Sunday, July 9, 1995
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
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
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!
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
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.