Top model

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:
Emily Tanimura, Patrick Pamphile/ Mathematicians

Chargée de projet:
Florise Pagès

Objectives:
Constructing a model - the main contribution of what’s known as “applied” mathematics - is always somewhat surprising in that it is a blend of intuition, survey and calculation in equal parts that involves selecting a well-defined “subject”, obtaining abundant information about it, translating this information into figures and then into a model that can predict how it will function. 

Workshops:
Everyday Life in Numbers
Using examples familiar to students, the contributor helped them see how maths can be used in everyday life and can, using predictions, provide answers to a question for which we lack information, e.g. the weather. The students made predictions and modelled the “chance”, “risk” or “probability” that something would happen using sports lottery cards, tossing coins or throwing dice, recording the results in a frequency table and simulating this on a computer.

14th June – 15th July 2018  
The students had to design a model that can predict who will win the next football World Cup (Russia 2018) using models they apply to their topic. To do this, they carried out a survey of the teams based on their recent matches to determine the significant factors that are easy to measure and temporarily defined, which they could prioritise: a good coach, already played in a world cup, already played against a particular team, already won the world cup, etc. The students then discussed these factors with sports journalists from Foot Citoyen who added empirical and uncertain aspects to the equation, explaining that in a World Cup, there is always a team that accomplishes a major feat and defies the odds, or that the host country has never lost its first match. From here, the students sorted and prioritised all the indicators they had collected: star players, coach’s profile, game strategy and previous wins, but also jet lag, injuries, etc.

Predictive Models
The class chose the ELO model, a model to predict the chances of winning used, among other things, for FIFA and chess players’ ranking. They then simulated the winning team from the quarter finals to the finals.  In the end, it is not one winning team that emerged but the teams the most likely to win. The class was aware of the system’s margin of error and that the “law of large numbers” can reduce this margin: the more simulations carried out, the closer one gets to reality. Above all, the students established a set of tools so that each of them could vote for a team, making informed choices. The model’s flaws were discussed and the results compared with the predictions made at the start of the project. 

Showcase:
Inspired by the shapes of mathematical objects, a giant ball was created using elements each representing the content produced by the class to reach the final result. Set up in the school grounds, the structure became a place to meet up and discuss the project. For one school, the most likely final was Brazil v. Germany, with Brazil the most likely to win; however, the chance that a different team would win was nonetheless 32%. On the contrary, the most unlikely final would have been Poland v. Portugal. For the other school Brazil was also the most likely winner, as was Germany, France… or even Portugal!

Acknowledgements:
Frédéric Hamelin and Nicolas Gettliffe/ Journalists from Foot Citoyen

Outing:
- Workshop on probability and statistics followed by a trip to the Maths Area of the Palais de la Découverte in Paris.

Participating schools:
- class 3è A, collège Paul Eluard, Montreuil
- class 4è Ellis Island, collège international, Noisy-le-Grand

Scenography: ELODIE DESCOUBES

Photos: PIERRE ANTOINE