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Interaction, Imagination and Community Building at the Math Forum

This chapter focuses on Drexler University's "Math Forum" web site (www.mathforum.org) , a site designed to support mathematics education. While the site offers resources for both instructors and students, the present discussion will focus on the instructors' use of the site as a "community of practice" in which teachers can collaborate to help develop their teaching skills and advance the profession in general.

INDIVIDUALIZED COMMUNITIES

Sociologist Barry Wellman suggests that networked communications has changed social interaction from the happenstance "groups" that emerge due to encounters in the physical world to one in which there are "individualized communities": that one may seek out and join, in a medium where distance and time do not govern the ability to freely associate.

He notes that communication is becoming more personal and more flexible, as evidenced by the evolution in the use of the telephone: homes and businesses began with a single telephone connecting the group to the outside world, then evolved to adopting on a more granular level (to the point where individual departments, then individual people, have their own numbers), and then going portable (such that a phone can be used by an individual in any location, or used to access that individual in any location). The core technology did not significantly change, but the way in which people used the technology evolved. The same is true of computers in education: from one computer for the entire school, to departmental labs, to a computer in each classroom, to a computer for each student.

From a sociological perspective, the adoption of technology is seen at first to atomize social groups: instead of interacting together, the members of a family are interacting with devices. However, in communication technology, the individuals are not interacting "with a device," but with other individuals, the device merely being a channel. In that sense, it is enabling individuals to cohere in social groups, of their own choosing, outside the limitations of their geographical location.

The author concedes that the virtual community is not entirely analogous to the physical one. Individuals who interact within the virtual space can share information, but their "virtual support group" does not follow them into the real world, where they find that when it comes time to turn thoughts to actions, they are very much alone in doing so, and in some instances, the physical presence of others at the moment of action may be functionally or psychologically necessary.

That limitation aside, there is still considerable value in enabling individuals to reach beyond their immediate surroundings to participate in virtual communities. In terms of the Math Forum, the professional support among teachers may not be possible in many locations (there may be only one "algebra teacher" at a rural school), and their needs are largely informational rather than physical.

The author also remarks on the "generational" nature of online communities, whose information is preserved in archives that are accessible to new members, enabling them to benefit more from the contribution of previous members (including those who may have left the group long ago) more effectively than is possible in live, person-to-person interaction.

The author also suggests a "most profound potential" of online communities to engender a benevolent spirit, in which community interest helps newcomers overcome their resistance and older members to be more sharing of their knowledge.

The author also draws on the work of Cobb, who suggests that schools promote a normative identity for students that may be in contrast with the "core identity" of students, which may cause a barrier to the development of a functional personal identity that causes resistance to learning. (EN: I think this is an oblique way of saying that that students who perform well are often socially ostracized by their peers and communities, such that a student is reluctant to participate in a classroom environment, and the virtual community gives them the ability to be "smart" in private, reaping the benefits of education while escaping the social consequences)

From the perspective of teachers, "professional development" is characterized as being dismal, and has little to do with improving their subject matter expertise or teaching skills in favor of catering to the political issues of the day. It's noted that, in their research, many teachers were using the resources as a means of self-initiated development for lack of development opportunities through their school systems.

Cobb also notes that the value of a learning environment (for teachers as well as students) requires participants have the sense of a "safe" environment where one is free to engage in speculative discussion and consider unorthodox ideas, as well as having a sense that the work is meaningful and their contribution matters. (EN: which are interesting points, and go far to explain why the attempt of companies to create communities for their employees fails to take off).

Another note, from an anthropological perspective, is that cultures are not intentionally homogeneous entities, but arise from the commonalities in ways of thinking and acting that arise from the individuals who participate in them. This same potential is shared, and greatly increased, by the use of internet technology to overcome impediments to cultural development.

(EN: I'm not sure if I entirely agree. This may be true in the early stages of cultural development, but I have the sense that, as soon as the culture begins to indentify itself as a culture, it explores that definition and creates a sense of what is required to be part of that culture. It may be an intentional grasp for power and control on the part of members of a culture to claim in as their own and arbitrate what others must do to be part of "their" culture, or it may be less sinister and more existential, but even the most innocent definition that claims "this is our culture" is a declaration that anything outside that definition is not "our culture" and has the same homogenizing effect, albeit by less aggressive means.)

TEACHERS' STORIES

The author presents four "stories" from teachers about their use of the Math Forum site to illustrate the benefits the site provides.

The first example is of a young teacher (under two years of experience) who felt inhibited to engage the older and more experienced colleagues, and turned to the online forum as a place where his youth and inexperience would be less of an impediment to being able to participate without being dismissed as "the new guy." His experience in the online medium helped him to be more confident in contributing to the discussions among his colleagues, both through practice, refining ideas, and having "connections" with others in the field. The author suggests that feelings of inadequacy are common among math teachers, whose education is often more focused on math than teaching skills, and who often specialize (an algebra teacher with years of experience is a neophyte at teaching geometry) And while many school systems encourage their staff to mentor one another, asking for help from colleagues can be seen as a sign of weakness that damages the credibility (and career) of a teacher.

The second story isn't a case study or testimonial, but a diatribe about the bureaucracy and the politics of the educational system, and the assertion that schools have become poor environments for actually learning. It's suggested that the Math Forum, being independent of the control of any school system or elected board, remains focused on the process of learning.

A third story mentions a teacher who was a "long-term substitute" who was in an area where there was little demand to hire new teachers. The resources provided in the Math Forum, including resources that he could provide to students and teachers, as well as networking with others in his situation about ways to improve his chances of permanent employment. It's not noted whether this worked out for him, only that this teacher was regarded by the local school community as a technical expert to be called upon to help out.

The last example is of a group of teachers in distant locations who used the Math Forum to organize themselves into a research group, primarily for the purposes of improving their own teaching skills. The author notes that there are "many things" that came out of the project and the participants learned "a whole host of other things" but is not terribly specific about the outcome.

(EN: While I wouldn't debate that an online forum such as this can be beneficial to its participants, I find the author's case studies to be extremely vague about the individuals involved and the benefits gained, to the point where it has the smell of marketing hype about it. I don't expect that's a motive, nor do I doubt that such outcomes are possible, but "fluffy" case studies harm rather than help credibility.)

DISCUSSION

The author further expounds on the (problematic) case studies, making a few further generalizations:

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