III. Background: The Geometry Forum and the Math Forum Proof-of-Concept Grants
The Math Forum began in January of 1996 as a proof-of-concept grant from the NSF to extend the work of the Geometry Forum into other areas of mathematics, and to investigate the viability of a virtual center for mathematics education on the Internet.The Geometry Forum: Communicating Mathematics on the Internet
The Internet held promise even before the existence of the World Wide Web. The Geometry Forum initially sought to exploit this potential by developing software that would facilitate the communication of mathematics, and by building a community through mailing lists, newsgroups, and resource archives designed to serve teachers, teacher educators, students, and research mathematicians. It quickly became evident, however, that Internet communities would not necessarily coalesce even when they had good reason to do so (e.g. researchers and teachers who were investigating and giving talks on similar topics in math education). At first the primary obstacle appeared to be a lack of Internet-savvy teachers who could participate and help generate materials for others to use. In response, the Geometry Forum began to offer Internet workshops, which soon became highly sought after professional experiences and a critical component of Forum research into and development of teacher participation. In addition to introductory workshops, the Forum established a week-long advanced summer program that brings together leading math educators on the Internet to identify the most promising uses for the Web, and to create classroom resources and projects.
An important outcome of the first summer program for teachers was a focus on interactive projects for students that would supplement existing classroom materials. The Geometry Problem of the Week (POW) and Project of the Month became staples of the geometry.pre-college discussion group, which in turn became a locus of activity for teachers, researchers, and students at all levels. Participants used the newsgroup to share teaching strategies, discuss mathematics, learn how to integrate the POW and other Internet resources, and connect with others facing challenges such as switching to block scheduling. Another element that has contributed to the quality of this public forum has been the seeding of mathematics education conversations through a 'Learning and Mathematics' series involving periodic postings of summaries of current research and ensuing discussions. The relatively narrow focus of the group's topic, regular infusions of high-quality mathematics and pedagogical material, and the building of a core group of participants have been critical to the success of this forum.
The next leap in growth of the Forum took place with the creation of a second interactive service, Ask Dr. Math. Here K12 students, teachers, and parents submit their math questions to a team of respondents initially composed of Swarthmore College students and world-class mathematicians associated with the Forum through the geometry newsgroups. Not only did this project greatly increase the level of activity and draw many more users to the Forum, but question-and-answer archives built from it have contributed significantly to a growing body of resources housed at the Forum that include previous newsgroup discussions, Problems of the Week and Projects of the Month, the Learning and Mathematics series, and other Forum activity.
Equally important, the interactive services such Ask Dr. Math and the Problem of the Week have been cultivated as opportunities for educational conversations with students and to support exposure to interesting mathematics and inquiry-based learning. From the beginning the Forum has attempted to reflect in its work evolving standards for mathematics education such as those published by NCTM. Students and teachers are encouraged to communicate mathematically, to explore, conjecture, build arguments and develop mathematical habits of mind, to become problem-solvers and value their mathematical power, and to experience mathematics at work and play in the world. The 'Learning and Mathematics' series provides a foundation for this orientation in exploring what we know about how people acquire and learn to use mathematical knowledge.
With the advent of the WWW and the increasing ease with which users can browse and search Internet resources, the wisdom of archiving Forum activities has become fully visible. It has also become clear that the multimedia environment of the Web will lend itself to our goal of designing public forums where math can be more easily communicated. Our software program has shifted its work on public discussion groups to the use of Web-based formats in which math graphics and formatted documents will be integrated into public conversations.
A notable example of substantive educational activity, the Forum has grown in popularity along with the WWW. It now hosts both the MathMagic program and the NCTM-L mailing list. The Forum has further developed its unique character as a professional site built on the activity of its users and has expanded its work to include the organization and development of online educational materials. For the last two summers the week-long advanced program has turned toward an investigation of the needs of teachers for Web resources and their contributions to the design, creation, and organization of online materials.
All of these developments reinforced the Geometry Forum's evolving focus on mathematics education as well as expanding its scope beyond geometry to other topics in math. Thus was born the Math Forum.(1)
The Math Forum: Phase I. Exploring the Possibility of a Virtual Mathematics Education Center on the Internet
The first task of the Math Forum was to design and implement a Web site that would make it easy for users to navigate a huge and growing number of Internet resources. Supported by the earlier work of our 1995 advanced summer program, we were able within one month to accomplish the shift from geometry to a more general focus on math education. There were, however, a number of dilemmas inherent in this effort. The Math Forum Web site alone currently has over 13,000 pages with links to hundreds of other useful sites.
A complex site that makes navigation and searching easy for new users may also render it difficult for them to grasp the powerful tools and the range of resources and activity at their disposal. This challenge has led us in the direction now being promoted by many advanced Web developers: to construct a site built on a database that can enable the material to be 'sliced' in many different ways to suit various user roles and the many categories by which those who come to us organize their work (topic, level, type of resource, standards, etc.).
Initially we addressed issues of quality control by concentrating on the quality of the sources rather than on a labor-intensive review process. Only the best newsgroups and mailing lists are archived. Only closely monitored projects such as the Problem of the Week, MathMagic, and Ask Dr. Math are featured. From our home page you can Search or Browse our Internet Mathematics Resource Collection, which contains annotated entries of hand-selected resources combined with cataloguing features based on American Mathematical Society categories that extend its value for our clients far beyond what is available from indexing agents such as AltaVista or Internet catalogues such as Yahoo. For guidance and in the hope that their efforts may eventually relieve us of some aspects of this work, we also participate in the current discussions taking place among librarians on the WWW.
While our site has received many awards,(2) the effective design and organization of our resource center is only one part of our effort. Our interactive projects such as Ask Dr. Math and the Problem of the Week are key attractors, and we have begun to develop software and to explore strategies for scaling up their level of activity. Additionally, we have begun to enlarge the online component of our workshops(3) in order to extend the benefit of this effort and make it possible for many more participants to learn online and after the fact. In keeping with our focus on math education, we have added sections focused on pedagogy, educational research, and key social and policy issues to our site.
A major undertaking in our role as a virtual center is to support, encourage the development of, and coherently integrate the online presences of key professional organizations and Internet mathematics providers. We began this effort by working with Patrick Ion of the AMS to hold a meeting of key players at the 1996 Joint Mathematics Meetings in Orlando that outlined the main areas to be discussed and identified leaders to be invited to a second session at the Seattle MathFest conference. While the coordination of this group and the development of useful conversations have not been quickly accomplished, we have begun a number of promising relations by following our overarching strategy of building resources based on existing user activity. First, we volunteered to enlarge and develop the Web presence of Math Awareness Week for the Joint Policy Board of Mathematics. Then, with the cooperation of the AMS, the MAA, and others we created a resource area for the math education components of the annual Joint Mathematics Meeting held in Orlando, contacting the presenters and offering to publish talks and related materials. In a similar vein, we worked with NCTM and the presenters at this year's annual meeting held in San Diego. Most recently we have hosted an area on our site focused on the 8th International Congress on Mathematics Education (ICME 8).(4)
The final major component of our work to date began in earnest during the summer of 1996, through collaborations with the National School Network project of BBN,(5) our own Forum Teacher Associates,(6) and the professional development programs of DIMACS,(7) Park City Mathematics Institute,(8) and Woodrow Wilson.(9) Through these three different contexts we are investigating training programs and online environments that will be effective for a range of teachers receiving various forms of professional support. Specifically, our involvement will enable them to learn about, integrate, and contribute to the mathematics resources and programs available via the Internet. On the one hand, we have found that these contexts and teachers are not nearly as far along in terms of Internet experience and connectivity as expected. On the other hand, the summer programs have been highly successful and have already resulted in significant online environments that are supporting ongoing relationships among participants and benefiting others in the Internet math education community.
As these last paragraphs indicate, the Math Forum has begun to develop a role for itself as an enabler, extending its value past the creation of its own Internet resources. It will be important to document this transition for the sake of informing future projects. Some factors are readily apparent: the Forum staff is a well-balanced team combining experience in programming, teaching, research, mathematics, and organizational development that makes for flexibility and responsiveness to emerging conditions and user needs. Central to this capacity is the ongoing gathering of formative data about what users need, how the Forum is being used, and what others are doing. While the Forum has specific programs and software projects that it develops and promotes, these are constantly in the service of its main goal of enabling others to participate in and contribute to the growth and effective use of Internet math resources. The ongoing formative evaluation process is used to align current efforts with new developments and in identifying new collaborations to be forged. Most of the Forum's current efforts, from the 'Learning and Mathematics' series and the Elementary Problem of the Week to the support of professional organizations such as NCTM, have evolved out of responses to user input. In essence the Forum takes seriously its status as a virtual center that exists by virtue of connecting the work of many individuals and organizations and being responsive to their needs and contributions.
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