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Math Tools Research Area Discussion Article
George Reese

Earlier in the year I had hoped to spark discussion by suggesting a set of applets that teachers could use and then share their results. That did not seem to strike a chord. On the other hand, without a prompt, a discussion began within a small group that illustrates the type of constructive conversation and growth that can go on around Math Tools, and I think it is worth documenting in this space.

The players include:
Jill Britton, educator at Camosun College in Victoria, BC
Suzanne Alejandre, educator at The Math Forum @ Drexel in Philadelphia, PA
George Reese, educator at MSTE in Champaign, IL
Pavel Safronov, programmer at MSTE
Mike Morton, chief technical officer at StreamSage, Inc.
Michael McKelvey, programmer at MSTE

The problem began with a small applet about Magic Squares. In November, Jill Britton posted to Math Tools saying that Mike Morton's Magic Square Applet, while "a terrific interactive teaching tool" was not working on the more recent browsers that she used. She asked if anyone was up to fixing it.

At MSTE, like some other places, we have groups of talented students to whom we can farm tasks like this, and so we began. There were two weeks of occasional emails between Jill and me talking about what the applet should look like. (These conversations are at I asked a gifted young Computer Engineering major, Pavel Safronov, to work on it. A day later he found a line of code he was sure had caused the problem. He recompiled it, put the new applet on the Web, and considered it fixed.

Then Jill discovered to her surprise that while the new tool worked on one set of new browsers, it didn't work on the older browsers. She copied to Sione Palu, a software developer in New Zealand. So this little applet had now become the problem and conversation for a growing and diverse group. In addition, Suzanne informed me that Mike Morton, the original programmer, was watching the conversation from the sidelines.

During this time, there were numerous side emails. I wrote to Suzanne; Pavel wrote to me. No doubt there were many more that did not happen to involve me. But the public forum for conversations was the Math Tools discussion page.

Suzanne tested the new applet on a variety of browsers. Some worked and some didn't. The conversation lagged for a few weeks before Suzanne started it up again by requesting that Jill and I both post to the list with which browsers work. She also brought up the issue of where the new applet should reside.

We decided on which server to place the applet, made decisions on how to credit the various people who worked on it, and added another feature (a 7x7 version of the magic square) to the applet. This last component brought Michael McKelvey, graduate student and programmer, into the discussion.

At that point Michael added his new knowledge to the group. He was able to improve the applet by removing a text box that was in the way. He added the 7x7 with little problem. He also revisited some old territory in the discussion regarding whether or not a plug-in or a cached version was the source of the problem. At this point, all conversations moved off the Math Tools site and onto personal emails. Several discussions happened simultaneously; the applet was being expanded, tested in different sites on different platforms, problems were identified and addressed, and solutions sought. Pavel was working from his home in Chicago. Michael was working from Champaign. Michael taught Pavel about the layouts. Messages passed by very quickly. At one point, Jill began an email with "Dear Magic Square Junkies."

By the time the conversation began to lag, the following had occurred:

  • There was a working Magic Squares tool.
  • It was revised and enhanced through a collaboration of several people in different locations.
  • Everyone (at least the major players) involved had learned something.
  • The credits and caveats for the tool had been worked out.
  • Some new relationships were formed.

These events began on November 28, 2003 and came to an uneventful close on January 22, 2004. During that time there were 80 email messages that went through my mail box on that subject. Of those, only 8 were posted to the Math Tools public site. Yet the site itself was the place for public "announcements" or questions about the applet. In the first eight days, there were 27 messages, followed by a three-week hiatus, and then discussion began again. From the time Michael joined the discussion on January 13th until it subsided on the 22nd, there were 40 emails, none on the public list.

I close with a couple observations on these interactions.

  • A key feature was the Math Tools site. Also a person, in this case Suzanne, who would act as a catalyst for conversations and a keystone for the structured conversations. Such a person is essential for moderating the feelings that come up as well as connecting people with different strengths and guiding them into the discussion.
  • The back channel communications are essential. Not all communication, perhaps not even most communication, will take place on the public forum. Instead, the safest and most productive way to work is with a small number of known, though not necessarily personally familiar people.
  • There was an authentic match of the problem with the abilities of the participants. The difference between my suggestions for a topic of inquiry and Jill's request for help is clear. Jill had a genuine and immediate need, and Michael and Pavel had the assignment, the ability, the curiosity, and the interest in helping. Everyone was able to contribute in a relatively painless way.
I look forward to observing and participating in more of these discussions.

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