Abstract:

The objectives, methods and results of the experiment of the MatCos programming environment obtained over the last ten years within the teaching-learning of Mathematics in Calabrian (Italy) secondary schools will be described. The Matcos programming environment has a dual pedagogic-educational basis:
- introducing students to programming using mathematical concepts suited to their age group;
- help the learning and mastering of mathematical methods and concepts by exploiting the potential of computers.
Programming therefore as a method, as an ‘ideal place’ where students have a concrete chance to explore mathematical concepts and formulate conjectures that can be validated or rejected, and to experience problem solving. The main characteristics of the MatCos environment are:
1) Modularity - structuring into graded modules, and precisely MatCos(2.1; 2.2; 2.3) respectively for classes I, II and III of lower secondary schools, MatCos(2.4; 2.5) respectively for classes I and II (two-year course) of higher secondary schools and MatCos (2.6; 2.7; 2.8) respectively for classes III, IV and V (three-year course) of higher secondary schools.
2) ‘Step-by-step’ - execution-allows control over each step of the algorithm and therefore the chance for the student to correct mistakes more easily, and not just syntactical errors.
3) Expressivity - MatCos is in the mother tongue, that is Italian (but translations into other languages are readily available) and uses commands with specific terminology which refers to precise mathematical concepts (point, line, straight line, segment, etc);
4) Easy to learn - MatCos comes without a declarative phase. This lightens the burden of syntactic rules that usually accompany any programming language, though without affecting the efficiency of the executable (file) and simplicity by the compiler.
The experiment of the MatCos programming environment has been carried out as part of the project by the same name on a representative sample of schools in the Calabria region (Italy). The schools were of a different type: lower secondary schools (age group of students 10-13) and higher secondary schools (age group of students 13-18). The experiment has been carried out with the supervision of the Interdepartmental Centre for Didactic Research (C.I.R.D.) of the University of Calabria.
The main results obtained over the last few years were presented at two national congresses called Progetto "Matematica e Computer" - Giornata di lavoro con gli studenti protagonisti (The Project ‘Mathematics and Computers’ - One-day workshop with the students involved), which took place in the months of November in the years 2005 and 2007 respectively.
Beside the encouraging results obtained throughout the various cycles of experiments from a purely scholastic point of view, students’ interest has been the most relevant aspect to emerge from the project, which learners expressed through the independent production -with the aid of computers- of prototypes of everyday objects, using mathematical concepts and related MatCos instructions. As a result, students have had the opportunity to come into contact with a vision of Mathematics that remains traditionally hidden in the didactics of this discipline in Italy. Some of these works will be shown during the presentation.

Keywords:

programming, matcos environment, research projects, secondary school, teaching-.