A Microworld Oriented Approach in a Multi-Functional Logo-Based Curriculum G. Bariamis, S. Chaimantas, Y. Kotsanis, L. Papathomaidi Doukas School EUROLOGO '93, University of Athens, 28-31/8/1993

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A Microworld Oriented Approach
in a Multi-Functional Logo-Based Curriculum
G. Bariamis, S. Chaimantas, Y. Kotsanis, L. Papathomaidi
Doukas School
Messogion 36-40, Maroussi
151 25 Athens Greece
tel: (301) 6822500, fax: (301) 6818277
e-mail: ikotsa@leon.nrcps.ariadne-t.gr
Abstract
Through the microworld approach and the project-oriented activities we can enhance both the learning process and the educational applications. Our main aim, in this microworld environment, is to approach the problem solving process in a "human" way, without having to adapt our thinking skills to a computational aspect of view. The presented powerful ideas emphasize the use of Logo as a student-centered tool in a generative active environment.
This paper will focus on four open-ended microworlds (polyspin, alphabet, lego-logo, speaking-turtle) that can be successfully included in any kind of computer-based curriculum or curricular school program (geometry, algebra, physics, etc.). These microworlds (except the last one) have been tested in our Logo-based curriculum which is included as an appendix. This curriculum has been resulted from an over-five year effort to introduce and apply a (one-hour per week, in a condensed way) class of Informatics into the school time-table, covering 4th to 8th grade.
Keywords: Logo, curriculum, microworlds, alphabets, functional programming, multimedia
George Bariamis was born in 1960. He received a degree in Electrical Engineering from Democritos University of Thrace. He has done post-graduate studies in Pedagogical and Technical School of Athens. He has also taken courses in Digital Electronics and Microcomputers at the Greek Center of Productivity. As a teacher of Informatics at Doukas School since 1987, he has been working with students from elementary level to high school level and also with adults interested in New Technology.
Sotiris Chaimantas was born in 1960. He received a degree in Informatics at the Fachhochschule of Konstanz Germany. He has been working in the field of Informatics in Germany and Greece for 4 years. As a teacher of Informatics at Doukas School since 1989, he has been working with students from elementary level to high school level designing and implementing educational software as well.
John Kotsanis was born in 1959. He has a degree in Electrical Engineering from the National Technical University of Athens (NTUA) and has done post-graduate research in Computational Linguistics. His interests include Educational Computing and Natural Language Processing. Logo Environments are of special significance to him. He is currently Co-ordinator of Department of Informatics at Doukas School. He is also active in software development and teacher training in various projects at Patras University.
Lena Papathomaidi was born in 1960. She received a degree in Mathematics from the Physics & Mathematics Department of Athens University. She has done post-graduate studies in teaching Mathematics at the University of Paris VII. She has also taken courses in Educational Computing at the Greek Computer Society. She is currently teacher of Informatics at Doukas School.
EUROLOGO '93, University of Athens, 28-31/8/1993

2. 2
A Microworld Oriented Approach
in a Multi-Functional Logo-Based Curriculum
Introduction
The experience we gained from an over-five year introduction and application of Informatics in primary and secondary education has led us, apart from various subtargets, to a significant teaching target: To develop the learner's ability in handling problems by planning, implementing, testing, improving and finally comparing them to the desired result. This can be achieved by choosing certain ideas and applications that will motivate the learner.
The use of microworlds and the powerful ideas they contain, has proved to be one of the best means in this educational process. These microworlds can include the following features which have been previously referred. They are:
- clearly defined parts of reality
- visualising and modelling process
- highly interactive and friendly
- able to manipulate, explore and be explored
- open-ended, extensible, cooperative, combinable
In the following chapters we will describe four microworlds (polyspin, alphabet, lego-logo, speaking-turtle) that can successfully be included in any kind of curricular school program.
The Polyspin Microworld
The “polyspin” microworld is based on a very simple idea of designing complex patterns from a series of movements and rotations on an initial pattern.
The experimentation with this microworld includes the following stages:
- a synthesis process, that is the description of a complex pattern from an initial pattern and a “generation rule”,
- an analysis process, that is the detection of the initial pattern and the “generation rule” of the given complex pattern, and
- a human repetitive process to achieve the desired goal through the trial & error approach.
We can use the microworld to design any kind of shapes (e.g. crystals, snowflakes, flowers, trees, etc.), to experiment with the changes that produce the variables, to also include recursively generated shapes and in this way simulate the nature.
The following procedures represent the basic structural elements of such a microworld (the initial pattern may be a procedure or an instruction list):

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POLY :NUM :SIZE :INSTR, puts the initial pattern (3rd input) on the edges of the regular polygon made from the number of its sides (1st input) and the size of them.
SPIN :NUM :INSTR, rotates the initial pattern (2nd input) as many times as the number (1st input) indicates, until it returns to the starting position.
TURN :ANGLE :INSTR, rotates the initial pattern (2nd input) as many degrees as the number (1st input) indicates, until it returns to the starting position.
The definitions of the procedures and sample examples are illustrated below (lcm function returns the least common multiple of two numbers):
to poly :n :side :instr to spin :n :instr to turn :angle :instr
repeat :n repeat :n repeat (lcm 360 :angle)/:angle
[fd :side rt 360/:n run :instr] [rt 360/:n run :instr] [rt :angle run :instr]
end end end
We can also include new inputs in the microworld (e.g. side and angle increments/decrements) or commands to change the colors of the shapes. The implementation of an “angle guess game” for randomly generated patterns should also be attractive for the students and beneficial for the teacher.
The fundamental challenge of the microworld is that in every new movement or rotation, the whole set of the previous patterns takes part and not only the first one. This reflects to the functionality of the microworld and to the interpretation of procedures as usual data.
We approach the problem solving process in a human way, giving the appropriate commands without having to adapt our thinking to the lower details of machine operation or a computational aspect of view. The previous possibilities emphasize the use of Logo as a powerful tool to which we can simulate and finally observe the way we are thinking.

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The Alphabet Microworld
Dealing with the description and designing of various alphabets (our mother tongue or foreign ones) can turn out to be very rich in exploring ideas, experiencing and assigning projects, as well as a flexible way of combining formal and concrete process. It can become the reason for someone to refer to the history of Typography, the various family fonts, the way of recognising, processing, representing characters on the computer, up to designing letters with detailed predefined pieces (as well as real objects used by young kids) and the making of banners by the use of floor turtles.
Using this microwold (and its combination with others, such as “polyspin” microworld) we can design letters and furthermore words and sentences of any heading and any size regarding their height (:h), length (:m), width (:w), (and depth if we tried to create 3-dimensional letters with perspective), color of the outline and filling of the letter, distance between letters and words, that can be placed in linear, curved or polygonal form. We can also include a “read” procedure to interactively input from the keyboard.
The following procedures represent the basic structural elements of such a microworld:
FDR/FDL: The turtle is moving on the hypotenuse of an hypothetical rectangular triangle (the two inputs define the size of vertical sides) preserving the vertical heading between starting and ending turtle position.
FDW/RTW: A moving/turning command that leaves a widened trace (if the used implementation of Logo does not support a “penwidth” primitive).
FDRW/FDLW: An FDR/FDL command with an additional width (it differs from FDR/FDL in that the ending turtle heading is the same of the start position).
As an example we design the Greek letter “Λ” in 3 different ways.
to La :h :m to Lb :h :m :w to Lc :h :m :w
fdr :h :m/2 lt 90 bk :w/2 rt 90 make "l Lambda :h :m :w
fdr :m/2 :h fdrw :h :m/2 - :w/2 :w fdr :h :m/2 - :l/2 fd :l rt 90
pu rt 90 fd :m rt 180 fdl :h :m/2 - :l/2 bk :l lt 90
rt 90 pd fdlw :h :m/2 - :w/2 :w fdl :h*(:m/2 - :l)/(:m/2 - :l/2) :m/2-:l
end pu rt 90 fd :m-:w/2 lt 90
rt 90 pd fdr :h*(:m/2 - :l)/(:m/2 - :l/2) :m/2-:l
end fd :l rt 90
end
(the general function “Lambda” returns the size “l” of a letter that differs from the width :w).

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The Lego-Logo Microworld
Dealing with Lego-Logo could be a wonderful experience to study various theoretical and practical subjects. The construction of an original machine, as a final goal, with a combination of hardware & software, make the student feel like an “inventor - engineer”. Every student could find, in every large or small project, something that suits his personal interests.
The understanding of automations, the clear distinction between hardware and software, the approach: experiment - evaluation - revision and finally the understanding of a part of our real world are some of the benefits that the student gains.
In small groups of 4-5 students, 9-13 years old, a set of projects are given from which they select one to implement. The available equipment is a portable specially formed work table, a Lego- Logo set, a computer connected to the school network, written material and manuals and TC- Logo. The interface control functions are also available in BASIC and PASCAL, so that the student can select their preferable programming language.
As an example we can refer to the task of implementing a Lego-Turtle construction, in a test- game form between the students of the same group, who check each other. Each student develops his own program on a computer of the lab and tests his work on the Lego-Logo work table, till he completes the whole job. The score refers to the total behaviour of the used model, containing also the handling process for the achievement of the final goal.
a. The Turtle Moves. The Lego-Logo turtle moves under the commands: XFD, XBK, XRT, XLT that are developed from the students themselves. The distances are calculated in centimetres, the angles in degrees. The vehicle should be moving in the most precise way and the test includes a difficult parking between obstacles that may fall with the lightest touch.
b. The Turtle Learns. The Lego-Logo turtle is being driven through two switches (one for each motor) only forward. The turtle must “learn” the path it has walked along and turn back (itself) to its initial position and heading.
c. The Turtle Avoids Obstacles. The Lego-Logo turtle has two touch sensors to detect the crashes. The test includes a speed race, with a procedure that drives faster to the exit. The initial position and heading was randomly set.

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The following procedures (defined by students) are an example of the XFD command and the ESCAPE command that drives the turtle to an exit (it is an interesting problem to study the relations between the topology of obstacles and the turning angle after a crash)
to xfd :distance to escape
fd :distance listento 6
talkto [a b] ifelse sensor? [xbk 2 xrt 50] [xfd 1]
seteven listento 7
on ifelse sensor? [xbk 2 xlt 50] [xfd 1]
wait :distance * 1.6667 escape
off end
end
Some of the microwold functions can be combined with other microworlds. For example in combination with the alphabet microworld the Lego-turtle can design letters on the floor.
The “Speaking” Turtle Microworld
Beyond the peripheral connections with specialized hardware (eg. floor turtles, lego-logo) working on Logo was limited until recently to its computational environment. With the development of multimedia this computational environment is expanded, enriched with the ability to include hypertext capabilities, to use colorful images, to drive any kind of devices (eg. CD-ROM, videodisks) and to control audio & video sources and functions.
Maybe, the first step in the construction of a multimedia microworld is to translate the written turtle commands, partly or wholy, into a verbal form. We create the sound files related to their respective commands or procedures and either Logo demands us verbally to execute turtle commands or we hear them being executed.
The following procedures represent the basic structural elements of such a microworld (based on MCI):
numtoword: A given number as input is put into words (eg. the command: numtowords 123, returns: [εκαηόν είκοζι ηπία] or [100 20 3]). This output can be related to respective sound files to produce the verbal form of the number.
say: A given instruction as input is converted in its verbal form (eg. the command say [fd 10 rt 90 pu fd 100 fill], return its verbal form: [μπποζηά δέκα δεξιά ενενήνηα πάνω πένα μπποζηά δέκα γέμιζε]).
startcd/playcd/stopcd: Starts, plays or stops a specified track (or time lenght) as input, on an audio compact disk.
playwav: plays the sound sample of the specified file, as input (in "wav" format).
The above procedures can fully be driven from a graphic user interface (GUI), an example of it is shown in the figure below.
We can take an example of a “multimedia turtle game”:

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A turtle, lost in the woods, is trying to find her nest. It can be moved by means of known commands (fd, rt, etc.) but can not see the location of the nest. With each move an overflying bird reveals the distance from turtle to nest but not the heading. The objective of the game is to lead the turtle to her nest by the fewest possible attempts (there is a unique solution with a precise number of attempts).

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A Logo-Based Curriculim (4th - 8th grade)
HoursSubject (4th grade)Objective1Lab Operating Instructionsname parts of computeridentify groups and codes, connect to the network, use basic keys2Basic Turtle Commands (I)move, turn the turtle, estimate (elementary) distances, angles2Basic Turtle Commands (II) Picture Managementuse penup, pendown and movement to any positioncolor, fill the shapes and the backgroundload, modify, save pictures4Drawing Project (I)draw,maintain, print a complete pictureanalyse (elementary) the stages for the constructionuse different shapes and stamps2Basic Geometric Figuresdraw squares and rectangulars, estimate distances, angles (of 90o) protect pictures from unwanted changes2Drawing Project (II)draw freely a project related to a season, adding small text3Project with Preparationprepare the desired drawing and shapesprecalculation of distances (the EEC-Flag project) 4Repetitiondraw regular polygons and circles (using repeat) 4Animationcreate animation using different shapes as turtlescreate animation using pen exchange technique2Writing, Typing a Textwrite, modify small texts on the picturesuse editing keys and punctuation marks2Procedureintroduce to name, write and execute procedure for simple shapesHoursSubject (5th grade)Objective2Turtle Commandsdraw simple shapes, use pen-background colorserase, stamp, fill, shade and use of different shapes2File Managementload, modify, save, print picturesuse function keys2Turtle Projectchoose, describe, implement pictures2Drawing Geometric Figuresdraw triangles, squares, rectangulars4Repetitiondraw regular polygons and circles (using repeat) understand "total turtle trip theorem" choose and implement a given composition of polygons2Animationcreate animated graphics (using different shapes and repeat) 2Writing, Typing Textuse word processing capabilities to add texts on the picture2Production of Drawingsuse interactive commands and record them on worksheets2Procedure Definitionuse the editor to name, write and execute a proceduremark and copy the interactive commands into a named procedure2Debugging Processdetect "errors" of procedures, edit and correct them (using slowturtle) 2Editor Exploitationfull use of editor capabilities to write and modify procedures2Modular Analysischoose, describe a drawing on a worksheetimplement by stages2Super/Subprocedures Buildingwrite procedures that call others

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HoursSubject (6th grade)Objective4Procedure-Subprocedure Buildingcreate, test, modify a procedureuse it as subprocedure within another procedure4Procedure Combinationsuse student completed procedures and combine them to create regular geometric figures and free designs4Turtle Geometry(with Euclidean Geometry Elements) familiarize with heading identify themselves with turtle-bodydiscover the relation between number of sides and angles of shapesidentify similarity, symmetryidentify divisors, multiples, complementary/supplementary anglesexperiment with circles and arcs4Animation - Sound Project (Multiple Turtles) draw using predefined shapesenrich drawing with animated graphics and sounds4Procedures with Variablescomprehend the use of variables and their effect on making flexibleprocedures4Variable Shapes Buildingexperiment with increments and decrements (grow and shrink) inparametric proceduresHoursSubject (7th grade)Objective4Alphabet Microworld (I)use and combine elements of the Turtle and Euclidean Geometryfind out the "symmetry" and the "similarity" as notions, by incrementing and decrementing patters, maintaining the proportions4Alphabet Microworld (II)understand effortlessly mathematical notions and numerical correlations by varying and trying different variables in given procedures4Microworld Enrichementcreate similar or different procedures by using the given Microworld and by having understood its philosophyextend its possibilities and enrich it according to their will and imagination2Analysis - Synthesisanalyse a given pattern, a group of patterns or a drawing, separating them in smaller pieces, create procedures which produce these pieces unite them properly to produce the whole (eg.theater project) 2Approaching throughDifferent Waysuse given or self made procedures compose a whole, being approached through different ways (imagination, personnal judjement) during the composition, even if they begin with the same procedures4Recursive Proceduresbe introduced to the notion of recursiondo research on the numerical and harmonious correlations of the produced graphicsrealize the level of one's own intervention in the variety of the produced patterns4Control StructuresPosition of Recursionwork on the continuous repetition, reproduction of patterns, understand the need of controlling repetition, recursionapply the recursion on other problems (such as the motion in the natural environment)

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Hours Subject (8th grade) Objective
2 Basic Commands
Procedure Building
review of Logo environment, commands and functions
distinction between interactive and procedural environment
2 Procedures with Variables create, test, modify a procedure with variables
distinction between procedures that returns or not values
2 Tail Recursion
N-gons (I)
understand the notion of tail recursion
analyze and use the N-gons procedures, estimate the value of
variables
2 Control Structures
N-gons (II)
use tail recursion to produce complex shapes from elementary ones
use if as control structure, rotate and center N-gons (proc: Spingon)
2 Parameters of Recursion identify and recognize the basic N-gons that produces a complex one
2 The "Angle Guess Game" estimate the angle of an incrementing recursive N-gons
(with score 80% for the first prediction & 95% for the last one)
4 Polyspin Microworld use the procedures of the microworld
combine "initial pattern" & "generation rule" to produce a complex one
choose a shape, describe the stages to produce it, implement the final
procedure
4 Embedded Recursion
Recursive Trees
identify the tail & embedded recursion (variables, control structures,...)
create proper stop conditions
describe in details the binary tree procedure
describe the effects of using different parameters in tree procedures
2 Recursive Levels describe the effects of using different parameters in recursive patterns
create synthesis of recursive patterns
2 List Processing be introduced to list processing, basic commands
identify and perform elementary list operations
2 Lists & Recursion use recursive procedures to define, search, sort, change a list
2 "Knowledge Trees" describe, organize & exchange knowledge, having the form of
binary trees
Remarks
- The computational environment consists of personal computers with color monitors (DOS &
WINDOWS based PC-386) connected to a network via a server that manages and shares the
available hardware & software resources (LogoWriter 2.0, TC-Logo 1.0, MSW-Logo 3.3,
etc).
- Students work one hour per week in groups of three, aiming to a better result (rarely do their
work in couples which has proved to have created difficulties).
- The presentation of learning material takes place in the first quarter of the teaching hour.
Students use the remaining time to deal with the given tasks, using their worksheets
accordingly.
- The evaluation of their progress is achieved through both their worksheets and the results of
their work on the PC.
- The teacher takes an active part throughout the entire process, filling in, skilfully, the lack of
personal contact while students get oriented to the PC.

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Acknowledgements
We would like to thank Y. Agellakis for the literary care of this paper, E. Marouka for her contribution in the Alphabet Microworld, our students P. Christeas & V. Tsaousopoulos for the multimedia support and Th. Kontonatsios for the telecommunication support, during the preparation of Eurologo '93 Proceedings.
BIBLIOGRAPHY
Harold Abelson, Andrea DiSessa (1981), Turtle Geometry, the Computer as a Medium for Exploring Mathematics, MIT Press
Michael Burke, Roland Genise (1987), Logo and Models of Computation, An Introduction to Computer Science, Addison Wesley
Eduardo Calabrese, ed (1991), Proceedings of the 3rd European Logo Conference, Eurologo 91, A.S.I. Parma
James Clayson (1988), Visual Modeling with Logo, A Structured Approach to Seeing, MIT Press
Andrea DiSessa, Celia Hoyles, Uri Leron, Seymour Papert (1985), Logo 85 Theoretical Papers, Massachusetts Institute of Technology, Cambridge, July 1985
K. Dunkan, D. Harris, eds (1985), Computers in Education, Proc. of the IFIP TC 3 4th World Conference, North-Holland
Paul Goldenberg, Wallace Feurzeig (1987), Exploring Language, MIT Press
Dennis Harper (1989), Logo Theory & Practice, Brooks/Code
Brian Harvey (1985, 1986, 1987), Computer Science Logo Style: Vol 1: Intermediate Programming, Vol 2: Projects, Style and Techniques, Vol 3: Advanced Topics, MIT Press
Celia Hoyles, Richard Noss, eds (1986), Proceedings of the 2nd International Conference for Logo and Mathematics Education, University of London Institute of Education, London
Yannis Kotsanis, Constantinos Doukas, eds (1991), Proceedings of the 1st Conference on Educational Computing, Athens, Doukas School
Robert Lawler (1985), Computer Experience and Cognitive Development, A Child's Learning in a Computer Culture, Ellis Horwood.
Seymour Papert (1980), Mind-Storms, Children, Computers and Powerful Ideas, Basic Books, New York, (Greek Edition: "Νοητικές Θύελλες", 1991, εκδ. Οδςζζέαρ)
Gilberte Schuyten, Martin Valcke, eds (1989), Proceedings of the 2nd European Logo Conference, Eurologo 89, Gent
Gilberte Schuyten, Martin Valcke, eds (1990), Teacher Education in Logo-Based Environments, Commission of European Communities
Cynthia Solomon (1986), Computer Environments for Children: A Reflection on Theories of Learning and Education, MIT Press
Tipps S., T. P. Riordon, G. Bull (1984), Nudges IBM Logo Projects, Holf Rinehart & Winston
Sylvia Weir (1986), Cultivating Minds: A Logo Casebook, Haper and Row

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