Some idea of math lessons

In his column, Etienne Ghys takes us to the challenges organized by the association MATh.en.JEANS, for students of all school levels. A nice way to give a taste of maths.

“Carte blanche”. The 2018-2019 season of the association MATh.en.JEANS ends. Since March, ten mathematical congresses have been held throughout France, and two more will be held in May, abroad. These congresses are very unusual: the participants and speakers are students of all school levels, from primary to high school. In 2018, 4,500 students participated (almost half of whom were girls) and 680 mathematical topics were discussed in 300 “workshops”.
The principle is as follows: teachers propose to students (volunteers) to reflect on a topic that has been suggested by a referent researcher. Small groups are formed, often straddling several schools, and the students meet once a week to reflect together on their problem. The big moment is the congress during which the students present their results in front of their classmates, but also in front of the teachers present in the amphitheater. These moments of exchange are magical; it is so rare to see a student on the blackboard explaining to a teacher what he or she has discovered! Some of these presentations are written and published by the association.

The themes covered are surprisingly diverse. Sometimes it is about number theory. For example: if I multiply all the integers from 1 to 1,000, how many 0’s will there be at the end of the result of my calculation? Other times, it is combinatorics that is in the spotlight: how can I place a certain number of points in the plane so that the line joining any two of them contains at least one more? Or again: if I place an even number of points in the plane, can they be joined two by two by segments that do not meet?
Other themes are much more “useful”. I remember, for example, a group of students who could no longer stand the long queues at the canteen at noon. They tried to optimize the timetable by suggesting to the principal to slightly modify the hours of classes so that the students did not all go out at the same time. Optimization is not as simple as one might think. There are also groups working on magic tricks or winning strategies in a (very) simplified version of poker.

Nice exponential behavior

The association was founded in 1989 and its growth shows a beautiful exponential behavior, a tripling every ten years or so: we should exceed one million students involved in… fifty years! All the surveys show a drop in the level of French students in mathematics. Should the number of hours of classes be increased? What should we think about the future disappearance of mathematics from the common core in the first grade? Shouldn’t we support more firmly initiatives like MATh.en.JEANS by moving to much higher orders of magnitude?
This would require massive financial support from the national education system, which is largely insufficient. Today, 600 teachers and 200 researchers are involved in the association, all volunteers. It should be considered that this kind of activity is an integral part of the mathematical training of students. Voluntary work and volunteering have their limits .
It’s an opportunity to do a little advertising. “The purpose of the André Parent Prize is to recognize research work, supervised or not, carried out by a group of young people (primary, middle or high school) during the school year, on a scientific subject in which mathematics plays a key role. “The prize will be awarded during the 20th Salon Culture et Jeux Mathématiques, to be held on May 23, 24, 25 and 26, Place Saint-Sulpice, Paris.

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