Cédric Villani

Bruises on the math hump.

What are the current strengths and weaknesses, the sticking points and potential levers that make us, the French, at the 26e place in the Pisa ranking? Making young French people love maths and improving their level in this subject was the mission entrusted in October 2017 by Jean-Michel Blanquer, Minister of National Education, to the mathematician and deputy Cédric Villani, and to Charles Torossian, Inspector General of National Education. Mission accomplished, the copy has just been returned this Monday, February 12 with 21 recommendations, one of which is particularly essential: the upgrading of teachers to change the way of teaching mathematics ...
Ne have nevertheless won the prestigious Fields Medal 13 times, including the one awarded in 2010 to our national Cedric Villani; the last time was the one awarded to our national Abel Prize (equivalent to the Nobel Prize) which, after the Fields Medal, is the most prestigious award in mathematics, was awarded in 2017 to Yves Meyer, for the fourth time to a Frenchman since its creation in 2003. In spite of such models, French students today are more than mediocre in this discipline, whereas until 1985, the teaching of mathematics in France was recognized as one of the best.  
The national assessments still confirm this worrying finding. For example, the Cedre of the Department of Evaluation, Prospective and Performance (Depp) reveals very fragile gains at the end of primary school. It shows that 42.4 % of pupils have a fragile mastery of mathematics, or even major difficulties. Multiplying 35.2 by 100 thus represents a major obstacle for half the pupils at the end of primary school. This fragility in mathematics persists thereafter, since the JDC survey (2014) shows that one young French person in ten has difficulty using everyday mathematics. To put it another way: 10 % of young French people suffer from a handicap in carrying out daily activities when numbers are involved, which hinders the achievement of their personal projects (business creation, etc.).

Why this degradation?

Let's go back in time ... From 1880 to 1968, following the Ferry Laws, French mathematics teaching was of exceptional quality. To understand the reasons for the drop in level, we must go back to the time when the teaching of mathematics in France reached excellence. For Jean Pierre Demailly, a teacher-researcher at the University of Grenoble, we must go back to the time of Jules Ferry, who in 1881 introduced free and compulsory education for all up to the age of 13: "II y had very extensive studies by educators such as Ferdinand Buisson in France and Wilhelm Grube in Germany, which led to the implementation of the best teaching strategies known at the time, and it worked extremely well, especially for calculus. I would say that from those years, from the 1880s until about 1968, French primary education did not change much, and was recognized as one of the best in the world, if not the best. Especially in the inter-war period, between 1918 and 1940; the only notable change was the abolition of higher primary education by J. Carcopino in 1941. » explains onFrance Culture last December Jean-Pierre Demailly, a teacher-researcher at the University of Grenoble.
This is one of the reasons why, from 1945 to 1970, France experienced a veritable scientific golden age," Jean-Pierre Demailly explains: "It was the time when all the people who benefited from this teaching were operating. From 1945 onwards, France experienced a period of remarkable development of its mathematical research; it continues today, but is seriously threatened by the current state of our education system. »
In the 1950s and 1970s, France was known for its excellence at the world level: "France was almost dominant, with exceptional mathematicians who alone produced a large part of the world's mathematics. There was the revival driven by the Bourbaki group in particular, and then some extraordinary mathematicians such as Jean-Pierre Serre and Alexandre Grothendieck. Extremely abstract, powerful mathematics were created. »
And then came "modern mathematics". In this same post-war period, new educational recommendations began to emerge in the world, based more on ideologies and smoky socio-psycho-educational theories than on a rigorous analysis of teaching practices, again according to Jean-Pierre Demailly. In France, they are nourished by the successes of mathematical abstraction. This will lead in particular to the reform of what will be called "modern mathematics", which was at the origin of an upheaval in mathematics teaching methods in the period 1969-1984, explains the academic:
"The reform of modern mathematics was based on a reasonable a priori idea: high school education at the time was not very close to the scholarly mathematics practiced by researchers. But there was the illusion that we were going to be able to bring some of this mathematics down to a very high level in general education, all the way down to kindergarten! »
In 1969, a first reform thus affected the teaching in high school, where they began to catechize this modern, rather abstract mathematics. The fiasco was not immediate, however, according to Jean-Pierre Demailly, who claimed that half of his Terminale C class was doing well:
"It was simply mathematics as it would be taught today in the second or third year of university, but made available to high school students. »
From 1970-1971, it is the beginning of the end: the teaching of modern maths is set up in secondary school, then in primary school... and even in kindergarten! And if the gifted pupils or those who had benefited from a family impregnation could possibly follow, the others were disoriented, at least as much as their parents, as Jean-Pierre Demailly still tells us: "At that time, children were taught in a very formal, axiomatic way. For example, they were given a completely abstract, bewildering definition of the right, in 4th grade. Correct, but I don't think any student could take advantage of that. As we pushed the excess of formalism at all levels and as the fundamental teaching of primary school, reading, arithmetic... deteriorated a lot in the meantime, from 1980 onwards we ended up with pupils who could no longer absorb these extremely ambitious contents. It was a failure. The first major planing operation took place under the Chevènement ministry. The pendulum swung back and then we threw everything out! » (Source : France Culture - Modern Mathematics. Les grandes avenues de la science moderne, 09/11/1971)

Objective of the Villani Report: "To formulate concrete proposals based on the most conclusive practices and in the light of international studies. »

No revolutionary proposal in the report, according to the statement by Cédric Villani himself this morning on LCP : "Let us finally do things the way the evaluations tell us, let us get on with it, and let us give ourselves the means to teach this discipline.
It would therefore not be a question of overturning the curriculum once again, but of changing the way of teaching, and therefore of better training teachers, especially school teachers. The report lists 21 measures and 32 additional recommendations to improve the level of mathematics among French students and to make them love this discipline, which The term "is indeed a special place in the school curriculum".
Indeed, it has become the queen subject for access to the best schools and "its symbolic weight far exceeds its real weight". The report notes that this "domination" exerts "a widespread feeling of self-deprecation among students and adults alike" and that as early as age 7, "students already declare themselves 'maths losers'.
"One of the conclusions of the report is to realize how deficient the human framework is in this area. Very few school teachers feel comfortable with mathematics and this is normal given their background and training", as many teachers come from literary backgrounds, said Mr. Villani. The report highlights a great deal of suffering in the teaching profession, correlated with this degradation, and equally worrying, fuelled by the deterioration of the image of the teacher in society. The heavy administrative burden, the impression of non-recognition, including salary...are contributing to this malaise. One third of school teachers say they do not like teaching mathematics. Classroom management problems (1), that encroach on actual time, generate additional job anxiety and increasing resignations.
Among the measures recommended in the report is the construction, starting in 2018, of initial training for teachers in schools starting at Bac+1, in the form of a bachelor's degree or a multidisciplinary course with a volume of teaching dedicated to fundamental disciplines. It is also a question of developing in-service training in mathematics for primary school teachers.
The report also suggests providing all schools with basic equipment, accompanied by tutorials, that encourages the manipulation of real or virtual objects. It is also necessary to "give back their place to the structured course and its written trace, to the notion of proof and explicit learning", to develop automatic calculation at all ages "through ritual practices" ("mental and intelligent calculation", repetitions) and "cultivate the meaning of the four operations from the first grade onwards".
Another idea: to offer high school students an annual "reconciliation" module with maths on new themes and approaches.

What about the fun in it?

"Teaching a math class, if you do it right, tomorrow will be more exciting than it ever was, assured Cedric Villani.
It is well known that pleasure and desire are fundamental drivers of learning. But, without effort, there is no progress either. It is necessary to develop a sense of effort in the pupil, to avoid underestimating his potential: to offer him ambitious and accessible content, thus developing a desirable but accessible difficulty, and to encourage him.
In elementary school, "let the numbers be your friends". In order for numbers to become "his friends", the child must become familiar with the transition to abstraction and mathematical writing at an early age. Thierry Dias, in his book "Manipuler et expérimenter en mathématiques" (Edition Magnard, December 2017) and Hervé Le MadecThe teacher of schools specializing in psychological disorders, stressed the reassuring and reassuring aspect of the simplification and stability of the abstract. It is of course not a question of freezing the childish representation in an empty abstract, but of constantly moving back and forth between concrete situations and mathematical expression, as soon as the pupil discovers the richness of alphabetic writing-reading. Many speakers pointed out a particular difficulty in learning numbers, due to the irregularity of the language used in France to numbers from 70 to 99 This is not the case in Switzerland or Belgium. (2). This irregularity is a real problem in many Western languages, but not so much in Asian languages. But modifying our language is an otherwise difficult problem, which is why students will have to be prepared to overcome this difficulty by spending more time constructing decimal numbers.
Fun through play. In order not to allow anxiety about the school task in mathematics to set in, one should draw inspiration from Canada, Singapore, the United States or Northern Europe, where school activities in mathematics are mostly associated with the notion of fun. Games, puzzles, contests, challenges and stories are all there! Contests, rallies and workshops such as MATh.en.JEANS are all part of this. In France, the largest initiative on this subject is the Kangaroo contestwhich is part of an international movement. We can only hope that this type of initiative will multiply.

Alternative methods: giving way to the child's intuition

There are a very large number of pedagogical methods that are supposed to make it possible to better involve the pupil in the learning process (e.g. in Finland, where methods of participation, group work based on socioconstructivism, etc. are practised). They can make it possible to give interest and attractiveness to the subject (changes of framework, link between mathematics and science, arts, etc.).
This sometimes makes it possible to "hang up" some students with little motivation and to better put them in a situation of success, according to Jean Cassou, a mathematics teacher and author of the book. "School: is it really better elsewhere? "(Edition Les impliqués, 2015).
It is also the approach of active pedagogies, mainly represented in France by Montessori schools and the Freinet movement. Manipulation holds a primordial place, but it is thought with a view to abstraction and this in a perspective of extended progressivity over the long term.
These methods are based on the child's senses and intuition, which has been the principle of the French School for over a century, knowing that "The moment when it is a question of passing from the intuitive form to the abstract form is the great art of a true educator", according to Ferdinand Buisson (3). This passage from the concrete to the abstract is at stake in different procedures depending on the methods, but many of them are based around the triptych manipulation - verbalization - abstraction.
If we take the case of Singapore, in one generation, that republic has gone from a third world economy to one of the highest levels of prosperity. Most indicators show that its students are excellent in all subjects. This success is the result of a political will that was affirmed in 1997. Schools that think" are described as learning organizations. "A learning nation' envisions a national culture and social environment that promotes lifelong learning for its enlightened, committed and capable citizens. meeting the challenges of the future at the dawn of the 21st century.
In order to become a leader in a technological world, the country has taken the decision to radically improve its mathematics programs. All parts of the education system, and its partners, have therefore mobilized to design the Primary Mathematics Project. Although it includes excellent tools for the teacher, what is called the "Singapore Method" is more than that: it is a harmonized, coherent and high-quality curriculum that includes a clear and ambitious vision, effective teaching tools, in-depth professional training, systematic assessment and evaluation, and a system of teamwork that supports teachers.
The method used in Singapore is not a "Singapore method" in the sense that it was invented in Singapore. ex nihilo It is a synthesis of effective didactic and pedagogical practices, based on the work of numerous researchers. (4) or drawing inspiration from older texts (5). For fifteen years, the method has been tested, corrected and improved thanks to feedback from the field. All teachers in the country have been trained in the National Institute of Education. These efforts have paid off: student performance has skyrocketed and the world has taken note. (6). (See Report p 19).

Mathematics, a national priority

This subject should also be included as a "national priority" with the mobilization of actors from the entire chain, from rectors to teachers. For, as the Villani report states, the current image of mathematics is worrying. Mathematics has a special place in the school curriculum: it has become one of the keys to gaining access to the most sought-after studies and schools. This means that, for many courses of study, its symbolic weight far exceeds its real weight.
Moreover, the impact of mathematics in today's digital economic world increases this pressure. This dominance is even on everyone's mind. The development of a sense of self-deprecation is widespread, among students and adults alike; because they are not part of the trio of students who turn out to be between 18 and 20, even students of quite satisfactory level come to see themselves as "Dummies in math." and sometimes hear themselves say it. By the age of 7, some students already declare themselves "math failures".
Faced with such a situation, one can only wonder. How does this sequence, which leads to a lasting loss of self-esteem, come about? How can a discipline, recognized for its usefulness and its formative virtues to the rigour of reasoning, be perceived as a repellent? The place and role of mathematics deserve to be clarified and brought back to their right proportion. At the same time, however, mathematics must be revalued, in simple terms. The place of families in the monitoring of pupils must be reinforced, and therefore authorized and instituted at the highest level, again in ordinary terms. Parents must be encouraged to meet teachers and to question their children's results, at the same time as teachers and supervisors must be encouraged to value all pupils.
(Sources: Report of the Ministry of National Education, AFP)
  1. Cnesco: According to the Talis survey (2013), priority education teachers estimate that they devote 21 % of class time in secondary school to creating and maintaining a favourable classroom climate (compared to 16 % outside priority education and 12 % in private schools).
  2. To avoid the failure of 1945, on the evolution of the Vaugelas Code, Guy Brousseau proposed the creation of a commission to study "the conditions of an experimental didactic transition of the mathematical repertoire of pupils from 5 to 8 years of age".
  3. Ferdinand Buisson, Dictionnaire pédagogique d'instruction primaire, 1887
  4. Jérôme Bruner, George Polya, Richard Skemp, Jean Piaget, Zoltan Dienes, Lev Vygotsky, Benjamin Bloom, Maria Montessori
  5. Ferdinand Buisson, Dictionnaire pédagogique d'instruction primaire, 1887.
  6. In the United Kingdom, since 2016, 45 million euros will be invested over four years to train nearly 700 teachers and extend the use of the "Singapore method" to some 8,000 primary and secondary schools.
To go further
- Book " Réveiller le désir d'apprendre " by Agnès Baumier-Klarsfeld - Preface by François Taddei - Editions Albin Michel, 2016
- Book " Jules Ferry et l'enfant sauvage - Sauver le collège " by Mara Goyet - Edition Flammarion, 2014
- Book " On acheve bien les jeunes " by Bernard Spitz - Edition Grasset, 2015
- Book " La réforme de l'école maternelle - pour éradiquer l'illétrisme " by Franca Lugand-Ciacci - Edition L'Harmattan, 2017
- Book " Teacher trapper, why not! Quand la nature réenchante l'école" by Philippe Nicolas - Editions Le Souffle d'or, 2017
- Book " Changer l'école - Maria Montessori " by Jacqueline Aymeries, Stéphanie Vailati- Editions à dos d'âne, 2016
- Book " Théorème vivant " by Cédric Villani - Edition Grasset, 2012

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