Designing Logo pedagogy for elementary education
Eötvös Loránd University
Dept. Informatics Methodology
1088, Budapest Múzeum krt. 6-8, Hungary
tel/fax: (36-1) 266-5196
Often the Logo language is considered to be just a toy, while teaching programming is approached in a scientific way. Thus the educational benefit of the Logo pedagogy is underestimated. This paper attempts to verify its use in elementary education, taking into consideration the developmental stages of children at that age.
Logo pedagogy, problem solving, elementary education
Future teachers of informatics are often puzzled when I ask them questions like: "Why do you think we should teach programming?" After many years of studies in PASCAL, programming methodology, data structures, etc. they are convinced that most of what they have learned is necessary to teach in schools of average setting in order to develop any kind of computer literacy and through that, organised thinking skill. Due to the past very scientific approach to computers and programming, the Logo language has not been taken seriously. It was just considered to be a toy or at most to be the first programming language just to get a taste of programming. Very often characterised by the following comment from teachers:
"I would introduce smaller children to Logo to let them believe they were programming."
"But they are!" would be my answer, not taken too seriously.
It is difficult for them to understand why it is not pure computer science that they are to teach and it is even more difficult to reason why to use Logo. Furthermore, I believe a better pedagogical background is needed in order for them to appreciate and understand the importance of the development of the thinking process during Logo work, and not just the correctness of the resulting program itself.
2 Teacher education at Eötvös Loránd University
Eötvös Loránd University has been training teachers in Informatics for about 15 years. Students graduating from our university would mainly teach at secondary school level, and due to the reorganisation of many schools, at elementary level too. Until recently schools have had a 4+4+4 years division of lower-higher elementary and secondary levels, nowadays you may find 4+8, 6+6, or even a combined 12 year setting too. This means that our teachers should be able to perform in an overall role of school education.
Our new National Curriculum does not directly require any form of informatics education till grade 5 and requirements are only defined till grade 10. This also means, that it gives no guidelines on how to approach the subject if a school decides to offer it in the curriculum for lower elementary, which otherwise every school has the freedom of doing so. On the other hand, the extent of our computerised society motivates parents to strongly require schools to prepare children on how to handle computers and give them any benefit that computerised education might offer. Thus teachers, given this task, often turn to us for help and advice on approaching this topics.
I offer an elective course on The School Implementation of Informatics for fourth year students, where I start out the semester by making them compose a draft curriculum, as if they were to teach through grades 1 to 12. The results I get are quite shocking, which gives us a warning sign to reconsider courses for teacher education. Students often list practically all subjects and topics that they have learned (DOS, maintenance, a bit of Logo just to introduce Pascal, history of computers, programming methodology...etc.) to be covered in about this sequence starting from early education. When discussing the question of why they think that all this knowledge is necessary for basic education, arguments could be summarised as follows:
"To introduce theoretical programming, which helps develop structured thinking."
On the other hand, they might choose to use no computers at all in basic elementary education, saying, that children at that age are not ripe for such activities. My arguments to change this rigid view throughout the semester consist of the introduction of various computer applications that can be integrated into subject areas, as well as the following Logo-like environment and approach.
3 Approaching Logo in elementary education
3.1 Reading and writing drawing
In my childhood, my favourite storybooks were pop-up-books, where characters could be moved around. Playing within the scene helps understanding the story. Children today have their own favourite storybooks that allow characters to be moved around, they are called "living storybooks". Interactivity, sound pronunciations, and animation certainly produces better understanding and much more enjoyment in the process of learning to read. The use of digitised speech for the pronunciation of requested words and/or sentences contributes to the acquisition of reading at the very early stage (lettering-reading) additional explanatory information of a requested word or expression enhances understanding of a more complex full story (understanding-reading).
Writing with a computer is far easier than with pencil on a piece of paper. Keying in the letters means reading (or identifying) the letters of the alphabet, and finding (comparing) the equivalent on the keyboard to press after one another. Learning to write by reading is a process that produces quick results, and chains the letters into words giving a meaning to them.
The Logo language can be used to accomplish such tasks, by extending a pre-programmed microworld in an easy way. The KIDLOGO microworld allows children themselves to create associations between words and their meaning by giving names to parts of their work as they progress. Meanwhile, the process of creation is in itself enlightening. The button driven system facilitates the design of drawings, music, animation, and their combination into a multimedia story. The summary of the KIDLOGO microworld can be seen in , illustrating, how the Logo-like development of a project refines the creating process, while other aspects of art education can be encountered as well, even at an early age.
3.2 A visual problem solving method
The Logo book that is mostly referred and its ideas re-implemented in Hungary, contains my contribution in developing a Logo programming style or method. This method is not based on technical programming tricks, but on natural problem solving techniques in Polyas style , that can be implemented in the ever motivating environment of visual constructions.
The main starting point in the creation of procedures is the overall comprehension of the idea that a new word is to be created with its definition composed as close as possible to the meaning of the word itself. This concept could be understood at any age level. The process of developing projects should involve vast amounts of exploration in connection with the plans, and make use of all possible mathematical knowledge already acquired. Several well noticeable phenomena can be investigated and recognised as Turtle theorems, like that of transformations (mirroring in several directions), turning and re-sizing properties, the Total Turtle Trip, ... etc. 
Further chapters cover topics of animation and their development, and visual modelling of graphic designs. The guidelines contain questions to ask oneself and advices to consider when trying to compose a desired image. The book contains a lot of illustrations and examples to visualise the method.
The main topics during visual problem solving can be summarised as follows:
Draw your plan on paper (preferably on squared paper).
Havent you already done something similar? Probably a bit different from present drawing. Could you somehow use your previous work? Or use it with a few minor modifications? Or can you use the same method? (fig 1.a)
Try to decompose your drawing into main parts. If a type of decomposition "does not ring a bell in your head" try to decompose it in another way. (fig 1.b)
Determine the starting and ending state of the Turtle in case of every part to be composed. (fig 1.c)
4 Findings strategies for teachers
4.1 KIDLOGO from kindergarten (5-6) to lower elementary (8-9 years old)
The characteristics described below form a short summary of findings of the past 13 years, mainly concentrating on kindergarten level, proving that even higher level operations can be used at such an early age. Drawings (fig 2.a - i) are those of kindergarten children.
Planning before doing
Children often started out by drawing their plan on paper, mainly due to the fact that teachers advised them to do so. Or sometimes while waiting for their turn, they planed their actions in order to be able to fulfil them while the tool was in their possession. However, children of very young age often changed their minds about plans, and turned to undecided territories. The pre-planned movements were attempted to be substituted by a trial and error method during the process of creation itself. Preparing plans and trying to hang on to them till fulfilled helps strengthen persistence.
Movements in relation to the pen (relative aspect)
Usually they acted first, even in a sequence of functions, and then reflected on what was done i.e. see if the pen was turned into the right direction. If they decided the action was wrong then, in most cases, they took a reverse action to undo the result and progress in the right direction. They repeated their mistakes several times, but bit by bit learned to think in relation to the pens and not their own state. When in trouble, or undecided on the proper direction to be taken, they just stood up and adjusted their hands, in relation to the pen (or their whole body) and tried to perform the necessary actions needed in this position. This diverted egocentric thinking into thinking in terms of another actor and its viewpoint.
Trial and error (debugging)
Introducing the undo button, which resulted in redrawing the whole picture except for the very last step, had a great effect on children. Seeing their own performances played back in front of their own eyes, the exact way it has been developed, thrilled them. Reproduction of their own uncertain movements, caused them to giggle and laugh, considering the movement of the pen, or their own actions to be funny. They enjoyed undoing the last step, which motivated these kinds of corrections, and at the same time allowed them to perfect their procedures with a better choreography. This developed concentration on tasks to be done in optimal number and type of steps, and made them think about their actions before performing them.
Modifying parameters (configuring environment)
Most of the children had a strong desire to fulfil a main aim, but the details were often adjusted to the limited possibilities. Depending on their determination to achieve the planned aim, they often went on to a higher level function, such as the use of some Logo commands printed on cards, to e.g. change colours, change angles or distance, ...etc. (fig 2.a).
Some drawings gave evidence of a very high level of precision in the development of a project. These drawings showed well prepared plans and strong determination to fulfil them (fig 2.b). Some works illustrated a good sense of symmetry, where the child performed reverse actions to produce the mirror image (fig 2.c).
Reading / writing abilities
Although most of these children did not know how to read and write, these activities greatly contributed to speeding up their learning in this field.
Reading and writing using these microworlds helps develop further abilities, since :
Naming drawings (procedures)
The ability to name their drawings first resulted in the use of their own names as the name of the drawing. The next picture was given their brothers or sisters name. Again the next was named after their parents or friends. But after some number of pictures they realised that they can identify their own products only if they assign a name to each picture drawn by using words that are meaningful to the picture itself. Thus they started to assign names that describe the image drawn.
The ease of KIDLOGO usage
Mastering the turtles movements gave an enormous amount of self-esteem to the child and the feeling of being in control.
The strong wish to modify the microworld, stimulated the children to attempt typing in a Logo command, that always resulted in a magical effect worth the effort. The use of cards gave them a further possibility for individual activity and autonomous control.
Naming parts of drawings (sub-procedures)
Undoing could result in an error message stating that the memory was not big enough to perform the undo function. They learned from this, to restrict the amount of steps taken in performing a specific drawing, which led to more optimal actions. On the other hand, when introduced to the possibility of naming the actions taken so far and reusing the name in a further construction, they began to give names that were most suitable for the actions performed. This in return, resulted in shorter procedures that would better coincide with a given name. They realised that if they assigned too many steps to a drawing, the turtle would not be able to learn it in association with a word, thus they tried to describe their drawings with a smaller amount of commands, more concisely, more meaningfully. This produced drawings that had meaningful names associated with them.
Reusing procedures (sub-procedure call)
Young children work on a project in one sitting, meaning that they would quit the project once they are forced to pause their actions. This is due to their limited patience and change of plans. However, there were several works evidencing that children, not having enough time to finish the project, asked to save the procedure itself and not the drawn end product (which could not be further debugged or continued later). They reloaded their saved programs at a later time and continued the refinement of the procedure to fulfil their plans (fig 2.d,e. done on two separate occasions). This proved their understanding of the difference between a drawing, as a product and the program that created it.
Thinking in terms of modules
It is not at all typical at this age, for a named procedure to be reused as a sub-procedure in drawing a desired plan. There were several instances, where this kind of higher level of combination was practised (fig 2.f). Furthermore, the named procedure was reused as an individual module to compose a more complex pattern by turning the modules direction (fig 2. g). And even more surprisingly, such procedures were passed on throughout time to be reused by others as well, or even recreated (fig 2. h,i were created in two consecutive years). Using such modules proved the better understanding of parts in terms of the whole.
In the beginning, it was always the teacher who showed
children how each microworld worked, how new functions performed,
helped in the debugging process, saved procedures or drawings,
i.e. did all higher level functions. Later on, as children became
more confident in using the tool, they asked for less and less
grownup help, but rather consulted with their peers and even had
collective debates or quarrels on how to proceed with a certain
problem. But the solutions were always very rewarding and created
more and more self confidence and independence. So, next year,
the absence of the teacher familiar with these programs did not
cause any hindrance in childrens performances. Actually,
the new teacher was the one who was taught by the children how to
use the microworlds. This fact produced an enormous amount of
self confidence in the talented ones and they became the
authority in problem
solving. These children, progressing into a higher class, were often asked by the teacher of the lower grade to aid her in specific tasks in which she was uncertain. Thus the bigger children became the aids, teachers, authority for the smaller ones, and these social activities and cognitive confrontations strengthened collaboration in a common aim.
4.2 Special education
This type of microworld proved to be very helpful for children with special needs. Motor disabled, hearing impaired, mentally disabled children were introduced to these tools. It is too cumbersome for children with disabilities to use full Logo features. A button-driven microworld reduces the fuss in performing the action, which the undo function further helps by making it easy to modify the steps to be taken. Such tools facilitate the performance of constructions that would probably not be achieved otherwise, or only with great effort. (Fig. 2.j,k,l shows the work of a child, with severe motor disabilities, using KIDLOGO, who has never been able to do such tasks with ruler and protractor as required).
4.3 Using visual problem solving from lower (9-10) to higher elementary (13-14 years old)
Planning before doing
In order to motivate children to tackle properly a desired problem, they should be asked to sketch down their plans on paper. In this case, preferably draw the desired drawing on squared paper, to better feel the ratios of line segments. This draft should be thought of, analysed, reflected upon to come up with a way in progressing with the creating process. The teacher has a great role at this stage in influencing the design process. Not in producing any sort of solution, but in understanding and clearing the reasoning of the children, letting them to be the leader in taking a desired path to fulfil their own plans. With trial and error, the children will notice the divergence of actual procedures from that planned, and consult with reasoning and adjust to the desired road. This allows the discovery of several occurrences which, upon repeated appearances, develops into common facts and later into concrete concepts. The teachers role is to absorb the chain of reasoning, and help clear it by giving some guiding advice, e.g. by suggesting that difficult details should be divided into smaller parts, or pointing out their similarity to other problems tackled previously. It is the advising process and not a solution that would be the greatest help for future progress. A thorough planning process at each stage helps develop abilities of analysis, abstraction, and the refinement of the logical thinking process.
Defining parts (procedures)
It is necessary to concentrate on every single part to be able to well define its exact procedural definition. Every procedure should be short and concise, defining as much as possible the task it should fulfil, and thus, a suitable name should be used to coincide with its meaning. Procedures should be as independent as can be, which could be achieved by the following:
Trial and error (developing - experimenting)
All thinking strategies should be welcomed and encouraged. Trial and error, partial solutions approach, or optimal strategies all lead to some kind of useful experience. All "intelligent mistakes", explored characteristics, well used mathematical theorems or those gained during experiments enrich learning and help in developing the thinking process. Results of well observed experiments can be composed into theorems to be used consciously at a later stage. All original approaches should be encouraged even if they do not seem to be leading to the desired aim. These individual roads might lead to rare solutions.
All solutions have to be experimented with and evaluated before use at the next level.
Developing level by level
Once basic definitions are clear, well constructed, general, state transparent, they become as natural as a primitive. These building blocks allow easy construction of more complex structures and let children concentrate on the next level of complexity. If some parts are better to be tackled by a top-down method, then the details can be substituted by simple state equivalent procedures to help in construction.
Developing problems through levels creates a thinking pattern that uses pre-defined procedures (past experiences that have been verified) to tackle present problems, with the possibility to project solutions into the next level (future constructions to be solved).
Implementations of Logo that allow the hiding of procedures provide a useful feature for extending Logo vocabulary in a specific direction, allowing new commands to behave as normal primitives.
The step-by-step development of programs allows partial solutions to develop with ease and little risk to progress closer to the desired goal.
Group work invokes communication, develops co-operative strategies, and topic related discussion that allow different forms of self expression. Success develops self-confidence, while failure strengthens togetherness in wanting to help peers accomplish desired a task. Sharing procedures presumes an understanding of the others solutions to further device new approaches.
Explorations are just as important as fulfilling a plan. Teachers should end problem solving sessions by initiating the reuse of defined building block to complete other possible figures either defined or invented. Also the application with different geometric transformations, leading to repetitive patterns should be investigated. These explorations invoke creative ideas and strengthen the importance of creating procedures that can be used in different constructions.
Application in other context
These problem solving techniques, methods, ideas, explorations, and metacognitive activities can be and should be transformed into other contexts as well, i.e. music, animation, and topics related to other subject areas. A good balance between context and process allows the development of higher order thinking skills in subject areas.
Why the case of Logo
The Logo programming environment is very supportive of such methods, being highly interactive, user (child) friendly, and its straight forward program development in terms of defining a new word, already invokes partially the methods referred. In this way, developing procedures becomes a rather natural phenomenon of expressing the meaning of a new word by using words already well understood.
Hiding and seeking procedures is a rather useful property for modelling level-by-level, revealing only the level of actual problem to be solved.
Constraining the use of primitives as well as the extension to specialised microworlds produces an environment that can be configured with ease and at the same time transfer from one to another is smooth. The possibility of defining a procedure, while on the run, gives a unique feature in the ease of developing button driven microworlds like KIDLOGO.
The KIDLOGO microworld is based on characteristics of children in the pre-operational period developing into those of the concrete operational period, while the problem solving method relies on the characteristics of the concrete operational period developing into that of the formal operational period . The choice of visual problem solving, as a topics, guarantees the motivation of most children and allow playful activities in a field that is very close to their world at the given age levels. The extendibility of Logo microworlds allow smooth transition from any Logo based open microworld to full Logo use. A longer period of Logo involvement with the method described encourages the appearance of concepts of analysis and abstraction , and the refinement of the logical, higher level thinking process that provides a strong base for developing formal thinking. Explicit problem solving instructions and Logo programming practice improves the ability to apply sub-goal formation, forward chaining, systematic trial and error, and analogy strategies. But "knowing how is not enough to insure the generalisation and transfer of complex procedural skills, rather that for such knowledge to be abstracted in one domain and applied in another, a learner must also know precisely what is being abstracted and applied". Problem solving strategies embedded within an environment  allows an automated connection between the planning and debugging process and a heuristic representation of the problem itself. However, this algorithmic rigidity in sticking to top-down development excludes other approaches and does not necessarily inspire the development of state transparent procedures, which can be a crucial characteristics of clear design concepts. The combination of convergent and divergent thinking patterns could lead to creativity, which should be well encouraged in elementary education.
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