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Still Crazy after all these Years
by Robert Berkman
with notes by Ihor Charischak

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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. 
Ihor's Notes
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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