**School Informatics in Logo
Style:
a Textbook Facing the new Challenges of the Bulgarian Informatics
Curriculum **

*D. Dicheva*^{1}* R.
Nikolov*^{1}* E. Sendova*^{2}

^{1}*Faculty of
Mathematics and Informatics, University of Sofia
5 James Bourchier Str., Sofia 1164, Bulgaria
email: *

8, Acad. G. Bonchev Str., Sofia 1113, Bulgaria

email:

**Abstract**

The paper deals with a textbook "Informatics in Logo style" for the Bulgarian secondary schools. It is written in the context of the significant changes Bulgaria is facing today which have influenced the whole school curriculum. An estimation of the advantages and the shortcomings of a previous version of the textbooks "Mathematics and Informatics for 8-12th grade" in which mathematics and informatics have been in a closer integration is presented. The new textbook is based on the informatics topics of "Mathematics and Informatics" taking into account the implications of transferring on a larger scale the positive results from a now 10 year old educational experiment in integrating informatics into the curriculum from the junior high school. In proposing to work in Logo style, the authors believe that the dilemma

programmers vs. userscould be solved in an elegant way.

**Keywords**

Informatics curriculum, integration, Logo

,glass-box toy system

**1 Introduction**

The problem of specifying an informatics curriculum matching
the educational demands of various countries in various
circumstances has been a real challenge for the specialists in
the field. A very successful attempt to solve this problem is *Informatics
for secondary education: a curriculum for schools* produced by
a working party of IFIP under the auspices of UNESCO. This
curriculum* is designed to be capable of implementation
throughout the world to all secondary age students *[1]*. *The
experts have designed the informatics units and modules on the
basis of their wide experience of developing effective
informatics education during the past quarter of a century. But
it is only natural that solving such a complex problem gives rise
to other problems:

- What software to use so as to cover all the informatics education objectives ?
- How to overcome the variety and the complexity of using the commercial application software packages at school?
- How to help teachers to address learners with different interests and motivation?
- How to overcome the variety of conditions in schools which are at different phases of development although in the same country?

The purpose of this paper is to give possible answers to some of the above questions taking advantage of authors' experience in teaching Informatics in the Bulgarian context.

**2 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 and in the special mathematical
classes in some other schools. The first textbook, addressed
mainly to teachers of informatics, appeared in 1974 and included
a short preface on the theory of algorithms and an elementary
idea of machine languages, illustrating concepts from the
algebra, geometry and numerical methods [2]. 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. (In the latter the
computers were introduced at the junior-secondary school.) [3,4]
Based on the positive experience of the RGE informatics project,
a team of researchers (including the authors of this paper) wrote
in 1987 textbooks named *Mathematics and Informatics for high
school students* (8th -12th grade) for the general educational
system. These textbooks have been in use since 1988 in many
regular secondary schools. Several university courses on school
informatics for future teachers have been based on them as well.

Some General ideas adopted in *Mathematics and Informatics*
textbooks are:

*Integrating informatics with other school subjects, mainly with mathematics*has been expected to be very useful for both informatics and the concrete subject matter since:

- informatics offers a means to clarify and extend the mathematical concepts studied and to illustrate the possibility of applying them to real situations;
- informatics offers appropriate tools for obtaining a great variety of solutions;
- working in a computer environment
of exploratory type (such as Logo and its
extensions) contributes to anticipating school
mathematics as a field for investigations and to
enhancing the scientists into the learner [5];

*Using problem solving scenarios*developed both vertically (in grades) and horizontally (with the same grade) [6];- Specifying branches in mathematics, informatics, linguistics and arts which students could choose according to their own interests;
- Offering the 'transparent software' approach through glass box toy systems [7].

**3 Lessons learned**

The most recent COMPED study reveals most of the problems in the Bulgarian schools (need for updating the computer equipment, for good educational software and textbooks, for re-training teachers etc.) [8] That these problems are a serious reason for the fact that the textbooks have not brought in life their full potential, is rather obvious. As authors we were more interested to see what were the advantages and shortcomings of the textbooks when used by experienced teachers in appropriate technical environment. What follows has been extracted from observations and discussions with such teachers.

The idea of having preliminary 2-week period of intensive work
with Logo (aiming at a more fluent transition to using it as
tool) could not be achieved. Thus even teachers who were
competent informaticians found it difficult to use informatics
tools for illustrating mathematical notions since the tools
themselves needed mastering. Besides the idea of integrating
informatics with mathematics (or possibly with other school
subjects) worked well mainly when the informatics classes
preceded immediately those of mathematics. *You do - you
understand, you explore - you invent* was the principle
applied. Having once experimented with mathematical objects in
Logo (or Logo-based) environment pupils were better prepared and
motivated to prove theorems. Practically though this would mean
dividing the form (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. Similarly
- when integrating informatics with other disciplines (like
languages and arts). Furthermore, in this case, teachers in
informatics had to joint the subject-matter teacher or the latter
should be trained additionally. With the smaller number of pilot
schools, highly motivated teachers and researchers to support
them, this idea worked reasonably well. But when attempted on a
larger scale the problems faced multiplied: for the sake of
better integration some mathematical lessons in the textbook were
re-arranged differently from the classical tradition, thus making
the novelty too big for the mathematics teachers (for them even
the attempt of integrating geometry with algebra was quite a
step, since till then these were two different school subjects
with separate grading). As a result very often the informatics
topics were left to the informatics teacher thus reducing the
chance for a real integration. The informatics teachers on their
part (especially in the case of non-mathematicians) did not like
the limitations imposed by mathematics lessons, or by the project
scenarios - they would prefer 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.
Last, but not the least, there is still prejudice among a
significant part of the education society (including some
parents) that Logo is a* children’s* language and
consequently students in the secondary school should learn
something more professional, like Pascal or C++.

**4 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 meeting the
challenges of the new economic situation in the country, in
general (and those of the Ministry of Education, in particular).
The new textbook entitled *Informatics in Logo Style* [9]
takes into account the lessons learned and a good deal of
teachers’ recommendations. This step was by no means giving
up the idea of *marrying* Logo-informatics and mathematics.
It wasn’t a* divorce. *It was rather getting wiser
after several years of *happy marriage*.

*4.1 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
*[10]. 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.

*4.2 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:

- to introduce the basic concepts, formal structures and methods of informatics;
- to acquaint the students with various computer applications in the real life.

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 [11]). 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 Contents of the Textbook*

The textbook is structured in three modules corresponding to the considered stages of studying Informatics:

- Introduction to Programming
- On more serious informatics topics
- 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 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 systems as *a black box* to experiment with and
thus to get an idea about their 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**

Our strong belief is that Logo is the language of choice for secondary school informatics. Logo is more powerful and cleaner than Pascal and directs the learner’s attention to interesting issues, rather than to syntactic details and implementation concerns [11].

When working on the textbooks it was a great advantage for us to develop them together with a relevant software environment. Some educational metaphors have been visualized and brought into life through an appropriate interface. Several consecutive versions of Logo in Bulgarian have been developed in parallel with the development of the textbooks.

The modular structure of* Informatics in Logo Style* will
hopefully meet the requirements for usability at different age
and different level of programming knowledge and skills. Thus its
first part could be used by younger children in the optional
primary level IT course (12-14-year old students). The first and
the second parts could be used in the regular informatics course
at the secondary school course (16-year old students). The third
part offers material for the optional secondary level IT course
(16-year old students).

The future perspectives of *Informatics in Logo style*
are in harmony with the Logo spirit: *no threshold, no ceiling *in
3-Dimensional space:

*contents*: extensions of the elective modules (both in variety and in volume) have been envisaged;*software:*the supporting software environment will be enriched with new glass box toy systems and microworlds;*authorship*: The authors of the textbooks see themselves as a part of a broader team (teachers, students at university and school level) endeavoring to improve and further develop the textbook and the supporting software.

Development in these dimensions will hopefully contribute to the achievement of educational informatics goals as formulated in [1].

**6 Financial Support**

This work is partly funded by INCO COPERNICUS Project 960106 - MATCh.

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