Morning

We began our first full day, as we will each day, with Connections. It's a time for people to spend in silent reflection, or to speak out if they have anything to share with the group.

The rest of the morning was spent exploring the software that we're going to be using. Some participants are new to the Mac environment, or to certain applications, so we spent some time getting set up on Eudora (mail), NewsWatcher (newsgroups), and Netscape (World Wide Web). In each case, we changed the basic preferences to be specific to the user and learned more or less how to perform basic functions.

All eight teachers have now finished their introductions, which are on geometry.institutes and the Web, and their Home Pages, which you can find at

http://olmo.swarthmore.edu/sum95/

The method suggested for constructing a home page was to take a look at the source for somebody else's page and work from that. It's a lot easier than taking out and studying an HTML handbook!

Lunchtime conversations

During our lunch (Philadelphia "hoagies" of course), we had an interesting discussion about the role of technology and visualization in the classroom. Why do students tend to resist drawing pictures? Perhaps, it was offered, students feel that drawing a picture is in some way cheating either the problem or herself.

We all seemed to agree that the best way to teach would be to incorporate as many different ways of thinking as possible. Clearly, it seems, the current system puts too strong an emphasis on algebraic computations and not enough on visualization. The tools that are being explored at this workshop, such as The Geometer's Sketchpad, are relatively easy ways to help manipulate visual pictures of mathematics, and the teachers here have found them very useful in their classes. However, we also must be wary not to get to the point where students are becoming dependent on technology. Somebody told a story about a kid who was trying to do 1 squared on a calculator. He obviously had no true concept of what it was to square a number.

There also seems to be a dependence on convention. For example, one teacher gave her class a test consisting of rectangles of which they were asked to find the area. They told her that she had forgotten to put the dimensions on, and when she responded that she had meant for them to actually measure the rectangles with rulers, they were "baffled".

The end of the afternoon

Our second afternoon/evening here at Swarthmore came more or less to a close (people are at their computers until the wee hours of the morning around here) with a discussion about potential projects for the week. When our ideas are better developed and work is begun in groups, we encourage all of you to join in from afar.

We first talked about what people had found on the Web -- what sites people found particularly good and bad, and why. People thought that sites should be more interactive. There really aren't all that many sites out there that are interesting enough to be sure to hold kids' attention for a substantial amount of time. There seem to be a lot of sites that have the potential to be really good, but don't go so far as to take full advantage of the immediacy that the the Net offers.

We all agreed that we have to stop sending kids to just browse the Web, because that wears thin quickly. So, we'd like to explore projects that involve the specific construction of something, or that involve interaction with other students, teachers or even professionals. The next step would be to offer recognition for achievement at such sites. It should also take full advantage of reaching and manipulating resources that would not normally be available at a school or somebody's home.

In a closely related conversation, we talked about resources that should be made available for teachers. Textbooks are no longer all that effective as a vehicle for distributing curriculum. They're simply not multi-media. The Net should be taking over that role, but it hasn't done so yet. It would be nice if it offered specific curricula, particularly for units not normally covered in classes. A goal for this Institute may be to formulate a model for such a developed unit. Where the problems lie are in organizing the material available on the Web and, most importantly, in getting teachers to contribute their resources. In answer to the latter, we explored the possibility of establishing a system in which teachers and students could be recognized for their work. One way would be simply to applaud them on the Net (perhaps offering a reward system similar to that of the Boy and Girl Scouts/Guides), while another might be to offer incentives such as increased access privileges, perks from software companies, or money (in the form of self-sustaining sites people would pay to visit).

I hope these summaries are useful to those wishing to follow and/or participate in the workshop.

Eric Sasson