In all probability

Since 2009, the Seine-Saint-Denis County Council has been backing “la Culture et l’Art au Collège (CAC)”. This project is based to a large extent on the presence in class for several weeks (40h) of an artist or scientist whose mission is to engage the students in a process of research and creation. 

Tutors: SARAH KAAKAI, EMILY TANIMURA, Danielle Tibi/ mathematicians, PIERRE BOISARD, NELO MOLTER MAGALHÃES/ sociologists

Project manager: Anna Mezey

Objectives:
This project was devised to offer concrete applications for notions of statistics and probabilities, to raise the question of uncertainty (often misunderstood by the general public) and to build bridges between mathematics and opinion polls.

Workshops:
The Measure of Things
The two contributors, a mathematician and a sociologist, introduce themselves to the students through the questions they tackle: How many students use social networks? How can Facebook data be used? What’s the probability that boys talk more than girls? They then study opinion polls to understand their objectives. The class also gets to grips with “the Law of large numbers”. At the end of this stage, the class chooses a survey topic.

Surveying and Coding 
The three classes choose different survey topics: food, free time and public transport. Depending on the theme and the target population (same-level classes, parents), the groups draw up a survey protocol with twenty closed-ended questions. The sociologist helps the group to formulate the questions properly so that the subject is respected and understood. After finalising the questionnaire, a paper or digital version of it is distributed. Once the questionnaires have been returned, the students encode the responses using Excel, and, with the help of the mathematician, they begin to establish statistics. 

Descriptive Statistics
Using the encoded data and Excel, the students represent this information in tables and graphs. The contributor shows them how to interpret patterns and estimations using methods to calculate probabilities. This gives the class the chance to learn about margins of error and the notion of uncertainty. The sociologist returns and analyses the final results with the students. Together, they make national comparisons. 

Outcome:
From 8th to 23rd June 2017, each middle school presented a selection of the findings from their surveys: “75% of Year 3è students have committed fare evasion”, “73% prefer travelling by car”, “37% play football”, “29% never eat chips”, “17% eat their evening meal alone”, etc. To accompany the installation, the students gave a detailed presentation of each stage of the process.    

Outings:
- Palais de la Découverte, trip to the temporary exhibition Faites vos jeux ! Quand les maths s'en mêlent (“Place your bets! When maths gets involved…”) and the presentation Du hasard aux mathématiques (“From Coincidence to Mathematics”)

Participating schools:
- class 3è A, collège PAUL ELUARD, MONTREUIL
- class 3è G, COLLÈGE JACQUES PRÉVERT, NOISY-LE-GRAND
- class 3è 4, COLLÈGE ROMAIN ROLLAND, CLICHY-SOUS-BOIS

Scenography: ELODIE DESCOUBES

Photos: PIERRE ANTOINE