The Computer
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The Computer


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Across the world there is a passionate love affair between children and computers.  I have worked with children and computers in Africa and Asia and America, in cities, in suburbs, on farms and in jungles.  I have worked with poor children and rich children; with children of bookish parents and with children from illiterate families.  But these differences don’t seem to matter.  Everywhere, with very few exceptions, I see the same gleam in their eyes, the same desire to appropriate this thing.  And more than wanting it, they seem to know that in a deep way it already belongs to them.  They know they can master it more easily and more naturally than their parents.  They know they are the computer generation.  --Seymour Papert, The Connected Family: bridging the digital generation gap, 1996

 

 

My children have never known a home that did not include a personal computer.  I often get requests from students in the computer clubs for information on how to get the software we use for use at home.  Most students in this particular elementary school have a computer at home.  Besides actual computers, familiarity with electronic controllers, “clicking”, visually taking in information, and even a concept of levels are a part of children’s playtime experience due to the presence of video game systems (the games have levels that you reach by completing some task or obtaining something from a prior level).  Dr. Papert attributes children’s affinity with computers as originating in part in their experience with video games.  He is careful to point out that though considered toys, these games were the first large scale merger of computer technology with toys and they are as demanding, and often are more demanding than homework.  (He says any adult that thinks otherwise need only to sit down and try one!)  Yet, children willingly devote time and effort to the games that they are reluctant to give to homework.  Dr. Papert believes educators have something to learn from Nintendo.  (Papert 1993)  

 

 

The activities presented in the cross-section in time, and the Lego robotics that I work with in computer clubs are part of this already familiar computer culture of kids.  Not having any knowledge of Seymour Papert’s theories or David Cavallo’s emergent designs, I observed children working with LOGO and the robots with the same enthusiasm as I have seen them engrossed in video games.  The materials themselves—Legos, computers, multimedia on-screen interactions—have the kids’ culture built in.  I found myself thinking, school should be this fun; after reading Papert’s books I find that he has been saying the same thing for over twenty years now.  The learning centers in Thailand (described in the sections linked to decentralized learning and emergent design) are evidence that school can be conducted in a decentralized, exploratory way when the true power of the computer is utilized.

 

So what is the “true” power of computers?  I think its very unfortunate that the popular image of computers revolutionizing life as expressed on TV and in magazine ads limits the concept in many adults’ minds to making business success and information faster and easier to get.  Computers are doing that, it’s true, but the hype about instant results is enormous.  I set up a website for a small business in Burlington, Vermont and know first hand how challenging it is to even get your site to appear in a standard Internet search.  Workshops are conducted on how to achieve this; the IBM ads with the smiling entrepreneurs with the Italian glassware don’t tell you about metatags and search engine fees.   The Internet is the other misrepresented hallmark of the computer “revolution”.  It is revolutionary, but there is also a lot of misleading hype about its uses.  The Internet was created to share current, perishable information in the scientific research community and it still serves this type of “immediate” information best.  If you want to find out about airline tickets, yes the Internet is fast, efficient and current.  If you want to find out about Holstein cows, as my daughter and I found out, it’s faster to get an encyclopedia than to run through the not-always-so-educational search results from the Internet search engines.  If you do find a great site on Holsteins, even book marking it will not guarantee it will be there in the format you need the next time you visit the site.  The Internet is not a huge library; it is a much faster, more easily accessible but temporary resource. 

 

I see the power of computers in educational environments such as the one in the cross section on many levels.  Computers used in a group setting allow a kind of individual learning to occur within the group; students move in and out of being on their own and being with others at their own pace and by choice.  It’s a free, fluid style of group learning.  Earlier segments of this document have elaborated on the children’s programming environment, LOGO, and one of its spin-offs, StarLogo.  Programming and observing computer simulations are in themselves examples of new types of learning.  Mitchel Resnick goes further to elucidate how a computer itself is a multi-level complex system.

 

Moreover, computers themselves are best understood by thinking in terms of levels.   At one level, the operation of a computer program can be described in terms of movement of electrons; at another level, in terms of gates and transistors; at another level, in terms of assembly language instructions; at yet another level, in terms of general algorithms and “intentions.”   Even more importantly, these computer inspired ideas about levels are providing new metaphors and models for understanding many other complex systems in the world, offering a productive framework for thinking about some of the most difficult issues of science, from evolution of species to the workings of the mind.

(Resnick and Wilensky 1996)

 

I reviewed such metaphors used by Marvin Minsky and Seymour Papert to form the theory of the Society of Mind in an earlier section.  Here’s one with a much lighter intent from “The Great Logo Adventure” by Jim Muller, formerly of Texas Instruments, who introduced the first commercial version of Logo, TI Logo, and helped found the Young Peoples’ Logo Association in the 1980’s.  He explains one of the powerful abilities of the computer, the ability to use recursion in programming, with a metaphor on life.  He writes an imaginary Logo program, “Get Through Life” as follows:

 

TO.GET.THROUGH.LIFE

GET.THROUGH.TODAY

GET.THROUGH.LIFE

END

 

What happens inside a computer is that the code “get through life” flies through the circuits, and is interpreted as “get through today”—OK, that is a subroutine and was defined previously, we must assume, so the computer executes “get through today” and then reads “get through life” again—and starts over.  It’s recursion: a continuous spiral of events and a powerfully efficient way to write a program.  This example is one for a being from Mount Olympus, however, because as you may have noticed, it will never reach the END line because the thing keeps starting over before it gets there.  Mr. Muller gives the final and mortal version of the “get through life” program as follows:

 

 

TO.GET.THROUGH.LIFE

IF LIFE=”OVER [STOP] {ELSE}

GET.THROUGH.TODAY

GET.THROUGH.LIFE

PRINT BOOK.OF.LIFE

END

 

 

He also includes a subroutine for a written record in this version of the “get through life program”.  Computers do extremely well using definitions that include the very thing they are written to define.   This is a new kind of thinking; I was taught not to use the word I was defining in the definition.   In programming, it turns out to be one of the best ways to define things, and a most efficient way to get things done. 

 

 

In the quotation above, Mitchel Resnick mentions how computers can provide models for understanding complex systems.   The science of complexity involves investigations of how complex phenomenon arise from simple components and simple interactions. (Resnick and Wilensky1996)  These investigations began when computers were first used in scientific research to model weather systems or graph specific mathematical problems and yielded unexpected results. The details of these investigations are beyond the scope of this paper but are numerous and well described in James Gleick’s book “Chaos” (1987). James Gleick likens the magnitude of the effect of computers on science to the effect of microscopes on previous generations of scientists.   Until the computer was invented, there was no way to perform millions of calculations in seconds; when computers did this and then graphed the results, a whole new science began emerging; new things could be seen.

 

 

These images are examples of one graph of the results of a math problem that could not be seen before computers with graphics capabilities. In 1979 Benoit Mandelbrot used huge IBM mainframe computers to be able to generate the first crude black and white images of this set that is now named for him.  The program I used to create these images is available on the Internet for $20.00. It is “careware”, software created by a group of programmers to raise money for helping the education of autistic children.  When I emailed the programmers to get permission to use images I create with the software on my web site, I received an enthusiastic reply.  Phillip Crews, the creator of the program said the children helped by the foundation use the program and create images to color.  I think that’s a powerful use of computers on a whole different level.

 

Zooming in on the smallest of the three white areas (to the left, the tip) of the first image yields the second image. 

Programs that create images like this are surprisingly brief because they use recursion.  Each point on this image was the result of a mathematical calculation for what is now considered university level mathematics.  Yet the whole image pops on the screen in a fraction of a second. Children can play with this program and discover relationships and even feel the imagination tingle by the view of trailing off into infinity—the “zooming in” theoretically never ends.  It’s “trial and error” geometry.   “…the Mandelbrot set allows no shortcuts.  The only way to see what shape goes with a particular equation is by trial and error…[emphasis mine]. (Gleick 1987)

 

This image is the result of zooming in on the tiny white area further to the left in the second image above seven times. 

 

So, what is it?  It’s the graph of a math problem—a set of points.  Mandelbrot investigated the set after years of thinking about the irregularities of markets, coastlines, and other behavior that the standard, neat textbook math problems dismissed as exceptions or anomalies.  These images became the symbol of the science of Chaos; the fringes of the set are areas where chaos arises from orderly calculations, but then orderly patterns emerge from the chaotic behavior.  The white area is the set; the colors are out of the set, and color-coded by how many times the recursive program executes calculations for the point it plots up to a preset limit (usually related to how many decimal places your computer can stand).  Without the preset limits, the recursion would theoretically go on infinitely.

In addition to the Mandelbrot Set above, graphics computers enable us to visualize structures in higher dimensions.  Think of a square with a side length a. Its area is a2.  If you make a cube from six of the squares is volume is a3.  The hyper volume (that is, the volume of a higher dimensional shape) of an n-cube (we describe higher dimension shapes in terms of three dimensional shapes because we are familiar with them) is an (Pickover 1999). These last few sentences are typical of the abstract language that I learned to decipher as I learned mathematics.  They would make little concrete sense to me if I were not also able to see the pictures of such shapes in Pickover’s book, pictures that can only be generated by a computer.  Looking at his pictures and trying to imagine what is “perpendicular to a cube” stretches my mind so that I can feel it thinking.  Our kids deserve to feel math like that. 

 

Research into complex systems touches on some of the deepest issues in science and philosophy—order vs. chaos, randomness vs. determinacy, analysis vs. synthesis.  In the minds of many, the study of complexity is not just a new science, but a new way of thinking about all science, a fundamental shift from the paradigms that have dominated scientific thinking for the past 300 years. (Resnick and Wilensky 1996)

 

Computers opened the field and study of complexity.  They have the power to open children’s minds to new ways of thinking.

 

Isn’t all of this a bit abstract for children in grades K—12?  That depends on how you approach the information.  As Seymour Papert eloquently describes, “the super valuation of the abstract blocks progress in education in mutually reinforcing ways in practice and in theory.”  (Papert 1993, 148)  Computers can allow children the very same opportunity to explore these concepts that they offer mathematicians.  Computers allow trial and error exploration of these pictures.  I enjoy opening the programs and allowing children to play with them and simply listening to the comments they make and the observations they express.  For me, listening to students as they explore such pictures or watch simulations running in StarLogo are inroads to understanding how that particular child perceives things.  When I first listen to a child’s own explanation of what she sees, I can better communicate about the math underlying the images.  Is this legitimate math education?  Well, I think of analogous learning experiences in my music teaching experience.  Writing music or learning even one part of a Beethoven symphony is extremely abstract; it involves a unique language, special symbols, and the ability to participate in real-time execution.  Yet from pre-school, children sing and play the “Ode to Joy” theme on instruments as a part of their school learning experience.  Why should math and computer science be any different?  Music escapes the stereotype of being an abstract field for higher grades and university level students that plagues math and science. I believe this is true because of the way math and sciences are presented in school, and not because of the inherent nature of the subjects. (Imagine requiring students to be able to read and write music before “allowing” them to sing.) With computers, kids can play with math and science more readily and in different ways—on the computer screen or with robots. 

 

Seymour Papert invented LOGO to give children a means to concretely explore, through trial and error, computer images and the programs behind them.  His theory of learning which he calls “Constructionism” values concrete thinking not as a step toward abstract thinking, but as a way of knowing equal to abstract thought and always co-existing with it.  He gives examples of how mathematicians and scientists themselves tinker and try things out and then write the results in something that resembles a format within the accepted confines of “the scientific method” (Papert 1993).  His point is that real science is a concrete process as much as it is abstract formalism.  Computers are the key to concrete manipulation of many abstract concepts and it makes them a powerful educational tool.  I consider the true power of computers in education to be the ability to use them to approach new material in new ways and honor alternate ways of knowing and styles of learning.  Using computers can change what children learn and how they learn it.

 

 

 

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