Winter 1999 Volume 17 f Number 2

PERSPECTIVES ON PAPERT

INSIDE The History of Mr. Papert Dreams, Realities, and Possibilities • Papert's Conjecture About the Variability of Piagetian Stages Papert, Logo, and Loving to Learn Mixed Feelings about Papert and Logo • Polygons and More • Explaining Yourself • Book Review, Logo News, Teacher Feature Gtste Volume 17 I Number 2

Editorial Publisher 1998-1999 ISTE BOARD OF DIRECTORS Logo Exchange is published quarterly by the In­ International Society for Technology in Education ISTE Executive Board Members ternational Society for Technology in Education Lynne Schrum, President University of Georgia­ Special Interest Group for Logo-Using Educa­ Editor-in-Chief tors. Logo Exchange solicits articles on all as­ Gary S. Stager, Pepperdine University Athens (GA) Heidi Rogers, President-Elect University of Idaho pects of Logo use in education. [email protected] Cheryl Lemke, Secretary Milken Family Submission of Manuscripts Foundation (CA) Copy Editing, Design, & Production Manuscripts should be sent by surface mail on Ron Richmond Michael Turzanski, Treasurer Cisco Systems, a 3.5-inch disk (where possible). Preferred for­ Inc. (MA) mat is Microsoft Word for the Macintosh. ASCII Founding Editor Chip Kimball, At Large Lake Washington files in either Macintosh or DOS format are also Tom Lough, Murray State University School District (WA) welcome. Submissions may also be made by elec­ Cathy Gunn, At Large Northern Arizona tronic mail. Where possible, graphics should be Design, Illustrations & Art Direction University Peter Reynolds, Fablevision Animation Studios submitted electronically. Please include elec­ pete @fablevision.com ISTE Board Members tronic copy, either on disk (preferred) or by elec­ Larry Anderson Mississippi State University tronic mail, with paper submissions. Paper sub­ Contributing Editors jose Calderoni ILCE. Mexico missions may be submitted for review if Dr. Douglas Clements, SUNY Buffalo Penny Ellsworth Western Springs School electronic copies are supplied on acceptance. Dr. Carolyn Dowling, Australian Catholic District 101 (IL) Send surface mail to: University Marianne Handler National-Louis (IL) University Gary S. Stager Alan Epstein, Metasoft Dennis Harper Olympia School District (WA) Dr. Brian Harvey, U.C. Berkeley 21825 Barbara St. Jorge Ortega FACE/Leon County SD (FL) Torrance, CA 90503 USA Daniel E. Kinnaman, Curriculum Administrator Neal Strudler University of Nevada, Las Vegas Magazine Sue Waalkes Upper Dublin School District (PA) Send electronic mail to: Dr. Julie Sarama, Wayne State University Peter Wholihan Sts. Paul & Peter School, Virgin logoexchange@moon. pepperdine.edu International Editor Islands Deadlines Jeff Richardson, Monash University, Australia ISTE Committees To be considered for publication, manuscripts International Editor Emeritus Lajeane Thomas Accreditation and Standards must be received by the dates indicated below. Dennis Harper, Olympia, Washington School Dave Brittain Awards Vol.l7,No.4 ...... Aprill5, 1999 District Cathy Gunn Distance Learning Michael Turzanski Finance "The Turtle Parties Like It's 1999" SIGLogo Officers Paul Resta and Gerald Knezek International Stephen Sesko, President jenelle Leonard Minority Affairs jeff Richardson, Vice-President LarySmith Policies and Procedures Hope Chafiian, Secretary/Treasurer M. D. Roblyer Publications Gary S. Stager, Editor ISTE Executive Officer SIG Coordinator for Research and Development Tom Magness David Moursund

Logo Exchange is published quarterly by the International Society for Technology in Education (ISTE). 1787 Agate St., Eugene, OR 97403-1923, USA: 800.336.5191. ISTE members may join SIG/Logo for $24. Dues include a subscription to Logo Exchange. Non ISTE member subscription rate is $34. Add $10 for mailing outside the USA. Send membership dues to ISTE. Add $4.00 for processing if payment does not accompany your dues. VISA. MasterCard, and Discover accepted. Advertising space in Logo Exchange is limited. Please contact ISTE's director of advertising services for space availability and details. Logo Exchange solicits articles on all topics of interest to Logo-using educators. Submission guidelines can be obtained by contacting the editor. Opinions expressed in this publication are those of the authors and do not necessarily represent or reflect official ISTE policy.

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Winter 1999 Vol. 17 I No. 2 Contents

ARTICLES

The History of Mr. Papert Martin Boyle 8 Dreams, Realties, and Possibilities Gail Marshall 15 Papert's Conjecture about the Variability of Piagetian Stages in Computer-Rich Cultures Anne McDougall 23 Logo News Logo Exchange staff 30 Polygons and More William]. Spezeski 31 Papert, Logo, and Loving to Learn Pam Gibbons 33

COLUMNS

EDITORIAL IN THEIR OWN WORDS Never Satisfied, Only Gratified Mixed Feelings about Gary S. Stager 2 Seymour Papert and Logo KenKahn 18 QUARTERLY QUANTUM Turtle and the Moon STARTING WITH STARLOGO Tom Lough 3 StarLogo Community of TEACHER FEATURE Learners Workshop Mr. Condom Vanessa Colella, Eric Klopfer and Mitchel Resnick 20 Seymour Papert 5 LOGO: SEARCH AND RESEARCH BOOK REVIEW Reading Papert or Papert's Perspectives, Research Responses Growing with Your Guru Douglas H. Clements Carolyn Dowling 7 and julie Sarama 27 FOR BEGINNERS THE LAST WORD: Simple Probability as a Vehicle Explaining Yourself for Understanding MicroWorlds Bernard Newsome 35 Data Structures Gary Stager 13 1ste EDITORIAL I GARY S. STAGER

Never Satisfied, Only Gratified

hose were the frequently uttered is an object to think with, both for the battlefield of ideas but rather in the Twords of my old trumpet teacher, learner and for the people who are marketplace. Logo is bad for business. William Fielder. You may enjoy the thinking about the thinking of the If kids construct their knowledge momentary pleasure of success, but learner. Seymour Papert has provided and express themselves in an environ­ persistence and hard work are required countless educators with the thrill as­ ment designed to have "no threshold if you wish to achieve greatness. This sociated with students performing in­ and no ceiling," then you are not simple poetic phrase reminds me of Dr. tellectual feats they never before be­ likely to buy lots of other software Seymour Papert. lieved to be possible. He invited products. Schools not disposing of old Papert' s life, work, and ideas have educators into a community of power­ computers because they are just per­ inspired countless people around the ful ideas by giving voice to their expe­ fect LEGO TC logo workstations world and acquainted millions of chil­ riences and encouraging the sharing of don't run out and buy as many new dren with the joy of learning. While learning stories. We have been given a computers each year. While the Soft­ reasonable people may differ about way in which to discuss profound ideas ware Publishers Association may whether Papert is the Father of Logo, without being overburdened by osten­ honor Papert with a lifetime achieve­ he can surely be considered its loving tatious vocabulary or overly technical ment award, its member companies mentor. In fact, Papert was one of the theories. Best of all, we are encouraged conspire to keep Logo-related presen­ first people to suggest (more than 35 to interpret these ideas in personally tations off far too many educational years ago) that computers could play resonant ways. technology conference programs. an important role in learning. Thirty Papert's books about education­ Logo is also bad for the business of years ago, Papert, Alan Kay, and Mindstorms, The Children's Machine schooling because it encourages con­ Cynthia Solomon were predicting that and The Connected Family-take the cerned adults to rethink the nature of every child would own a portable com­ reader through the development of his teaching and learning. puter. Papert's previous accomplish­ thinking about learning with comput­ The most noxious attacks on Logo ments in mathematics, cognitive psy­ ers. We are challenged to question our are acts of omission. As a university chology, and artificial intelligence led own assumptions in order to take steps teacher educator, I receive countless credibility to such predictions. toward enriching the learning experi­ textbooks on the theory, history, and In Papert you find the rare futurist. ence for children. (Carolyn Dowling practice of educational computing for He not only launched the idea of explores these books later in this issue.) my consideration. The majority of these learner-centered computing, but then It has always pleased me that texts don't disagree with Logo research spent several decades expanding his Papert's books have enjoyed no serious or the theories of Seymour Papert. They theories while actually building things criticism in academic circles. People don't mention them at all. Most of these (both software and ideas) used by oth­ may disagree with a point or two in books purporting to provide an intel­ ers. His work shares more with Tho­ the books, but there has been no seri­ lectual and/or historical understanding mas Edison than most "ivory tower ous piece of scholarship arguing of educational computing ignore four academics." against the ideas found in Mindstorms. decades' worth of research and class­ Logo offers learners a powerful in­ This does not, of course, mean that room practice. This is unacceptable and tellectual laboratory and vehicle for Logo, or even Papert personally, has intellectually dishonest. One rare excep­ self-expression while providing teach­ been free of criticism. tion is Designing Multimedia Environ- ers with a catalyst for rethinking the The attacks on Logo, with few ex­ nature of teaching and learning. Logo ceptio~s. have not been fought on the See NOT SATISFIED (Page 4)

2 LOGO EXCHANGE Vol. 17 I No.2 QUARTERLY QUANTUM I TOM LOUGH. FOUNDING EDITOR

Turtle and the Moon

t started out as an ordinary event. I around the earth as it moved appar­ right, that of the child or that of the I took my son Kyser outside one ently eastward beneath Jupiter! turtle? evening to observe the moon in its first We decided to come out again in Intellectually. I knew that the same quarter. Before long, however, it turned three more hours, and discussed what side of the moon was illuminated each into an extraordinary event and then it might look like then. Sure enough! night. But I had to do some real men­ (a bit later) into an amazing event! We saw that the moon and Jupiter had tal gymnastics to picture why the left And finally, it gave me another per­ moved further west across the sky. But side appears to be illuminated for ob­ spective about what we can learn from the moon had also moved eastward servers in the Southern Hemisphere. the turtle. with respect to Jupiter. The shining Like many children wondering about But I'm getting way ahead of myself! planet now appeared above and to the the upside-down turtle, I found myself Let me back up and tell you what hap­ right of the moon. Relative motion in contorting my body. turning sort of pened. action! upside down to look at the moon and When we went outside, it was on Such extraordinary events are won­ Jupiter, so I could better imagine what the downside of dusk and the sky was derful opportunities to observe and it must look like for someone in south­ just darkening. The moon was spec­ contemplate the rather complex move­ em Africa. Finally, I could make com­ tacular. We could see the brilliantly il­ ments of the heavenly bodies. fortable sense of it. luminated right side of the moon and Now, here's the amazing part. Dur­ This ordinary, extraordinary, and the uneven shadows along the termi­ ing the next afternoon, I logged onto a amazing series of events reminded me nator between light and darkness. We live camera site on the Internet once again that some turtle aspects are also noticed that Jupiter was shining (www.africam.com) that was situ­ challenging for young minds; yet, they brightly above and to the left of the ated by a waterhole in southern Africa. are accessible. Ideas such as relative moon. It was simply beautiful. I wanted to see what animals might be motion and relative direction sound About three hours later, I had to go drinking there at dusk. complex, but they are all around us. outside for something. While out, I Instead of seeing animals, however, The rich learning environment of the happened to take a look at the moon. I was treated to a beautiful view of the Logo turtle provides the stimulus to What I saw sent me running back into moon! The camera host had recognized examine these ideas in ways that are the house to get Kyser! the spectacular sky scene and had meaningful to us. From their earlier position, the trained the cam's lens on it for others We could wish no better for our stu- moon and Jupiter had moved across the to enjoy as well. There on my computer dents. f8 sky toward the west. But Jupiter was screen was Jupiter, but it was below no longer to the left of the moon; it was and to the left of the moon! And the FD 100! directly above it, lined up with the ter­ moon was lighted on the left side in­ minator. stead of the right! Amazing! Tom Lough, Founding Editor, We discussed what we were seeing, Kyser and I enjoyed this series of Murray State University and concluded that the westerly move­ observations very much. But it also Department of Elementary and ment of the moon-Jupiter system was reminded me of the Logo turtle. All of Secondary Education, due to the rotation of the earth. Just us have seen the fascinating situation PO Box 9, Murray, KY 42071. like the sun, it was moving from east of a child trying to figure out how to phone: 502.762.2538 to west. But we could also see the re­ turn a turtle that is facing towards the fax: 502.762.2540 sult of the revolution of the moon bottom of the screen. Whose "left" is tom.lough @coe. murraystate.edu

Winter 1999 LOGO EXCHANGE 3 I

BACK TO SCHOOL / Continued from Page 2

ments for Children by Allison Druin and Papert' s enormous contributions to the Cynthia Solomon. world of ideas in three ways. Ask a room full of educators who know something about Logo to brain­ 1. His ability to generate brilliant storm a list of the most frequently theories. heard criticisms. The list always in­ 2. His willingness to risk criticism cludes things such as: it requires teach­ for generalizing how those theo­ ers to learn new things; it requires too ries would look in practice. much class time to do something 3. His ability to predict how those worthwhile; it's hard to assign a letter ideas would be assimilated and grade; or it doesn't fit neatly into tra­ misinterpreted by the institu­ ditional curriculum areas. These are tions they challenge. Jeff Richardson's not criticisms of Logo as much as they are criticisms of school. Logo is an em­ In many ways, Papert reconcept­ Wild Ride bodiment of that criticism. ualizes Dewey, Montessori, Vygotsky, by JEFF RICHARDSON. Seymour Papert possesses qualities Piaget, A.S. Neil, and other progressive INTERNATIONAL EDITOR that set him apart from many other educators in a contemporary com­ great thinkers. He not only loves to puter-rich world. His ideas are built on I rode with him learn, but he relishes other people's the shoulders of the great educators inctaxionce learning and helps us see the magic in who came before. Moreover, Papert OIJly fora p1ile and a half our own learning. One of Seymour's helps us see the tactical errors of our s~edligeit. took ?:Coupleofmonths 0 prize pupils, ldit Harel, speaks in a glo­ predecessors and the new opportuni­ C"~e~nY.~~~~~:9Y:~~l:>ylan) : rious interview for next issue about ties that emerge with the widespread Papert's playfulness. He loves toys. availability of personal computing de­ ··Si~:i~~:ni~i:~=~:~~:~: ••: games and puzzles. His sense of humor vices. We are encouraged to use our ~!;}nat ComplitmgitfSytme)'m1990. • is infectious and he is fueled by the imagination, to dream, to play. . Iotttenderl:.the conference:a$ahtim~ bl~deleg~te. . . .· .... · ··· · .. · · hard-fun of children. Papert's humor My answer is that if you have a vi­ and playfulness often lead to very im­ sion of Someday you can use this to . . ·Our pathS crossed it1adowni9wn portant research. guide what you do Monday. But if your radio studi(); Seymour was thereto ·do a"serious interview.'' I was us­ Papert also cares a great deal about vision of where it is going is doing the ing Tardis booth to make myregu­ educational equity and believes that same old stuff a bit (or a lot) better, a larweekly spot on Mei~bourne radio. learning provides a vehicle for over­ your efforts will be bypassed by history We both finished up at the same time. (Seymour Papert, 1998). coming social injustices. His work has So I introduced· myself and sug­ always been concerned with disadvan­ This issue contains a collection of gested we share a taxi. back to the taged communities, whether they be in perspectives on Papert from an inter­ conference center. During the ride he New York, the Roxbury section of Bos­ national cast of contributors. Many of generously listened to my crazy re­ ton, or developing countries. Sey­ these contributors know Seymour search ideas, interjecting ideas, and mour's current projects include work­ Papert through only his work. I am .·elaborations of.his OwR We were still ing in Thailand (see his Teacher grateful for their contributions and as '· talking animatedly when the eab Feature in this issue) with the job always thank Peter Reynolds for his ' :pulled up af'the coriference center, Corps as well as a juvenile girls prison wonderful illustrations. Point to http:/ ·.:W.h~t:e ,dignitaries wer,e waiting tQ, in Maine. /www.stager.org/planetpapert.html ····tishef·Seymourinto•some innef5anc· His willingness and ability to work for an extensive collection of articles, :'turiiand his .next appointment' with the corporate world has led to papers and speeches by and about .•..•.... He stayed·in the eab talkmgwith criticism from within the Logo commu­ Seymour Papert. ~ i: me for a further quarter of an hour;. nity but has also produced actual prod­ . >~he meter running. and frustrated ucts that benefit children. Papert does suits on the footpath calling "Dr; not view popular culture with disdain Papert, we teally MUST GO!" He made them crazy as he ignored them but as a variable necessary in any for­ Gary mula for understanding the way chil­ and continued our conversation dren learn now and in the future. Gary Stager, Editor-in-Chief about the usual things: children, I have come to appreciate Seymour [email protected] computers, and powerful ideas. ~

4 LOGO EXCHANGE Vol. 17 I No. 2 TEACHER FEATURE

Mr. Condom

by SEYMOUR PAPERT

recently came back from a trip to ing so would be irrelevant to the real port for learning the programming Thailand where I am working on problem. These villagers know about skills needed to carry out their projects I a project to develop uses of digital sex and would be perfectly capable of using Logo (Logo Writer at the time) as technology for learning in so called figuring out how to use a condom if their programming language. "developing" countries. While there I they were not so uptight about it. What All students were expected to deal met a remarkable educator who has was needed was to make them have a with some aspect of fractions. But they provided me with what has become my more relaxed relationship with the could choose which. Most chose some favorite learning story. thing. aspect of schoolish knowledge about He earned the title Mr. Condom Contrast his approach with what manipulating fractions. But some did (though when they are being polite he happens in many American sex edu­ something very different. is more usually addressed as Mr. cation classes. Teacher draws on the Debbie's software was very differ­ Mechai Viravaidya. Chairman of the board, or puts up a chart showing the ent indeed. She described the insight Population and Community Develop­ plumbing of the human reproductive she wanted her software to convey as ment Association (PDA), by bringing system. "Now this is how a condom "There are fractions everywhere. You a brilliant educational methodology the works ... " can put them on top of anything." To problem of encouraging villagers to The difference between Mr. Mechai show this she would draw a picture and practice birth and STD control. His and the approach of the American sex show that you can find many fractions procedure is this. education class applies much more in it. She spent a lot of time doing that He goes to a village meeting. holds widely than to condoms. In fact I be­ and programming the computer to up a condom and asks if anyone knows lieve that Mr. Mechai has as much to show the result. what to do with it. The tension and tell us about math education as about Now I forgot to say that before this silence is palpable. So he says: "Well, sex education. Because if kids were not experience Debbie was a very poor look." He unwraps the condom, puts too uptight about fractions to play with math student and when interviewed it to his lips, and blows it up like a bal­ them, they would find it easy to figure about fractions showed not only a piti­ loon. The tense silence is broken by a out how they work. ful lack of knowledge but also an ex­ few giggles. So he continues in the So let me tell you another story in treme reluctance to apply her mind to same spirit ... bouncing the balloon, which my then doctoral student ldit thinking about them. After her soft­ blowing up another, trying to juggle .. Harel did something for fractions very ware writing experience she scored, for . generally fooling around. When the similar to what Mr. Mechai did for the first time in her life. at a superior crowd seems to entering the spirit of condoms. level on standardized school math tests. fun he hands out condoms to everyone It happened in the Hennigan School What happened? This goes against urging them to join in the fun. in Boston. Idit had given a fourth-grade the grain of conventional wisdom in Then he goes away. class an assignment to make software the school world. "If you want students And if you look at the statistics you that would teach something about frac­ to score well on tests about fractions, see that in the places where Mr. Con­ tions. The students had access to teach them the stuff they will be tested dom has performed the birth rate has enough computers for each one to on." From this point of view Debbie gone down. work on an individual product. They was wasting her time with the soft­ Mr. Mechai explained to me that if had enough time-a school period a ware. Just like the villagers were "wast- he stood up there and spoke about sex, day for most of a school year-to do a people would not listen. Besides, do- serious job. And they had enough sup- See MR. CONDOM (Page 12)

Winter 1999 LOGO EXCHANGE 5 manner of teaching possibilities and edu­ tives and concepts of Mindstorms mir­ Dandng cational applications dancing in my rored in his ideas and guidance. I feel this mind! This was one of the most signifi­ underpinning was one of the keys to the cant moments of my life. success of the series of MIT conferences. with Shortly after that. I had the opportu­ By then, Terry Cannings had demon­ nity to encounter Seymour more directly. strated that a regional Logo conference Once the National Logo Exchange (as it could succeed by hosting the West Coast Seymour was called back then) was launched in Logo Conference. With Logo '86 conclud­ September 1982, the Logo folks at the ing the MIT international conferences, by TOM LOUGH. University of Virginia began to think UVA and Meckler Publishing joined to FOUNDING EDITOR about how to connect with even more host the East Coast Logo Conference Logo users. The idea of a Logo confer­ (ECLC) in 1987. Naturally. we wanted e dance is a powerful metaphor in ence spurred a series of telephone calls Seymour as the keynote speaker. many contexts. However. I was un­ to MIT, and we eventually agreed to host We set up ECLC using many ideas prepared for how deeply such a a planning meeting at the 1983 National from Mindstorms. Jock McLees from Ter­ metaphor might affect me when I first en­ Educational Computing Conference rapin taught us how to juggle. Andy countered Logo and Seymour Papert. Let (NECC '83) in Baltimore. David taught us how to construct a geo­ me tell you how it was ... Immediately prior to this meeting, desic dome. Dan and Molly Watt taught In the fall of 1981, I was a us contra dancing. One of the physics graduate student at the hallmarks of contra dancing is University of Virginia. By a se­ that traditional male-female ries of fortunate circum­ couples are not necessary. stances, I was able to audit a Anyone can dance with any­ new course offered by a couple one else, following the Logo­ of education professors named like procedural instructions of Glen Bull and Steve Tipps that the contra caller. What fun! focused on a new computer On the final day of the con­ language called Logo. ference, I was given the oppor­ The class used recently un­ tunity to introduce Seymour packed TI-99A computers for the keynote address. Dur­ with TI-LOGO cartridges. ing my remarks, I made refer­ Glen and Steve taught in a ence to the earlier conference highly interactive manner. al­ activities and the contra danc­ lowing each of us to "play" ing. and then said, "Last night with the turtle and to try out marked a highlight of my life. many different ideas. I asked Seymour to dance with The assigned text for the course was Seymour and I had a telephone conver­ me ... and he said, 'Yes!"' a paperback book called Mindstorms. It sation to sketch out the idea of an inter­ In that moment, my personal meta­ was my first encounter with Seymour national Logo conference to be held at phor of dancing with Seymour came full Papert. I found it to be one of the most MIT. Heady stuff, indeed, for a UVA circle, from that initial encounter in the engaging books I had ever read. In the graduate student. It was an exciting time! pages of Mindstorms. through the tele­ book, Seymour established and developed But for me, the dance was only beginning. phone calls and various conference meet­ the metaphor of the samba school as an­ Shortly afterwards, I was lucky ings. to the opportunity to enjoy his com­ other way of looking at learning. It cer­ enough to be named to the Logo 84 con­ pany as a partner in a contra dance in tainly made sense to me, especially with ference steering committee and attended the midst of hundreds of other Logo en­ the exciting classroom environment of several planning meetings with Seymour thusiasts. the Logo course I was taking. and many other MIT Logo legends. I was Looking back, I can see that dancing Learn to dance the samba by dancing touched by Seymour's consistent gentle with Seymour has heavily influenced my the samba! Indeed! demeanor and his genuine interest in oth­ life. But, more importantly, because of I can still remember the depth of the ers and what they were doing and think­ this dance, I have been able to pass on "Aha!" experience Seymour provided to ing. He listened intently to ideas, and of­ something of the promise, the potential, me in Mindstorms with the simple rev­ fered many of his own. and the excitement of Logo to teachers elation of writing a procedure named This was a dance of a different nature. and students all around the world. Heady HOUSE that contained the names of since its context was more official and stuff. indeed! other procedures named SQUARE and administrative in nature. At the same Thank you, Seymour. for saying, TRIANGLE. Suddenly, I could see all time, I could still see clearly the perspec- "Yes." I still dance with your ideas! ~

6 LOGO EXCHANGE Vol. 17 I No.2 BOOK REVIEW Reading Papert or Growing with Your Guru

by CAROLYN DOWLING

s we move through life it is cus ticular set of circumstances. Things ism-the recognition of individual learn­ tomary to discard our gurus. New change. and the idea is no longer so rel­ ing styles and multiple ways of represent­ Apre-occupations seduce us from evant, although this does not deter many ing knowledge. their teachings, their inspiration no gurus from continuing to voice their The Children's Machine, published in longer moves us, we've been there and original message, with little modification, 1993, consolidated a number of aspects done that. The guru becomes last year's long after its use-by date. of Papert 's thinking and writing over the news, and we move on. This is not Papert's style, but neither previous 10 or so years. It did so in the So what's the matter with Papert? Why is he a reed blowing in the wind of every context of an impassioned appeal for the hasn't he done the decent thing by now new educational fad and fashion. His radical reconceptual-ization and refor­ and become boring? Why do we continue special genius has been to allow his origi­ mation of the school system as we know to scour the Web for the latest speeches and nal ideas to grow and develop, to evolve, it-indeed, of the whole notion of articles? Why do we still await forthcom­ if you like, in response to changing edu­ "schooling." ing books with eager anticipation, besieg­ cational contexts, while all the time re­ More recently The Connected Family ing book stores for the first copies, import­ maining true to his fundamental commit­ with its associated Web site and CD, re­ ing them in far-flung parts of the world by ment to the creation of environments in viewed in volume 16, no. 1 of this publi­ all sorts of creative and devious means, which children are empowered to learn. cation, acknowledges a potential new passing them around as treasures from The publication of his seminal work, force in children's learning-the presence friend to friend? Mindstorms. with its roots in his own of powerful computing technology in the There's no denying that in the circles learning experiences and in his earlier home. The possibility now exists to re­ that count (largely, but not exclusively, work in the field of Artificial Intelligence, shape the balance of power between child, education), Papert is still hotter than mobilized a generation of teachers who home, and school in relation to learning. Windows 90-anything. and seems likely were enthused by the educational poten­ and to foster within the home a learning to remain so. tial of computers, but were unsure as to culture embodying the principles long What's his secret? I'd suggest that one where this lay in practice. It was the foun­ advocated by Papert and his followers, but reason why we don't outgrow Papert is dation stone of a whole educational "cul­ seemingly all but impossible to implement that he has also kept on growing and ture" possessed of a way of thinking about within existing school environments. moving forward. Way back when com­ learning that was sufficiently distinctive, Papert's mind will not stand still. puters were first sneaking into schools, profound, and clearly articulated as to be Things do change, but rather than dimin­ he had already traveled to the far end of widely dignified with the label "philoso­ ishing the force of his thinking, change the street and was peering eagerly 'round phy." Today the term "Logo philosophy" serves to create new opportunities and the corner, while the rest of us were still is applied far more broadly than to Logo contexts for the expression of his vi­ plucking up courage to follow him out alone, and "Logolike" as a description of sion-for he indeed is a visionary. For of the driveway. Papert has always been learning environments is well understood this we are grateful. May he keep on ahead of the game-far enough ahead to outside what has sometimes been termed keeping on! ® inspire us with his vision. but not so far the "Logo community." that the vision has seemed impossibly out Subsequent work focussed on the de­ of reach. His concerns are grounded in velopment and refinement of a number Carolyn DowUng our experiences, and his solutions engage of powerful educational ideas, including Australian Catholic University with our dreams. "constructionism," a realization in prac­ 412 Mt Alexander Rd We can all think of revolutionary tical terms of key aspects of Ascot Vale, Victoria 3032 thinkers who have had one big insight, a constructivist theories of learning, and AUSTRALIA single powerful idea, applicable to a par- the importance of epistemological plural- c.dowli ng@ mercy.acu.edu.au

Winter 1999 LOGO EXCHANGE 7 FEATURE ARTICLE The History of Mr. Papert

by MARTIN BOYLE

ABSTRACT hers of the family to turn their hands This paper outlines the life and career in whatever direction was required of Seymour A. Papert. We follow the and, for a young boy, must have been development of Papert from his early more than just compensation for an ec­ formal and informal education in the centric upbringing. South Africa of the 1930s through to Indeed: his sage era in The Children's Machine of the 1990s. On the way we will trace The Papert family's way of life was the formative influence of Papert's straight out of a Hemingway story. work with Jean Piaget in Geneva, his (Crevier, 1993, p. 84) first serious collaborative work with Marvin Minsky, leading to the bomb­ The story tells of following bush I I shell of Perceptrons, through to the suc­ trails, hunting for food, and falling in cess of his greatest educational achieve­ love with the transmission differential ment-the development of the of broken-down trucks-strong forma­ computer programming language Logo. tive experience for the young mind. We will see how, in the later part of By the nature of things, the Paperts his academic career, Papert has drawn were the only white people in the area. out the constructivist principles of enabled him to enjoy a childhood spon­ This led the young Seymour into Piaget into his own constructionism at sored by Henry Ford! trouble when he had to eventually at­ work in the classroom. Anecdote spices Papert further reveals a love for tend school in Johannesburg. U nfamil­ the life of Papert with real humour and Daisy, who left me with an 11th com­ iar with the strict and convoluted unexpected actions will give insightful mandment: edicts of the political and social conse­ glimpses into the workings of the great quences of apartheid, the 10-year-old man's mind. "Thou shall invent three theories organized evening lessons for the illit­ every day before breakfast and erate black domestic servants of his EARLY LIFE throw them away before dinner." area and found himself in serious Seymour A. Papert was born on March (Papert 1993b, p. 58) trouble with the authorities for such 1, 1928, in Pretoria, South Africa. The illegal activities; the consequences man himself seems shy or unwilling to Such is the eclecticism of Papert's were to have interesting future rever­ divulge many details of his early life, subsequentendeavoursthatoneisin­ berations: though in Mindstorms he owns to an clined to accept that he fell, hook with interest in gears from early childhood the lot, for that beloved teacher's ad­ This was just the first of Papert's experiences, indeed: vice. anti-apartheid activities, activities Papert's childhood gives every ap­ that would later lead the United Before I was two years old I had de­ pearance of being outside the norm. States immigration authorities to veloped an intense involvement with His father was an entomologist who deny him a visa for many months. automobiles. (Papert, 1980, p. vi) spent the best part of Seymour's early (Crevier, 1993, p. 84) childhood roaming the east coast of Had the world then developed as it southern Africa in pursuit of the tsetse The logic of the situation was lost has now such precocity may even have fly-a lifestyle that required all mem- on the young boy, because:

8 LOGO EXCHANGE Vol. 17 I No.2 Adults justified their reluctance to then an opportunity opened and Papert of Microworlds, StarLogo, Lego robots, let blacks sit at school desks by cit­ was to spend a fascinating episode of and magic bricks, a decade on, strengthen ing fear of contagious disease. But, his life as a researcher at the Interna­ that assessment of Piaget's worth. reflected Papert, these are the same tional Centre of Genetic Epistemology, servants who take care of babies and at the University of Geneva, working The Artifidal Intelligentsia cook the food in the whites' homes. under Jean Piaget. and Perceptron Sagas How can the ruling class think like that? (Crevier, 1993, p. 85) ... the Parisian discovery that had Following the four years in the biggest impact on my life was Geneva, I became a professor of Such interest in matters logical and Jean Piaget, who at that time was mathematics at MIT. Many factors illogical soon earned the talented boy giving a course at the Sorbonne. I made the move attractive. There an invitation to attend seminars in got to know him and was invited was the prospect of access to com­ philosophy at the University of to work in his center in Geneva, puters and of working with Johannesburg! where I spent the next four years Marvin Minsky and Warren and became passionately inter­ McCulloch, as well as a wonderful Early Career ested in children's thinking. sense of playfulness that I had ex­ Before long Papert was a philosophy (Papert, 1993b, p. 33) perienced there on brief visits. student in his own right at the Univer­ When I finally arrived, all this sity of Witwatersrand where he was Although Papert was to deviate from came together in all-night sessions awarded his BA in 1949. After this his the gospel of the master in terms of the around a PDP-1 computer that had interests switched to mathematics, rigidity of the stages of child cognitive been given to Minsky. It was pure leading to a doctoral degree from development stages, the Piagetian influ­ play. We were finding out what Witwatersrand in 1952. ence pervades the remainder of his work. could be done with a computer, In order to widen his horizons, Piaget. fundamentally and overtly, con­ and anything interesting was Papert then moved overseas. He was tributing to such diverse concepts as the worthwhile. Nobody yet knew awarded a Commonwealth research establishment and efficacy of computer­ enough to decree that some things scholarship to St. John's College, Cam­ rich microworlds through to the layer­ were more serious than others. We bridge, UK, which would eventually ing development of societies of mind. were like infants discovering the enabled him to complete a second doc­ Allow Papert, with metaphor as ever world. (Papert, 1993b, p. 33) torate and while in England he ran into his telling servant, to make his own elo­ one of Americas foremost workers in quent point: One wonders how many of us have the emerging field of Artificial Intelli­ shared that heady experience with gence, Ed Feigenbaum, at the National When Piaget is poured into a new Papert when computers are new, com­ Physical Laboratory outside London. decade, much will change. Whether puters are an unknown quantity­ one has conservation of Piaget will with computers anything goes! Feigenbaum was a Fulbright Fel­ depend on what one perceives as In 1958 Marvin Minsky and John low for the year, and he had a most important in the thinking of McCarthy had founded the Artificial memorable friendship with a the great master. My own view is Intelligence Group at MIT. Minsky had young and somewhat eccentric that the essential aspects of his not forgotten the young Papert who South African scholar named work have not fallen by the way­ had made such an impression on him Seymour Papert. (McCorduck, side. On the contrary they are at their London meeting. 1979, p. 275) stronger and more relevant than ever. (Papert, 1988, p. 3) "... for it was at the 1960 London More significantly for the future, at Symposium on Information a symposium in London itself, he first And later: Theory organized by Colin Cherry met Marvin Minsky. The encounter that an event happened which with Minsky was to prove the genesis In my Piaget, stages and even most changed my career path and made of the second great collaborative effort stages of "active learning" are quite me follow the course that brought of Papert's professional life; but first secondary. I focus instead on his me here. I came to that meeting as he turned his interests toward France. constructivism and structuralism. a mathematician interested in Papert spent the year 1956-57 as a (Papert, 1988, p. 4) computational ideas and Informa­ researcher at the Henri Poincare Insti­ tion Theory. I came there with a tute at the University of Paris to com­ The developing influence, within the paper in which I had a little theo­ plete the research for his doctorate, but constructionist movement in education rem. And what happened was the

Winter 1999 LOGO EXCHANGE 9

------worst nightmare of somebody com­ In fact the Logical Theorist discov­ wasn't all pathetic and sad be­ ing to a meeting with a theorem. ered a shorted and more satisfying cause he was quite convincing. He The speaker before me an­ proof to Theorem 2.85 than was going to beat it very easily. nounced exactly the same theorem Whitehead and Russell had used. And that also said something and proved it at least as well as I Simon wrote this news to Lord about him, almost naive. We did, not quite the same, but you Russell, who responded with de­ didn't know. About halfway can't get much credit for just hav­ light. However the journal Of Sym­ through we all thought Dreyfus ing a slightly different proof. Now bolic Logic declined to publish an was going to win." (McCorduck, that could have been a nightmare; article co-authored by the Logical 1979 p 198) in fact. it turned into a great gift. Theorist describing this proof. That person was Marvin Minsky. (McCorduck, 1979, p .142, foot­ Herb Simon had this to say: Marvin and I came to the meeting note) with essentially the same paper Dreyfus thought that MacHack and this led to a collaboration that Minsky was building robots; would play bad, mechanical, non­ continued for many years and is Minsky and Papert were designing vi­ human chess. But it was a wonder­ responsible for almost everything sion machines; and then there was ful game-a cliff-hanger between we did in the next decade and has chess ... two woodpushers with bursts of certainly colored everything I have All day long the argument ebbed and insights and fiendish plans ... done since then. (Papert, 1998) flowed on the matter of intelligent great moments of drama and disas­ machines. The philosopher Hubert ter that go on in such games. After the previously mentioned visa Dreyfus published in 1965 a report for (McCorduck, 1979 p 199) problems were sorted out with the U.S. RAND called Alchemy and AI (later immigration authorities, Papert was in. expanded into the book What Comput­ Dreyfus was soundly defeated. Re­ He strode into Minsky's office, sat ers Can't Do.) generally panning what venge for the artificial intelligentsia down, and they were away-never to Dreyfus termed the artificial intelligen­ was very sweet; but, as throughout his­ look back! tsia. The ensuing battle was bloody and tory, successful houses soon turn upon is, indeed, far from over! themselves. Rarely had co-operation between Papert wrote the paper to refute Frank Rosenblatt had been a class­ ,, ,I two researchers been so productive: Dreyfus, also for RAND. but the attor­ mate of Minsky at high school in the Colleagues no longer said "Minsky­ neys would not touch it! early '40s. In 1962 he introduced to the and-McCarthy," but "Minsky-and­ press with, it must be said, some fan­ Papert." The two soon initiated It was eventually brought out as a fare the perceptron. The perceptron new research programmes in the Project MAC report with no law­ was a simple neural network. a model theory of computation. robotics, suits ensuing. (McCorduck, 1979, of artificial intelligence at odds with human perception, and child psy­ p. 196) the then fashionable symbol manipu­ chology. When the Artificial Intelli­ lation models. Minsky had toyed with gence Group formally became the There's still great debate about who neural networks; in fact. his PhD dis­ MIT AI Laboratory in 1968, did what and who said what in the sertation concerned them and had dis­ Minsky and Papert acted as co-di­ great chess debate. The fact is that a missed their worth at that time. Thus rectors. (Crevier, 1993, p. 86) chess playing software package that we the claims made by Rosenblatt purport­ will call MacHack throughout for sim­ ing to demonstrate the learning pow­ It was an exhilarating time in AI. plicity had been beaten by a 10-year­ ers of the perceptron were viewed right Sane men and women with earned old boy to the delight of Dreyfus who from the start with skepticism in the PhDs from highly respected seats of was alleged to have claimed that chess Papert camp. learning were claiming that the office playing computers could never beat The MIT faction did take the situa­ thermostat was intelligent! Perhaps any human player. The program was tion seriously though. David Waltz, a with hindsight and the passage of time strengthened (in fact it was a different graduate student recalls: they deserve to retain their now found program) and somehow Dreyfus, who anonymity! was a poor chess player, was persuaded Marvin and Seymour really were Alan Newell and Herb Simon back to play it. interested in Perceptrons. I and a in 1956 had produced software that bunch of other students took a could churn out proofs of theorems Papert, smiling recalls, "I organ­ seminar from them, where the goal from Russell and Whitehead's ised the famous chess match. That was to figure out as much about Principia Mathematica. was beautiful. He was-well, it Perceptrons as possible. We were

10 LOGO EXCHANGE Vol. 17 I No.2 merely to explore in a methodical powerful network mechanisms is work to present first the Images of a sense what they were capable of seriously exaggerated) to be mis­ Learning Society to entice the elemen­ and what they weren't. and try to leading attempts to use connec­ tary reader further into the plot. characterize them in some way. tionist methods in practical appli­ Papert is also concerned with the (Crevier, 1993, p. 107) cations. But most of the motivation notion, which he suggests some have for Perceptrons came from more read into the work, that computers will The result of all ofthis activity was fundamental concerns many of cause changes in the way children the publication of a book by Papert and which cut cleanly across the divi­ think. He replies: Minsky in 1969 that they called sion between networkers and pro­ Perceptrons, and which demonstrated grammers. (Papert, 1992, p. 346) What I was saying, and still say. is mathematically and most ably that the something slightly more subtle: I simple Perceptron was totally inca­ see Logo as a means that can, in pable of solving a wide range of impor­ Mindstorms and Logo principle, be used by educators to tant mathematical problems. We turn now to that most famous epi­ support the development of new The repercussions of their book were sode of Seymour Papert's educational ways of thinking and learning. immediate and dramatic, for Rosenblatt life-the development of the computer However. Logo does not in itself and his collaborators were totally un­ programming language Logo. We will produce good learning any more able to rebut the book's arguments. Neu­ mention only very briefly matters of than paint produces good art. ral network research was dead in the common knowledge. Suffice to say that (Papert, 1993a, p. xiv) water amid claims of deliberate sabotage the language had its beginnings in to divert federal funding away from net­ Papert's thoughts of the late '60s and The emphasis in the first edition on works and into symbol manipulation culminated in the publication of his structured programming is also regret­ programmes. No self-respecting re­ seminal work, Mindstorms-Children, ted. Papert would much have preferred searcher would dare touch neural net­ Computers and Powerful Ideas, in 1980. to introduce the tinkering bricolour as work research for a decade until the The Logo Language was an offshoot an alternative programming style much connectionist movement of the '80s, of the list-processing language known earlier in the piece and he stresses his which has proved greater potential for as LISP and its genesis from lists gave subsequent work in this field with his fruitful results. Connectionist research­ rise to its name-the Greek for word, then wife, the techno-psychologist ers in AI blame Papert and Minsky to Logos. The famous turtle probably Sherry Turkle. (Turkle, 1984). this day for the decade of neglect! finds its antecedents in a similar liv­ The recent developments in Logo. In the 1972 printing of Perceptrons. ing model that used to roam the Bristol in particular the MicroWorlds, are seen there is a handwritten dedication to the UK laboratory of brain physiologist as a move toward the encouragement memory of Frank Rosenblatt who was Grey Walter in search of food by way of a richer, wider epistemological range lost in a boating accident, by all ac­ of power outlets! The rest, as most and, we may say, a more expansive in­ counts a broken man, shortly after the would say, is history. terpretation of activities that constitute Perceptron affair. A second edition of Papert's book computer programming. We will leave the last word on the Mindstorms was published in 1993 and matter to Papert; he wrote in 1988: it is to the introduction ofthat edition Constructionism and to which we turn our attention. The Children's Machine Did Minsky and I try to kill As is right and fitting, Papert uses In recent years the writings of Seymour connectionism, and how do we feel the introduction to the second edition Papert return ever more strongly to his about its resurrection? Something as a debugging exercise for the first Piagetian intellectual roots. In the late more complex than a plea is edition, practising his preaching on not '70s, his collaborative work with needed. Yes, there was some hostil­ getting things right the first time! Marvin Minsky on the development of ity in the energy behind the re­ Papert acknowledges that he failed to Society of Mind concepts is significant, search reported in Perceptrons, and anticipate the pick-up rate of though noticeably unreported on there is some degree of annoyance Mindstorms by teachers-especially el­ Papert's part. Such societal metaphors at the way the new movement has ementary teachers-and is disappointed show, in their layering of different bands developed; part of our drive came, that many of his exemplary microworlds of cognition in the developing mind, an as we quite plainly acknowledged are classically physical and an impedi­ echo, of Piaget's stages of readiness. In in our book, from the fact that ment to such readers going beyond the the '80s, Papert's work with Sherry funding and research energy were early part of the work where the field Turkle on epistemological pluralism and being dissipated on what still ap­ is rich in Newtonian physics! Papert with ldit Harel (Harel, 1991) on chil­ pear to me (since the story of new, suggests that he would reorganize the dren as software designers carries for-

Winter 1999 LOGO EXCHANGE 11 ward the constructivist notions of build­ carry the reforms as far in their structionism, Norwood, NJ: Ablex. ing knowledge structures into construc­ realm as Gorbachev did in his. Papert, S. (1992) 'One AI or Many?' in tionist principles which are driving (Papert, 1993b, p. 206) Beakley, B. & Ludlow, P (Eds.) The Phi­ children's activity in this decade. losophy of Mind, Cambridge MA: the Papert would, I suspect, consider a Perhaps the computer is The Chil­ MIT Press. Papert, S. (1993a) Mindstorms-Children, definition of constructionism as an dren's Machine and the vehicle for free­ Computers and Powerlful Ideas, Second oxymoronic concept. We will have to ing thought. Edition, New York: Basic Books. do with the banal, flat, and constrained Papert, S. (1993b) The Children's Machine learning by doing-especially physi­ Endnote -Rethinking School in the Age ofthe Com­ cally making something. We end with this vision of Papert: puter, New York: Basic Books. Papert, S. (1998) The 11th Colin Cherry Constructionism shares construc­ Absent-minded like many driven Memorial Lecture on Communication, tivism's connotation of learning as intellectuals, Papert is said to have London: www.connectedfamily.com/ "building knowledge structures" once realised, mid-way across the frame 4/ c fO 4 1 3 seymour I irrespective of the circumstances Atlantic, that he had left his wife recent_essays/ciD413_cherry_l.html of the learning. It then adds the behind in a New York airport. Col­ Turkle, S. (1984) The Second Self Comput­ ers and the Human Spirit, London: idea that this happens especially leagues report that he sometimes Granada. felicitously in a context where the forgets to show up at lectures and, learner is consciously engaged in when he does, tends to get carried constructing a public entity, away into whatever topic fasci­ Martin Boyle whether it's a sand castle on the nates him at the moment. A man Faculty of Education beach or a theory of the universe. of dramatic personal magnetism, Monash University (Papert, 1991, p. 1) he is likely to startle interviewers Victoria 3168 Australia with juggling demonstrations at [email protected]

Constructionism finds a true home airport terminals or by stopping his MR. CONDOM/ Continued from Page 5 in a computer-rich culture and herein car in the middle of aU-turn to lies the heart of Papert's objection to formulate a thought. Papert's apho­ ing their time" (and their condoms) current educational practice. He is not risms, like Minsky's, tend to stick. blowing balloons. But this conven­ as might have appeared from Mind­ One of his favourites is that we are tional wisdom entirely misses the storms anti-teacher; rather, he is to thinking as the Victorians were point. Neither Debbie nor the villag­ against the prevailing school culture to sex. (Crevier, 1993, p. 86) ers were wasting time-by playing that constrains children, physically and with the condom or the fraction they epistemologically, in the pathway of its I will leave you to unwrap that say­ were taking these things into their own liking. ing ofPapert's for yourselves! e heads. They were letting themselves In his closing address to the 1990 think about them. World Conference on Computers and References Education, he appealed, in the spirit of Crevier, D. (1993) Artificial Intelligence, About the Author those times as a comparison with the New York: Basic Books. Dr. Seymour Papert is fondly known political structure of the then USSR. for Harel.l. ( 1991) Children Designers, Ablex: as the "Father of Logo." He is a re­ perestroika in epistemological politics. Norwood, N]. spected mathematician, educator and McCorduck, P. (1979) Machines Who Think: As Papert says: artificial intelligence pioneer. Papert's A personal Inquiry into the History and numerous honors include awards from Prospects of Artificial Intelligence, San the Software Publisher's Association His [Mikhail Gorbachev] slogan of Francisco: W H. Freeman & Company. and the Smithsonian Institution. Dr. perestroika (which literally means Papert, S. (1980) Mindstorms: Children, "restructuring") became synony­ Computers and Powerful Ideas, New Papert occupies the LEGO Professor of mous with a policy of struggling to York: Basic Books. Learning Chair at the MIT Media Lab's reform a system in serious crisis Papert, S. (1988) 'The Conservation of Epistemology and Learning Group. without calling into question the Piaget: The Computer as grist to the Seymour Papert's books including foundations on which it was built. Constructivist Mill' in Forman, G. & Mindstorms: Children, Computers and It should be clear by now that I see Pufall, P. (Eds.) Constructivism in the Powerful Ideas, The Children's Machine. most of those who talk loudly Computer Age, Hillsdale N]: Lawrence and The Connected Family are required about "restructuring" in education Erlbaum. reading for anyone interested in edu­ Papert, S. (1991) 'Situating Construction­ in much the same light ~though cational computing and the future of ism' in Harel.l. & Papert, S. (Eds.) Con- few of them have the courage to learning.

12 LOGO EXCHANGE Vol. 17 1 No. 2 FOR BEGINNERS Simple Probability as a Vehicle for Understanding MicroWorlds Data Structures An Activity for Advanced Beginners by GARY S. STAGER

ow that most of you can be con­ Recording data to flip Nsidered advanced beginners in us­ with text boxes ifelse 1 = random 2 ing Micro Worlds, this activity will ex­ This part of the project will flip a coin [recordheads] [recordtails] plore a bit more of the language and in FLIP. and change the value in the settotalf1ips headscount + data structures. This activity will ex­ textboxes, headscount, tailscount and tails count plore probability while demonstrating totalflips. If you name turtles, text end how sliders, text boxes turtles and even boxes or sliders with you unique Do NOT use more than one of the the screen may be used to collect and names, you may change them even if flip procedures in your project! report data. All of these objects are data they are on different pages. This allows structures in MicroWorlds you to have some action going on be­ to coin The core of this project will flip a tween the scenes. if 1 = random 2 [output coin numerous times and record num­ "heads] ber of times heads and tails appear. 1. Make a startup button on the first output "tails page. end 1. Start a new project. 2. Create a new page from the pages to recordheads 2. Name the turtle. coin. menu. coin, setsh "heads 3. Create two coin shapes in the 3. Create text boxes named, setheadscount headscount + 1 shapes center. Name one heads Headscount. Tailscount and end and the other tails. Be sure to Totalflips. make them appear different in 4. Show the names of the text boxes to recordtails some way so that the user can so the user knows what they are coin, setsh "tails clearly see which one side of the reading. settailscount tailscount + 1 coin lands face-up. 5. Click the Startup buttonType the end 4. Change the turtle's costume to following procedures on the pro­ to startup one of the coin shapes. cedures page. setheadscount 0 settailscount 0 to flip end ifelse coin "heads [recordheads] [recordtails] settotalflips headscount + tailscount end

5. Create a Many Times button with The flip procedure could also be ' <'',• the instruction, flip. written: ':.·,··

Winter 1999 LOGO EXCHANGE 13 Click the flip button to start and stop 1. Type Startup to initialize the settails tails + 1 the experiment. You may wish to make variables, click on the flip button tailsgraph, fd 1 stamp the flip button run Many Times if you and switch between pages. end want it to keep flipping the coin. Can you make a text box that reports Do you see the sliders changing to startup the standard deviation of the coin flips? their values? settailscount 0 setheadscount 0 Recording data Extra bonus! settotalflips 0 with sliders Adding a histogram settails 0 setheads 0 headsgraph, setpos [-170 - Sliders may be used as reporters (in­ to graph our data put devices) to change the value of a It is easy to add simple graphing func­ 145] tailsgraph, setpos [200 -145] variable or they may be used as indica­ tionality to our probability lab with the tors (output devices) displaying the creation of two turtles and a bit more page2 clean page1 current value of that reporter. Let's Logo programming. end experiment with sliders on a second 1. Type Startup and click on the flip page of our coin flipping project. 1. Hatch two turtles on the same page as the sliders. button to set the experiment in action! 1. Create a new page from the Pages 2. Name one turtle, headsgraph. and menu. the other, tailsgraph. (for heads You may even want to figure out a 2. Create two sliders, heads and graph and tails graph) way to stop the graphing when a bar tails, with a minimum of 0 and 3. Place those turtles above their re­ reaches the top. How about a textbox maximum of 300 at the bottom spective sliders. reporting the experimental standard of the new page. 4. Create two different turtle cos­ 3. Optional: Create buttons to tumes consisting of blue and red deviation? switch between the two pages of horizontal bars. Name the shapes our project. hline and tline. 4. Make the following changes to your procedures.

to recordheads The magic of MicroWorlds' paral­ coin, setsh "heads lelism allows the coin to be animated, setheadscount headscount + 1 text boxes to change, sliders to report setheads heads + 1 and a histogram to be created all at end once. You can use lots of software to generate random numbers, but no to recordtails other title allows all of these things to coin, setsh "tails happen at once. I am confident that settailscount tailscount + 1 5. Make the following changes to your procedures. you can figure out exciting ways to in­ settails tails + 1 tegrate these programming techniques end to recordheads into much more complex simulations coin, setsh "heads and experiments. ~ Change the startup procedure as fol­ setheadscount headscount + 1 lows. setheads heads + 1 headsgraph, fd 1 stamp to startup end settailscount 0 setheadscount 0 to recordtails settotalflips 0 coin, setsh "tails Gary Stager, Editor-in-Chief settails 0 setheads 0 settailscount tailscount + 1 logoexchange@ stager.org end

Vol. 17 I No. 2 14 LOGO EXCHANGE

·- ~··--·---.~------Dreams, Realities, and Possibilities

by GAIL MARSHALL

Introduction longer would they respond to pre-pro­ ing with problems they generate them­ Sometimes. on waking from a deep grammed questions in workbooks; no selves and profit from the realization sleep. you can recall fragments of a longer would they go through tedious that education can be a constructive dream: "First this happened and then manipulations with protractors or act. Wise teachers will use Logo as a suddenly that happened, but how did blocks or rods to create new realities. means of freeing students from the rou­ the end of the dream fit in with what Instead the student would be given tine, the hum-drum, the merely aver­ went before?" We often have trouble tools that would challenge. stretch. ex­ age and stimulate students to plan, to making sense of our dreams because cite and strengthen the mind. think, to act and to analyze in ways they are made up of bits and pieces of But. for the most part. the dream that are difficult. if not impossible. in events-some real, some imagined, or was rejected by American schools. In other educational contexts. Thought­ changed beyond recognition in our spite of the enthusiasm of teachers, stu­ ful school administrators will under­ consciousness or unconscious states. dents and parents who saw Logo as a stand that Logo use achieves many, if Looking back at the history of Logo in powerful stimulus for children's intel­ not all, of the goals deemed important American schools is, in some ways, like lectual development, many educators by professional educational organiza­ a dream. We can reconstruct the impe­ resisted change and resisted possibil­ tions such as NCTM, NCTE. ASCD. tus for introducing Logo, mark the ity of using computing power to change and by policy groups. both in govern­ milestones on its implementation in schooling for the better. ment and the business world. But if one or another school but then the pic­ The problem lies not in Logo and Logo is to achieve more widespread use ture becomes clouded. "What hap­ not in the stars-undefined forces of fate than it now enjoys. changes must oc­ pened?" we ask. "How did the flow of pushing us this way and that-but in the cur. Changes not in Logo itself but in events go from recognizing that Logo conflicts over what to teach and how the way Americans-policy makers, par­ was a powerful tool that allowed stu­ to teach that have made education a ents. researchers. teachers and admin­ dents to use computers as mediums of quiet but bloody battleground for de­ istrators-view education. expression to the present day. where, cades. For all its ingenuity. for all the for the most part, computers are driv­ possibilities that Logo provides to open The Reality ing students?" up the world of mathematics and art So':l-e say that American education and computing and general thinking started with Horace Mann or George The Dream Logo's potential on the wide scale it Peabody sitting on one end of a bench Even before yesterday's primitive desk­ deserves-used as a matter of course in and a student sitting on the other end. top computers appeared in American classrooms around the country-has not In truth, a variety of forces have shaped classrooms, Seymour Papert and other been reached because a mindset domi­ American education. Some of those visionaries had the dream that comput­ nates American education that is es­ forces were based on Romantic, ers could be used to free students from sentially inimical to change. to educa­ Rousseauian. ideals about how stu­ the constraints of traditional educa­ tion as a constructive act, and to the dents learn; others were based on in­ tional media and could serve as the empowerment of students as agents in strumentalist goals-teaching vast num­ impetus for students' engagement with their own learning. As a bold, creative, bers of students, some of whom had important ideas, strategies and prod­ purposeful endeavor Logo will have a only the day before arrived from other. ucts. Logo broke the mold. No more life of its own for years to come. Fortu­ non-English-speaking countries to would students be driven by the linear nate students will work with Logo, re­ read, write, count, and move quickly flow of text on a printed page; no alize the power that comes from work- into factories and foundries.

Winter 1999 LOGO EXCHANGE 15 Callahan (1962) recounts the de­ out students deemed acceptable for and factory world of earlier days to the pressing story of a great shift from the higher education from those judged investigation of information world of quality of instruction as an issue to the suitable only for low level jobs. By the the future, we can also begin to make a quantity of services delivered by late 1930s the acceptance of standard­ case for changes in what and how we schools. During the 1920s and 1930s the ized tests was widespread and the "fill test (Marshall, 1999). "Taylor" movement, based on the ideas in the blanks/check the correct box" While many of the new curricula of the efficiency expert, Frederick Tay­ mode of assessment reigned supreme probably deserved to fail others de­ lor, changed the face of American as a way of telling students, teachers served to flourish and become part and schools as the formula for deciding on and the community at large whether parcel of the American educational the worth of schools was decided by di­ Johnny and Jane could read. experience. Remnants of some of the viding the number of students graduat­ While the tests were efficient and projects persist-indeed some of the ing (the "output") into the total cost of were effective in that they provided a early innovative software developed in schooling (the "input"). Schools across quantitative measure of one student the late 1970s and early 1980s owes the country were advised to drop the against another or all students against much to the ideas developed through teaching offoreign languages when only a pre-set standard, the tests were reduc­ earlier curriculum development ef­ small numbers of students in any school tive. What was judged to be important forts. But the public's resistance to elected to take those courses. That such was what could be counted and what changes in teaching and testing has moves were penny wise and pound fool­ can be counted isn't always important. been a constant. Such was the climate ish was demonstrated years later when The problem with American testing when Logo was introduced. the federal government had to pour mil­ methods was made especially evident The situation was made even more lions of dollars into emergency training as the curriculum reform movement of problematic by the methods usually of foreign language teachers during the the late 1950s and early 1960s collided used in the conduct of research on the Sputnik "crisis." But the underlying head on with the problem of assessing effects of instruction. During the 19th problem, the use of" input/output" ways the effects of the new curricula with century men of science looked for ways of evaluating education, has persisted. tests that were judged to be "scientific" to explain numerically how things and As a result, American education has by the public at large. So ingrained was people were alike or different. Some sci­ been driven by utilitarian goals-how the habit of using standardized tests, entists filled the skulls of members of many students are graduated, how many and only standardized tests, as accept­ different ethnic groups with beans or of those students getjobs in factories or able outcome measures, that the public stones in an attempt to prove that Cau­ foundries, how many remain in their came to believe that the use of any other casians were more intelligent than other jobs? Such utilitarian goals are incon­ kind of test was a "fudge factor" con­ groups. Agriculturists sought a math­ sistent with many of the educational nived at by educators who were unwill­ ematical shorthand to explain how the innovations designed to generate higher ing to subject their curricula to "real" ears of corn grown in one plot of land levels of student thinking, promote tests. The problems faced by the "New were superior to those grown in another mathematical thinking beyond low level Math" and other curriculum reform plot of land. As the fledgling research computation and increase humanistic efforts were, in no small measure due industry in America began to measure values (Marshall, 1994). to the public's rejection of any outcome first corn and then students' progress The situation is complicated by the data that didn't look and feel like the through the school years, the methods major role that testing plays in deci­ good old tests of yesterday (Marshall, of earlier scientists were adopted whole­ sion making. Today's standardized 1994). The curriculum developers' cau­ sale. Like the standardized tests used achievement tests are nothing more tions that those tests didn't capture the without question in schools, the pre-/ than elaborations of the types of sort­ complexity of performance fostered by post-test method of looking for effects ing instruments designed during WWI the new curricula was hooted at by edu­ became a standard-never mind that such to ensure that recruits for the Army cational conservatives, who wished to methods focused on a limited set of could read and write. Easy to adminis­ maintain the status quo. questions and those questions not nec­ ter and quickly scored, the tests iden­ DuBois, in a comprehensive history essarily the ones to ask when looking tified draftees who couldn't read and of the testing movement that focuses on for what students know. streamed them away from induction. needs and conditions for testing as well The research methods popularized as After the war the growing testing in­ as on the traditional formulaic approach a means of asking if instruction had dustry used the models and methods that characterizes many psychometrics made a difference were rooted in a be­ of Army-driven testing for a wide textbooks, tells us the Chinese, who haviorist epistemology that asked how range of assessments-industry used invented testing, were able to change much students learned or how long it some measures for job placement and their tests as their civilization changed. took them to learn. The possibility of an counseling, schools used them to sort Surely, .as we move from the foundry alternative epistemology, a construe-

16 LOGO EXCHANGE Vol. 17 /No. 2 tivist epistemology that asked how stu­ ment need to be studied. Stories of how researchers who frame questions that dents acquire knowledge, how they ap­ one goes from adoption to implemen­ are appropriate for the Logo environ­ ply it over a wide range of situations, and tation need to be collected, analyzed ment and not researchers who are bent what strategies are needed to help in the and disseminated. in applying research questions that may acquisition and use of knowledge, was Similarly, we need to decide, in re­ fit their own epistemologies but have either ignored or derided within the edu­ alistic terms, what we expect Logo use nothing to do with Logo. Logo users cational community at large (Marshall, in students to produce. Is it reasonable, need to pose the questions and not 1993). Once again, as with testing and for example, to expect that first grad­ leave the generation of research to curriculum reform, resistance to any ers using Logo for only a few minutes people with little understanding of chil­ other method was offered as a means of a day a few weeks in the school year dren or mathematics or the possibili­ maintaining the status quo-never mind learn "planning skills?" Or is it reason­ ties for technology in the 21st century. that the status quo might not be useful able to expect that students who work Seymour Papert and others who have now or in the future. with Logo, in the ways Logo was de­ brought Logo and Logo-like materials to signed to be used, grow more confident market have done 99% of the work. The The Possibilities about asking mathematical questions 1% remaining, however, is the critical just because something has been done and more skilled in answering those percent that will ensure that more stu­ a hundred or a thousand or a million questions? If we ask such questions we dents have an opportunity to go beyond times doesn't mean that the way it's also need to be able to demonstrate that mere key punching and use technology supposed to be. But change is difficult, acquiring such skills has positive ben­ as a means of stretching the mind, en­ especially today in the contentious at­ efits. Maybe students with a solid foun­ gaging the imagination and satisfying mosphere that cloaks everything from dation in Logo do as well or better than the quest for dissonance that Piaget tells human behavior to the design of com­ their peers in algebra or geometry or us is built into every organism. It's puter interfaces in an "either/or" set of calculus-or maybe they elect to take worth the effort, don't you think? conditions. To bring about change calls more mathematics courses or maybe for strategies that go beyond the "You're they become more fluent in spatial re­ References wrong, we're right" chanting that quells lations. A wealth of well-designed tests, Callahan, R. ( 1962). Education and the Cult the advance of new models and meth­ Raven's Progressive Matrices comes to ofEfflciency: A Study ofSocial Forces that ods. In short, like it not, changes in edu­ mind, are regarded within education Have Shaped the Administration ofPub­ cational policies and practices will prob­ and the world at large as reliable, valid lic Schools. University of Chicago Press, ably only occur when and if indicators of intellectual performance. Chicago. DuBois, P.H. (1967). The History of Psy­ constructivists take on the task of ac­ Those tests and others we may need chometrics. Washington University, St. cumulating evidence, telling the stories to design, subject to rigorous scrutiny Louis, MO. presented by the evidence, and making and apply in order to answer the ques­ Marshall, G. (1999). Exploring assessment, a coherent case for alternatives in cur­ tion, "What difference does Logo (in press, Educational Information riculum, testing and research. make?" can assuage the public's doubts Technology). Here's a scenario that might make a about the worth of Logo's possibilities Marshall, G. (1994). Cautionary verses: convincing case for change-but the sce­ as a permanent part of a school's in­ Prospects and problems in achieving the nario needs all the pieces working to­ structional program. aims of the computer revolution, in ]. gether in order to make the convincing Above all, we need the students' Wright and D. Benzie, (eds.) Exploring case that reassures the doubting and ad­ performance to tell the story. Videos a New Partnership: Children. Teachers vances the use of educational methods of students engaged for long periods of and Technology. Elsevier Science, that differ from the "ftll in the blanks" time with complex problems can be Amsterdam. Marshall, G. ( 1993). Informatics and or the "cut and paste multimedia" that compelling evidence for people whose changes in learning: The American di­ have captured educational technology. only knowledge of Logo is "It's new lemma and opposing epistemological In the first place, applications of and it isn't computation." Presenta­ perspectives and unanswered ques­ Logo in the classroom as Logo was tions of the types of innovative spatial, tions, in D. C. Johnson and B. Samways meant to be need to be identified. The numerical and logical thinking that (eds.) Informatics and Changes in Learn­ conditions that gave rise to good imple­ occurs in the best Logo classrooms may ing. Elsevier Science, Amsterdam. mentation-is it specific staff develop­ go a long way towards convincing the ment practices, is it time and model­ dads and moms who never met an In­ ing and support and a belief in the structional Learning System they worth of the outcomes-need to be ana­ didn't like that Logo is not a toy. lyzed. The types of implementation We need teachers helping other GaU Marshall that foster student interest and engage- teachers in a systematic way. We need 7 4055.652 @compuserve.com

Winter 1999 LOGO EXCHANGE 17

--~--~--~- -~ ------' IN THEIR OWN WORDS Mixed Feelings about Seymour Papert and Logo

by KEN KAHN

eymour Papert and one of his Years later I was at Xerox PARC do­ ways of describing Logo changed ing programming language research and Smy life. I recall a Logo group had stopped doing research on comput­ meeting in 1977 where Seymour de­ ers and learning. Then around 1990 I scribed Logo as an attempt to take the heard a talk by Mitchel Resnick about best ideas from computer science and LEGO Logo. I was impressed and told () make them accessible to children. Most my colleagues at PARC about the talk. I of those ideas had come from the Lisp also repeated Seymour's description of programming language. It felt good to Logo as taking the best ideas in com­ hear that since I felt as if I was con­ puter science and "child engineering" tinuing this tradition by making a them. At the time I was working with child-friendly programming language Vijay Saraswat and others on new pro­ called Director. Director was inspired gramming languages based upon con­ Figure 1. An Executable Hand-drawn by ·the ideas of Carl Hewitt on actor current constraint programming. Vijay Pictorial Janus Program programming (roughly concurrent ob­ asked why we couldn't make a "Logo of ject-oriented programming}. Little did the 90s" based upon our research. That That experience led me to think of I anticipate that over the following 20 led to our research on Pictorial Janus. a language that was more concrete and years I would make three more at­ Pictorial Janus is a completely visual based not upon static pictures but upon tempts to "child engineer" advanced programming language. The programs animation. And yet I wanted a lan­ programming languages. are pictures-they can even be drawn guage that was as powerful and expres­ In 1980 I left MIT and drifted away on paper, scanned in, automatically sive as the ones I had been working on from Logo and the like. I began work­ parsed, and executed. Program execu­ at PARC. I hit upon the idea of ing on Prolog and other logic program­ tion is shown as an animation of the ToonTalk (see www.toontalk.com}, ming languages. Cynthia Solomon, original drawing. After showing it to a where a child does all her programming who by 1982 was the director of the few children and non-programmers, I by manipulating concrete objects in­ Atari Lab in Cambridge, was excited realized that despite its completely vi­ side of an animated game-like world. I about the possibilities of kids and logic sual nature it was not well suited for founded Animated Programs in 1992 programming. While consulting for non-experts. While Pictorial Janus was to build ToonTalk. ToonTalk is a con­ Atari, I did research on making the visual, it was based upon sophisticated current language where a child pro­ Prolog programming language acces­ formal abstractions. And these abstrac­ grams by training robots, giving birds sible to kids. tions were hard for people to learn. messages to deliver, manipulating

18 LOGO EXCHANGE Vol. 17 /No.2 boxes, text pads, and number pads, naturally "data parallel." children. He has been a faculty mem­ using animated tools, loading trucks, I recall thinking in 19 7 5, while ber at MIT, the University of and more. The child is a character in teaching kids Logo, "Wow, here I am Stockholm, and Upsala University. For this world and can even fly her heli­ successfully teaching this kid a pro­ more than eight years, he was a re­ copter to travel between houses or to gramming language that is much more searcher at Xerox PARC. He has made see an overview of an ongoing compu­ advanced than what all the 'profes­ several animated films that have been tation. sional' programmers in the world are shown in film festivals, theaters, and cable TV. In 1992, Ken founded Ani­ mated Programs with the mission to make computer programming child's play. He received a patent covering the underlying technology of ToonTalk (US Patent Number 5,517,663). ID References Kahn. Ken. Director guide. Technical Re­ port 4828, MIT AI Lab, December 1979. Kahn, Ken. A grammar kit in Prolog. In M. Yazdani, editor, New Horizons in Educational Computing. Ellis Horwood Ltd .. 1984. Also in Instructional Science and Proceedings of the AISB Easter Conference on AI and Education. Exeter, England. April1983. Kahn, Kenneth M .. and Saraswat. Vijay A.. Complete visualizations of concurrent programs and their executions. In Pro­ ceedings of the IEEE Visual Language Workshop, October 1990. Figure 2. Programming Inside ToonTalk Kahn, Ken, ToonTalk-An Animated Pro­ So why did I title this article "Mixed using." Today I look at Logo and think gramming Environment for Children. Feelings about Seymour Papert and it isn't that different from Visual Ba­ Proceedings of the National Educa­ tional Computing Conference. Balti­ Logo"? Because I think Seymour and sic and is weaker than popular lan­ more. Maryland. June 1995. Also ex­ others did a great job designing Logo guages like Java. I am disappointed that tended version appears in the journal in the late '60s. But by 1975, new pro­ Logo and its successors are no longer of Visual Languages and Computing. gramming language ideas were floating based on "cutting-edge" computer sci­ June 1996. around and yet Logo stayed the same. ence. Cutting-edge computer science Resnick. Mitch. Turtles. Termites. and Traf­ There has been great progress in pro­ research on programming languages fic jams: Explorations in Massively Par­ gramming language research in the last leads to languages that are simpler, allel Microworlds. Cambridge. MA: MIT 25 years and yet I don't see significant more elegant, and yet more powerful. Press. 1994. changes to the Logo language that im­ These are good things for programmers Saraswat. Vijay A .. Concurrent constraint pressed and excited me 25 years ago. and for kids. I still believe in Seymour programming languages. Doctoral Dis­ LCSI' s MicroWorlds Logo adds some and powerful ideas. I have learned a sertation Award and Logic Program­ ming Series. The MIT Press. 1993. nice user interface gadgets and a very lot from Seymour and am very grate­ impoverished way of running pro­ ful. I just think Logo could be so much grams in parallel. (Concurrent pro­ better than it is. grams can't really synchronize and can only communicate via global vari­ About the author ables.) StarLogo is more interesting but ToonTalk was designed and built by its SIMD model of computation is not Ken Kahn who, after earning a doctor­ flexible enough for the wide range of ate in computer science from MIT, things that kids might want to program spent 20 years as a researcher in pro­ Ken Kahn , Animated Programs computers to do. It is a good thing only gramming languages, computer anima­ [email protected] when dealing with problems that are tion, and programming systems for www. toontalk.com

Winter 1999 LOGO EXCHANGE 19 STARTING WITH STARLOGO

Starlogo Community of Learners Workshop

by VANESSA COLELLA. ERIC KLOPFER. & MITCHEL RESNICK

ew technologies can shape both versity of Maine combined forces to what and how people learn. Though Starlogo has help high school students and teach­ NBefore the advent of computer been available online ers from a variety of disciplines learn modeling. complex. dynamic systems and many illustrative about modeling and complexity. The were inaccessible to all but the most workshop aimed to engage participants advanced mathematicians. The oppor­ sample projects have in building StarLogo models of com­ tunity to address these ideas using been created, it has plex systems and, in the process, to computer technologies has improved embrace new and powerful ideas. their accessibility to novices and in­ remained creased their presence in educational "unapproachable" for Challenges environments. StarLogo provides a many people. One of our primary motivations when way for students and teachers to build we organized the workshop was to and analyze models of these systems. achieve a balance between structure But too often, people believe mistak­ The Community of and exploration. We designed the work­ enly that the mere presence of a new Learners Workshop shop to foster a playful, cooperative, technology will be sufficient to effect This past summer, high school stu­ creative spirit while at the same time change. Though StarLogo has been dents and teachers transformed a con­ providing adequate structure for learn­ available online and many illustrative ference room at the Santa Fe Institute ing how to build models. To accomplish -sample projects have been created, it into a buzzing interdisciplinary mod­ this balance, we organized the work­ has remained "unapproachable" for eling workshop. The two-week Star­ shop around a set of open-ended chal­ many people. In particular, the avail­ Logo Community of Learners Work­ lenges and activities that guided par­ able materials have been insufficient shop brought together 25 participants ticipants' explorations and provided a to facilitate its seamless integration and five workshop leaders from around means for critical review while main­ into classrooms. As with other tech­ the country for a hands-on experience taining an investigative atmosphere. nologies, the effectiveness of complex, in model building. Participants in the Each challenge was a problem state­ dynamic models in education is influ­ workshop explored a variety of social ment that was meant to get partici­ enced greatly by the way in which they and scientific models, including preda­ pants' creative juices flowing. Here is are presented. Creating an environ­ tor-prey dynamics, population growth, a short excerpt from one challenge: ment that encourages and supports and traffic patterns, StarLogo2 uses, learners' intellectual curiosity is just and a variety of participatory activities. As you observe behavior in the real as important as providing the tools for The StarLogo Community of Learn­ world, you can make guesses about building and exploring new phenom­ ers Workshop was created to help the reasons for some of these behav­ ena. Thus, we saw a critical need to people develop new ways of under­ iors. Think about the last time you develop new educational approaches standing and describing phenomena in were "people watching." If you saw for helping teachers and students use the world around them. The Santa Fe a woman in a business suit running StarLogo to learn about complex, dy­ Institute, the Massachusetts Institute to catch a bus, you might have as­ namic systems. of Technology Media Lab, and the Uni- sumed that she was late for work. If

20 LOGO EXCHANGE Vol. 17 I No.2 you saw a young man pacing in 1. covered a StarLogo modeling con­ of complex systems. These experiences front of a movie theater, you might cept that was appropriate for par­ helped participants as they designed have assumed that his date was late ticipants' current level of experi­ and created their own final projects to meet him. If you saw a small ence later in the workshop. child throwing a temper tantrum, 2. enabled participants to build a you might have assumed that he was coherent and interesting model, Design Studio tired or hungry. In each of these even before they knew much of Because we designed the challenges to cases, you were drawing conclu­ the StarLogo language catalyze a variety of possible solutions, sions about people's internal states 3. supported a wide variety of solu­ we wanted to incorporate a structure based upon the behavior that you tions. Often challenges contained into the workshop that would to help observed. Often, internal states-like pointers to sample projects, participants evaluate these solutions. being hungry, anxious, happy, or en­ which illustrated possible imple­ We borrowed a few ideas from the de­ ergetic influence the way people act. mentations of the key concepts sign studio teaching model, which is Many other creatures and objects, in the challenge. This format standard fare in the visual and creative even subatomic particles, are also af­ minimized direct instruction, in­ arts. In integrating these ideas, we fected by their internal states. Mod­ stead fostering an environment hoped to foster the kinds of creative eling the internal states of individu­ in which specific programming thinking that we feel should be a part als provides you with an information was available when of the scientific enterprise, while at the opportunity to understand a great needed. same time providing a time-tested variety of real-world systems. structure for community-based learn­ We adopted two key ing and peer review. Challenge We adopted two key components of You have seen that turtles have components of the the design studio, the "desk-crits" and several properties (e.g., heading, design studio, the the "pinups." These mechanisms pro­ color, etc.) that allow them to re­ vide learners with generative feedback member information. Turtles can "desk-crits" and the during the design and building pro­ remember additional information "pinups." These cesses. While participants worked on about themselves if you add new mechanisms provide the challenges, workshop leaders peri­ turtle variables. The different types odically visited each group. During of information that turtles remem­ Learners with generative these "desk-crits," the workshop lead­ ber are referred to as "states." feedback during the ers encouraged participants to describe Can you create a StarLogo design and building what they wanted their models to project with a turtle "energy" state? show, reflect on how well their mod­ How will you enable the turtles to processes els achieved this goal, and think about gain and lose energy? How might the next steps they wanted to take. your turtles behave or look differ­ Many of the challenges were accom­ About two-thirds of the way through ently as their energy level increases panied by "off-screen" activities that each challenge, "pinup" sessions pro­ or decreases? How does their be­ provided another way for participants vided a public forum for participants havior help you visualize the to connect abstract notions of complex­ to articulate the rationale behind their turtles' changing states? What as­ ity and decentralized behavior to their models. During these sessions, special sumptions do you make about a own personal experience. One morn­ attention was paid to how well the turtle's state based on its behavior? ing, participants "flew" around the models communicated ideas to other Are your assumptions accurate? parking lot trying to form cohesive people. After each brief presentation, "bird flocks" without a leader. Group participants and leaders gave feedback The challenges facilitated model activities like this one enabled partici­ to the model builders, enabling people design and construction, built familiar­ pants to develop a personal perspective to improve their models. Participants ity with the StarLogo environment, on concepts like exponential growth, developed both the abilities to design, and introduced the principles of com­ local versus global information, and implement, and explore simulations plex systems. group decision-making. We found that (through the challenges) and the facili­ As we developed the challenges, we integrating the group activities into the ties to describe, analyze, and critique made sure they fulfilled three require­ challenges was a great way to help simulations (through the "desk-crits" ments: people develop deeper understandings and "pinups").

Winter 1999 LOGO EXCHANGE 21 Moving Ideas media can help bring about deep Beyond the Workshop One teacher introduced changes in how people think and learn. Written evaluations from participating Starlogo to the Santa Fe Resnick led the development of the pro­ students and teachers showed consis­ Community CoLLege, totype for the award-winning LEGO tent approval for the content and the Mindstorms product (a robotics con­ format of the workshop. More impor­ where students are struction kit based on programmable tant, the enthusiasm from the summer addressing Local LEGO bricks). and he is the developer workshop has poured into participants' community problems, ofStarLogo (an environment for mod­ daily pursuits. The teachers and stu­ eling complex dynamic systems). dents continue to explore what they such as the declining Resnick was also co-founder of the began at the workshop. One teacher water table. Meanwhile, Computer Clubhouse, a network of af­ introduced StarLogo to the Santa Fe more than a dozen ter-school learning centers for youth Community College, where students from under-served communities. are addressing local community prob­ students are building Resnick earned a B.A. in physics at lems, such as the declining water table. Starlogo projects for Princeton University (1978) and M.S. Meanwhile, more than a dozen stu­ and Ph.D. degrees in computer science dents are building StarLogo projects for this year's New Mexico at MIT (1988, 1992). He is author of this year's New Mexico High School High School the book Turtles. Termites, and Traffic Supercomputing Challenge. Another Supercomputing jams, published by MIT Press in 1994. teacher wrote "[my] students are very playful with StarLogo and have devel­ ChaLLenge. Endnotes oped models of evaporation and cloud 1 Vanessa Colella (MIT Media Lab), formation, processionary caterpillars, Larry Latour (University of Maine). city rioting, and traffic flow." taught junior high and high school sci­ Eric Klopfer (University of Massachu­ We plan on running similar work­ ence. She currently works on Partici­ setts, Amherst). Nigel Snoad (Santa Fe shops at the Santa Fe Institute and in patory Simulations-computer-sup­ Institute), and Gil Munden (University the Boston area during the summer of ported activities that enable immersion of Maine) were Workshop leaders. 1999. In addition, we are currently in and investigation about "life-sized" Special thanks also to Ginger Rich­ writing a workbook that includes chal­ dynamic systems. In addition, she is co­ ardson (Santa Fe Institute). without lenges and activities inspired by the authoring a book on StarLogo for stu­ whom the Workshop would never have StarLogo Community of Learners dents and teachers. She holds an S.M. happened. Workshop. The workbook will include in media arts and sciences from MIT, 2 Developed by Mitchel Resnick, MIT sample projects for each of 10 chal­ an M.A. in communications, comput­ Media Lab. StarLogo is available for lenges, hints and strategies for complet­ ing, and technology from Teachers Col­ free on the Web at www.media.mit. ing the challenges, and ideas for pre­ lege, Columbia University, and an S.B. edu/star logo. senting the challenges in a variety of in biology from MIT. 3 Thanks to David Shaffer for his as­ Ij learning environments. It will describe Dr. Eric Klopfer is a National Science sistance. See http://dws.www.media. how to run "off-screen" activities that Foundation postdoctoral fellow at the mit.edu/people/dws/papers/ can help learners understand more University of Massachusetts at Amherst. designstudio/index.html for more about complex dynamic systems and He received his Ph.D. from the Univer­ details. will include a short section on why and sity of Wisconsin, and his B.S. from how you might use individual-based Cornell University. Dr. Klopfer's re­ modeling environments like StarLogo search focuses on the use of computer in your own pursuits. ® models in science and math education. He is currently investigating the effects About the authors of teachers developing their own com­ Vanessa Colella is a doctoral student at puter models. In addition to the Star­ Vanessa Colella MIT's Media Laboratory, where she Logo book that he is co-authoring. he is [email protected] investigates how innovative computa­ also developing software (code-named tional tools can transform the processes "Weevolution") for modeling learning Eric Klopfer of science education. Her research fo­ and evolution in animals. [email protected] cuses on ways to help people teach and Dr. Mitchel Resnick, associate pro­ learn about complex dynamic systems. fessor at the MIT Media Laboratory, Mitchel Resnick Before her work at the Media Lab, she studies how new techological tools and [email protected]

22 LOGO EXCHANGE Vol. 17 I No.2 - Papert's Conjecture about the Variability of Piagetian Stages in Computer-Rich Cultures

by ANNE McDOUGALL

Introduction From the earliest work with chil­ very "abstract" powerful ideas made One of the most interesting and impor­ dren and Logo, anecdotal evidence sug­ accessible through Logo, but apart from tant aspects of Papert's work in gested that Papert's view was correct, Logo contexts, it is not normally con­ Mindstorms (1980) is his conjecture and I became interested to see whether sidered appropriate for formal presen­ that children in a computer-rich learn­ it could be substantiated by more for­ tation to children at elementary school ing environment using Logo might be mal research. level. able to engage in learning activities I began my investigation of these The study was focused by several involving abstract or formal thinking ideas with an intensive case study, the themes from Papert's work: the impor­ at ages considerably younger than data collection for which spanned the tance of the culture in which children would be expected from Piagetian years 1984-86. In 1988 I spent a term learn in providing suitable resources theory. teaching Logo in a Grade 5 classroom for building intellectual structures, the to investigate the possible extension of power of computing to "concretize" This book is about ... using com­ my findings from the case study into a abstract ideas, and the idea that learn­ puters to challenge current beliefs more generalizable classroom situa­ ing with a computer might change the about who can understand what tion. More recently, through a project way other learning takes place. and at what age. It is about using "Children as Programmers" funded by Support ofPapert's conjecture in the computers to question standard as­ Charles Sturt University, a colleague, case study environment would not of sumptions in developmental psy­ John Oakley, and I have been working course imply its necessary transfer to chology and the psychology of apti­ with teachers in well resourced class­ classroom settings. However, if his tudes and attitudes.... I take from rooms to investigate the conjecture ideas were not supported in the study, Piaget a model of children as build­ further. This paper describes my ear­ the chances of their being substanti­ ers of their own intellectual struc­ lier research on this question, and out­ ated in real classrooms would be very tures .... All builders need materi­ lines the current work. small. als to build with. Where I am at The subjects for the study were my variance with Piaget is in the role I A Case Study 1984-86: two children, aged 9 and 6, when data attribute to the surrounding cul­ Children, Recursion, and collection commenced in 1984. They tures as a source of these materi­ Logo Programming were provided with a home learning als .... In many cases where Piaget For my doctoral research project environment rich in materials and op­ would explain the slower develop­ (McDougall, 1988; 1990a) I undertook portunities for learning about recur­ ment of a particular concept by its a case study to investigate Papert' s con­ sion, including an Apple II computer greater complexity or formality, I jecture. I studied the development of with Logo, a robot turtle and a printer, see the critical factor as the rela­ understanding and use of the concept a teacher well versed in Logo and re­ tive poverty of the culture in those of recursion, a topic usually considered lated issues of learning and teaching, materials that would make the difficult for undergraduate computer books and other materials, and, as far concept simple and concrete. science students, in children of elemen­ as possible, unrestricted time for work­ (Papert, 1980, 4-7) tary school age. Recursion is one of the ing with these things. The learning

Winter 1999 LOGO EXCHANGE 23 environment was informal, with a Detailed descriptions of the A Graphics Project: sense of playfulness; there was no set children's development of under­ Display Procedure for curriculum to be covered and no assess­ standing of recursion and skills of re­ Nested Reflected Polygons ment. cursive programming have been re­ This project stretched over two ses­ In one sense, it was not an ideal ported elsewhere (McDougall, 1985; sions on consecutive days; the total Logo culture such as Papert described 1988; 1992). I'll present the briefest time was three hours and 15 minutes. in Mindstorms. The ultimate agenda summary here. The children had previously written an for our activities was inevitably The case-study children's early ongoing "display" of spirals of differ­ mine-the carrying out of a research work with recursion did not involve ent shapes, each spiral being drawn by project-rather than being completely programming at all. Both children the turtle, then erased before the next the children's own. Within that con­ recognised and made many situations was drawn. They planned to make a straint, however, as far as possible the involving self-reference, repetition similar display. built on a procedure children had control over our activities. with small variation, and nesting of they had already written to draw Very detailed, though not constant, levels with pictures, story fragments, nested reflected squares. observations of the children's program­ toys, and everyday materials. Following are the final versions of ming and other activities in this envi­ Since the younger child's program­ their procedures for the display of ronment were made over three years. ming work did not involve procedure nested reflected polygons. Some of the In particular, all incidents relating to writing, she did not use recursion in designs generated by running the pro­ the development of their understand­ Logo. The elder child's first recursive cedure 0 with inputs 45 and 5 are ing of recursion were recorded. The programming project was the develop­ shown in Figure 1. criterion I set for substantiation of the ment of a tail-recursive procedure to conjecture in this case was confident draw a nested squares design, which TO 0 :N :'1' and independent writing and debug­ she completed with help at age 9. A few FULLSCREEN ging of Logo procedures using embed­ months later, I wrote for her an em­ IF :'1' = 360 [STOP] ded recursion (Leron, 1985). bedded recursive Logo-like procedure FP :N :'1' I used a peer-teaching technique for for the story The Cat in the Hat Comes REPEAT 2000 Back (Suess, 1958), and showed her a data collection. While I planned to ob­ cs tain some data about the two children's graphics procedure emphasizing the 0 :N ( :'1' + 5) learning from sessions in which they unwinding part of embedded recur­ SPLITSCREEN worked alone with Logo, greater in­ sion. END sights into their learning would be pos­ Her understanding of and compe­ sible if, having learned Logo them­ tence in programming with recursion selves, each child were to teach it to a developed unevenly but clearly. until TO FP :N :T friend. Reports of the discussions oc­ the third year of data collection for the PU HOME PD curring with pairs of students work­ study when the elder child and her IF :N = 0 [STOP] ing together (see, for example, Hayles friend, both then aged 11, worked on a PU HOME PD et al.. 1984; 1985) gave me the idea that series of recursive programming F :N :T peer teaching could be a very valuable projects, showing competence, confi­ PU HOME PD and revealing situation for the Logo re­ dence and independence in using re­ FP (:N - 15) :T searcher. First, my children would cursion in Logo. Various areas of diffi­ PU HOME PD learn what they might about Logo and culty they encountered during these F :N (-:'1') recursion; then each would teach Logo projects, and their overcoming of these PU HOME PD to a chosen school friend in whatever are described in detail elsewhere END way she wanted. (McDougall. 1988; 1990b). The diffi­ Seventy-nine Logo sessions were culties included problems with inter­ TO ABS :NUM spread unevenly over the data collec­ pretation of the function of the STOP OP IF :NUM < 0 [ -:NUM] [ tion period. For most of the first year, command, appreciating the scoping of :NUM] the two case-study children worked in­ variables. passing of values between END dividually with me. Then for more procedures, and multiple inputs in re­ cursive calls. than a year, each child worked with her TO F :N :'1' I shall present here two of these friend. Finally, for two months toward REPEAT ABS 360/:T [FD :N R'l' the end of the third year, the elder child children's most advanced projects to :T] and her friend worked on projects par­ illustrate the level of their program­ END ticularly involving recursion. ming at the end of the study.

24 LOGO EXCHANGE Vol. 17 I No.2 A List Processing Project: BIG MEDIUM SMALL Too Many Bears DADDY MUMMY BABY The elder case study child had previ­ DINAH'S BED ously read the story "Too Many Bears" ??? (Ahlberg & Amstutz, 1983), recog­ ALLAN. AHLBERG TELLS ABOUT nised its structure as recursive, and DINAH GOLDILOCKS suggested that her friend read it as well. DINAH TELLS ABOUT GOLDILOCKS Figure 1 They planned to "write the story in GOLDILOCKS TELLS STORY Logo". This project was done in one GOLDILOCKS FINISHES STORY one-hour session. I helped with the IF DINAH FINISHES STORY test in the TELL.STORY procedure, ALLAN. AHLBERG FINISHES STORY suggesting that it test for [GOLD­ GOODBYE ILOCKS] instead of the empty list, and GOODNIGHT with the syntax of the PRINT state­ SNORE ments. The children's procedures for the project were the following. Conclusion for the Case Study Both the case study children, at ages 9 TO CH.l and 6, respectively, were able to recog­ BEARS . IN. BED Figure lA nize and generate examples of the fea­ QUESTION tures of recursion in pictures, stories TELL.STORY [ALLAN.AHLBERG and everyday situations, although they DINAH GOLDILOCKS] found it difficult to define or talk in SLEEP general terms about recursion. The el­ END der child, working at first (at age 9) TO BEARS . IN. BED with the researcher, and later with a friend (until age 11) developed Logo PRINT [BIG MEDIUM SMALL] programming skills including confident PRINT [DADDY MUMMY BABY] PRINT [DINAH'S BED] use of controlled embedded recursion. These children, in an environment END rich in opportunities for working with TO QUESTION recursion, were able to understand and PRINT [???] use this abstract idea when one of them END was as young as 6 years of age. At age 9, the elder child was able to read with TO SLEEP understanding Logo procedures using PRINT [GOODBYE] embedded recursion and to prepare :u~~:.~ PRINT [GOODNIGHT] with help a procedure containing tail . puHOM£<~ PRINT [SNORE] recursion. At age 11, she and a school END friend together operated as competent ::!:j~=:~~:> and independent programmers with .:*·'~·sr.::t~:;.'.f~ii:: TO TELL. STORY : L full recursion in Logo. Thus Papert' s ;'"tlt:•• IF :L = [GOLDILOCKS] [PRINT conjecture was supported, in the case [GOLDILOCKS TELLS STORY] of recursion, by this study. PRINT [GOLDILOCKS FINISHES My next step was to use the experi­ STORY] STOP] ence I had gained from the case study (PRINT FIRST :L [TELLS ABOUT] and try to test the conjecture in a class­ BUTFIRST : L) room situation. TELL.STORY BUTFIRST :L (PRINT FIRST :L [FINISHES Work in a Grade 5 Classroom 1988 STORY]) ~ r :ui·:T .... In the first half of 1988, I was able to •:u..~mias i6o 1 END work with Logo in a Grade 5 classroom RT :~: tt::m~m.i .. at Balwyn North Primary School in END .. ,,:••:;::.·:· Running the procedure CH.l pro­ Melbourne. There was one Apple lie ,,l''' duced: computer in the classroom, a fairly

Winter 1999 LOGO EXCHANGE 25 typical level of resourcing in elemen­ taking programming projects as part of McDougall, Anne (1988) Children, Recur­ tary schools here at the time. I had the their regular learning activities. sion and Logo Programming. Unpub­ computer connected to a large televi­ We chose classrooms with teachers lished Ph.D. thesis. Monash University. sion monitor so all the children could who were highly competent and expe­ McDougall, Anne (1990a) Children, Re­ see what was on the screen, and I rienced in this type of work (Oakley cursion and Logo Programming: An Investigation of Papert's Conjecture brought in a Logo disk, books, manu­ & McDougall, 1997a) sited in schools about the Variability of Piagetian Stages als, other materials, and a robot turtle that provided supportive environments in Computer-Rich Cultures. In Mc­ for the class to use. for this type of work (Oakley & Dougall. A and Dowling. C. (eds.) Com­ We worked together as one large McDougall, 1997b). We interviewed puters in Education. Amsterdam: North group on directing the robot turtle to the teachers about their work and that Holland. 415-418. move and draw pictures. I showed the of their students. McDougall, Anne (1990b) Student Diffi­ children the format for writing proce­ This work is ongoing. We have a culties in Programming with Recursion dures, and we had the turtle draw geo­ collection of disks of individual stu­ in Logo. Proceedings of the Computer metrical figures and more complex pic­ dents' projects, and we are examining Education Group of Victoria Annual tures. Our projects were, I think, these systematically to investigate the Conference. Melbourne: Computer Edu­ typical of the Logo activities under­ programming concepts used in the cation Group of Victoria. 108-115. McDougall, Anne (1992) Structure and taken in many elementary classrooms. projects and evidence of any other ab­ Process Microviews: Partial Under­ However, with the limitations imposed stract concept development supported standings of Recursion in Logo Pro­ by the use of a single computer for the by the programming activity. gramming. In Nevile, L. (ed.) Logo and whole class, it was quite impossible to Mathematics Education. Melbourne: create anything like a level of unre­ Conclusion A.C.E.R. 109-118. stricted time, and of learner ownership Papert's description in Mindstorms of McDougall, Anne (1995) Integration of of our activities, sufficient to investi­ the power of his early experiences with Portable Computers into Australian gate Papert's conjecture. gears in enabling his later understand­ Classrooms: Issues and Outcomes. In Mulling over the unreasonableness ing of a variety of more abstract con­ Watson, D. and Tinsley, D. (eds.) Inte­ of the arguments that "Logo didn't de­ cepts is still, for me, one of the most grating Information Technology into liver what it promised" in environ­ exciting learning stories I have encoun­ Education. London: Chapman & Hall. ments similar to the one in which I tered. His conjecture about the potential 281-284. Oakley, john and McDougall, Anne was working, I decided to defer fur­ of computing to support and enhance the (1997a) Issues in the Preparation of ther investigation of the conjecture learning of abstract concepts remains an Teachers of Programming for Children. until computers were sufficiently extremely important one, and its inves­ In Passey, D. and Samways, B. (eds.) In­ widely available in schools for each tigation warrants a considerable and sus­ formation Technology Supporting child to have his or her own. The op­ tained research effort. ~ Change through Teacher Education. Lon­ portunity came with the adoption by don: Chapman & Hall. 108-114. a number of Australian schools of the References Oakley, John and McDougall, Anne use of portable notebook computers Ahlberg, A. and Amstutz, A. (1983) Too (1997b) Educational Environments for (see for example McDougall, 1995). Many Bears. In Ten in a Bed. London: Research on Cognitive Development Often these schools required that in­ Granada. 9-17. through Programming. In Johnson. D. dividual students own the computers, Hoyles, C., Sutherland, R. and Evans. ]. L. and Maddux. C. D. (eds.) Logo: A Ret­ rospective. New York: The Haworth so issues of access and available com­ (1984) A Preliminary Investigation of the Pupil-Centred Approach to the Press. 83-93. puter time no longer limited what chil­ Learning of Logo in the Secondary Papert, Seymour ( 1980) Mindstorms: Chil­ dren might achieve with Logo. School Mathematics Classroom. Univer­ dren, Computers and Powerful Ideas. sity of London Institute of Education. Brighton, U.K.: Harvester. The Children as Programmers Hoyles. C.. Sutherland, R. and Evans, ]. Seuss, Dr. (1958) The Catin the Hat Comes Project 1996-9 (1985) And Then She Had the Idea of Back. New York: Random House. With a colleague, John Oakley, from Dividing It by 360. Times Educational Charles Sturt University, I embarked Supplement. March 1, 52-53. in 1996 on a project we called Children Leron. Uri (1985) Logo Today: Vision and as Programmers. With funding from Reality. The Computing Teacher. Febru­ Charles Sturt University, we planned ary. 26-32. McDougall, Anne (1985). Teaching and to carry out further investigation of Learning about Recursion. In Palmgren, Papert's coi"Uecture, collecting data in Anne McDougall M. (ed.) Logo85Pre-proceedings. Massa­ Anne.McDougall@education. technology-rich elementary school chusetts Institute of Technology. 155-6. classrooms where children were under- monash.edu.au

26 LOGO EXCHANGE Vol. 17 I No.2 LOGO: SEARCH AND RESEARCH

Papert's Perspectives, Research Responses

by DOUGLAS H. CLEMENTS AND JULIE SARAMA

eymour Papert has made myriad was that the turtle was "body syn­ mathematizing familiar processes is a contributions to education, but tonic" -firmly related to children's fluent, natural and enjoyable activity, Sperhaps none so great as provid­ sense and knowledge of their own bod­ then is the time to talk about mathe­ ing new visions (Papert, 1980; Papert, ies and the way they move. Research matizing mathematical structures, as 1987; Papert, 1993; Papert, 1996). In supports Papert's contention that ideas in a good pure course on modern alge­ this brief space, we can mention only of turtle geometry are based on intui­ bra." Richard Noss (1986) tested this a few of these perspectives that have tive knowledge (Kynigos, 1992). In one idea. Children who had used variables been investigated by researchers. What intensive study of the learning of one in their Logo work were more able to does empirical evidence say about the child, we found that Logo helped con­ use algebraic ideas to represent vari­ vision Papert has shown us? nect the two ideas of tum-as-body-mo­ ous situations. Noss states that it is not tion and tum-as-number. Only after necessary that they have learned some­ 'Spontaneously' learning making this connection did the child thing about algebra per se. The alge­ mathematical ideas begin to understand the measurement braic thinking that they learned in One of Papert' s early notions was that of angles and turns (Clements, Battista, Logo was used to build algebraic mean­ more ideas could be learned "precon­ Sarama, & Swaminathan, 1996). ing in non-computer contexts. So, sciously" and "spontaneously," as sim­ Papert also argued that new knowl­ Logo learning may aid in forming ple ideas about counting are learned edge acquired in Logo has to compete primitive conceptions of algebraic no­ (Papert, 1980) . That is, certain pro­ with existing knowledge. This notion is tions at an early age, which may be­ cesses, such as combinatorics, are not supported by findings that Logo has more come part of a system of algebraic normally learned without formal effect on children's ideas about angles thinking later. teaching. However, such domains than about length (Noss, 1987). So, could be learned in a "Piagetian," natu­ teachers need to be active helping chil­ Building a conceptual ral way, if experiences were provided dren integrate what they are learning in framework for learning by the culture. Papert argued that the Logo with their existing knowledge. It mathematics computer could provide such experi­ may be fine for children to be confused Papert (1980) claimed that Logo can ences. In support of such a notion, (as between the angle of turn and the make the abstract concrete, accelerat­ Wright says 4-year-olds have been seen measure of the resulting angle)-Papert's ing cognitive development. That is, systematically combining the primary "transitional theories" -but then an im­ Logo can help build a conceptual paint colors in a computer simulation portant role for the teacher involves ar­ framework on which later mathemat­ program to build the three secondary ranging experiences that prevent stu­ ics learning can build. Using this ap­ colors so that they could create a pic­ dents from simply evading the problem proach, some researchers have re­ ture with all sizes and colors (Wright, (Simmons & Cope, 1990). ported gains (Miller, Kelly, & Kelly, 1994). We do not know how frequent 1988; Rieber, 1987), but others found such learning might be. Making a transition between no significant differences (Clements & informal and formal ideas: Gullo, 1984; Howell, Scott, & Dia­ Learning geometry The case of algebra mond, 1987). With teacher planning through 'body syntony' Papert believed that Logo could be a and mediation, however, computer Papert introduced turtle geometry to transition between informal and for­ programming can facilitate mathemat­ the earliest versions of Logo. His idea mal mathematical experiences. "When ics achievement and higher-order

Winter 1999 LOGO EXCHANGE 27 thinking (Billings, 1986; Reed, tiation (Clements & Nastasi, 1988; • focus students' attention on par­ Palumbo, & Stolar, 1988; Roblyer, Hoyles, Healy, & Sutherland, 1991). ticular aspects of their experience Castine, & King, 1988; Wiburg, 1989). This should not be taken to mean that • educe informal language and pro­ So, research reports that the use of children should always work together, vide formal mathematical lan­ Logo can afford opportunities for chil­ however; a balance of cooperative and guage for the mathematical con­ dren to explore mathematical ideas in individual work may be ideal. A com­ cepts a meaningful context and in doing so bination of structured interdependence • emphasize planning for algorithm generate a more active exploration and and individual autonomy, with a high­ development understanding of concepts and pro­ status student coordinator, may be best • suggest paths to pursue cesses (Yelland, 1995). Such benefits (Hoyles, Healy, & Pozzi, 1994). • provide metacognitive prompts occur more frequently and more pow­ and ask higher-order questions erfully when teachers are actively in­ Learning and teaching • facilitate disequilibrium using volved mediating students' work with Many researchers interpreted Papert' s computer feedback as a catalyst Logo. In general, there is research sup­ early writings as indicating no need for • provide tailored feedback regard­ port for Papert's "power principle" -stu­ teaching. One researcher for example, ing students' problem-solving ef­ dents use the mathematics first for a used "a 'standard' play-oriented ver­ forts personally meaningful goal, then sion of the LOGO curriculum as de­ • discuss errors and common mis­ deepen that initial understanding scribed in most published accounts understandings (Papert, 1996). (e.g., Papert, 1980)" (Mitterer & Rose­ • continually connect the ideas de­ Drasnor, 1986, p. 178). This researcher veloped to those embedded in Learning powerfully found very little Logo-specific change other contexts through projects in problem solving behaviors, however, • provide modeling and coaching This power principle is consistent with leading to the conclusion that learning • promote both student-teacher and another perspective: Papert strongly Logo will not enhance general problem student-student interaction. advocated learning through in-depth solving skills. engagement in projects. Here there is Interpretation is individual. I. for It is also noteworthy that positive strong research support (with the ca­ example, can not read about the Samba effects also take a considerable time. veat that they are all from Papert's schools without imagining learning Liu (1997) found 150hoursofexperi­ group). Whether they designed proj­ and teaching beyond simple versions ence was necessary. In the case of al­ ects to teach others about fractions of play. Nevertheless, as we discussed gebra, for example, the extent to which (Hare! & Papert, 1990) or mathemati­ previously, "learning without being the researcher prompted for a Logo cal games (Kafai, 1993), students learn taught" is also a Mindstorms theme. connection were instrumental in stu­ more and learn more deeply, when The definition of teaching is critical: dents' generating meaningful notations engaged in projects. teaching-by-telling in a narrow sense for the unknowns (Noss, 1986). or guiding learning in the broadest Learning responsibly and sense? Changing schools learning together Researchers consistently report that Papert stated that the computer by it­ Papert also predicted that Logo could the most positive results have involved self was not an agent of change (a per­ help children take responsibility for teacher mediation based on a well­ spective he called "technocentrism", their learning and work together more developed theoretical foundation Papert, 1987). This has been clearly powerfully. Logo experiences posi­ (Clements, 1990; De Corte & Ver­ supported by research. It is less the tively affect students' (both boys and schaffel, 1989; Delclos & Burns, 1993; inherent features of computers and girls) internal locus of control Lehrer, Guckenberg, & Lee, 1988; more people's experience with the (Bernhard & Siegel, 1994). Overall, Lehrer, Harckham, Archer, & Pruzek, machine that determines learning and research suggests that educators build 1986; Littlefield et al., 1988). Effective social change (Mehan, 1989). classroom cultures that encourage stu­ teachers appear to plan and oversee dents to take responsibility for their computer programming experiences to Final Words own learning; to engage in tasks that ensure that students reflect on and This is not, and could not be, a com­ are challenging, but not too difficult or understand the mathematical concepts prehensive review ofPapert's perspec­ too easy; and to work cooperatively, (McCoy, 1996, p. 443). Research indi­ tives or research responses. It is but a asking each other questions (King, cates that they: small selection illustrating the power 1989), engaging in cognitive conflicts, of Papert's vision and the empirical and always working to resolve them • select or create tasks designed to support-and enrichment-that research through discussion of ideas and nego- acpieve educational goals has offered. We need additional re-

28 LOGO EXCHANGE Vol.17/No. 2 search across the spectrum-from the Hayles, C., Healy, L., & Pozzi. S. (1994). Mitterer, J.. & Rose-Drasnor, L. (1986). traditional hypothesis tests that will Groupwork with computers: An over­ LOGO and the transfer of problem solv­ evaluate the many (usually post hoc) view of findings. Journal of Computer ing: An empirical test. The Alberta jour­ nal of Educational Research. 32, 176- conjectures and initial results in the Assisted Learning. 10. 202-215. Hayles. C., Healy. L.. & Sutherland, R. 194. literature to exploratory studies that ( 1991). Patterns of discussion between Noss, R. (1986). Constructing a conceptual stretch the conceptions of what com­ pupil pairs in computer and non-com­ framework for elementary algebra puter programming and education puter environments. journal of Com­ through Logo programming. Educa­ might be. ~ puter Assisted Learning, 7, 210-228. tional Studies in Mathematics, 1 7, 335- Kafai. Y. B. (1993). Minds in play: Com­ 357. 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The Computing Teacher. 17(2), 8- Delclos, V. R., & Burns, S. (1993). Media­ McCoy, L. P. (1996). Computer-based 11. tional elements in computer program­ mathematics learning. journal of Re­ Wright,]. L. (1994). Listen to the children: ming instruction: An exploratory study. search on Computing in Education, 28, Observing young children's discoveries journal ofComputing in Childhood Edu­ 438-460. with the microcomputer. In]. L. Wright cation, 4, 137-152. Mehan, H. ( 1989). Microcomputers in & D. D. Shade (Ed.), Young children: Harel, I., & Papert, S. (1990). Software de­ classrooms: Educational technology or Active learners in a technological age (pp. sign as a learning environment. Interac­ social practice? Anthropology & Educa­ 3-17). Washington, DC: National Asso­ tive Learning Environments, 1(1), 1-32. tion Quarterly. 20, 4-22. ciation for the Education of Young Chil­ Howell, R. D., Scott, P. B., & Diamond,]. Miller, R. B., Kelly, G. N., & Kelly, ]. T. dren. (1987). The effects of "instant" Logo (1988). Effects of Logo computer pro­ Yelland, N. ( 1995). Mindstorms or a storm computing language on the cognitive gramming experience on problem solv­ in a teacup? A review of research with development of very young children. ing and spatial relations ability. Contem­ Logo. International journal of Math­ journal of Educational Computing Re­ porary Educational Psychology, 13, ematics Education, Science, and Technol­ search, 3, 249-260. 348-357. ogy, 26(6), 853-869. Winter 1999 LOGO EXCHANGE 29 J Time to prepare this material was elementary geometry curriculum, Logo has studied teachers' use of computer partially provided by a National Sci­ Geometry (published by Silver Burdett, innovations and students development ence Foundation Research Grant. "An & Ginn, 1991). With colleagues, he is of mathematical constructs while Investigation of the Development of working on the previously mentioned working in computer microworlds. She Elementary Children's Geometric NSF research grant and is finishing a is co-author of several Investigations Thinking in Computer and second NSF-funded project, Investiga­ units and of Turtle Math and has de­ Noncomputer Environments," NSF tions in Number, Data, and Space, to signed and programming new versions MDR-8954664. Any opinions, find­ develop a full K-5 mathematics cur­ of Logo and other computer micro­ ings, and conclusions or recommenda­ riculum featuring Logo. With Sarama, worlds. She is co-principal investiga­ tions expressed in this publication are he is co-authoring new versions Logo tor on the new Building Blocks project. those of the authors and do not neces­ for learning elementary mathematics. sarily reflect the views of the National One, Turtle Math, is currently available Douglas H. Clements Science Foundation. ~ from LCSI. Sarama and Clements are SUNY at Buffalo co-PI's on the aforementioned Build­ Dept. of Learning and Instruction About the Authors ing Blocks project, which is developing 593 Baldy Hall Douglas H. Clements, Professor at the mathematics software for preschool to Buffalo, NY 14260 State University of New York at Buf­ grade 2 children. [email protected] falo, has studied the use of Logo envi­ Julie Sarama, Ph.D., is an assistant ronments in developing children's cre­ professor at Wayne State University, Julie Sarama ative, mathematics, metacognitive, where she teaches mathematics con­ Wayne State University problem-solving, and social abilities. tent courses for pre-service teachers Teacher Education Division Through a National Science Founda­ and research courses for graduate Detroit, MI 48202 tion (NSF) grant, he developed a K-6 mathematics education students. She [email protected]

30 LOGO EXCHANGE Vol.17/No. 2 ---- Polygons and More

[ by WILLIAM J. SPEZESKI

s a Logo practitioner, I am always looking for inter­ to poly.round :n :1 :r esting ideas to build a project around. One of my re­ local "adj Acent thoughts was to use Logo to design buttons that make "adj :r * tan 180 I :n could be used as clickable links for Web pages. The tool pu fd :adj pd that I felt would be very useful was a procedure to draw a repeat :n [ fd :1 - 2 * :adj arcr :r 360 I :n] square with rounded corners. More generally. it would be pu bk :adj pd valuable to have a procedure that would draw different poly­ end gons with rounded vertices. And so I begin the article in search of a procedure to do just that. Don't panic! This is not as bad as it looks. Here is a sum­ Drawing regular polygons with Logo is accomplished very mary of what this procedure POLY . ROUND will do: easily by using a procedure like 1. Its third parameter r controls to poly :n :1 the size of the arc radius. repeat :n [ fd :1 rt 360 I :n ) 2. It produces a polygon with end rounded vertices whose line segments coincide with por­ f:""'" where the parameters n and I are used to control the num­ tions of the enveloping regu­ ber of sides and the side length, respectively. The slight lar polygon drawn by POLY alteration with the same values of n and 1. (Its size is control­ lable.) to polyr :n :1 3. The starting (and stopping) position of the turtle is at repeat :n [ fd :1 arcr 15 360 I :n ) a vertex of the corresponding enveloping regular poly­ end gon drawn by POLY. is a procedure that produces something close to the desired In order to round the vertices of a polygon and preserve result, rounded vertices. The RT command in POLY is re­ the polygon's size, each side of the polygon must be short­ placed with ARCR (arc right), the usual procedure that draws ened (adjusted) a little bit at each end. That "little bit" (AD]) an arc in a clockwise direction. Here the radius of the arc is is equal to R * TAN 18 0 I N in our case. Here R is the fixed at 15 and the span of the arc is identical to the exte­ radius of the arc and TAN is the trigonometric function rior angle needed to draw anN-sided polygon. tangent. You may have to substitute sIN xI cos x if the Procedure POLYR is quite usable. but it has a few defi­ 1. ciencies: version of Logo that you are using does not have the TAN function available. Creating round vertices with procedure 1. The radius of the arc is fixed. POL YR also shifts the starting position of the turtle. Com­ 2. The size of the figure is not easy to control. pensating adjustments are made in procedure POLY. ROUND 3. The starting position is no longer at a vertex. to position the turtle initally at a (virtual) vertex with the initial FD and closing BK commands. After a using a little trigonometry, the procedure can be Coming back full circle to Web page button design, pro­ rewritten to do exactly what we want. A revised version of cedure POLY. ROUND is a very useful drawing tool that will procedure POLYR is shown below: produce a scalable polygonal button shape. But so much for Winter 1999 LOGO EXCHANGE 31 J Web buttons. Designing Web buttons is truly a very inter­ The figures were generated with the following esting Logo project. Having said that, however, I will leave superprocedure: that discussion to another time. What is more interesting at to showit the moment is exploring procedure POLY. ROUND. cs fs set -320 160 0 polyb 5 100 Procedure POLY.ROUND set -150 100 0 po1y.round 5 30 145 Yogi Berra is famous for his quote "If you come to a fork in sat 30 110 0 poly.round 3 20 50 the road, take it!" Web page button design was the impetus set 150 100 0 poly.round 7 50 155 for developing procedure POLY. ROUND. But now we will set -300 -100 0 poly.round 15 20 450 leave the world of Web page buttons and take the fork in set -70 -100 0 poly.round 30 5 750 the road, digressing with a brief discussion of the proce­ set 140 -100 18 poly.round 5 50 180 dure that was developed above. end Procedure POLY. ROUND will draw polygons with rounded corners as long as the radius of the arc r remains a reasonable It uses procedure SET below to arrange the objects on length. Looking at the expression the screen:

L 2 * R * tan 180/N to set pu setxy list :x :y pd in the procedure, it is clear that for appropriate large values seth :z of R. this difference will take on negative values. When we end get negative values of this expression, however, the fun be­ gins! Going FORWARD a negative amount results in moving Editor's Notes the turtle BACK, while going BACK a negative amount re­ The Logo programs in this article were written to work in sults in moving the turtle FORWARD. In fact, for larger val­ Terrapin dialects of Logo. If you are using an LCSI dialect, ues of R. procedure POLY. ROUND behaves a lot like like Micro Worlds, make the following changes. to polyb :n :r • You can eliminate the 1 o c a 1 "ad j line in repeat :n [ bk :r arcr :r 360/:n ] poly. round. end • Change the SET procedure to SETUP. Set is a primi­ The above procedure is similar to procedure POL YR with tive in MicroWorlds. FD replaced by BK and parameter 1 replaced by r. Both • Change cs fs to CG in the SHOWIT procedure. POLY. Band POLY. ROUND (with R>L/2*TAN 180 /N) will produce some very dramatic effects. Let's look at a few Conclusion examples. This article discusses an interesting procedure POLY. ROUND that draws regular polygons with rounded vertices and has some interesting side effects. But more importantly, it hope­ fully illustrates more of the hidden surprises and sense of discovery that Logo has provided over the years. Seymour Papert' s gift to all of Logo is truly a gift that keeps giving. Thank you, Dr. Papert. ®

About the author Bill Spezeski teaches at Massachusetts College of Liberal Arts and is a long-time contributor to Logo Exchange. Look for other articles by him in future issues.

But Spezeski wspezeski@ mcla. mass.edu

32 LOGO EXCHANGE Vol. 17 I No.2 Papert, Logo, and Loving to Learn

[ by PAM GIBBONS

Mindstorms-where it spired by Papert's notions of such The fact that this phenomenon was all began ... things as objects to think with, think­ widespread but not absolute suggested, In preparing to write this paper, I went ing about thinking, computational however, that it was not inevitable, and to the bookshelf and retrieved my yel­ metaphors, sub-procedures and mind­ if not inevitable, then perhaps lowed, dog-eared, now almost loose-leaf sized bites, and the wonder of recur­ conquerable. Stated as a truism, copy of Mindstorms (Papert, 1980). It sion. Most gratifying, however, was Papert's comment (1980:42) that had been quite awhile since I returned Papert's ready and emphatic recogni­ to the book that started it all for me, so tion of the cognitive-social universe of "The extent to which adults in our I read it again. Perhaps mirroring what programming and the quality of human society have lost the child's posi­ Papert described as how "we all forget relationships in Logo environments. tive stance toward learning varies about our thinking as children" While the Papertian roots of many of from individual to individual" (1980:41), I was surprised to read in these themes may have faded in my those pages so many ideas, hopes and memory, one of Papert's observations begged for serious investigation. Why dreams about Logo and learning that I has stayed with me clearly and was this so? What can educators do had long since internalised and ac­ strongly-that which he describes as the about it? cepted as part of some Logo commu­ mathophobia (fear of learning) endemic nity collective consciousness. in our society. In an alarming recogni­ Why doesn't everyone At first, I greatly admired Papert's tion of what once was a way of being love to learn? writing probably because I agreed with for all of us, Papert observed that "Chil­ Years later, my doctoral research fo­ what he was saying. It seemed so hard dren begin their lives as eager and com­ cused on individual differences, cogni­ to make other educators understand petent learners"(1980:40). I found this tion, and recursion in Logo program­ what could happen if you put children observation alarming because, particu­ ming-truly Papert inspired themes and Logo together in the right environ­ larly in schools, it was clear that most (Gibbons, 1993; 1995). Based on the ment-the things I was observing on a children had lost this eagerness and com­ neuro-psychological cognitive theories daily basis-that it was very exciting petence very early on in their formal of Luria (1973) regarding individual to find that a respected researcher was education. Papert (1980:42) noted that: differences, and Activity Theory actually writing about the same things. (Leont'ev, 1981; Vygotsky, 1978) re­ I was fascinated by the theoretical dis­ "An unknown but certainly sig­ garding tl:le plasticity and cultural situ­ cussion underlying Papert's observa­ nificant proportion of the popula­ ation of cognitive abilities, I explored tions. I was inspired by his proposi­ tion has almost completely given the ways in which individuals used and tions of educational revolution and up on learning. These people sel­ conceptualised recursion in Logo pro­ what the future of education could dom, if ever, engage in learning gramming. Two types of individuals' hold. I entered the Logo community and see themselves as neither com­ dominant cognitive styles were identi­ and conducted my own research, in- petent at it nor likely to enjoy it." fied and studied-for ease of discus-

Winter 1999 LOGO EXCHANGE 33 sion in this paper, these are char­ these subjects, learning is embodied in erately promote simultaneous process­ acterised as either simultaneous (rela­ the memorisation of unrelated pieces ing abilities that in my research were tional) thinking or successive (proce­ of information or ritualistic proce­ associated with learners who enjoyed dural) thinking. dures. The notion of education thus learning. Efforts to encourage the de­ From this research I discovered that becomes onerous and cumulative; the velopment of simultaneous abilities simultaneous learners demonstrated presentation of new information in­ should not, however, be confused with an eagerness and curiosity for new volves the extension of the long list of Papert' s (1985) ideological concerns knowledge; they placed high value on things to be remembered rather than regarding the "forcing" of style. Rather, "understanding" concepts rather than supporting existing knowledge through it is proposed that attention should be on memorisation-their activity was the development of a more robust men­ given to the development of both simul­ characterised by the pursuit of knowl­ tal model. For the simultaneous learn­ taneous and successive information edge for its own sake. In marked con­ ers, however, new learning experiences processing modes so that learners trast, the successive learners demon­ were welcomed in their promise of pro­ might be better placed to manifest a strated resistance to receiving new viding further clues in the construction style preference instead of, by default, instruction and reluctance to adopt of uniform and universal mental mod­ an inappropriate style necessity. new techniques or modify old ones. els. New information is, for the latter This discrepancy was reflected in the type oflearner, thus linked to the long­ Full drcle pairs' widely divergent perceptions of term reduction of mental activity (at Traditional school environments eas­ what constituted knowledge and learn­ the expense of short-term intellectual ily create environments in which suc­ ing; So polarised were these percep­ effort} and, in a programming context, cessive thinking reigns supreme-the tions that widely divergent educational to the ultimate ability to implement time to design learning environments outcomes between these cognitive pro­ efficient and elegant procedures. to cultivate simultaneous thinking is cessing types were inevitable. long overdue. So, what would such The identification of the existence How can a love of learning environments look like? of a polarity of beliefs between indi­ learning be encouraged? Learners will be engaged in tasks that viduals regarding the very nature of Traditional Western learning environ­ demand relational thinking, that in­ learning itself, was entirely consistent ments have been marked by an empha­ volve keeping a number of items in with diSessa' s ( 1985) observations of sis on activities supported by succes­ mind at once, that demand the identi­ contrasting "intuitive epistemologies" sive processing strategies. Although fication of non-sequential relationships held by two case study subjects. using different terminology, this obser­ between components, that require DiSessa observed that one student vation was also noted by Papert in planning and contemplation. Learners maintained a view of "understanding Mindstorms (1980): the mnestic out­ will concentrate more on solving prob­ physics" that was consistent with comes of tasks favouring successive lems than on knowing facts (resonance diSessa's own p-prims epistemology processing are easily defined and mea­ with Brian Harvey's comments regard­ (1983). In contrast, the other student sured with educators thus being more ing the Internet (1997). There will be · was perceived to hold the view that readily accountable for their work. discovery; there will be creativity, there knowledge of physics resided in its This is in contrast to the problematic will be a richness of human relation­ equations and formalisms (with intui­ nature of assessing the development of ships; learners will have time to play tive knowledge only serving to con­ thinking or problem solving skills as­ and to think; variety will be valued as found understanding). DiSessa noted sociated with simultaneous informa­ an educational outcome; educators will the resistance of the latter student to tion processing. If schooling almost ex­ not be driven by time limits, stand­ adopting a more systemic approach and clusively encourages successive ardised test scores or expediency. forwarded the expectation that this stu­ abilities through the nature of tradi­ Learners will love learning. dent would be at a distinct disadvan­ tional task demands then successive It sounds like Mindstorms. It sounds tage in learning physics. The findings abilities will progressively improve by like Papert. I have conducted my Papert­ of my own research were consistent default and without deliberate inter­ inspired research and have analysed its with diSessa's observations and sug­ vention at the expense of simultaneous findings, and yet it simply confirms gested a theoretical foundation for his abilities. Papert's 1980 call to arms. Papert's call and Papert's propositions. The concern is that we may then be may have ended up being more of an In my research, successive learners "breeding" learners who dread learn­ evolution than a revolution and the demonstrated the assimilation of ing when we should be actively pursu­ technology may have marched on, but knowledge by remembering sequences ing the type of tasks that will invoke. his ideals have stood the test of time. of processes or instructions for indi­ and thus develop, simultaneous abili­ vidual instances of similar cases. For ties. In this way, educators may delib- See LOVING TO LEARN (Page 36)

34 LOGO EXCHANGE Vol. 17 I No.2 THE LAST WORD: COMMENTARY

Explaining Yourself

by BERNARD NEWSOME

itting here at my Power Mac G3 Power: Keys to the New Learning of But I can't see schools giving up 266, struggling to adjust the color the Digital Century. their position in the educational sys­ Sin PhotoShop in order to print Much there to admire, I thought. (I tem, nor governments allowing it to out a red rather than a brown image of thought the Internet had little of in­ happen. Why? One particular reason a small French cake, Le Melodie. I mar­ terest in it until recently.) Empower­ is we assume that if a child is not suc­ vel at what a distance computers and ing children because the computer cessful in a traditional school it is the their programs have come since I was gives them, through their extraordi­ child who has failed, whereas if the at University in the Fifties. That ma­ nary method of playway learning. an child is unsuccessful in an alternative chine. which seemed only to deal with advantage over goops like me. school. or in an alternative program, exam correlations, or the playing of then it is the school or the program that Nim. kept two large rooms humming has failed. The corollary of this, of to the gentle sound of many valves. Could their wisdom course, is that if the child is successful Possibly before I die, every man. added together give us in the first place, it is to the school's woman, and child will have on their pedagogy and a program credit. But, if successful in the second, kitchen tables a vast improvement on he/she was clever enough to make up what I have today. and breakfast will for educating for the the leeway. consist of multiple connections to the future-a theoretical America has had some outstanding Internet instead of rushing out to the theorists and practitioners in educa­ office or school. The American predi­ base operating on, and tion, I mused. Dewey was a profound lection for fast foods, though, is likely being informed by, a initiator; in modem times Bruner, and to increase. practical understanding? in even more recent times, Donald Like most of my generation, I just Graves. And of course Papert himself. use the power of the computer to do Running sideways across that tradition what I want to do. Most of that is lim­ Radicalizing and subverting traditional is George Kelly, the psychologist of per­ ited, and my wife is even more hesi­ learning establishments, called schools. sonal construct theory, and then side­ tant than I am at learning a new set of is possible when multiple ages and ways to the Russian trio of Vygotski, procedures. It was only just yesterday multiple activities go along together. A Bachtin and Luria, sideways to Piaget. that I clicked on Internet Explorer, and social setting of relative experts or rela­ and head on to Polanyi. (I know you did a bit of surfing for the first time. A tive beginners, offers a context for have your favorites too!) Could their couple of my mates said I could with online help of the human kind. And wisdom added together give us peda­ benefit clock onto The Connected then the use of the computer for con­ gogy and a program for educating for Family's Seymour Papert Web site structing, rather than transmitting. the future-a theoretical base operat­ (www.connectedfamily.com). and Yes, I remember being taught Micro­ ing on, and being informed by, a prac­ revisit Mindstorms in an updated. I did Worlds and turtle graphics program­ tical understanding? that, slid into the site of master and ming by a tidily 9-year-old. Goodie, When Dewey advocated learning disciples, and read the lecture, Child Goodie. through experience, he promoted a

Winter 1999 LOGO EXCHANGE 35 problem~solving environment. Every does not matter-study the behaviors LOVING TO LEARN / Cont. from Page 34 new personal or social venture, in of Salmon and Eskimo and you will whatever educational context, requires find similar conceptual schemes ap­ As educators, we can pay no greater adjustment of previously internalized plied to make sense of the data. Indeed, homage than to continue to pursue the routines for dealing with what we find. he argues that the same concept can fulfilment of these ideals. ® These internalized routines. some call be learnt by children at all ages, albeit them skills, are all very well whilst the at different levels of complexity and References diSessa A ( 1983). Phenomenology and the earth stands still, or whilst all experi~ inter~relatedness. If that is right, it evolution of intuition. In D. Gentner ence is predictable. But, as we all know, would suggest that vertical sequencing and AL. Stevens (Eds), Mental models. if we could predict accurately which in curriculum makes sense when con­ 15-34. Hillsdale, NJ: Lawrence Erlbaum horse will win the next race, or which tent provides richer pastures for explo­ Associates. poker machine, operated by a program, ration of already familiar conceptual diSessa A (1985). Learning about know­ is set for the jackpot on the next turn structures. ing. In E. Klein (Ed.), Children and com­ of the wheel, we'd have no need to But enough of the big boys. What puters: New directions for child develop­ learn anything new; what's more, we'd about those three Xs I found on the ment (28). 97-124. San Francisco: all be on holiday in the Bahamas. Mamamedia site (www. mamamedia. Jessey Bass. Part of what we do requires little ad­ com) developed by Papert disciple ldit Gibbons. P. (1993). Recursion: An analy­ justment. We have learnt the routines; Harel into a practical program of mul~ sis of individual differences in Logo pro­ gramming. Unpublished doctoral thesis. we carry them out. and are satisfied. (I timedia learning: EXploring, EXpress~ know how to make the bread I like.) ing and EXchanging? All the theories University of Sydney. Gibbons, P. ( 1995). A cognitive processing But the future, at all levels, is not grounded in children's learning activi­ account of individual differences in known. Thus our tacit knowledge, ties. I'd like to add one more, Explain~ novice Logo programmers' conceptual­ which Polanyi clearly saw as the cru~ ing. The How of the doing, or the ques­ isation and use of recursion. journal of cial mechanism for understanding tion of learner to knower, How do I do Educational Computing Research 13(3). what confronts us, is continually in that?, promotes the acquisition of 211~226. need of more than recursive resetting; skills. The Why for the doing, or the Harvey. B. (1997). Stop the internet, I want the storehouse needs to be expanded question of learner to learner, Why are to get off. Logo Exchange 16(1). 18-19. to cope with the ever present newness you doing that?, or Why do it at all?, Leont'ev, A (1981). Problems of the devel­ of the changing circumstance. Equally, develops the higher order understand~ opment of the mind. Moscow: Progress. though, our tacit knowledge is not to ing of the relationship between things; Luria, A R. (1973). The working brain: An be abandoned, for what we have is the makes the practitioner into the theo­ introduction to neuropsychology. Mid~ dlesex: Penguin. fruit of past encounters. Unless what rist. The problem for most schools is Papert, S. ( 1980). Mindstorms: Children. we find is totally unknown, we have that the control of the why is with computers and powerful ideas. New enough to dig into the slippery slope those who can do, and know why they York: Basic Books. and stabilize, although to climb upward do, which has tended to be seen as the Papert, S. (1985). Computer criticism ver­ may require expansion of the system. teacher. sus technocentric thinking. Logo85: Extrapolating to curriculum content Papert's work suggests a better Theoretical Papers. Cambridge. MA: and structure, the learner in any area route. Massachusetts Institute of Technology. brings to the task a body of expectations Vygotsky, L.S. (1978). Mind in Society. and a repertoire of routines which have About the author Cambridge MA: Harvard University worked in the past, repertoires both Bernard Newsome is a retired profes~ Press. personal (Kelly) and social (any post­ sor oflanguage and literature. He is the '70s guru). Likely, today's encounter author of Understanding Children About the author will be familiar. But when it is not, new Writing and Talking, Writing and Dr. Pam Gibbons teaches at the Aus­ procedures have to be learnt and incor­ Learning. He makes Shaker furniture tralian Catholic U niversity~Mount porated before a satisfactory outcome and is artist's assistant to his wife, Saint Mary Campus, 179 Albert Rd., can be achieved. Curriculum content Mary, who is a printmaker, painter, Strathfield. NSW. 2135 Australia. thus should be not totally new, and it and photographer. Since retirement, he should be structurally related to what has become an enthusiastic computer went before. Build on the old so that user and Logo hacker. Bernard lives in the learner doesn't drown. Melbourne, Australia. On another tack, Bruner, in Man A Course of Study, made the audacious Bernard Newsome Pam Gibbons claim that curriculum content of itself news holm@ bigpond.com [email protected]

36 LOGO EXCHANGE Vol. 17 I No.2 ulti

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