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Inspired
by Seymour Papert's notion of a computer as an object to think with,
Robert's ideas about learning and teaching took a dramatic step forward.
Here's his story
I encountered LOGO early on in the second year of my teaching career,
in the winter of 1986. I was just starting out teaching mathematics, and
I knew that many of the things in that were going on in my classroom were
rather dry and technical, and that there had to be some way of making things
more interesting. I always had a good eye for humor, as well as games and
puzzles, but technology didn't interest me. I had a Tandy Model 100 "notebook"
computer which was excellent as a word processor, but the computer programs
in my school seemed to be just as silly and inane as the textbook I was
using. I had heard something about LOGO from our computer teacher, who
had started teaching at about the same time as me. I knew that it had something
to do with a turtle drawing squares, but despite all my colleagues prompts,
I made little effort to visit the computer lab to see what it was all about.
All this changed one Saturday morning when Ihor Charischak, who at
that time was working as an independent staff developer and educational
consultant, came to give a workshop at my school. He began by describing
something called a "dynamic notebook"(1) which could be opened and all
kinds of amazing mathematical things could happen, which he termed a "microworld."
I was intrigued by his vision, and he proceeded to show us a game he had
written in LogoWriter called Dr. Factor (2) As we played, I slowly glombed
onto the idea Ihor was advocating: that this thing he called a "microworld"
could transcend the pedestrian "drill and kill" computer games which I
saw as having little relevance to a deep understanding of mathematics.
Ihor continued by playing a LogoWriter movie he had made called Number
Town (3) where all the whole numbers lived in perfect harmony, until a
nasty fraction called 1/4 came to town to rob the local bakery. As I watched
the numbers move around in their story, I realized that in a microworld,
a turtle didn't have to be a turtle: it could be a character in some unfolding
drama that dealt with some fundamental idea of mathematics. From that moment
on, I was a confirmed LOGO head. I immediately went out and purchased what
seems like now (and was then, also) a very primitive Apple IIe knockoff
known as a Laser which I propped up on my dining room table along with
a secondhand black and green monitor. During my Christmas break, I pulled
out all my old copies of Scientific American and promptly taught
myself how to program worms, cycloids, fractals and any number of other
computerized entities I could find in the Mathematical Recreations column.
My earliest microworlds were primitive by any stretch of the imagination.
Some just involved drilling students on addition or multiplication facts,
rewarding them with a stamped "light bulb" every time a fact was recalled
correctly. Others were more interesting: one program asked students to
place numbers in the proper place value column; at the conclusion of the
game, the letters under each column would spell out the answer to a joke
or riddle that had been posed at the beginning of the activity. As I learned
more LogoWriter "tricks," my microworlds became more sophisticated. At
one point, I had my students program an entire Carmen Sandiego chase game
which took place within the periodic table. To give you an idea of how
complex this was at the time, my students needed three 5 1/4 floppy
disks to run the game: one with the program, which was then swapped with
two data disks. For me, there was no going back: I would never be the same
teacher after encountering LOGO and internalizing the microworld concept.
Even when I wasn't using LOGO, or technology for that matter, I was always
thinking of embedding the mathematical skills and concepts I was
teaching in some kind of compelling context, whether it was a game, puzzle
or story. While the first microworld I saw was on a computer screen, I
understood that it was not so much a technical term for where an experience
was taking place, but how it unfolded. Encountering LOGO was a transformative
experience in my educational development; though LOGO may not be on people's
minds like it once was, the concept of the microworld will always be as
important, meaningful and compelling as it was 15 years ago.
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Ihor's Notes
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1. I first heard about the idea of a "dynamic notebook" from
Alan Kay. He called his vision of a personal computer a Dynabook.
2. Dr. Factor is a variation of Taxman,
a game that appeared in David Ahl's book, 1001 Computer Games. Antonia
Stone of Playing to Win included Dr. Factor as one of the programs
in a collection called Playing to Learn which was published by HRM.
In the Connected Mathematics Project (CMP) unit Prime Time: Factors
and Multiples (published by Dale Seymour) Taxman (called the
Factor Game) is used to motivate a unit on prime numbers and factors.
This program is available from the CMP website. http://www.math.msu.edu/cmp/This
version is also one of the java-based activities on NCTM's Illuminations
website. http://Illuminations.nctm.org/imath/6-8/FactorGame/
3. Number Town was a LogoWriter version of the animated
movie called The Weird Number published by Xerox Publishing in 1971.
Not currently available in an updated form.
You will find some examples of microworlds that Robert
and I have created on the CLIME website at http://clime.org/microworlds |
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