"Hour of Code": Back to the roots... [1987-1993]

1

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: [email protected]

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

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)

Hours Subject (4th grade) Objective

1 Lab Operating Instructions name parts of computer

identify groups and codes, connect to the network, use basic keys

2 Basic Turtle Commands (I) move, turn the turtle, estimate (elementary) distances, angles

2 Basic Turtle Commands (II)

Picture Management

use penup, pendown and movement to any position

color, fill the shapes and the background

load, modify, save pictures

4 Drawing Project (I) draw,maintain, print a complete picture

analyse (elementary) the stages for the construction

use different shapes and stamps

2 Basic Geometric Figures draw squares and rectangulars, estimate distances, angles (of 90o)

protect pictures from unwanted changes

2 Drawing Project (II) draw freely a project related to a season, adding small text

3 Project with Preparation prepare the desired drawing and shapes

precalculation of distances (the EEC-Flag project)

4 Repetition draw regular polygons and circles (using repeat)

4 Animation create animation using different shapes as turtles

create animation using pen exchange technique

2 Writing, Typing a Text write, modify small texts on the pictures

use editing keys and punctuation marks

2 Procedure introduce to name, write and execute procedure for simple shapes


2 Turtle Commands draw simple shapes, use pen-background colors

erase, stamp, fill, shade and use of different shapes

2 File Management load, modify, save, print pictures

use function keys

2 Turtle Project choose, describe, implement pictures

2 Drawing Geometric Figures draw triangles, squares, rectangulars

4 Repetition draw regular polygons and circles (using repeat)

understand "total turtle trip theorem"

choose and implement a given composition of polygons

2 Animation create animated graphics (using different shapes and repeat)

2 Writing, Typing Text use word processing capabilities to add texts on the picture

2 Production of Drawings use interactive commands and record them on worksheets

2 Procedure Definition use the editor to name, write and execute a procedure

mark and copy the interactive commands into a named procedure

2 Debugging Process detect "errors" of procedures, edit and correct them (using slowturtle)

2 Editor Exploitation full use of editor capabilities to write and modify procedures

2 Modular Analysis choose, describe a drawing on a worksheet

implement by stages

2 Super/Subprocedures Building write procedures that call others

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4 Procedure-Subprocedure

Building

create, test, modify a procedure

use it as subprocedure within another procedure

4 Procedure Combinations use student completed procedures and combine them to create regular

geometric figures and free designs

4 Turtle Geometry

(with Euclidean Geometry

Elements)

familiarize with heading identify themselves with turtle-body

discover the relation between number of sides and angles of shapes

identify similarity, symmetry

identify divisors, multiples, complementary/supplementary angles

experiment with circles and arcs

4 Animation - Sound Project

(Multiple Turtles)

draw using predefined shapes

enrich drawing with animated graphics and sounds

4 Procedures with Variables comprehend the use of variables and their effect on making flexible

procedures

4 Variable Shapes Building experiment with increments and decrements (grow and shrink) in

parametric procedures


4 Alphabet Microworld (I) use and combine elements of the Turtle and Euclidean Geometry

find out the "symmetry" and the "similarity" as notions, by incrementing

and decrementing patters, maintaining the proportions

4 Alphabet Microworld (II) understand effortlessly mathematical notions and numerical

correlations by varying and trying different variables in given

procedures

4 Microworld Enrichement create similar or different procedures by using the given Microworld

and by having understood its philosophy

extend its possibilities and enrich it according to their will and

imagination

2 Analysis - Synthesis analyse 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)

2 Approaching through

Different Ways

use 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

procedures

4 Recursive Procedures be introduced to the notion of recursion

do research on the numerical and harmonious correlations of the

produced graphics

realize the level of one's own intervention in the variety of the

produced patterns

4 Control Structures

Position of Recursion

work on the continuous repetition, reproduction of patterns, understand

the need of controlling repetition, recursion

apply the recursion on other problems

(such as the motion in the natural environment)

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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.

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