Informatics in Logo style: Today
Informatics in Logo style: Today
 Darina Dicheva
Faculty of Mathematics and Informatics,
University of Sofia
e-mail: darinad@fmi.uni-sofia.bg

Abstract: This paper is an attempt to discuss the benefits and shortcomings of using Logo based on the recent Logo related research and practice. It reflects the Bulgarian experience in teaching and using informatics in a Logo context.

1. Introduction

The title of this paper suggests presenting an overview of learning and teaching in a Logo context. This may sounds rather assuming. However, the current research and practice in relation to Logo is so developing, so diverse, so widespread that giving an overview would be doomed to failure beforehand. This presentation does not pretend to give the overview. It is rather an attempt of the author to discuss the benefits and shortcomings of using Logo based on the Bulgarian research and experience in teaching and using informatics in a Logo context and on the presentations at the recent Logo conferences.

2. Logo today

2.1. Logo - Philosophy

Logo language, developed by Seymour Papert at MIT, is based on the philosophy of discovery learning. The turtle is used as an object to think with while the user is playing with Logo. The emphasis is on exploring, experimenting, experiencing, and acquiring powerful ideas that relate to mathematical concepts and problem solving strategies simply by way of discovery (Papert, 1980). Papert's work on Logo language was greatly influenced by Piaget's theories about child development and learning processes at various stages of development. According to Papert, Peagetian learning is learning without being taught or learning without a curriculum. Children instead build their own intellectual structures through interaction with the environment (the Logo environment in this case).
In his famous book Mindstorms. Children, computers, and powerful ideas Papert advocated Logo learning in children on the basis of two major hypothesis: Moreover, according to the self-discovery approach, which supports the constructivist view of learning, Logo programming skills can be acquired in the same natural and spontaneous way in which the child learns to speak.
What the experience with Logo shows fifteen years later? If we look in the Proceedings of the European Logo conferences we could get a pretty informative picture of the current state of research, use, and new implementations of Logo.

2.2. Logo - Research

A good number of studies have been carried out aiming at testing Papert's two hypotheses. A series of those investigations based on Papert's self-discovery pedagogy did not report any supporting evidence for a cognitive effect of Logo learning (De Corte & Verschaffel, 1989). In fact the discovery approach wasn't rejected but instead was questioned. Consequently the view that the acquisition of the programming skills would somehow happen to the children due to the unique characteristics of Logo language (Leron, 1985), was largely abandoned, and a broad consensus emerged that Logo environments - while still stimulating students own construction of their knowledge and skills - should at the same time provide systematic guidance and mediation to support their acquisition of problem solving skills in programming, and possibly their transfer to other domains and situations (De Corte, 1993; Noss & Hoyles, 1992). Consequently, lots of research efforts have been put in investigating issues related to effective teaching, learning, and using Logo and Logo-based environments.
An expending tendency in the recent Logo research is the development of Logo-based microworlds. Though the concept of microworld is a key notion in the Logo approach, this notion seems to be rather vague and its definition varies with the different authors. For example, for Lawler (1987), they are virtual worlds for creative actions, Papert (1987) insists on the notion of transitional object, that help to manipulate abstractions. Valcke (1989) summarizes the arguments for the development of microworlds in an educational framework: The latter argument is important. Indeed, the full Logo version offers too many learning opportunities to the pupils and it is difficult for the teacher to control, direct or support the different learning processes going on. Thus microworlds make it possible to use Logo in fairly conservative teaching settings.
Microworlds cannot be considered merely as a piece of software. A microworld is also the activities, the didactical material, etc. In order to take full advantage of using a microworld a well chosen set of assignments should be given to the students. Lapidot & Rachman (1993) suggest that a typical way of using their combinatorial microworld consists of the following steps: (1) letting the pupils play with home-made games that concentrate on a specific topic; (2) discussing the problem that arise from the game (still in the game level); (3) introducing assignments that the class solves together, and, (4) formalizing the problem. These steps follow well the Constructivism philosophy, in which the formalism comes at the end.

2.3. Logo - Practice

As one could expect, Logo is most popular in the primary school level. The Becker study in the USA revealed that about 40 000 primary school teachers use Logo in their classroom. Logo is quite used in Europe, too. The EUROLOGO conference proceedings include many reports on using Logo in most of the European countries. Logo seems to be widely spread, but we can also ask questions in relation of the type of use of Logo. Is it only turtling as Doyle reported in relation to using Logo in the National Curriculum in England? (Doyle, 1989, 1993)
Though the most natural integration of Logo is in the area of mathematics, most of the projects reported are not related to direct use in mathematics. Lots of attention is given to projects aimed at developing general thinking and problem solving skills in the children. Other areas in which Logo has been widely used include language, design, and technology.
With the development of more powerful versions of the language and associated hardware Logo has become popular even in the senior secondary school. I will mention just three examples: In Holland a curriculum for a fundamental course in Informatics and a textbook Informatics with Logo has been produced for junior secondary school level (Jansen, 1989). The textbook is in two parts, the first one being an introduction to programming and the second one focusing on data handling. In Bulgaria, Logo is used in a number of secondary schools in the regular Informatics classes (Sendova et al., 1989b; Dicheva et al., 1996b). Au (1995) reports that in Australia, the use of Logo and Lego/Logo is having a very important place in both the junior and the senior computing studies syllabi. In particular, it has been used rather commonly in the teaching of certain parts of the syllabi such as monitoring and control systems and graphical systems.

2.4. Logo - Technical Developments

Logo has undergone many generations of development in the last fifteen years. After Apple Logo which gained a good popularity in the early 1980, we have witnessed the continual development of the Logo language with more recent versions of Logo Writer, TC Logo, LCN Logo, Object Logo, Comenius Logo, Microworlds, StarLogo, to name just a few. The new developments of some versions of the Logo language are beginning to incorporate various multimedia features which makes it easier for the students to use graphics, animation and sound in their work. For instance, one of the latest versions of Logo, Microwords, includes typical multimedia features such as buttons, graphics (similar to this used in common draw applications) and hypertext. StarLogo includes thousands of turtles and patches which allows students to investigate creature-environment interaction through simulation. These new features allow the students to keep up to date with the latest development of computing technology and to develop new and vigorous ways of thinking about ideas, which correspond to the original aims of the Logo language. We should also mention the Logo versions based on the development of hardware to be used with the language, and specially the availability of Lego/Logo. At last, let us mention the project LogoNet - a Logo telecommunication project (started in MIT Media Lab), which is aimed at combining Logo and Internet. It would allow students and teachers to share ideas and projects over the Internet via a LogoExpress and LogoNet software interface (Dickinson, 1995).

2.5. Logo - Teacher Training

It is obvious that teacher training initiatives (pre- and in-service) are of great importance to reach one of the final goals of educational computing: integration into the curriculum. The question is how teachers should be trained. The problem is that it is not only familiarizing with the Logo language what the teachers need. In order for them to use effectively Logo and Logo-based environments a change of their pedagogical attitude is also necessary. And the last takes lots of time and is not exactly a question of training (Correia & Carvalho, 1989). For example, for young teachers, the problem is often that they do not fully appreciate what children are capable of doing for themselves. Many of them feel that if they are not actively teaching then they are not fulfilling their role. From the other side, many experienced teachers need convincing that they do not need to be Logo experts to encourage their pupils to investigate situations using Logo as a tool. Another problem for some teachers is that of transfer of control of the learning process and class control. They feel that their classroom control is threatened if pupils are allowed to explore situations freely (Eyre, 1989).
Taking into account the slowness of the pedagogical changes of the teachers we consider that it is very important to produce manuals with multiple and different suggestions which would give the teacher some reassurance in the exploration through Logo. Another contribution to solving the teachers' difficulties in using Logo is the construction of structured contexts in Logo language in order to give a stimulating point of start for the exploration of concepts, the development of capabilities, the creation of alternative solutions, in the freedom and reversibility which Logo environment offers (Correia & Carvalho, 1989).
An opinion shared by many is that teacher training will become successful (i.e. causing changes in the actual teaching behavior of the teacher) when a long-term approach to training is adopted and if the progression during this training is carefully planned. Logo should be integrated into a variety of courses and in relation to a variety of objectives.
In the Faculty of Mathematics and Informatics, University of Sofia, we traditionally teach two pre-service teacher training courses related to Logo: the first one is called Problem-oriented languages and major part of it is devoted to learning and using Logo; the second one called School Informatics discusses Logo use across the curricula. Recently, a new course of teaching mathematics in a laboratory-type computer environment was introduced. At the end of this course the future teachers work out projects containing different mathematical topics suitable for the discovery-learning and experiment their proposals in a real class situations. In addition, a variety of in-service teacher training courses are available.

3. Application of logo in mathematics

Most of the attempts to apply Logo within subject matters fields are concentrated in mathematics and specially in geometry. This is quite natural giving that Logo comprises the famous microworld - Turtle Geometry which is a different style of doing geometry, namely a computational style (Abelson & DiSessa, 1981). In the Turtle Mathland the educational question is not how to teach the existing school math but rather how to reconstruct mathematics or knowledge in such way that no great effort is need to teach it (Papert, 1980).
It is believed that using Logo would make mathematics explicit. When developing their projects the pupils use implicitly many mathematical concepts and skills (which haven't been necessarily formally studied), e.g. they use symmetry, they use variables, they practice estimation in various ways, they break problems down into more manageable parts and learn to work more systematically. So pupils who use Logo are engaged in various mathematical processes, though they don't really realize this since their goal is, for example, just to draw a picture.
Despite the numerous attempts toward a real integration of Logo in school math, a widespread view is that Logo has until now not had substantial impact on mathematics education in general, and geometry teaching in particular (see also Noss & Hoyles, 1992; Kaput, 1992). According to Noss and Hoyles this is partly attributed to the discrepancy between doing Logo and doing mathematics: it is mostly taken for granted that interacting with Logo objects is identical to doing mathematics, or will spontaneously lead to mathematical activity. However, it has now become clear that working with Logo does not necessary induce in children searching for mathematical structures and relations.

3.1. Mathematical Microworlds

In the Logo community, there is a consensus about the advantages of using microworlds. The main purpose of Logo-based mathematical microworlds is to enable teachers to provide an environment in which pupils might focus more explicitly on some areas of mathematics. At the same time the pupils will be able to retain all the benefits of working with Logo. Most of the microworlds just provide a number of extra primitives. The user always has the full power of the Logo language available to him and whatever the microworld provides is additional to that power. Many microworlds projects have been presented at the European Logo conferences, e.g. A.T.M. Logo microworlds, including MULTI - a microworld allowing multiple turtles to be used to explore problems such as curves of pursuit, and LOCUS, which extends the use of multiple turtles to allow the exploration of loci (Pratt & Ainley, 1989); 2-D and 3-D Coordinate Systems Microworld (Klotz & Close, 1991); MicroBridge - a microworld in the area of combinatorics based on using a Bridge-like card game (Lapidot & Rachman, 1993), to mention just a few.
There are a few examples of really powerful Logo-based mathematical microworlds enriching the language with tools and resources so as to support creating in the classroom an effective learning environment in which students become active learners of mathematics guided by their teacher. An example of such a learning environment is GEOMLAND, a computer system developed at the University of Sofia under the scientific guidance of B. Sendov.

3.2. GEOMLAND - A Powerful Learning Environment in Geometry

The GEOMLAND project was inspired of observations that some children could not always understand the mathematically talking turtle. Furthermore, the mathematical objects the pupils come across in the secondary school become more and more complicated and the basic Logo possibilities - not quite adequate.
GEOMLAND represents a mathematical laboratory (Sendov & Dicheva, 1988) designed to stimulate pupils at formulating and testing conjectures, which are considered to be the main activities of doing mathematics. This laboratory offers tools for constructing, manipulating, and measuring geometrical objects. By using them the student can carry out various experiments with the objects, can explore their properties, and on the basis of these experiments can formulate conjectures and verify them.

3.2.1. GEOMLAND - the language

GEOMLAND is a language-based system, as opposite to some similar geometric systems for direct manipulation of objects, e.g. Cabri-Geometry (Laborde & Laborde, 1991; Bellemain & Dagdilelis, 1993) and Geometry Sketchpad (Jackiw, 1991). It is designed as a Logo extension enriched by tools for working directly with geometric objects such as points, segments, lines, circles, vectors and sets of such objects. The pupil could work either in Logoland or in the Flatland - the world of the plane-geometric objects. There, the child cannot control the turtle anymore but can create geometric objects and manipulate them. All the other Logo tools are common, e.g., the assignment, loop, and conditional commands. An important aspect of GEOMLAND is that the program remember the instructions performed as a procedure which could be observed, changed and executed again afterwards.
Each object in GEOMLAND is characterised by a name, a value, an image and its relationships to other objects. The geometric values match the data types POINT, LINE, RAY, SEGMENT, CIRCLE, VECTOR SET, VISUAL and are specified by a number of components. For instance, the components of a point are its X-coordinate and Y-coordinate, the components of a circle are its center and radius, etc. Three basic types of primitives are included for manipulating with geometric values: (i) constructors - to create an object given its components; (ii) selectors - to extract components of an object; (iii) modifiers - to modify a specified component of an object. Here are some examples:
Objects can be constructed and modified by the OBJECT command. It creates an object with a given name and displays it on the screen. The following commands would construct a triangle ABC and display it on the screen:
The OBJECT primitive is richer than MAKE since it not only assigns a value to the name but also displays it if the value is of a geometric type. It is possible to modify some of the components of an object in which case the object is automatically modified too, obtaining a new value and a new image.
If we want further on to construct the altitude in the above triangle ABC passing through the vertex C we could use the following commands:
The above solution could be also represented functionally with a single OBJECT command:

3.2.2. Advantages of using GEOMLAND

Among the main advantages of using GEOMLAND are the following:

3.2.3. Using the GEOMLAND in a class setting

The first version of the system was developed in 1986 (Sendov et al., 1987). Since then it has been popularized among the teachers in mathematics and informatics. Since 1987 it has been used in the regular math classes in some specialized mathematical schools and in optional mathematical courses at other schools. Since then lots of joint efforts of researchers and teachers have been put to prepare appropriate teaching materials and to answer various questions related to the effectiveness of using GEOMLAND in a real class setting, like: Can we support an exploratory, trying-things-out mode of learning geometry in the class? Could the traditional curriculum be made learnable if it is taught in a new and different type of school environment? How can teachers be encouraged to take a new role - the one of a partner of the students in their mathematical discoveries? (Kolcheva & Sendova, 1993)
The experience of using GEOMLAND in regular classes (7th to 9th grade) shows that a new teaching style responding to the natural wish of students to learn rather than to be taught has readily been adopted. Teachers have adopted a new image in pupils' eyes - that of people daring to take risks by saying: I am not sure. Let us try and see what will happen... instead of the traditional one of people always knowing at least one solution of each problem. As for the students, they got used to exploring a given math situation by varying its key aspects so as to extract the maximum from it; they happen to reinvent known theorems and even to formulate problems whose answers could be a challenge even to professional mathematicians (Sendov & Sendova, 1991).

4. Teaching informatics in logo style

Littlefield (1992) in a review of Harel and Papert's book Constructionism (1991) argues against the assumption that there are educational magic points, and claims that effective learning still requires good mediation and teaching Logo. Our own experience in using Logo at school showed that there should be a good balance between discovery learning by the students, on the one hand, and systematic guidance, and instruction, on the other. A crucial component in such an environment is the direct instruction of problem-solving skills within the Logo context (see also De Corte, 1993).
This section describes the Bulgarian experience in teaching Informatics in a Logo context and is based on the paper (Dicheva et al., 1996b).

4.1. Background

Bulgaria has a relatively old tradition in having informatics in the secondary curriculum. The first steps go back to 1967 when programming was included as a separate subject in the curricula for the mathematical schools. With the introduction of the microcomputers in the schools on a large scale (1984 - 1986) different educational strategies have been experimented including such ambitious projects as the Research Group of Education (RGE) projects on integrating the school curriculum on the basis of informatics. Based on the positive experience of the RGE informatics project, a team of researchers (the author included) wrote in 1987 textbooks named Mathematics and Informatics (8th -12th grade) for the general educational system (Nikolov et al., 1988). These textbooks have been in use since 1988 in many regular secondary schools. Among the general ideas adopted in Mathematics and Informatics textbooks were:

4.2. Lessons Learned

Unfortunately, our initial idea for the students to have preliminary 2-week intensive introductory work with Logo failed. Thus even teachers who were competent informaticians found it difficult to use Logo for illustrating mathematical notions since the tools themselves needed mastering. Besides, the idea of integrating informatics with mathematics worked well mainly when the informatics classes preceded immediately the mathematics ones. (Having once experimented with mathematical objects in Logo environment pupils were better prepared and motivated to prove theorems.)
For the sake of better integration some mathematical lessons in the textbook were re-arranged differently from the classical tradition, which made the novelty too big for the mathematics teachers. As a result the informatics topics were often left to the informatics teacher thus reducing the chance for a real integration. The informatics teachers on their part did not like the limitations imposed by mathematics lessons - most of them preferred a more systematic introduction of the informatics topics. The exploratory spirit of Logo where debugging sometimes is substituted by de-goaling confronts with the rigid time-table of the regular classes in informatics.
From the organizational point of view using the textbook required splitting the class (usually about 30 pupils) in 2 groups for the informatics part and finding another appropriate configuration (e.g. learning foreign language) to make a shift with.
Last, but not the least, there is still prejudice among a significant part of the education society (including some parents) that Logo is a childish language and consequently students in the secondary school should learn something more professional, like Pascal or C++.

4.3. The New Textbook

Despite the technical, organizational and other problems encountered in using Mathematics and Informatics these textbooks became popular and were appreciated by most of the teachers and loved by the pupils. This was the reason for considering the idea of developing a new version of the textbook entitled Informatics in Logo Style (Dicheva et al., 1996a) taking into account the lessons learned and a good deal of teachers' recommendations. This step was by no means giving up the idea of integrating Logo-informatics and mathematics. It was rather getting wiser after several years of happy marriage.

4.3.1. Requirements

The idea for the Informatics in Logo Style was that it would be an alternative of the textbook Informatics with Pascal which was recommended by the Ministry of Education as a basic textbook for the 10th grade school subject Informatics. The Ministry asked the authors to write the new book so that it could cover in addition the optional informatics courses in the junior high school. Eventually, the new textbook had to be a Logo based informatics book for students from 5th to 10th grade (11 to 16 year old students) in different forms of training at school: regular, optional, and extra-curricula activities. This was quite a challenge!

4.3.2. The design principles

As its title suggests, the textbook was not meant to be an introduction to Logo programming but an introduction to Informatics in Logo style. This means that it would hopefully bring the spirit of the educational philosophy of the Logo community, which sees learning as a constructive process.
When thinking of a school informatics curriculum we should mention the two common perspectives: to prepare students for computer programming jobs or to help them become competent users of informatics tools. Neither of these perspectives in its extreme form seemed to us satisfying from educational point of view. In the informatics classes the students should not learn to program but rather should program (in order) to learn.
In our view the school informatics should pursue two main goals: An elegant way of achieving these goals is to bridge the gap between the two extreme approaches programmers vs. users.
Based on the view of recognized researchers in the field and on our personal experience we consider as important three stages in students' study of informatics. In the first one they must learn the rules of the game, i.e. the syntax and the semantics of the programming language (see also Harvey, 1985). At this stage the novices need much practical experience. At the second stage the students get acquainted with ideas, formal structures and methods of Informatics. At the last stage the goal is twofold. On one hand - to give the students an idea of reasonable use of computers in various fields, on the other - to make them familiar with the basic principles of developing computer systems.

4.3.3. Contents of the textbook

The textbook is structured in three modules corresponding to the considered stages of studying Informatics:
  1. Introduction to Programming
  2. On more serious informatics topics
  3. More informatics and applications
The user-friendliness of the Logo environment was naturally transferred into user-friendly textbooks. In the introductory part we have minimized the formal presentation and the technical details and have provided in a meaningful context even the unfortunate necessity of learning the rules of the programming language. This module starts with brief historical information about computers and programming. Then some basic concepts such as commands, loops, variables, procedures, recursion, conditionals and Boolean expressions, words and lists are introduced using the Bulgarian version of Berkeley Logo. The presentation is based on examples which serve as a skeleton for developing informatics ideas. Such an example is a spiral procedure where we start with a tail recursive rectangular spiral and proceed with stepwise enrichment by introducing: inputs for the angle and for increasements; then - a stop condition, and finally - complex logical expressions to check the data validity, i.e. to make the procedure foolproof. The co-ordinate turtle is introduced intentionally late so as to support cultivating a more geometrically consistent programming style in which absolute and relative positioning of the turtle are not mixed. (This observation has been triggered off by a remark of Sean Close's.)
The second module deals with more serious informatics topics. The importance and the role of the local variables is considered as opposed to that of the global ones. Then the embedded recursion is introduced by both a graphical and a word version of a typical recursive problem. To reveal the most essential features of the recursion we involve this concept in different contexts: word and list processing, number problems, and fractals. Further on the most common data structures are discussed: list, array, set, queue, stack. Finally, such important informatics topics as sorting, searching and coding of information are included.
The third module contains three branches which could be used by preference: (i)Informatics; (ii) Arts and design applications; (iii) Linguistic and natural language applications. In the first branch we give high priority to the approach of using glass-box toy systems. These are simplified models of computer systems such as data base systems, electronic dictionaries, spreadsheets, etc. Students could use such a system as a black box to experiment with and thus to get an idea about its functions. Furthermore, the texts of the glass box toy systems are available to the interested readers and can serve as windows to a more penetrated study of the software implementation principles. The remaining two branches are meant to those who think they don't like the subject. Working in a field of their own interest (arts, design, linguistics) would hopefully raise the motivation of pupils and would let them choose their own way towards making best use of informatics.

5. Conclusion

It seems that there is still a long way to go to find Logo fully integrated into the normal classroom setting. It is important to ensure that children are not subjected to a repeating sequence of writing fairly trivial procedures, but are led towards using Logo as a proper investigation tool, finding out when Logo is an appropriate tool and when it is not. Developments are needed in a wide variety of fields, e.g. curriculum development, teacher training, linking Logo to other curriculum contents than mathematics, etc.
Our personal future perspectives of Informatics in Logo style are in harmony with the Logo spirit: no threshold, no ceiling in a 3-Dimensional space:

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Tornar Tornar a les Pončncies del Vl Seminari Logo