M.G. Frassia

University of Calabria (ITALY)
"Chance only favours the mind which is prepared"
Louis Pasteur

The science of chance, or the mathematical theory of probability, is involved in everyday life and in fields very different from that of gambling. In the social sciences the influence of mathematics has grown steadily. Important political choices in technology or economics are subjected to analysis based on probability theory.

The key notions of probability theory and the traditional method of calculating probability are at the basis of the education and shaping of sensible citizens capable of informed decisions. Therefore such notions should be part of our culture and of school education. The teaching of probabilistic reasoning from an early age means educating to critical thinking, it means to train students to "bring order" to their ideas in order to approach events rationally and correctly interpret real-world phenomena. This also means raising awareness in the learner of the fact that- since certain outcomes are more probable, easier to occur than others - you can make predictions or ‘bets’, in other words you can control rationally the forecasting of uncertain events. This contribution is related to the above framework, and it shows a didactic example aimed at strengthening the concept of probability taught in high schools. This teaching proposal, implemented in conditions of problem-solving, has a playful approach with simulations which are first real, then virtual by implementing simple algorithms with the aid of the computer programming environment MatCos. The analysis of the results obtained allows for a direct comparison with the theoretical model. The design teaching setting based on games intended as "knowledge space" enables students to practise their critical thinking as well as their problem-solving, creativity and collaboration skills (Prensky, M., 2001; Caine, Renate M. and Geoffrey, 2011).

The virtual simulation of games allows students to reconfigure aspects of sensible reality to be analyzed and studied through the computer used as an educational tool in the programming environment MatCos (Costabile, F.A. and Serpe, A., 2012 and 2013).
The choice of presenting some random phenomena through programming experiences stems from the need to suggest alternative methods to traditional teaching. In most cases in schools the study of probability is approached as a guide to properties and results to be applied in contexts often restricted, a methodology which is insufficient to understanding the true meaning of probability.