integrating informatics into the curriculum

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269 Integrating Informatics into the Curriculum Rumen NIKOLOV Research Group on Education, bul. Vitosha 19, Sofia, Bulgaria Since 1979 a new curriculum and new methods of teaching, closely related to informatics and its applications have been explored in Bulgaria. This paper deals with a set of problems which could be used for introducing and acquiring some basic notions of informatics, e.g. 'cycle', 'recursion', 'coding'. Keywords: Integral Approach, Logo, Cycle, Recursion, Cod- ing. 1. Introduction Our children will live in a society, supplied with computers, robots and other devices based on new technologies. The most important task of the school is to prepare the pupils in such a way that they should not feel they are new-comers in the future society. This is the most important task of the Research Group on Education (RGE) at the Bulgarian Academy of Sciences and the Ministry of Education. Since 1979 the RGE has been ex- perimenting with a new curriculum and new meth- ods of teaching, closely related to informatics and its applications. Since 1982 the schools of the RGE have been supplied with microcomputers and software, based on the programming language Logo. Rumen Nikolov was born in 1955 in the town of Pernik, Bulgaria. He graduated from the Faculty of Mathematics at Sofia University in 1980, his speciality being Computer Sci- ence. In 1987 he has obtained a PhD in the field of Informatics and Education. Since 1982 he has been involved in the activi- ties of the Research Group on Education at the Bulgarian Academy of Sciences and the Ministry of Education. North-Holland Education & Computing 3 (1987) 269-274 2. Basic Goals of the Initial Teaching of Infor- maties The systematic teaching of informatics in the schools of the RGE begins at the fifth class (pupils 11 years old) and aims at: - acquiring fundamental skills and habits for work with microcomputers; - obtaining ideas about the present and the future applications of the computers; - acquiring skills and habits to use software tools within various fields of application; - acquiring basic programming notions, princi- ples and methods; - acquiring and using the basic Logo construc- tions; - using the computer as a tool for solving problems from various subjects and activities; - becoming familiar with some basic informa- tion structures and applying them effectively when solving various problems; - learning to look for reasonable applications of the computers in activities close to the pupils' interests. The goals of the initial teaching of informatics correspond to the leading principle of education in the RGE activity--an integral approach to the acquiring of knowledge [1,2,3]. This principle can 0067-9287/87/$3.50 © 1987, IFIP

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269

Integrating Informatics into the Curriculum

Rumen N I K O L O V Research Group on Education, bul. Vitosha 19, Sofia, Bulgaria

Since 1979 a new curriculum and new methods of teaching, closely related to informatics and its applications have been explored in Bulgaria. This paper deals with a set of problems which could be used for introducing and acquiring some basic notions of informatics, e.g. 'cycle', 'recursion', 'coding'.

Keywords: Integral Approach, Logo, Cycle, Recursion, Cod- ing.

1. Introduction

Our children will live in a society, supplied with computers, robots and other devices based on new technologies. The most important task of the school is to prepare the pupils in such a way that they should not feel they are new-comers in the future society. This is the most important task of the Research Group on Education (RGE) at the Bulgarian Academy of Sciences and the Ministry of Education. Since 1979 the RGE has been ex- perimenting with a new curriculum and new meth- ods of teaching, closely related to informatics and its applications. Since 1982 the schools of the RGE have been supplied with microcomputers and software, based on the programming language Logo.

Rumen Nikolov was born in 1955 in the town of Pernik, Bulgaria. He graduated from the Faculty of Mathematics at Sofia University in 1980, his speciality being Computer Sci- ence. In 1987 he has obtained a PhD in the field of Informatics and Education. Since 1982 he has been involved in the activi- ties of the Research Group on Education at the Bulgarian Academy of Sciences and the Ministry of Education.

North-Holland Education & Computing 3 (1987) 269-274

2. Basic Goals of the Initial Teaching of Infor- maties

The systematic teaching of informatics in the schools of the RGE begins at the fifth class (pupils 11 years old) and aims at:

- acquiring fundamental skills and habits for work with microcomputers;

- obtaining ideas about the present and the future applications of the computers;

- acquiring skills and habits to use software tools within various fields of application;

- acquiring basic programming notions, princi- ples and methods;

- acquiring and using the basic Logo construc- tions;

- using the computer as a tool for solving problems from various subjects and activities;

- becoming familiar with some basic informa- tion structures and applying them effectively when solving various problems;

- learning to look for reasonable applications of the computers in activities close to the pupils' interests.

The goals of the initial teaching of informatics correspond to the leading principle of education in the RGE act ivi ty--an integral approach to the acquiring of knowledge [1,2,3]. This principle can

0067-9287/87/$3.50 © 1987, IFIP

270 R. Nikolov / Integrating Informatics into the Curriculum

be best performed by the means and methods of informatics.

3. Our approach

The classical approach to using Logo is based on Turtle graphics and fist-processing. This ap- proach has been borne in mind both in the textbooks of informatics [4,5] and in the corre- sponding software. In order to carry out the basic goals of the initial teaching of informatics in the RGE schools we had to create a uniform language environment, covering wider applications of com- puters. Logo extensions for programming of music, drawing, animation, textprocessing and training games have been developed. A Bulgarian version of Logo was developed as well. We are going to make a language extension for manipulating different kinds of training robots and robotized toys. The variety of problems that could be solved using the Logo environment has been shown in the textbooks in informatics. This enables us to create a suitable learning environment in which every pupil should be motivated to work with computers. We do not think that all pupils should become good programmers but everybody should be given the chance.

In order to illustrate what was said above we propose a set of problems which could be used for introducing and acquiring some basic notions of informatics, e.g. cycle, recursion, coding.

3.1. Cycle

The cycle is one of the basic programming notions. It can be introduced and used when solving problems, demanding repetitive actions to be programmed. The problems should correspond to the pupils' individuality.

3.1.1. Drawing geometric figures Turtle geometry proposes a variety of prob-

lems, suitable for introducing the notion cycle. The experience of using Logo shows that Playing turtle--a game in which the pupil identifies him- self with the turt le--contributes to the intuitive acquiring of a given geometric notion. The follow- ing problem (a jocular story) can be a good reason to take part in such a game:

Figure 1.

The testament of the old pirate:

. . .you will find a high tree. Stand in front of the tree and turn to the north. Go forward 5 km and turn to the right 60 degrees. Having executed these operations 6 times you will get to the place where the treasure has been buried.

The quick-witted will find the treasure at once. To save walking one could also use the following procedure, where 1 step = 100 meters, whose ef- fect is shown in Figure 1.

TO SEEK REPEAT 6[FORWARD 50 RIGHT 60]

END

But everybody should realize that the naive treasure-hunters would hardly succeed.

A well exploited example is to find out a proce- dure for describing a circle. How does one go over the contours of a circle? A little bit forward, a tittle bit to the right, a little bit forward, a little bit to the right . . . . Here is the corresponding proce- dure, which produces Figure 2:

TO CIRCLE REPEAT[360 FORWARD 1 RIGHT 1]

END

Figure 2.

R. Nikolov / Integrating Informatics into the Curriculum 271

3.1.2. Modelling A good way to become familiar with the notion

of a cycle is to solve problems in which a physical interpretation of graphics commands is de- manded. Such an example is the modelling of a rectilinear uniform motion:

TO MOVE :T :V REPEAT :T[FORWARD :V]

END

When executing the procedure MOVE with in- puts 5 and 100 respectively the turtle will move 100 (computer) seconds with velocity of 5 steps/s.

Similarly a uniformly accelerating motion can be modelled:

TO ACCELL :VO :T :A MAKE "V :VO REPEAT :T[FORWARD :V MAKE "V :V+ :A]

END

This project can be extended further. For in- stance one could make the models more realistic by adding suitable pictures as a background to the motion. A picture-editor can be used for this purpose. By means of a shape-editor one can draw different objects--cars, trucks, rockets, ships. De- pending on the problem which pupils have to solve they could then change the shape of the turtle, or even introduce more than one moving object. The program could be edited so as to print a result--e.g, the covered distance.

Other physical phenomena, for instance mea- suring the time, could be modelled too. The cyclic nature of the clock hand motion is intuitively clear to every pupil. This can also be cleverly used to make the notion cycle more familiar. Consider the example:

TO DAY REPEAT 24[HOURI

END TO HOUR

REPEAT 60[MINUTE] END TO MINUTE

REPEAT 60[SECOND] END TO SECOND

RIGHT 6 END

ter, a cuckoo clock, and a chess-clock being devel- oped.

3.1.3. Music Pupils who have a particular interest in music

would possibly best acquire the notion of cycle by programming appropriate tunes, such as the one shown in Figure 3. Here is the same tune ex- pressed in Logo:

TO SONG REPEAT 2[TUNE]

END TO TUNE

PLAY[F1 G1 A1 F1 F1 G1 A1 F1 A1 B1 C2 A1 B1 C2 C2 D2 C2 B1 A1 F1 C2 D2 C2 B1 A1 F1 F1 C1 F1 F1 C1 F 1 ] [ 4 4 4 4 4 4 4 4 4 4 2 4 4 2 8 8 8 8 4 4 8 8 8 8 4 4 4 4 2 4 4 2 ]

END

Furthermore, the computer could play as a street-organ:

TO GRIND :N REPEAT :N[TUNE]

END

3.1.4. Animation All pupils are fond of animated cartoons. What

a pleasant challenge it would be for them to make such a movie by themselves, say one called The dancing little man. The consecutive poses of the man being drawing are shown in Figure 4. The program for animating the man is easy to write:

TO DANCE :N REPEAT :N[FIGURE]

END TO FIGURE

SETSHAPE :POSE1 SETSHAPE :POSE2 SETSHAPE :POSE3 SETSHAPE :POSE4 SETSHAPE :POSE5 SETSHAPE :POSE6

END

The project The dancing little man could be enriched by a suitable background and new danc- ing figures, the dance to be synchronized with music and so on.

3.2. Recursion

This project could also be extended and en- riched, e.g. a procedure for decelerating could be added in order to make the clock keep real time, leading to programs for an electronic chronome-

Recursion is one of the most complicated pro- gramming notions. All the same, pupils could acquire this notion intuitively and write recursive procedures (although of the simplest possible kind)

272 R. Nikolov / Integrating lnformatics into the Curriculum

eA

Figure 3.

provided that the problems to be solved involve programming of some recursive phenomena. For this purpose many of the problems for introducing cycle could be used.

3.2.1. Getting into orbit In order to simulate a rocket moving into a

circular orbit one should not use the procedure CIRCLE for drawing a circle. This motion is better described by the following procedure:

TO ORBIT REPEAT 360[FORWARD I RIGHT 1] ORBIT

END

It is clear that the procedure can be shortened:

TO ORBIT FORWARD 1 RIGHT 1 ORBIT

END

Further the procedure ORBIT can be modified in a natural way in procedures describing a mo- tion in orbits of different kind:

TO SQ.ORBIT :SIDE FORWARD :SIDE RIGHT 90 SQ.ORBIT :SIDE

END TO POLY.ORBIT :SIDE :ANGLE

FORWARD :SIDE RIGHT :ANGLE POLY.ORBIT :SIDE :ANGLE

END

Figure 4.

3. 2.2. Inertial motion To write a program in order to simulate the

motion of bodies under their own momentun is a good reason to meet recursion:

TO INERTIA :V FORWARD :V INERTIA :V

END

3.2.3. An eternal clock The programs producing an electronic chro-

nometer and a clock can be easily transformed into programs for an eternal chronometer and an eternal clock [6]. The recursive motion of the second hand could be described as follows:

TO HAND SECOND HAND

END

3.2.4. Listening to a gramophone which is out of order

It happens sometimes that due to some damage the gramophone plays a tune fragment over and over again. This recursive playing can also be described by a recursive procedure:

TO D.C.AL.FINE TUNE D.C.AL.FINE

END

where T U N E is a procedure for performing an arbitrary music fragment.

3.2.5. Marathon dance The animated cartoon The dancing little man

could be projected without limitation if one uses

R. Nikolov / Integrating Informatics into the Curriculum 273

the procedure:

TO M A R A T H O N . D A N C E F I G U R E M A R A T H O N . D A N C E

END

3.2.6. An endless fairy-tale Endless fairy-tales are very popular among

pupils. An interesting task would be to make the computer tell such stories, e.g:

TO FAIRLY.TALE PRINT [THE F I S H E R M A N C A U G H T A G O L D

FISH] PRINT [AND IT AS KE D HIM: " L E T ME GO AND] P R I N T [I W I L L F U L F I L T W O WISHES OF

YOURS." " O . K " - ] PRINT [ANSWERED THE F I S H E R M A N A N D LET

THE FISH GO.] WISHES

E N D TO WISHES

PRINT ["MY FIRST WISH IS TO GET A G O L D COIN.]

P R I N T [MY SECOND WISH IS T H A T Y O U FULFIL]

PRINT [TWO WISHES OF MINE:"] WISHES

E N D

3.2. 7. Further projects It is very important to become familiar with the

notion of recursion especially when using Logo. Having obtained an intuitive idea of the notion, the pupils will understand that the solution of many problems becomes easier if described in terms of recursion. The rest can be left to the computer. The only thing to be done is to describe how the solution of a given problem can be re- duced to the solution of a simpler one, and when the computer is to stop the recursive execution. For instance:

TO G C D :A :B IF :B = 0 T H E N O U T P U T :A O U T P U T G C D :B R E M A I N D E R :A :B

E N D TO L E N G T H :WOR D

IF :WORD = " T HE N O U T P U T 0 O U T P U T 1 + L E N G T H BUTFIRST : W OR D

E N D

3.3. Coding

Coding is a basic notion in informatics. To become more familiar with it the pupils should obtain a more general understanding of it. This

Figure 5.

could be achieved by solving problems from different fields of interest to them. Here is an old music problem of such a kind:

In the fragment given in Figure 5 a great composer has coded his name. Who is he [7]?

Knowing the latin notation of the notes (which is the same as in the Logo extension for music) one could easily guess that the composer is BACH.

Other interesting problems are connected with the coding and decoding of messages by using the Sherlock Holmes code Dancing figures [8] shown in Figure 6.

Afterwards the figures could be made to dance by using animation.

Messages can be coded using the ASCII code but with a certain shift. Here is a procedure of this kind:

TO CODE :STRING IF :STRING = " T H E N O U T P U T " M A K E SYMB FIRST :STRING M A K E " C O D E (ASCII :SYMB)+ 13 IF :CODE > 90 THEN M A K E " C O D E 64+

( : C O D E - 90) M A K E "NEW.SYMB C H A R :CODE O U T P U T W O R D :NEW.SYMB CODE BF :STRING

END

4. H ow can one learn some Bulgarian

Learning by doing is one of the greatest educa- tional advantages of Logo. If the pupils take part in a project and refine and enrich it, many goals of the initial teaching of informatics could be achieved. A project of this kind is to teach the computer a foreign language--say an English speaking one to understand Bulgarian. This will motivate pupils too to begin learning a foreign language. One could start with the translation of the basic commands of Logo:

TO HAHPE~ :SIZE F O R W A R D :SIZE

E N D TO HA/IMCHO :ANGLE

R I G H T :ANGLE E N D

274 R. Nikolov / Integrating Informatics into the Curriculum

Figure 6.

The computer could be taught to understand and illustrate in an appropriate way whole

sentences:

"Can, mteTo ~arp~raa." (The sun is rising.) "KauT~r~T Jaa~a." (The stone is falling.) "FiTmIaTa nee." (The bird is singing.) "Caon~T 6ara." (The elephant is running.)

The syntax of these sentences is the following: (noun)(verb) . Using the shape-editor the pupils draw objects corresponding to the nouns. The p r o c e d u r e s C J V b H I I E T O , K A M ~ b K ~ b T , I I T H I I A T A and CJIOH~bT are supposed to change the shape of the turtle, while the proce- dures H3FPHBA, IIA]IA, I IEE and BHFA il- lustrate the action corresponding to the verb. Afterwards every one of the above sentences could be illustrated on the screen.

The project can be enriched further, involving sentences which reflect different phenomena from reality. Every pupil will find his own topic for conversation with the computer. A program gener- ating random sentences and illustrating them rep- resents a good test of the pupil's knowledge of the

language.

5. The final Big show

Everyone is proud when winning public recog- nition, the more so the pupils. A Big Logo show,

organized at the end of the term or the year would give the pupils additional stimuli for work. The best individual and collective programs could be presented in front of a large and appreciative audience--schoolmates, parents, friends.

Acknowledgement

The research is supported financially by the Committee of Science at the Council of Ministers of Bulgaria under the contract No. 554.

References

[1] CemloB, Ba. ~ zlp. (1982), lip~n~m~ B pa6oTaTa Ha lIFO, paroTeH aoKy~en'r FIFO, CoOp~.

[2] Cen~on, Bn. ~ ~p. (1980), Kum-a aa ym~Te.~ aa ory~em~eTo B r,~,pBK maac lIFO, Codpml.

[3] Coa/IoB, Ba., HoBa~oBa, P. (1983), Ea~ a MaTeMaTm~a FIFO, Codpm~.

[4] HmcoJloB, P. (1983) JIOFO. F_xc~epm~elrraneH yqe6max FIFO, Codp~t~.

[5] Hnxonoa, P., Cenaoaa, E. (1985), Eam~ ~ MaTeuaTmca, JIOFO-2 liFO, CoqbH~.

[6] Nikolov, R., Sendova, E. (1985), Informatics Textbooks for Beginners, International conference "Children in an infor- mation age: tomorrow's problems today", Varna, Bulgaria.

[7] Hofstadter, D. (1979), GSdel, Escher, Bach: an Eternal Golden Braid (The Harvester Press).

[8] Jacobs, H. (1970), Mathematics. A Human Endeavour, (Freeman, San Francisco).