Turtle geometry: Logo Language


1. Academic level of the *students: pupils 11 – 14 years old; first class, second class and third class of Italian lower secondary school.

2. Reflection on the *mathematical content* from a didactical point of view which might focus in epistemology, history, social issues, etc:

History - the evolution of geometry, in some examples:

  • Greek ceramics and Roman Mosaics
  • Cartesian Geometry and the geometrical Transformations

From this last step we can come back until the ancient Greek with some simple uses of Logo, sometimes it will be possible to study the same problem with a different point of view: for example the constructions of the regular polygons with Logo or with Euclidean way.
So it is very important to study the structures of geometrical figures in a dynamic approach ( see the Erlangen’s Program), with transformations of modulus etc..

3. Description of the *used materials*, availability, and classification according to the process followed (v. gr.: initial assessment, classroom presentation, homework, group work, final assessment, etc.):

At the beginning the class works without computer only with pencil and paper and a pupil behaves like a robot to understand the difference between to teach a procedure and to execute a procedure.
Then the teacher shows the program (we use Berkeley’s University MSWLogo, with a little translator from English instructions to Italian instructions).
The first times the pupils work in pairs, so they can help themselves.
This work is completely operative: the used materials allow both an help and an autonomous resolution of the problem.
The realization of the project is often the final assessment, some things are important:

  • conformity beetwen the final object and the starting project;
  • choice of the more economic way;
  • presence of original observations and reflections…

Slide show of some works