GAMES DESIGN WITH PROGRAMMING ENVIRONMENT MATCOS FOR ENHANCED LEARNING OF PROBABILITY THEORY: A DIDACTIC EXAMPLE FOR HIGH SCHOOLS Maria Giovanna Frassia Department of Mathematics and Computer Science, University of Calabria (ITALY) Abstract This paper presents a didactic proposal, based on the use of the computer as a tool for programming and aimed at enhancing the debate around the meaning and interpretation of probability. In the school of the third millennium, it is important to provide alternative methods to the classic lesson with other pedagogical-didactic approaches that favor cooperative learning, peer tutoring and resources of the class. Keywords: random phenomena, problem solving, programming environment, game-based learning in high school, mathematics education, civic education, technology-enhanced learning. 1 INTRODUCTION 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. Nowadays, the number of teenagers attracted to gambling (slot machines, scratch cards, games and online lotteries), is constantly increasing. Tempted by: chance winnings young people invest “small” amounts of money in the game. The problem of gambling addiction is rampant and school as an educational agency cannot remain helpless and cannot ignore the problem. 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. In ministerial programs for Italian high schools, the topic of probability plays a very important role in the teaching of mathematics. In fact, it is already taught in the first two years and then it is taken up and studied in more depth in the following three years. However, despite the started social and educational benefits, emphasized by distinguished mathematicians 1 , the theme of probability continues to remain marginal in school. The possible causes for neglect of such an important issue for the education and training of future citizens are: teachers are ill-equipped to deal with this particular area because of the minor importance that it frequently plays in university curricula; the difficulty of finding practical applications of probability theory that are close to the reality of the students; the difficulty of contextualizing the teaching of probability in the formation of the high school student's though process (13-15 years for the first two years; 16-18 years for the final three years); etc. It is important, then, to reflect on the topic of probability and on the development appropriate of didactic activities, in order to develop a greater awareness of the importance of the subject within upper secondary school [12]; at the same time we should provide a series of tips and tools to help instructors to teach of probability with greater confidence and pleasure. 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 [13], has a playful approach with simulations which are first real, then virtual by 1 Bruno De Finetti (1906-1985), Federico Enriques (1871-1946), Giancarlo Rota (1932-1999) and still other.