.•. Volume 2, Number 3-Spring 1994 BY) Q~ In This Issue e ~ -r: Advancing Logo' In the last issue we were grappling with the theoretical problem ofdefining By Seymour Papert 1 what kind of Logo is advanced Logo. Soon after writing my contribution I MicroWorlds Project Reports found myselfin a meeting ofLogoteachers who were grappling with a related by Kathryn Verzoni 3 but very practical problem. They felt that many of their students were not by Gerald Crisci 5 advancing in programming skills. For example even after several years of Logosium 4 doing Logo, students still composed long and intricate strings of Logo Logo Tool Box 6 instructions and resisted all suggestions of organizing their work as Where Does Programming Fit In? subprocedures. The teachers saw the situation as a "bug" in their own work by Mark Steinberger 8 and had tried, so far with limited success, a number of strategies to remedy Turtle Math it. Some of them, working on the assumption that the students did not by Douglas Clements and understand the idea ofsubprocedure, had developed teaching units to explain Julie Meredith 9 some principles of structured programming. Others tried to influence the New Product Information 11 students by showing concretely how their code could be written differently. Courses and Workshops 12 The teaching materials they developed were excellent and I am sure that these teachers would have exercised great skill in engaging students in discussion about the relative merits of different styles of programming. Why The first version of Logo that I then did their strategies not succeed? played with was TILOGO. It had In the course ofthe discussion I came to appreciate more sharply than I had fast-moving sprites that could change before the force of another factor that enters into this kind of situation. One color and shape, and a rather anemic might call it "the Piaget insight" which I formulated in the following way back turtle which ran "out of ink" when it in the days I when worked in Geneva. One ofthe major contributions Piaget tried to draw anything complex. made to the investigation ofchildren's thinking is understanding that it is not Meanwhile, the Logo implement- right to label as "wrong" children's declarations that there are more red beads ations for the Apple II had no sprites than blue beads or more water in the tall glass. If you truly succeed in putting and few colors, but the turtle could yourself in their intellectual framework (no easy task!) you will understand fillthe screen with elaborate graphics. that "the children are correctly answering the questions they are really The kinds of projects that emerged answering ... only their questions are not the same as yours even ifboth use in each environment - games and the same words." This does not mean that children, like the rest of us, aren't animations onthe one hand; drawings sometimes just plain wrong. But the whole point of Piaget's empathic and and patterns on the other - reflected interactive way of conducting these conversations is to distinguish between these differences. errors or slips or "mere misunderstandings" and what the children really Nowwe have MicroWorlds, the first believe. radically different Logoto come along The Piaget insight applies to programming. For example, in the early days in many years. What will emerge in of our work at the Hennigan School a remarkable fifth grader, Nicky Brown this environment? This issue ofLogo (now an MIT undergraduate), put me right when I tried to advise him to break Update includes two tentative up a program into subprocedures. He systematically refuted all my arguments. answers with articles by Kathryn No, it would not help him understand his program more clearly: he Verzoni and Gerald Crisci about their demonstrated by his ease of debugging and modifying his work that his own students' MicroWorlds projects. way ofunderstanding it worked perfectly well. Well yes, subprocedures might The software environment help others take over parts of his work, but this wasn't his main goal and influences, but does not determine besides he didn't really think that they were interested anyway. Finally it was the direction that people take with it. clear from his discussion that he just didn't like the kind of structuring of his What you dowith any version ofLogo (Continues on next page, second column) is a matter of choice. In "Advancing Logo,"Seymour Papert reflects upon a discussion with a group ofteachers * The following is based on an interaction with a group of teachers who will about moving in new directions with surely recognize themselves in it. I decided not to identify them because the limited space available here forces me into an oversimplified presentation that Logo: introducing new kinds of casts me in the role of "the expert" coming with "answers" to problems that (Continues on next page, first column) other people ("just teachers") couldn't solve. I hate this role. In reality the discussions were far richer and more creatively interactive. A fuller narrative would cast me as a catalyst rather than as an expert. page 2
(By Seymour Papert, continued from page 1) Logo Foundation project that would be produced by the subprocedurization I suggested. 250 West 57th Street Remembering Nicky Brown - and many other talented young programmers New York, NY 10107-2228 - was a sharp reminder that there is something wrong with describing the Telephone: 212765-4918 problem raised by these teachers as if their students lacked "programming FAX: 212765-4789 skilL" They m!ly have lacked one particular programming skill, but what email: [email protected] their style ofprogramming required was another kind of skill- and when one Board of Directors looks at how fluently many students debug their "spaghetti code," one is Seymour Papert, Chair impressed by the level of that skill. Clotilde Fonseca This diatribe against imposing structured programming on these children Tessa R. Harvey is not intended to avoid the issue that it would be immensely valuable for them Geraldine Kozberg to learn new programming ideas. Quite the contrary, it led me to a crisper Michael Tempel formulation of an alternative strategy to achieve this not by trying to force Takayuki Tsuru new ways to write the children's old programs but by introducing them to new The Logo Foundation is a nonprofit programming domains in which other ideas would come up more naturally. educational organization incorporated My new insight consisted oflooking more closely at the development ofthe in New York State. practice of Logoin the schools from which these teachers came - and when it was finally formulated I see that it applies on a much larger scale perhaps to Logo Update is published three times yearly by the Logo Foundation. the way that Logo programming in schools has developed across the board. Subscription is free. One ofthe most positive educational benefits that came with the introduction of Logo into the schools I was looking at was a shift towards project-based © 1994 Logo Foundation learning. An excellent progressive step. But every progress risks bringing a You may copy and distribute this document for educational purposes certain kind of conservatism in its wake. In this case the conservatism took provided that you do not charge for the form of establishing a certain model of "project" and this model of project such copies and that this copyright carried with it a match to a certain style of programming, in fact precisely the notice is reproduced in full. style from which the teachers were now trying to wean their students. The style of project in question developed a wide presence with the introduction ofLogoWriter. Schematically described, it consists ofusing Logo (In This Issue, continued from page 1) to make a presentation of the results of research conducted by students. In projects, approaches, and program- the best cases Logoserves as more thanjust presenting ideas that are already ming techniques. formulated; the struggle to represent material is part of thinking about it. This issue of Logo Update also Some examples of this kind of work have become well known in the Logo includes readers' responses to earlier community. Early examples included a project on the life cycle of the fly articles, and news about courses, developed by Marian Rosen's computer summer camp group, and projects by workshops, and new products. One of students in Joanne Ronkin's class at Hennigan on such topics as the human these new products is Turtle Math, a skeleton. From Costa Rica came a bold students' project onhuman reproduction specialized version of Logo which is and many on historical and ecological themes. There was no doubt in the described in an article by its creators, minds of the teachers at the meeting I am reporting here that such projects Doug Clements and Julie Meredith. were educationally valuable and a good use of Logo. What emerged only And don't forget the National slowly during the meeting was an awareness that the projects favor a certain Educational Computing Conference, style: they are essentially narrative projects and favor a "narrative" style of which will be held in Boston from programming that looks in the end more like a page full of text than like a June 11to 15. In addition to the many structured piece ofmathematics. Indeed I would gofurther and say that there Logo workshops and presentations has been a co-evolution of this kind of project and this style of programming. planned for the conference, there is The best way to diversify the style of Logo programming is to diversify the Logosium, a full-day Logo kinds of projects for which Logois used. A clear example is provided by Lego- symposium, scheduled for Sunday, Logo. Programming a Lego turtle to follow a light requires programming June 12. This event is sponsored by based on repetitive runs of conditionals. But there is room for infinite ISTE's SIG-Logo, the Logo diversity without hardware beyond the computer. Writing a video game in the Foundation, and the MIT Media Lab. style of Pacman or Mario requires efficient testing for new conditions and Turn to page 4 for more information. thinking carefully about a user interface that will permit rapid response. I look forward to seeing you there. Simulations involving probability lead into issues of representation. All of these put so much of a real premium on small self-contained tool-like procedures that there is no need to persuade students to use them. They are what comes naturally in these contexts ..•.
Logo Update / Spring 1994 page 3 .Modeling Real Life with MicroWorlds Project Builder by Kathryn Verzoni "
What factors affect the probability The project design problem: and interactions in ways they (and 1) that Joe will get a date? How do diet, Analyze some aspect of real life for never had before. and timing and dosage ofinsulin affect cause and effect relationships. Define During the early stages of blood sugar levels in juvenile at least four factors that would have simulation development, defining an diabetics? How accurately can I significant effects upon some effect and distinguishing it from the simulate a wheel on an inclined plane dependent variable or outcome. causes proved to be quite a stumbling using Logo? These are just a few of Develop equations that will describe block. On several occasions when I the questions my seventh grade the relationship between the factors was called over for help, a student students pondered as they used and the outcome. Finally, use would say, "Here are my factors, but MicroWorlds to model real-life cause MicroWorlds to build your model. now I don't get what to do next." My and effect relationships. Your model should be dynamic and question was, "Well, what are you MicroWorlds' slider is a wonderful interactive. Any user (even your five- trying to model here? What do these vehicle for developing understanding year-old brother) should be able to factors affect?" "Oh, .. I don't know .. of variables. The ability to both manipulate values and witness the , , I mean, wait, .. !' Often, they had display and change a value directly effects of such changes. included the "effect" as one of the on the screen enables kids to get a What followed was an onslaught of causes. Their befuddlement and concrete feel for a concept that is too ideas ranging from the very silly to subsequent progress toward ultimate often abstract. Our experiences with the serious. No matter what the resolution was fascinating and raised this new feature led naturally into its selected domain, each learner needed issues relating to differences between use in projects. to think about concepts, relationships, correlational and causal relation- ships. i~D Cat's Health (neue 1) Learners continually found themselves faced with the problem of STRIPE".TflE CAT., HAS VERY BAD HEALTH. howto describe a relationship in terms BY MOVUIC!. THE 5.UDERS YOU CAJMAKE IT of an equation that Logo would BETTER. understand. One student decided to develop a simulation of four factors that affect acat'shealth. In Angie's mind, "mood rating" and "number ofnuisance dogs as neighbors" had straightforward, linear effects. The better the eat's mood rating, the better his health. The more nuisance dogs he had to co- exist with, the worse his health. However, thinking about "hours of sleep" and "amount of food eaten" caused her more trouble. Angie asked, "How would I make it so that the tr Cat's ."~~ Logo Update / Spring1994 page 4 (Continued from page 3) to message talkto "textl ct ~ would work in real life. print [under these conditions the cat's health rating is ...] It wasn't until a few weeks after repeat 8 [insert char 32] the kids had completed their projects setfontsize 20 setstyle "bold that I started to make connections insert :healthrating between the business of causal repeat 2 [insert char 32] modeling and school duties such as end solving for x, making "x y" tables, and plotting functions. Too bad I to calc.health didn't make these connections if food> 5 [make "food minus food] nineteen years ago. if food < 6 [make "food food] With modeling experiences like if sleep> 8 [make "sleep minus sleep] < these under their belts, maybe - just if sleep 9 [make "sleep sleep] maybe - our future high-schoolers make "healthrating :sleep + :food + mood - nuisance.dogs + 38 might begin to make some connect- end ions between school math and to see.health everyday life. ..•. calc.health message end Kathryn Verzoni teaches at the to continue to go.back West Point Post Schools, West getpage "page2 getpage "page2 Point, NY. textl, ct end end to see.explanations to clear.message getpage "page3 textl, ct end end Logosium - Sunday, June 12, 1994 • Sponsored by ISTE's SIG-Logo and the Logo Foundation • Hosted by the MIT Media Lab • An ISTE Pre-Conference Activity at NECC '94, Boston For Registration Information Contact: NECC '94 Office, Lesley College 29 Everett Street • Cambridge, MA 02138 Phone: (617) 349-8965 • Fax: (617) 349-8968 Internet: [email protected] Discussions, Sharing Sessions, and Presentations (Partial Listing) Long Lasting Logo Environments Logo and High School Mathematics Global Logo Links Logo and the NCTM Standards Action Research Logo and Physics Inservice Teacher Education Logo for Little Kids College Logo Courses Children as Game Designers Logo in the Lab and in the Classroom Lego Logo Robotics Contests Programming Tricks and Techniques Computer Science Logo Style Linking Logo with Other Software Logo Curriculum Materials StarLogo: Learning with Thousands of Turtles The Programmable Brick Lunchtime Keynote Speech by Seymour Papert And Jitterbug Logo Style. It's Procedural! Important Note: The NECC '94 Advanced Program, and ISTE Update printed the Logosium fee as $100. This is an error. If you have already registered you will receive a refund. If you have not yet registered, send the correct amount, which is $50. Logo Update / Spring 1994 page5 I' I Pinball Wizards ,. by Gerald Crisci One of the challenges of using the pinball games using the Macintosh elementary schools were involved in project approach when teaching with version of LogoWriter. Since these the project. It lasted approximately Logo is to develop activities which projects were very successful and four months. Students were provided have some structure, yet allow 'motivating, I decided to repeat them with examples of new MicroWorlds children to express their individual with this year's classes. This time commands and shown how to creativity. students used MicroWorlds to create incorporate them into a program. I When my students reach the fifth more sophisticated games. They were introduced concepts by meeting with grade, I introduce them to new Logo encouraged to use their imaginations classes approximately once every concepts that allow them to explore in creating their designs within a three weeks. The regular teachers more sophisticated ideas like structure I provided. brought the classes to the computer variables and conditionals. During Each project had three basic lab for additional sessions. Most this time, students use Logoto create requirements: students worked in pairs. a simulation ofa physical object, such • The game should contain non- The pinball projects helped as a working analog watch. This violent subject matter. students to integrate many Logo model allows them to construct fairly • The game should have clear ways concepts and techniques. They used complicated projects while to win and to lose. • sliders to keep score and to vary the demonstrating their knowledge of • Instructions should clearly explain speed of their games. advanced Logo features. how to play the game. • conditional statements (if Last year, my students designed Fourteen fifth-grade classes in five commands) to make the ball react to objects on the screen, detect collisions with other turtles, and set winning and losing thresholds. • multiple pages to provide for different game levels and for instruction screens. • the Paint Tools to create background graphics and the Shape Editor to create screen objects. • buttons to link pages together and to control the action. • coordinate commands (setpos, setx, sety, mousepos) to move a "paddle" and to position objects on the screen. Some students created musical sequences which played at the end of the game, and some made use ofthe reporters timer and random. When the project began, I showed students examples ofpinball games I had created myself. These games featured a ball bouncing offobjects on INSTRUCTIONS the screen and a paddle keeping the If you hit the blue/ green ball in play. Most of the students' initial game circle you will get five points! designs mimicked what I had shown Once you get 80 points you win them, but many went on to create the game!! If you hit the other types of games, including hockey, soccer,and basketball. Others orange rectangle you lose! built games with themes based on units studied in school,like acid rain. Many based their projects on fantasy (Continues on next page) Logo Update / Spring1994 page 6 (Continued from page 5) themes involving space aliens, -" pirates, or "smiley faces." As the year went on, I began to notice a subtle difference between Logo Tool Box . by Michael Tempel the boys' and girls' projects. Boys generally created games which were functional, yet visually unattractive. Lines on the screen might be crooked The Tool Box column in the last issue of Logo Update included a Logo and graphics haphazardly placed. program which I used to randomize the order of the six authors o~the lead Most girls, on the other hand, took article, ''What is Advanced Logo?" Brian Harvey, one of the SIX, has a great care in the visual design of complaint. their games. I conferenced with some boys and helped them to "clean up" To the editor: the appearance of their screens. Your shuffling algorithm is unfair! Although everyone has an equal Wrapping up the project was chance of being first, the probability of ending up last depends on the difficult forthe young game designers. starting position. The person who starts first has only about a .015 chance Many students wanted to add of ending up at the end, whereas the person who starts last has a .402 additional levels, game options, and chance of staying last. To be fair, the probability should be .167 for more graphics. We could have spent everyone. . the rest of the year improving the A person moves toward the end of the line at each call to shuffle if games and adding new features. someone who was after that person moves to the front. So,in order for the As the year comes to an end, fifth first person to end up last, here's what has to happen: grade students will invite third First shuffle: anyone else moves to the front, p=5/6. Second shuffle: one graders to their classes to play the of the four last people moves to the front, p=4/6. Third shuffle: one ofthe games they have created. This will three last people moves to the front, p=3/6. And so on for the remaining allow third graders to see how they two shuffles, p=2/6 and p=1/6. These five probabilities are multiplied will use their own knowledge of Logo together to give the result .015 as above. . in future years to create their own By contrast, in order for the person at the end to remain at the end, all exciting projects ..•. that has to happen on all five shuffles is that someone else be chosen to moveto the front, soit's p=5/6 each time. Multiplying these fiveprobabilities Gerald Crisci is District Elementary together gives the result .402. Computer Teacher with the Scarsdale I double-checked my math by simulating several trials in Logo. Showing Public Schools. He also wishes to off the array facility of UCBLogo, here's what I did: thank Alan Alterman, Scarsdale's Math / Science Enrichment Teacher, for his help in developing this project. to sim :n For more information, contact the local [lasts this] author at: make "lasts (array 6 1) Curriculum Center for [i 1 6J [setitem :i :lasts 0] Scarsdale Public Schools repeat :n [make "this last shuffle shuffle shuffle - Brewster Road shuffle shuffle [1 2 3 4 5 6] ~ Scarsdale, NY 10583 setitem :this :lasts (l+item :this :lasts)J 914 721-2430 print :lasts [email protected] end I did two separate trials of sim 1000, with these results: First trial: 14 46 83 163 262 432 Second trial: 21 49 91 144 292 403 Each number represents the number oftimes that the person originally in that position ended up last, soout ofthe first 1000trials, the first person ended up last 14 times, the second person ended up last 46 times, etc. (Continues on next page) Logo Update / Spring 1994 page 7 (Continued from page 6) To make your algorithm fair, whenever someone moves to the front, OOPS! that person should be exempt from further shuffling (so the next shuffle is of a smaller set). Here are my modified versions of your procedures: In the previous issue of Logo Update, part of Carol Sperry's Book ~ 198 163 140 161 176 162 169 155 159 169 176 172 Brian Harvey, who started third and ended up second, is a Lecturer in Computer Science at the University of California at Berkeley. He is the How to Order DeB Logo author of the three-volume Computer Science LogoStyle and is the creator ofUCBLogo. UCBLogo is available in versions for MSDOS, Macintosh, and UNIX computers. It is in the public Here is the original shuffle program as it appeared in Logo Update, domain, and may be obtained via Volume 2, No.2: anonymous FTP from to shuffle :deck anarres.cs.berkeley.edu. output move. to. front (pick :deck) :deck Get the file publREADME for end details. Ifyou donot have FTP access, but to move. to. front :item :list can read a 3.5-inch disk, send $3.00 output sentence :item (remove :item :list) to cover costs and specify whether end you want the Mac or the MSDOS version, or send $6.00 for both, to: to remove :it :them if :it = first :them [output butfirst :them] Brian Harvey output sentence (first :them) (remove :it butfirst :them) 2634 Virginia St. end Berkeley, CA 94709 to pick :group Outside North America, please output item (1 + random count :group) :group send US $4.00 for one disk or US end $7.00 for both. Logo Update / Spring 1994 page 8 Where Does Programming Fit In? .' by Mark Steinberger The questions, "Is Programming a purely 'cognitive' terms. Something these menu-driven applications, GoodActivity for Children?" (Papert, very personal happened, and one programming can be introduced as a Logo Update, Fall 1993) and "Is could not assume that it would be meaningful solution to the student's Programming Obsolete?"(Clements repeated for other children in exactly real life problem. and Meredith, Logo Exchange, Fall the same form." I love working with Logo, as do 1993) are important questions for us Papert, as an adult, has clearly many of the hundreds of children because they go to the heart of the fallen in love with Logo the way he with whom I have worked. I have issue, "Why do we want children to was in love with gears as a child. discovered, however, that there are work with computers?" The answer That is why he uses it to solve a many teachers and students who do to that question is rooted in our vision myriad of daily problems. In his not share that affection. It seems to of schools and their role in a young column Papert argues that me that ourjob as educators is to help person's life.The most important task programming is a good activity for these people find other paths to of formal education is to facilitate children because it can be used to computer literacy. children's development into lifelong create anything from whimsical I am interested in environments independent learners who take doodles to microworlds that assist in accessible to children that include a control of their own destinies. They the exploration of a variety of programming language for purposes must be imbued with a strong sense interesting situations. Papert relates ofextending the environment, but do ofthemselves and their ability to act a number ofstories that describe how not require use of that language to in this world. For this kind of he used programming to explore cross the threshold. HyperCard, education tobe meaningful, children's interesting relationships and Hyperstudio, MicroWorlds and self-confidence must be backed up phenomena. Control Lab all fit into that category. with competence in a variety of life Papert tells the story of a Logo They all have reasonably powerful skills, orliteracies. Computer literacy alarm clock. He used Logo because menu-driven capabilities while is one of those skills. he loves it and didn't have access to a having an integrated programming A computer literate student clockradio. Someone else might have language that expands those understands that a computer is a tool used the Mac's microphone to record capabilities. that people use to accomplish self- a loud, repetitive sound. His The HyperCard model provides a defined, real-life tasks. They have a Macintosh alarm would have then goodexample. At its less sophisticated realistic understanding of what a played that sound, rather than the levels, HyperCard is a very powerful, computer can do, even if they don't simple beep, at the appropriate time. menu-driven, creative environment. know the specifics of how to get it Not as elegant as Logo,but it gets the When and if a student wants to create done. Implied is an understanding job done. If he had a telephone (How something that can't be accomplished that computers are not mysterious or many classrooms do?)he might have with the commands available in the magical, but useful and controllable. called a friend and asked him to call menu she can opt to learn something Our goal as educators is to nourish back and wake him. Perhaps someone about scripting. This is needs-based students whosee themselves as actors would have built something out of teaching at its best. The student is in the computer arena, not passive tinker toys. not learning to script because it will bystanders, or worse, victims. We When Logowas first introduced, it improve her mind. She is learning it want students to grow into adults provided the only avenue for children because she has an authentic need who will not be intimidated by to control a computer. It promoted for it. From this need an emotional computers but will go out and use the idea of a low threshold and high connectionmay form and that student computers to achieve their personal ceiling. Today there are open-ended may share a love of the elegance, and professional goals. powerful tools that have lower challenge, and flexibility of In the forward to Mindstorms, thresholds for children. While not yet programming that I share with Seymour Papert describes his love of obsolete, programming does have a Seymour Papert ..•. gears. They were an important narrower role than it did when Logo learning model for him because he was first introduced. Mark Steinberger, who has taught was in lovewith them. He specifically I no longer see programming as an with Logo for many years, is the did not proposeproducing sets ofgears entry level computer activity for Computer Coordinator in Community for all children to study because "... children. Word processing, computer- School District 4 in New York City. this would miss the essence of the ized paint programs and hypermedia story. I fell in love with gears. This is production are more accessible. As something that cannot be reduced to children begin to feel limited by Logo Update / Spring1994 page 9 Turtle Math by Douglas H. Clements and Julie Sarama Meredith ing symbols and drawings, as well as Can Logohelp teach mathematics pattern searching. Further, students effectively? Research and classroom R command for can easily modify the code. This practice over the years provides an this turn is encourages experimentation and answer: "Yes, but, it takes some rt 45 supports later work with procedures. doing!"Fortunately, research has also (See the illustration on the next provided some answers about what (001 page.) to do and how to do it.! We've used Thesecondbasicissue isthe direction what we've learned to design a Logo ofthe symbol-drawing connection.One environment fine-tuned for the symbols (code)and drawings explicit. of Logo's main strengths has been its learning of geometry and other That's good, but they often lose these support of linkages between drawings mathematical topics. The result is connections. Turtle Math encourages and symbols. One of its limitations has Turtle Math, a version of Logo immediate mode programming - been in the lack oftwo- way connection accompanied by activities geared to students type commands into the between these modes. That is, one the upper elementary grades. We command center and see them creates or modifies symbolic code to based Turtle Math on five principles immediately enacted. Students produce visual drawings, but not the we gleaned from research. (especially novices) often prefer this reverse. Turtle Math provides a II draw 1. Encourage building exploratory mode and find it easier to commands" toolthat allowsthe student mathematics from visual and make sense oftasks. Hoyles and Noss to use the mouse to turn and move the found that having students record intuitive knowledge turtle, with corresponding Logo their commands while working in commands created automatically. The Research supports Papert's idea immediate mode encouraged them to cursor changesto acrosshairs,the turtle that Logo's turtle can encourage take a more global perspective on the continually turns to face it, and the students to build mathematical task and to look for structure within corresponding turn command is knowledge out of their personal, their program design." In contrast, dynamically updated in the Command visual, intuitive knowledge, such as use of procedures can lead to a Center. knowledge of walking and moving. separation between symbols and However, it also warns that children drawings. Further, students working It 45 have a lot of difficulty with in immediate mode are also more measurements. For instance, turns likely to abandon inappropriate and angles can become stumbling solution strategies before they make + stones for children trying to use turtle incorrect generalizations. This keeps geometry meaningfully. To help, them on track. Turtle Math's Turtle Math features a turtle that command center displays all the turns slowly and, optionally, a ray commands, in sequence, even as they The turtle is then dragged forward or turns with it, showing the change in work in immediate mode. back and the corresponding fd or bk heading throughout the turn. Turtle In Turtle Math, students enter command is placed in the Command Math also provides measurement commands in "immediate mode" in a Center. tools; for example, an on-screen command center. Any changes to protractor, placed at the turtle's commands are reflected auto- It 45 fd 100 position and heading, measures turns. matically in the drawing. For One arrowhead shows the turtle's example, if you change the fd 40 to fd heading. The other followsthe cursor, 50, the drawing automatically shows which students move with the mouse. that change when you press When they click the mouse, this Logo Update / Spring1994 page 10 Pull down to choose menus. ." Cl ick to choose I. File Edit Font Windows Motions EHtras Helpl Ii CI tool. square (Continued from page 9) for such analysis. Several of Turtle are immediately reflected on the construction of a Logo-based Math's tools provide such support. In graphics screen upon exiting that school mathematics curriculum," addition to the structure of the window. 1987, International Journal of Command Center, a step function Mathematics Education, Science, allows children to "walk through" any 5. Provide freedom within and Technology, 18,581-595. procedure, or the commands in the constraints command center. As they do so, they Douglas H. Clements is Professor of may edit any command inthe sequence. Our goal is to encourage problem Education and Julie Sarama The change is immediately reflected solving within structured activities as Meredith is aPh.D. candidate at State on the screen. well as student directed exploration, University of New York at Buffalo. Students can also step through both within the constraints ofthe Turtle procedures with inputs. This is Math environment. We provide a set of particularly important given that, activities, but they are not intended to otherwise, they tend to lose sight of be static. Teachers and students can what the numbers specified as inputs invent and save their own. mean and how they function within Turtle geometry has long been a rich the procedure. mathematicalmicroworld. With Turtle Math we aim to extend and enhance it 4. Encourage procedural still further ..•. thinking 1 Clements, D.H. and Meredith, The benefits of using the command J.S. Research on Logo: Effects & center and immediate mode Efficacy, 1992, Logo Foundation programming have already been CUse the Response Form on page described. Turtle Math's structure 11 to order.) encourages use ofproced ures from the beginning. First, the teach tool walks 2 Hoyles, C. and Noss, R., students through the steps of defining "Synthesizing mathematical procedures. Second, changes made to conceptions and their procedures within the teach window formalization through the Logo Update / Spring1994 page 11 New Products LOGO USERS GROUPS Crystal Rain Forest TM, from Terrapin Software will be available for Macintosh computers in June. This Long Island Logo Users Group adventure game teaches Logo throughout, and provides Contact: Marilyn Tahl for learning about environmental topics. It incorporates 516333-4018 (evenings) Crystal LogoTM, a simplified Logo, which may be used 516627-8110 (days) separately as well as within the game. Contact Terrapin at 800 972-8200. Los Angeles Logo Users Group Turtle Math TM, the program described on pages nine Contact: Carolina Goodman and ten ofthis issue, is available for Macintosh computers. Campbell Hall For more information and a free demo disk contact LCSI 4533 Laurel Canyon Blvd. at 800 321-5646. North Hollywood, CA 91607 Also from LCSI, MicroWorlds Project Builder" and 818980-7280 ext.234 Micro Worlds Math Links ™ will be available for the MSDOS environment in June. An MSDOS version of New York Logo Users Group MicroWorlds Language ArtTM will follow later this Contact: The Logo Foundation year. 212765-4918 While They Last Philadelphia Logo Users Group During the summers of 1984, 1985, and 1986, Logo Contact: Mel Levin conferences were held at MIT. We have a few copies of Prince Hall School the Logo '85 and Logo '86 Conference Proceedings, and Godfrey and Gratz Avenues Logo '86 Bibliographies. They're yours for the cost of Philadelphia PA 19141 shipping and handling. Use the Response Form below to 215276-5369 order. ------~ •. Logo Foundation Response Form •. D Enter my free subscription to Logo Update. D Send me the full list of Logo Foundation publications. Enter my order for price quantity amount D Research on Logo: Effects & Efficacy $ 4.75 $--- o Logo '85 Conference Proceedings $ 5.00 $--- o Logo '86 Conference Proceedings $ 5.00 $--- o Logo '86 Bibliography $ 5.00 $--- o Mindstorms (Second Edition) by Seymour Papert $ 13.00 $--- o The Children's Machine by Seymour Papert $ 22.50 $--- Tax-deductible contribution to the Logo Foundation $--- Total $ _ Name _ Please enclose payment or a school purchase Organization order. Address Overseas shipments require additional City State Zip _ charges. Please inquire before ordering as the amount depends upon Day Phone ( ) Evening Phone ( ) _ destination and carrier. Logo Update / Spring 1994 page 12 Summer Logo Courses FLORIDA MASSACHUSETTS OHIO Programming with Applications Boston Computer Museum LogoWriter Course 6/13 - 6/24 in Education: Logo 715- 8/13 Computer Clubhouse Contact: George Shirk Contact: Dr. Joel Levine (For Children ages 10 to16) SciMaTech Barry University Contact: Education Department University of Toledo Miami Shores, Florida 617426-2800 Toledo, Ohio 305 899-3608 419537-2079 MINNESOTA GEORGIA Logo St. Paul 6/20 - 6/24 TEXAS Summerscape Contact: Logo Foundation Logo in Your Curriculum July and August sessions 212765-4918 6/20 - 6/24, 7/25 - 7/29 or (For Students, grades 7 to 9) 8/8 - 8/12 Contact: Scott Shepherd NEW YORK Contact: Theresa Overall Georgia Institute of Technology Logo Course 7/11 - 7/15 Lamplighter School Atlanta, Georgia 30332 LEGO Logo 7/18 - 7/22 Dallas, Texas 404 894-9544 Contact: Joseph Sede 214369-9201 Long Island University ILLINOIS 516299-2199 Logo Course 7111 - 8/5 If you are offering a Logo LEGO Logo 7/11 - 7/15 Contact: Doris Dale course or workshop, please Southern Illinois University Contact: SCOPE let us know so that we may at Carbondale Staff Development include the information 618453-4245 516360-0800 ext. 13,21, or 25 in Logo Update. 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