Informatics in Logo for High School Alexandra Yudina Moscow State Fifty Seventh School, Moscow ORT Technology School 7, Kuusinena, apt. 95, Moscow, 123308, Russia email: [email protected]

Abstract In Russian schools Logo environments are almost exclusively in the hands of Informatics teachers. Therefore, the important way to get the educational benefit of Logo pedagogy is to develop Logo courses of Informatics. The paper describes the Logo course of Informatics for high school that has been used in many of Russian schools for several years. A characteristic distinction of the course is that it is based on the special system of tasks. This system provides a rapid and suitable way for students to gain experience in solving problems and then introduce them to research activities in the fields of mathematics, physics and informatics.

Keywords: Logo in high school, system of tasks, exploring activity

1.Informatics in Russian schools

Informatics is a separate subject in Russian schools. As a rule, all computers in a school are installed in a computer lab (or labs). These labs are mostly used for teaching Informatics. Only a small number of schools use computers for teaching other school subjects. In Russian schools teaching is still based on a strong separation of subjects. Therefore, the only person in an ordinary school who can introduce progressive ideas and bring in new approaches related to applying computers in education is a teacher of Informatics. Whether or not to use Logo is a decision of each individual teacher. The important way to get the educational benefit of Logo pedagogy is to develop Logo courses of Informatics. Informatics as a compulsory subject was established in Russian schools in mid-80s. At that time, the function of the new subject was to disseminate ‘computer literacy’. The subject was supposed to focus on teaching programming. Attention was also paid to fundamentals of hardware and to such topics of computer science as number systems and Boolean logic. At the beginning, for about 10 years, the content of the course remained nearly the same. However, rapid development of hardware and software caused gradual changes in the educational content of the subject. By mid-90s, the meaning of words ‘computer literacy’ had changed. It became clear that everybody does not need to be a programmer, and, on the other hand, user skills are of great importance for future employment of students. By that time Russian educational system had been to a great extent decentralized. Schools were allowed to determine curriculum on their own to some degree. In schools with well-equipped computer labs Informatics began to transform from programming to making computerized documents. No doubt that from the merely utilitarian point of view studying Windows and Microsoft Office is very useful for students. But if the focus in class is on user skills only, main educational possibilities of computer remain untouched. This question sparkled a lively discussion on the pages of pedagogical periodicals; the debates resulted in developing and setting up the State Minimum Curriculum in Informatics. It covers the following main topics:

165 Information (concept, representation, transmission, storage, processing); Number systems and Boolean logic; Computer (main components, their functions, system software); Algorithms and programming; Modeling and simulation; Information technologies (text and graphic editors, spreadsheets, data bases); Networks and Internet. The compulsory course is to cover at least 68 hours (for example, in 10th grade, two hours a week). However, schools with computer labs usually extend the course and determine at which stage it would be best started (grades 7-9 or 10-11). Every school has the right to compose its own, individual curriculum in accordance with the local features – human conditions and equipment. But it should be based on the requirements of the Minimum Curriculum. There are several recommended textbooks which introduce different approaches to the course. Informatics teachers can build up their own sequence of topics and select learning materials and kinds of activities that they think are most suitable for their students. On the whole, in the framework of the Informatics curriculum, computer is considered mainly to be a practical instrument and an object of study. It is only to a little degree that computer is regarded as an exploratory tool or a universal laboratory, and never – as a tool that gives the learner better opportunities to construct knowledge.

2. Informatics in Logo

Logo appeared in Russian schools in early 90s. Applying it was not closely connected with the standard curriculum. Logo lay outside the educational mainstream. One of the main difficulties in Logo implementation was shortage of literature for teachers. Usually Logo was applied in ‘after class’ activities and mainly in lower grades of secondary school. This means that children just had fun playing with the turtle and then, in 8th or 9th grade they were to study Basic as ‘serious’ informatics topic. Logo potential remained unemployed. I have been using Logo environments in class since 1990. The experience of work with Logo in high school has convinced me that Logo is an adequate instrument for informatics teacher. Several years of using Logo in teaching practice had resulted in a course for high school students. The first variant of the course was published in 1995. It was appreciated by Informatics teachers and then adopted by officials. The last edition of this course titled ‘Informatics in LogoWriter’ was published in 1999. The edition included two books: the textbook and the teacher’s guide. Russian Ministry of Education has recommended the textbook for a core course. In this article I am going to describe the course and to propose examples of teaching materials. Initially the course was intended for those teachers who applied LogoWriter only. Then MicroWorlds, MSWLogo, and even Control Lab appeared in Russian schools. Presently I am preparing my next book for informatics teachers, which is based on experimental work in Moscow State Fifty Seventh School and Moscow ORT Technology School. Some of the examples given below are taken from this book. Logo-related materials in most cases are collections of project ideas and project descriptions. The proposed Logo course, on the contrary, is based on well-defined sequence of problems. This decision was motivated by several factors. As has been mentioned above, teachers have a choice among several textbooks with different approaches to teaching Informatics. To win recognition of teachers, an author of a new schoolbook should take into account a number of factors: how to motivate students, satisfy parents, meet requirements of standards, fit with the interests of administrators. But first of all, teaching materials should be well elaborated and convenient for everyday teaching practice.

166 Advantages of the project-oriented method are well known. However, it is not widespread, especially in high school. Project approach confronts rigid timetable of regular classes in Informatics. Students usually have one or two lessons a week; the curriculum is vast, so the lessons should be managed in an intensive manner. The project-oriented method cannot make sure the curriculum would be fully covered. Limitations imposed by project scenarios represent additional difficulties for teachers, who would prefer a more systematic introduction of the Informatics topics. In most cases, teachers prefer to know exactly what they have to do in class this week, next week, and so on … How to overcome these difficulties and make it easier for Logo approach to find the way into high school? A possible answer is to develop a special system of problems that would serve as some kind of a ladder both for teachers and students: a simple problem – a micro project – a mini project – and, maybe, large and complex project in the end.

3. System of Logo tasks

The system is intended for a course of Informatics arranged for three years – 8th, 9th and 10th grades – with two lessons per week, i.e. 68 hours a year. A significant part of lessons is devoted to Logo activities that cover a number of Informatics topics and provide the integration with other school subjects: geometry, algebra and physics. The Logo book for students is a textbook and a book of problems at the same time. It is divided into small sections containing all the needed explanations and examples as well as a series of tasks at the end of each section. So a teacher has no need to explain new material at every lesson to the whole group of students. Students as a rule work at the computers performing the tasks one after another at their individual pace according to their abilities and background. Thus a teacher’s role is to look after the process of solving problems, to be an expert and an adviser, to facilitate discussions.

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th 8 grade (50-55 lessons)

Turtle geometry Procedures 72 tasks Parameters Students master Logo tools Variables, loops User input, conditional branches 55 tasks Recursion

th 9 grade (20-25 lessons)

Drawing graphs of functions 42 tasks Modelling different kinds of motion 23 tasks Students apply Logo tools toward

the explorations th in the fields of math, physics and 10 grade (15-20 lessons) informatics Words and lists 12 tasks

Tasks connected with data representation 22 tasks (coding systems that represents numbers, characters, graphics, sounds inside a computer)

Table 1: System of tasks The first three parts of the system contains only graphic tasks. These parts play an important role in the course. A detailed description of these parts given below illustrates the suggested approach to teaching Informatics.

4. At the first stage students should gain experience of solving problems

1. Turtle geometry

Figure 1: Sequence of tasks from the Chapter 1 of the textbook

Students learn to describe a simple algorithm in sufficient and complete detail so that it can be performed precisely by another person or device.

168 At the same time they are engaged in geometrical explorations. This gives an appreciable support to the students in their studies of traditional geometry.

2. Procedures

Figure 2: Sequence of tasks from the Chapter 2

Students learn to analyze a problem, to subdivide a task into subtasks, to plan program’s structure before writing program, to write well-structured programs. The following scheme is taken from the teacher’s guide. It explains and illustrates the possible ways of performing the tasks. However the teacher should encourage the students to invent their own solutions.

Level I Level II Level III

Figure 3: ‘Constructing’ different shapes from semicircles

The tasks for this chapter were selected meaningly to convince learners that structuring is the best way. These tasks can hardly be performed in ‘spaghetti’-style. One of the first tasks is the ‘Chessboard’. The following scheme and the program are taken from the teacher’s guide. This task is a deep argument for modularizing programs.

169 Level I Level II Level III Level IV

Figure 4: One of the possible ways of ‘building up’ the chessboard

to SQUARE Level I setc 9 repeat 4[fd 30 rt 90] rt 90 fd 30 lt 90 end to SQUARE+ SQ Level II lt 45 pu fd 10 pd setc 5 fill bk 10 rt 45 end to ROW1 Level III repeat 4 [SQUARE SQUARE+] pu fd 30 lt 90 fd 30 * 8 rt 90 pd end

to ROW2 repeat 4 [SQUARE+ SQUARE] pu fd 30 lt 90 fd 30 * 8 rt 90 pd end to BOARD repeat 4[ROW1 ROW2] Level IV end

3. Parameters

Students learn to identify the main parameters of an object or a process and to control them.

Figure 5: A series of similar tasks from the Chapter 3

The figure shows the tasks in which similar building blocks – polygons – are used. These blocks are procedures with one input; the input is the length of the polygon’s side. Primarily the students should define and use procedures with one input, then with two and three inputs. This activity claims ‘transfer from

170 concrete to abstract’ and vice versa thus promoting the development of students’ abilities to generalization and classification. The following fragment from the teacher’s guide shows the way of solving the three last tasks in the chapter. The latter should be a procedure with three inputs. to CURL :S fd 3 * :S rt 90 fd 3 * :S rt 90 fd 2 * :S rt 90 fd 1 * :S rt 90 CURL 30 fd 1 * :S lt 90 fd 1 * :S lt 90 fd 2 * :S lt 90 fd 3 * :S lt 90 RANGE 10 7 end RANGE 7 10 to RANGE :S :N repeat :N[CURL :S] end to FRAME :S :width :height repeat 2[RANGE :S :width rt 90 RANGE :S :height rt 90] end

FRAME 10 11 5 FRAME 6 15 5 Figure 6: Greek ornament as a procedure with three inputs

5. From separate tasks to trial research

The described three chapters of the textbook contain 72 tasks. It takes usually about 20-25 lessons for every student to perform all of them. The system of tasks provides a rapid and suitable way for students to gain experience of solving problems. At this stage diversified opportunities of the Logo environment should not distract students. The number of technical details was minimized in this part of the textbook; only 15 Logo commands are needed for performing all the tasks. The next three chapters are devoted to traditional programming tools: variables; assignment, input and output operations; loops and recursion. Students should perform 55 tasks; usually it takes about 25 lessons to fulfil the work. The described set of tasks really represents a system because there are multiple interconnections between the tasks. The problems are coming in such a way that many of previous ones could serve as building blocks for the next ones. Although all the students perform the same tasks, their results differ in appearance. The way in which most of the tasks are formulated gives children enough opportunity to express their creativity. Step by step the complexity of the tasks increases; they gradually expand into small projects. Teachers are supposed to use the sequence of Logo tasks as a skeleton for a variety of activities in the framework of Informatics curriculum. One of the most important for high school activities is a training investigation. At the following stages of the presentational course students should carry on a number of simple investigations; three of them are described below.

171 Typically, every project is built in three stages. Firstly, a model should be built; i.e. Logo program is to be written. Then the model become an object of exploration: students run the program varying parameters, collect and interpret the results; hypothesize possible relationships between inputs and outputs; find out regularities. At last, students should make up a report with formulas, illustrations, graphs; or create a multimedia presentation. This kind of class work provides a close integration of a number of activities: modelling; programming; text processing; Web design; working with multimedia, and so on.

Exploring triangles in 8th grade

Students should produce a program that constructs a set of right triangles. The length of the hypotenuse should be constant and the angle should vary. Then students are offered to output the quotient of one of the legs to the hypotenuse for every triangle and to formulate how this quotient varies with the angle value. After this students transfer their results from the MicroWorlds project page to a MS Word document. Then students prepare a presentable report with illustrations, the numerical data placed into a table and conclusion.

Figure 7: Results of the work on MicroWorlds project page

to tri :angle seth 90 lt :angle fd 200 make "b ycor pr (se [A=] :angle [b=] :b [b/c=] :b / 200) sety 0 setx 0 end

to triangles make "angle 5 repeat 17 [tri :angle make "angle :angle + 5] end

Drawing graphs in 9th grade

Students should produce a program for drawing a graph of preset function. Then they draw different sets of graphs having some common characteristic. The pictures should be imported into MS Word document. Then students make up a report; they are to specify common formula of the whole set and formulae for every curve.

172 Another type of activity is related to Web design. Students create ‘live’, animated graphs and put the GIF- animation into Web page. Firstly students write additional Logo program that produces a series of images and saves each graph into separate file. The program must increase or decrease one of the coefficients over some range. Then students work with Microsoft GIF animator assembling their movies. The last stage of the work is making a Web page.

Figure 8: A set of parabolas with fixed zeros on the MicroWorlds project page and in MS Word document

to graph :F setsh 13 make "x -350 / scale repeat 700 / (step / 10) [make "y run :F dot :x * scale :y * scale make "x :x + (step / 10) / scale] end

to dot :x :y if and :y > -200 :y < 200 [pu setx :x sety :y pd stamp] end

Figure 9: Several tasks from the Chapter 7

Encoding images and sounds in 10th grade

Learning about coding characters, images and sounds students create programs which load external files, treat them as very long words and save transformed sequences of characters into new files. One of the tasks is to write a program that inverts black-white BMP file. The second example is a small project ‘Sound editor’. WAV file is to be loaded; then its ‘sound shape’, i.e. graph, is to be drawn. Then a number of transformations of the sound can be performed. In fact, students explore different coding systems.

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Figure 10: A fragment of the ‘Sound editor’ page with reversed WAV file

6. Conclusion

The described three year course of Informatics for high school is based on Logo environments: LogoWriter, MicroWorlds, MSWLogo. On the whole, Logo activities cover about 50 % of class time. Sequence of Logo tasks serves as a skeleton for a variety of activities related to different topics of Informatics curriculum and provides the integration with other school subjects. The ‘task-oriented’ approach is convenient for teachers because at the beginning they have enough time to become more familiar with Logo in the classroom and its potential for learning. Everyday work with the described system of Logo tasks gives the teachers a deeper understanding of Logo and confidence in using the software. Teachers can plan their work in advance. The elaborated sequence of tasks provides an intensive character of learning process and stable motivation. The tasks are attractive and interesting both for students and teachers, all off them lie within an average students powers. Step by step the tasks expand into projects. The trend is to engage students in making small investigation. Thus the described course bridges the gap between traditional methods of teaching Informatics and project- oriented approach. The described book for students and the teacher’s guide received positive response from informatics teachers. The author hopes that Logo would be increasingly used at high school level and more and more informatics teachers would consider Logo as the most suitable instrument for their own work.

References

Yudina A (1997) Research projects in Logo for high school students Proceedings of the Sixth European Logo Conference 141-153 Yudina A (1999a) Informatics in LogoWriter Mnemozina, Moscow (In Russian) Yudina A (1999b) Teacher’s guide for the textbook ‘Informatics in LogoWriter’ Mnemozina, Moscow (In Russian)

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