Schola Europaea European School Brussels II

110
PANORAMA
The ‘code’ is then translated into an
action by the student. An interpreter
or a compiler takes over this task for
the respective programming language.
The use of computer-aided dynamic
geometry systems in the lessons makes
this analogy even more obvious.
Without comments and/or instructions,
the expert reader also needs some
time to understand which figure will be
constructed. In exactly the same situation
is the computer scientist, if confronted with
an unknown/uncommented program.
Before writing down the description of
the construction the actual work is done
by the brain: the problem is analyzed
and different solution types are run
through. This is often done in a trial-anderror
manner. The analogy of solving
a construction problem and writing an
algorithmic program is perfectly obvious.
The concept of the subroutine or
function becomes clear in step (2): also in
geometry often-used construction steps
can be summarized in a metalanguage
OBJECTS
The attempt to model a certain part of
physical reality led both to the development
of geometry, and modern programming
languages and to complex structures with
certain properties.
To every student it is intuitively clear that
a finite line has the property of "length".
One point, however, does not (compare
with Euclid’s definition). In a similar way
a floating-point number has the property
of additive potential. A multidimensional
array, however, does not—except if one
defines this in any (reasonable) way.
term. Programmers also archive often
used algorithms in a library.
The instruction summarizes:
{line parallel to AB, distance h c}
(1) S 1 = {line perpendicular XY in X} ∩ k (X ; r = z)
(2) S 1 = {line perpendicular XY in X} ∩ k (X ; r = z)
(3) S 1 S 2
Again one can see the close link to the
concepts of programming languages:
New subroutines are allowed to use
already existing subroutines (line
perpendicular, circle k(X ; r = z)...).
There’s a handing over of variables
unknown prior to the actual execution
of the construction (X, Y, z).
Subroutines can use/define local
variables. (S1 and S2)
Naturally the geometry teacher does not
refer to these facts, but the brain structures
of the students adapt to these new concepts
enabling them to understand the programming
techniques very quickly later on.
Modification and combination of the
geometrical basic objects enable us to create
sets of new objects with various properties
dealt with in a large number of the geometrical
theorems. The triangle for example helps us
to understand the properties of polygons. To
consider the polygon just as set of Cartesian
points would be impractical and hinder
deeper understanding.
In a very similar way the programmer
combines simple data types to objects
with various properties (array, record
etc.). These again can be combined to