastructure.

How to Learn More

NewMedia magazine is probably the best single source for keeping up with what's new in multimedia. It appears monthly and publishes an annual buyer's guide. NewMedia contains dozens of full-color pictures that illustrate the products it describes, and the layout is visually appealing. To subscribe to NewMedia, write to P.O. Box 1771, Riverton, NJ 08077-7331. Phone (415) 573-5170. Fax (415) 573-5131. Be sure to ask about a free subscription, which is available to qualified readers. NewMedia is also available on the Web at http://www.hyperstand.com, where you will find even more information than what is contained in the printed version.

Another free magazine is T.H.E. Journal. T.H.E. stands for Technological Horizons in Education. T.H.E. Journal appears monthly; each issue contains application highlights and dozens of new product announcements. Subscribers also receive special multimedia supplements from vendors like IBM, Apple, and Zenith. T.H.E. Journal is free to qualified individuals in educational institutions and training departments in the United States and Canada. To subscribe, phone (714) 730-4011 or fax (714) 730-3739. The mailing address is 150 El Camino Real, Suite 112, Tustin, CA 92680. There is also an online version at http://www.thejournal.com. The online version lets you download product demos, search back issues, and read articles that did not appear in the printed journal.

Also free is an online listserver called EDUPAGE. Three times a week, the EDUPAGE listserver sends you an e-mail message containing a digest of ed tech news, concentrating on issues related to the Internet. Personally, I find this to be the most valuable single source for keeping up with what's happening in educational technology. To subscribe, send an e-mail message to listproc@educom.unc.edu. Leave the subject line blank, and as your message, type:

Subscribe EDUPAGE Firstname Lastname

Replace Firstname and Lastname with your first and last names. You can also find EDUPAGE on the Web at http://www.educom.edu.

Finally, you may be interested in visiting the Instructional Technology Center's Web site at the University of Delaware, which is at http://www.udel.edu/educ/itc. There you will find information about courses in Multimedia and Internet Literacy that are offered throughout the year, and the Summer Institute in Educational and Assistive Technology, which will offer twenty-two courses in the summer of 1997 in several locations across the state. UD is also in the final stages of creating a doctoral specialization in educational technology. To request information about the doctoral program, send me an e-mail message stating that you are interested in learning more about it. My e-mail address is fth@udel.edu.

References

Brown, J. S., Collins, A., and Duguid, P. Situated Cognition and the Culture of Learning. Educational Researcher 28 (1989): 32-42.

The Cognition and Technology Group at Vanderbilt. Anchored Instruction and Its Relationship to Situated Cognition. Educational Researcher 19 (1990): 2-10.


This Web page is owned by Dr. Fred T. Hofstetter, Professor and Director of Instructional Technology at the University of Delaware. Copyright © 1997.