I Participate, We Decide: Decision Analysis enters Italian high school and students win

Authors: Anna Ippolito and Fabrizio Ruggeri, Liceo Giulio Casiraghi, Cinisello Balsamo, and IMATI CNR, Milano, Italy


Since 2015 high school students in Italy have to take part in activities known under the name of Alternanza Scuola/Lavoro (School/Work Alternation) so that they will spend 200 hours, over their final three years, on projects involving partners from industry, business, government, academic world, NGOs, etc. The purpose of the projects is to make students familiar with the work environment first hand. This article will outline the results of the activities of a class of third year students during the school year 2015-2016. It is worth mentioning that the Italian school system is based on 13 years of compulsory classes (5 in high school) before students can attend university. Therefore, the students involved in the project were, in general, 16 years old when they started it.


The students had to get acquainted with topics and models which are not part of the high school curriculum: Bayesian Networks and Decision Analysis. The students went through the typical stages of a decision process: problem structuring, uncertainty modelling, preference modelling, expected utility maximisation and sensitivity analysis. The experience went well beyond the scientific aspects since the students were induced to think about how complex problems can be tackled, identifying what really matters, from the goals to achieve to the other factors involved and their causal relationships, from the uncertainty in the occurrence of events to the value they assign to the consequences.

The students of the 3GS class at Liceo Giulio Casiraghi in Cinisello Balsamo (Milano) were involved in a year long project, named “I Participate, We Decide”, in cooperation with the Institute of Applied Mathematics and Information Technologies of the Italian National Research Council (IMATI CNR) in Milano. As a result of the project, they took part in the TEDxYouth @ Bologna event (http://www.tedxyouthbologna.com/un-nuovo-inizio/) and won in the Mathematics and Economics category. For the event, held in Bologna on November, 12th, 2016, the students prepared a video available at http://web.mi.imati.cnr.it/fabrizio/doc/ruggeri/Filmato.mp4.

TEDxYouth @ Bologna is a national competition, realized in collaboration with MIUR (Ministry of Education, University and Research), aimed at developing the excellence of Italian high school and increasing students’ competences and public speaking skills.

The project, conducted under the guidance of their Math teacher, Prof. Anna Ippolito, and Dr. Fabrizio Ruggeri, Research Director at IMATI CNR, aimed to choose the optimal way to spend (hypothetical) 100,000 Euros to improve school life. The students, who complemented their Math work with reflections on participatory democracy during their Philosophy classes, first created a Facebook group, open to all students in the school, where anybody could suggest possible purchases and express opinions on the various proposals. After identifying possible purchases (e.g., material for labs, multimedia boards, locks), a search was made to know their costs. Eventually, 18 options were found on how to spend the available hypothetical funds.

Subsequently, the most important factors were identified to determine the goodness of a purchasing option: school welfare, formative success, security and number of enrolled students. Other relevant factors were identified and causal relationships were studied, first through a brainstorming session, which produced a graph on the whiteboard, and then through a matrix where the relationships between the 26 factors identified were expressed by 0 (no relationship) or 1 or -1 (actual relationship, with implication determined by the sign).

At the same time, students learned the use of GeNIe software (https://www.bayesfusion.com/), originally developed at the University of Pittsburgh, which allows building Bayesian networks in a relatively simple way. The Bayesian network is based on the conditional probability assignment on the nodes (the factors mentioned above), e.g., on the likelihood of better school reputation as the thefts diminish and the results of INVALSI trials (a nationwide test on the students’ skills) are good. First of all, students began to assign probabilities to a network prepared by Dr. Ruggeri on the purchase campaign of a soccer team (AC Milan), also assigning a value (gain) linked to the victory in the national championship and the qualification for an European Cup, and then choosing the option maximizing the expected gain. Subsequently, the students themselves built a simple Bayesian network on the choice of the place to go on holiday and, finally, once they learned how to structure a problem, assign probabilities and utility, they built the Bayesian network for school expenses based on the matrix previously described. A subset of the network built with GeNIe is shown in Figure 1 with parents and children of the node “Learning” (“Apprendimento” in the original network, in Italian). The probabilities shown in Figure 1 are the marginal probabilities about improvement or not, whereas the conditional probabilities assigned by the students to the node “Learning ” are presented in Table 1 where “>” means “Improves” and “<” means “Not” (i.e. it does not improve).

Figure 1: Marginal probabilities of parents and children of node “Learning”

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Table 1: Conditional probabilities of the node “Learning”

In the end, the optimal solution, i.e., the one that maximized the expected utility, was to repair 50 ceilings, 100 locks and 4 bathrooms, buy 70 school tables and make a contribution to 50 students for a school trip. It is clear that care and maintenance of school facilities has been a priority for students!

During the project the students had also the opportunity to visit IMATI CNR and discuss with researchers about their work, especially about application of stochastic methods in engineering, biology, agriculture and earth sciences.

More details on the project are available in the recently published paper (in Italian, sorry!):

Anna Ippolito, Fabrizio Ruggeri (2016), Le reti bayesiane come strumento per l’analisi di problemi complessi: il caso del bilancio partecipato in una scuola secondaria superiore, INDUZIONI: Demografia, Probabilità, Statistica a scuola, vol. 53, pp. 78-89, DOI: 10.19272/201600902006