The Math Forum
15 August 1996
Grant Proposal
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VI. What We Will Do
C. Online Educational Mentoring and Professional Development
Online education is tightly integrated with community building and with user involvement in the shaping of online resources. The existence of a lively, wide-ranging, and productive community with substantive resources makes possible online instruction and professional development that is connected to a wider set of colleagues and materials than are normally present in inservice workshops. By the same token, conducting education online offers the chance to generate new members and more materials for the community. This benefit results from using the same medium to conduct the education as to record the process. As yet the online environment does not supply the richness of the face-to-face workshop, but since our own tentative experiments in this direction and those conducted by OII and others indicate the promise of integrating the two, we plan to do so wherever possible. We also expect emerging video and virtual reality technologies to greatly enhance the quality of the online environment.
Our focus here, however, is not on the technology but on exploring a representative range of promising online education contexts for both mathematics and math education. We plan to work with and draw on the experience of pioneers like Jim Levin and Margaret Riel, Margaret Honey and the Bank Street online courses, Judi Harris and her various telementoring projects, and other programs such as PBS's Mathline. In most instances the Forum will simply serve as a technology transfer agent and facilitator of information exchange and dissemination so that these efforts can build on our collective experience and resources. In others, funding from our grant will jumpstart their entry into this field and commitments have been secured to bring the costs and responsibilities under others' budgets in years two and three.
Professional development programs. With each of our main teacher groups (NSN, Union City, and the Princeton coalition) we will build an online component of the summer programs so that participants unable to attend in person can join in, and to produce a record of the activity that can be packaged as a self-pacing unit after the event has taken place. In the second year we will aggressively build online working groups during the school year both to follow up on the previous summer's work and in preparation for a developed online component during the following summer. In the third year we will package online-only versions and experiment during the school year with marketing and disseminating these models.
Pre-service education. John Olive of the University of Georgia plans to experiment with Internet forums and a question-answer environment for pre-service student teachers based on the Forum's Ask Dr. Math program. Over a four-quarter sequence his students will use Ask Dr. Math to become familiar with the questions and thinking of students, and will then use our software to conduct their own project with local students. In the third quarter they will employ Internet forums to exchange resources and support each other while they are involved in a full practice-teaching experience. These conversations will be archived and used in the fourth quarter for analysis and reflection on their teaching experiences. Evaluation from year one will contribute to a revised plan for a tri-semester system in year two. Year three will focus on refining the program and preparing conference presentations and articles on this project. (See the accompanying letter of support for more detail.)
Continuing professional education. The Educational Testing Service has been contracted by the National Board for Professional Teaching Standards to develop an assessment process for these new standards. ETS realizes that many teachers are not accustomed to the new forms of assessment and the new standards, and would therefore like to offer professional development opportunities for teachers preparing for assessment. Mentored groups will help to create a professional development online curriculum that will include examination of standards, annotated examples of teaching activity and analyses of student work, pedagogical analyses of mathematical problems, and 'live' online question-and-answer sessions with mentors. We will aid and advise ETS on the Internet and Web aspects of this project and in the process will learn more about professional development and the practices of a self-sustaining commercial education institution.
Question and answer services for students. Ask Dr. Math has already begun experimenting with enlarging the pool of 'math doctors' and the development of an improved interface for managing the load of questions. Plans have been laid for preparing this environment to serve as a general question-and- answer product that can be disseminated to other sites on the Internet. The use of Ask Dr. Math in the pre-service teaching environment as indicated in John Olive's project suggests one direction we will pursue for scaling up the capacity of this resource. In turn, it also provides an opportunity to focus the attention of professional educators on assessing and improving the quality of the exchanges taking place. Topic-specific areas such as Jim King's Dynamic Geometry Center (described below) will become another resource for sharing the responsibilities of the Ask Dr. Math program.
We are also interested in expanding the reach of this program into other linguistic communities. We recently received e-mail from a program in Quebec asking whether we would mind having Ask Dr. Math extended into French and offering to run the operation. We are of course enthusiastic, and we have also begun discussions with Nora Ramirez about setting up a Spanish version. By year three we aim to have established Ask Dr. Math as either a fee-based service or a distributed program housed at various topic- specific math centers or offered through MAA's student chapters.
Puzzle and Problem-based programs for students. The idea of a Problem of the Week has already been carried by Forum Teacher Associates into the realms of high school calculus and middle school and elementary level math. The Elementary POW project includes a nice component in which students from different schools share responsibility for posing problems and responding to solutions.(29) Another area that cries out for attention is high school algebra, and the Forum is pursuing possible collaborations to support the development of resources in this area. We also believe, however, that the traditional algebra curriculum should yield to more interdisciplinary courses. In any case, both software programming to improve project management capabilities and recruitment and dissemination efforts will be essential to the successful scaling up of these projects.
Locating good problems is a difficulty faced by all POW projects. We need a good collection of problems. We have a subcontract with James Levin at the University of Illinois to revise his Grand & Everyday Challenges for Education framework to take advantage of recent advances in telecommunications technologies and other sources of problems and to construct a widely accessible database of challenges for mathematics students and teachers. During the first year, he will work to set up a small Web- accessible database and will in the process contact and begin developing a community of 'problemists'-- teachers and others who are interested in collecting, constructing, and grading problems by level. The database and its classification scheme will be tested with a wide range of students and teachers and modified accordingly. Levin will involve a broad range of people in posing real challenges that they face in their everyday life which would be of interest to mathematics students and teachers, and will develop network-based mechanisms for allowing students and teachers to work collaboratively with the challenge posers. He will also evaluate the impact of working on Grand and Everyday Mathematics Challenges on mathematics learning and teaching. During year three we will help the problemists and challenge posers to establish their own organization to continue the operation of the Challenge framework.
Team-based student math mentoring. One of the most successful Internet mentoring projects is a team-based model, Judi Harris' Electronic Emissary project at the University of Texas College of Education [see Harris, J. (1996), "Practical Lessons in Telementoring," her 'Mining the Internet' column to appear in the October '96 issue of Learning and Leading with Technology ]. This project makes use of volunteer experts who work over the Internet with teachers and their students, and the activities are mediated by an Education graduate student facilitator. Although the program has not had a great deal of experience with mathematics, this is a well worked out approach to mentoring students, and we would like to learn with them. Consequently, we propose a contract in year one for forty Classroom/Subject Matter Expert Teams. We will monitor their activities and suggest changes for year two, when we will subsidize twenty teams. We expect these outcomes: valuable mentoring experiences for sixty groups of students, online materials resulting from the exchanges, an increase in our experience and a widening of our perspective, and the development of a relatively inexpensive method of Internet mentoring together with some notion of its value for the mathematics community. As an added bonus, Emissary is currently studying the professional development that results for teachers who are in contact with subject-matter specialists during the mentoring process. (For further details see the budget explanation accompanying the subcontract.)
Teachers mentoring teachers. A Master Teacher Forum for Teachers will be run in tandem with the Master Teacher Forum for Parents project outlined in section A, with Presidential Awardees responding to teachers' questions and the results being archived. This effort complements the broader and less math-specific work of the Online Internet Institute (OII) with which we will collaborate, as described in section A above.
Curriculum Development Projects. Many now realize that it is not enough simply to present teachers with new curriculum in a few workshops. Teachers need ongoing sources of support and mentors to turn to for quick advice, and ways of quickly getting revisions and supplemental software. It is also important to make it possible for teachers to contribute supporting materials they have developed. The Web is ideal for all this and more, so we have approached three curriculum development projects that are of interest to the LITMUS 2000 Project, one at each level of K12 education.
With the help of the Math Forum, TERC's Investigations in Number, Data, and Space will develop its own teacher leader network. As its curriculum has begun to be disseminated and implemented, TERC has gradually developed a cadre of teacher leaders who are working to support other teachers as they implement Investigations. Discussions among the leaders will focus both on their use of Investigations in their own classrooms with regard to issues of pedagogy and children's thinking, and on their own development as teacher educators, a new role for many of these teachers. In year two we will work with TERC to create contexts in which some portion of this network activity can be shared with others. In year three we will support the transition to self-management of this online network.
The Connected Mathematics Project is at the point where experienced teachers from its original pilot sites will be interested and available to serve as 'CMP on-line coaches'. There is also a teacher enhancement effort, with sixteen major sites in New Mexico and elsewhere that have made a three-year commitment to CMP. These sites, which represent many teachers, will serve as a nucleus for online efforts. All of them have some funding for holding workshops in their locales and CMP has funding to bring leadership teams to the Michigan State campus over the next two summers. At some sites an effort has already been made to get teachers e-mail accounts, and at the urging of participants a low-tech listserv has just been set up for the leadership teams. Between its in-house staff and its corps of experienced teachers, CMP is well-positioned to cover on-line coaching. The Forum will lend its technical and training expertise as well as software support to this project.
The high school Interactive Math Program is being handled a bit differently. We are currently negotating with its publisher, Key Curriculum Press, for a contract that will pay us to construct Web pages for IMP. This will give us experience in becoming self-supporting and in dealing with publishers. Key will also provide a resource person who will moderate discussions. The IMP collaboration is also different in that our local high school is in the process of adopting its curriculum and we will be able to work closely with local teachers to test the new IMP site.
Topic-specific resource center. Prof. James King, of the University of Washington, has been actively engaged in summer workshops with the Park City Mathematics Institute. He is also an authority on Dynamic Geometry, the new discipline spawned by the 'dynamic' software programs Sketchpad and Cabri (King, James & Schattschneider, Doris, Dynamic Geometry, is to be published by MAA in January). King will operate a mentored dynamic geometry Web center for teachers. He will facilitate discussion on our dynamic geometry newsgroup with regular postings of pedagogical issues situated concretely in terms of dynamic geometry problems and classroom-based case studies. He will also conduct an 'Ask Dr. Dynamic' discussion group for teachers and a special challenge problem for students, as has been done for the Problem of the Week. In all this, King will be assisted by an undergraduate and a graduate student in mathematics. (See the budget explanation in the subcontract for details.) In years two and three we will help King locate ongoing support from a commercial publisher such as Key Curriculum Press or through regional mathematics centers associated with the Park City Mathematics Institute.
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