The DREI Web Site as a Mathematical Resource for the Classroom


It is generally accepted among professional educators that students who realize the practical applications of their studies can perform better in the classroom and are more likely to use their skills, both academically and professionally, in the future. Unfortunately, the resources required to provide real-world examples of classroom studies have been somewhat limited. If recent criticisms of America's public school system are to be believed, teachers are using outdated textbooks and teaching methods. Schools are operating under their own organizational inertia: doing the same thing that they have been doing for years with little incentive for change. How will Americašs schools meet the challenge of educating its students to be competitive in today's technology-driven workplace?

The purpose of the DIMACS DREI program is for secondary mathematics teachers to meet with university faculty and mathematics researchers to discuss cutting-edge mathematical topics on the frontiers of research that will be of interest to the average high school student. Faced with the "Nintendo generation" student of the 1990s, teachers are compelled to look beyond the four walls of their classroom, and indeed the confines of their own building, to find new and interesting topics to challenge their students. In order to promote this philosophy to other educators and students, the World Wide Web seems an obvious tool.

This is the spirit and intent of the DIMACS DREI home pages on the World Wide Web. The specific goals of the web site are threefold:

For a period of three weeks in the summer of 1996, a group of teachers and researchers participated in a unique sharing experience: researchers exchanged the details of their research with teachers, and teachers shared their everyday classroom experiences with researchers. As a result, the participating teachers learned of many examples of real-world mathematics that could be shared with students in their classroom to make mathematics "more real," which is a concept endorsed in the current NCTM Standards for Mathematics. Likewise, researchers learned much about the academic abilities and interests of typical American students.

The DREI web site introduces the visitor to four such areas of current mathematical research: computational geometry, Voronoi diagrams, art gallery problems and tilings and tessellations. Although each of these topics is rich in post-doctoral research, the concepts behind them are easily understood and explained within the confines of the secondary mathematics curriculum.

For instance, consider a seemingly innocuous problem, namely a typical art gallery question suitable for classroom use.




"On a rainy Saturday afternoon, you decide to visit a local museum to view the paintings hanging on the walls. By looking at the floor plan of the museum, you wonder: What is the minimum number of seated security guards required such that all the paintings on the walls can be guarded at all times."





Students of almost any age can certainly use the technique of trial and error to determine that, for this particular example, two security guards is the minimum number. Older students may even develop a sense of intuition about solving these problems. It is left to the more mature student to rigorously prove that the solution of this example is indeed two guards. (Incidentally, the proof also provides a means to predict this minimum number of guards for nearly any floor plan simply by counting the vertices of the simple polygon. See the section on Art Gallery Problems for further details.)

The web site provides a central forum for developing supporting materials such as these to further encourage dissemination, collaboration and discussion of these topics. Teachers, both individually and in groups, have developed lesson plans and other resources based on their experience at the DREI 1996 conference for publication on the web site. Teachers are encouraged to try these lessons in their own classroom and share their experiences by providing feedback to the authors via the Internet.

Further, a mechanism exists whereby the lesson itself can be modified by other colleagues. The very researchers who presented their respective topics at the summer conference are welcomed and encouraged to visit the web site occasionally and make their own contributions to these lesson ideas. Teachers are encouraged to stay in touch with the researchers in order to keep up on the latest news and developments in their respective fields. As a result, the curriculum improves through a constant cycle of implementation, evaluation and revision. The free flow of information between researchers and classroom teachers is vital to the success of the DREI program and the web site itself.

Most classroom teachers lack the time, support and resources to investigate such high level mathematical topics as those presented on the DREI web site. Given the demands upon both a teacheršs and studentšs limited time in the classroom, a resource such as the DREI web site should prove to be a valuable tool in several respects. For example, it allows teachers to preview and learn about real-world applications of mathematics that may be used in their own classrooms. Additionally, the availability of prepared and tested materials is an essential ingredient in any successful classroom lesson. Furthermore, the web pages include a forum where teachers and students alike can directly contact the DREI participants, teachers and researchers alike, via the Internet.

As with nearly all content on the World Wide Web, the DREI home pages are in a constant state of evaluation and improvement. And Internet sites which provide educational resources vary greatly in approach. As a result, there are various aspects of the DREI web site that are planned for the future. The site in its present state is mostly a static resource of information. Planned upgrades to the site might include such ideas as interactive tutors, simulations and educational games to further pique the interest of the student.

In sum, the philosophy of the web site is to provide and promote an open forum for a community of learners who otherwise would not have an opportunity to experience some mathematical concepts on the frontiers of research. It provides background materials, concrete lesson plans, lesson ideas and a forum for open collaboration and discussion. It is hoped by its creators that the web site serves as a useful and entertaining tool to increase mathematics interest and awareness in the classroom.

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