Languages and mathematics, the same battle!

A recent survey published by the daily newspaper Le Figaro¹ , revealed that according to a 2013 memo from the Ministry of Education's Statistics Directorate, 40% of CM2 teachers reportedly said they had received no training on the French language, its learning and teaching. This is troubling, to say the least.

Then it was the Express, in its 30 June 2022 edition, which published an alarming report on the state of mathematics with the declarations of three tycoons.

A reality too long questioned

All this has been known for a long time.

Some thirty years ago, the first PISA surveys and the recruitment tests for the military service made it possible to diagnose that about 20% of each generation had no command of the fundamentals, i.e. French and mathematics, which are nevertheless conditions for continuing a normal education at secondary school.

A 2013 study carried by the French Ministry of Education had compared the written results performance of CM2 pupils in the same dictation. While an average of 10.7 spelling errors of a grammatical or lexical nature were found in their papers in 1987, in 2007, 20 years later, there were 14.7, i.e. almost 40% more² .

A study carried out in 2017 had already shown that the level of spelling proficiency of the French was dropping at all levels. The Voltaire Barometer is clear: from school to higher education, it not only confirmed what could be predicted, but showed that the evil had spread to the different strata of society. Only 35-40% of people know and apply the basic rules of language. This is true at all levels: in schools, in higher education and in companies. And mistakes are costly... because they damage the image of the writer and, in a professional context, that of the company as well.

So what has been denied for decades is now coming to light, and if the company directors are alarmed, it may be that the situation is really serious. So they start teaching French in higher education and in companies, as if it were their vocation. In fact, we're trying to fix in a hurry what we had had all the means to see and do for a long time.

A late but happy reaction

It should be acknowledged that the ministry of Education has started reacting with rather encouraging results.

An information note from the Ministry in February 2022 (No 22-04)³, concerning the assessments at the beginning of the sixth grade in 2021, reports a slight increase in performance in French and more marked progress in reinforced priority education (REP +), including in mathematics.

In the most socially advantaged « collèges », the mastery rates are 95.9% in French (+3.5 points compared to 2019) and 85.8% in mathematics (+3.1). In the least favoured schools, the mastery rates are 77.3% (7.3 points) and 51.1% (+1.9) for French and mathematics respectively. Clearly, the doubling of classes in CP and CE1 and the renewed emphasis on the fundamentals, advocated in 2002 by Jack Lang and implemented fifteen years later by Jean-Michel Blanquer, are yielding promising results, as part of the vast education project which is off the point here.

We will not mention the low teachers salaries, the teacher training, the length of the school year, timetables, social networks etc., subjects on which there is much to say, but this is not our domain.

We would like to focus on the language itself. Because, if it takes so long to react to a situation that has been known about for decades, it is because there may be a problem with the relationship between language and society.

The question of the relationship to language

How many times have we heard comments like: "Spelling doesn't count. What counts is intelligence. ?

If for so long we let children (who had not been given the basics, starting with the French language), move up to the sixth form and fail, it is undoubtedly because we did not measure the consequences of this deleterious choice and because we imagined that the child would end up learning French, the important thing being elsewhere.

If we don't set the record straight now by exposing all the flaws that could take us in the wrong direction, we can expect a difficult, very difficult future.

The magazin L'Express dossier, mentioned above, only deals with mathematics, because it is said the mathematics are intelligence, and if the level drops in mathematics and not only in language (mother tongue or schooling language) or in languages (including foreign languages), it becomes really serious. In fact, the Express study refers to language only marginally.

So when Alexandre Richard, CEO of Pernod Richard, says, for example, "Like Monsieur Jourdain with prose, we do maths without knowing it, and I have to admit that these equations and rules of three of everyday life are a little personal recreation for me", he is right, but he is very much below the mark.

If they were all manifestations of the same phenomenon. Of course there are mechanical aspects. If school teachers are essentially arts teachers, one should not expect an optimal treatment of basic arithmetic exercises. The same can be said of dictation, which is still considered by many to be a silly exercise, like playing scales in music.

Worldwide statistics indicate that IQ has been dropping for some time. It would seem that France is not an isolated case.

We argue here that language and mathematics go hand in hand and that the collapse of language and mathematics reveals and leads to a collapse of individual and collective intelligence.

Without getting into scientific and philosophical discussions, if we admit that "intelligence is the set of thought processes of a living being which allow him or her to adapt to new situations, to learn or to understand"⁴ and if we admit with Vygotski that thought and language, although different in nature, are inseparable processes, then we can make progress. To quote Vygotski again: "The meaning [of the word] can be considered both as a phenomenon of a verbal nature and as a phenomenon in the realm of thought."⁵

It is possible that our habits of thought, which separate everything, break them down and analyse, only see in language a communication activity, i.e. a surface phenomenon. And some will find it silly to link language, mathematics and intelligence.

Basic knowledge

We will limit ourselves to the question of the relationship between language and mathematics by remaining at the level of a "lesson in things", a word that evokes the « school learning qualification » of our parents or grandparents.

The first point is to say that when we speak, we can say anything and everything, but we also sometimes, even often and in crucial situations, do mathematics without knowing it.

Here are two examples, among dozens of others, of what we might call the logic of everyday life.

First principle: since it happened to me, it can happen to anyone. It's a kind of principle of generalisation of personal experience.

This is a very valuable principle, because our lives, our culture, are shaped by our personal experiences. But is generalisation legitimate? This is a fundamental question. "Truth this side of the Pyrenees, error beyond", said Pascal.

So it would be interesting to count, while listening to the radio or in simple conversations, the number of times you consider as true for everyone else what you personaly have observed. Another formulation of the same question: is my personal truth somehow universal?

Of course life is complicated and what 'I' think is true, often interferes with pre-established beliefs. It is true because it is what 'I' believe, or it is what 'I' believe because it is true. This is how common sense works. To stick to mathematics, the question of whether I have the right to make a general case out of a particular case remains unresolved. For example, after a vaccine, my neighbour got sick, so I believe that everyone will get sick after a vaccine, regardless of any metaphysical considerations about acting or not acting on the course of life.

An interesting experiment would be to count the number of times over a week when we are in a position to ask ourselves whether we are entitled to make a general rule from a particular case. This is a permanent issue, the problem being that, in terms of individual or collective behaviour, we are not aware of it. Nor are we aware of the fact that everything passes through language.

Following on from this first example, and moving up a level of complexity, let us talk about probability.

Mathematics of the « Fables de La Fontaine »

The example is fictitious, but everyone will recognise the connection with the current pandemic.

A person is vaccinated, but has one chance in 10 of becoming infected within three months. If this person are infected, he/she have a 1 in 50 chance of being hospitalized. Once in hospital, he or she has a 1 in 50 chance of being admitted to critical care, and if they enter critical care, they have a 1 in 10 chance of being admitted to intensive care, and then a 1 in 5 chance (risk) of not making it. The vital risk for the vaccinated person is thus 1 in 10x50x50x20x5 = 2,500,000 (fictitious example, I repeat). So the protection of the vaccine is not total, but if the same person is not vaccinated, let's do the same calculation again with slightly different coefficients. Let's say they have a 1 in 10 chance of being infected (the same rate as with vaccination, to simplify), that once infected their risk of going to hospital is 1 in 20, that once in hospital their risk of going to critical care is 1 in 20, then ending up in intensive care is 1 in 5 and finally, in intensive care, there is a 1 in 2 risk of not making it. In this case, the probability in relation to the vital risk is 10x20x20x5x5 or 1 in 100,000.

Thus, in the fictitious example and only in this example, an unvaccinated person is 2,500/100, or 25 times less protected against the virus than a vaccinated person (with three booster shots for example).

What is important here is that everything is done in natural language with a few reminders of mental calculation. So probability calculation is part of our daily life, as well as lottery games. Nevertheless, the mental representation of 1/2 500 0000 and 1/100 000 is not something immediate. Some people may not be able to make any representation.

In everyday language, two probabilities can be set against each other. One might say that a fully vaccinated person is 25 times more protected than a non-vaccinated person, whereas the risk of a side effect is statistically, for example, 1 in 100,000, given that behaviours are otherwise assumed to be the same. So the person who agrees to believe in the statistics will have to weigh up the risk incurred without a vaccine against the risk of side effects. But the journalist who makes the commentary and doesn't want to upset anyone remains vague. For example, he or she may say that opinions are divided and that some fear the side effects of vaccines while others have more confidence in the effeftivness of the vaccine, but the choices become almost impossible insofar as the risk, whether one is vaccinated or not, is seen as equivalent. It will become difficult to deduce from it an effective collective attitude.

So, behind these examples, there is indeed quite complex mathematical or statistical reasoning, but it is part of the "mathematics of everyday life" which passes through natural language with some quite simple mathematical expressions, understandable and likely to act on individual and collective behaviour.

Moreover, if you reread La Fontaine, The Cicada and the Ant and The Hare and the Tortoise, like many other fables, call for more complex mathematical reasoning than one might think, but unless there is proof to the contrary, fables cannot be translated into mathematical language.

This remark leads us to emphasise that all teaching, whether scientific or artistic, requires natural language.

Each subject has its own way of using language. Linguists call these discursive genres. There is a way of talking about mathematical matters just as there are different languages for law. A code is not written in the same way as a plea. But every subject, like every social usage, uses language in its own way, and so every subject, like every social context, requires access to and mastery of the language.

Thus, teaching mathematics, but also physics, chemistry, history and geography, also means teaching the language. The teacher is always interacting with language.

The same applies to the student.

Ah, the subjunctive!

To learn mathematics, students must be able to understand the wording. They need to understand the logical sequences and to integrate the probabilities and the possibility of hypotheses into these sequences. In everyday French, uncertainty, doubt, convenience, obligation, wish, probability, require in principle the use of the subjunctive. It is also very systematic in Italian, Spanish and Romanian. The subjunctive has a bad reputation, because it is said to be a difficult tense. If you give up the subjunctive, you have to replace it with something else, otherwise you lose your intelligence. Which comes first, language or intelligence, is a never-ending, almost pointless question, like the chicken and the egg, the processes are so intertwined that they cannot be separated.

Banalities?

We do not feel that we are stating new ideas here. And in fact, the 2006 Common Base⁶ said essentially the same thing in Article 1.

"Knowing how to read, write and speak French is a prerequisite for access to all areas of knowledge and the acquisition of all skills. The French language is the primary tool for equal opportunities, for the citizen’s freedom of citizenship and civility: it enables people to communicate both orally and in writing, in a variety of situations; it enables them to understand and express their rights and duties.

Ensuring that all pupils have a command of the French language and are able to express themselves accurately and clearly in both spoken and written form is a matter for the teaching of French, but also for all subjects.

Every teacher and all the members of the educational community are accountable for this priority mission of the school institution.

The acquaintance with the French literature is a major tool for the acquisition of the command of the French language.

...

"Written and oral expression must be worked on throughout compulsory schooling, including through the memorization and recitation of literary texts. Learning spelling and grammar should lead pupils to understand that respecting the rules of French expression is not contradictory to freedom of expression: on the contrary, it encourages precise thinking as well as rigorous and easily understandable reasoning.

The student should master the language tools of vocabulary, grammar and spelling sufficiently to be able to read, understand and write texts in different contexts.

Learning grammar and spelling requires specific exercises separate from the study of texts.

Things are extremely clear, at least in the wording, but were they really that clear at the level of those in charge and of society as a whole? It sounds like a refrain that is repeated out of habit without paying attention to it.

The comparison with the 2015 Common Core⁷ is significant in this respect.

"Article 1 - Articles D. 122-1 to D. 122-3 of the Education Code are replaced by the following provisions:

"Art. D. 122-1. - The common base of knowledge, skills and culture provided for in Article L. 122-1-1 is composed of five areas of training which define the major training issues during compulsory education:

"1° languages for thinking and communicating: this area covers the learning of the French language, of foreign langages and, where appropriate, regional languages, scientific languages, computer and media languages, as well as languages of the arts and the body;"

...

Domain 1: Languages for thinking and communicating

"The field of languages for thinking and communicating covers four types of language, which are both objects of knowledge and tools: the French language; foreign or regional languages; mathematical, scientific and computer languages; languages of the arts and the body. This domain allows access to other knowledge and to a culture which makes it possible to exercise a critical mind; it implies the mastery of codes, rules, sign systems and representations. It brings into play knowledge and skills that are used as tools for thinking, communicating, expressing and working and which are used in all fields of knowledge and in most activities.

Confusion on a large scale!

It should be noted that the notion of "mastery of language" has disappeared. Moreover, domain 1 covers four types of language without any prioritization. There is only mention of "codes, rules, sign systems and representations", whereas the specificity of natural language is precisely that it is not a code. And the four types of language have the same two functionalities of "thinking" and "communicating" and are both "objects of knowledge" and "tools". The idea expressed in an official document that language (French language and modern foreign languages) enables us to think is rather pleasant, but the use of the notion of tool opens up an abyss of interpretation. Confusing artistic creation with the paintbrush, the poet with the pencil, the axe with the executioner, bothers us, but it is very much in keeping with the times.

The level of abstraction of the very definition of this field is such that translation into programme terms may seem problematic.

Of course, learning the French langage has not disappeared from the curricula, and the mastery of French remains a priority for each of the three cycles throughout compulsory schooling. But there are doubts about the reality of this priority.

This sets out the main guidelines for the 2015 curricula.

Table 8: Allocation for each cycle of the main guidelines
prescribed by the 2015 curricula⁸

Cycle	Class levels	Orientations in the 2015 syllabus
2	CP - CE1 - CE2	"The mastery of languages, and in particular the French language, is the priority of the first three years.
3	CM1 - CM2 - 6ème	Cycle 3 has a "dual responsibility": "to consolidate basic learning" and "to allow a better transition" between primary and junior high school.
4	5th - 4th - 3rd	From the 5th year onwardse , the pupil has become familiar with the organisation and rhythm of the collège. They continue to build their skills, their citizenship and their career plans.

 

In this perfect ideal world, one imagines that by the end of primary school the child has mastered the French language and that the fundamentals are consolidated.

This is why we are now obliged to relearn spelling at university and even in companies. In 2017, a salutary change of direction was taken, which consists, as far as primary and lower secondary schools are concerned, in taking up the main thrust of the 2002 programmes, with the doubling of the first classes of primary school and an effective rather than theoretical emphasis on the fundamentals.

The first results are promising, but will be judged over time.

What about plurilingualism?

Dear reader, you may be wondering what this has to do with plurilingualism.

The answer was given in advance by François Rastier at the first European Conference on Plurilingualism held in Paris in November 2005, which gave birth to the OEP, in these terms

"In order to access to plurilingualism, one has to rely on quality monolingualism monolingualism: in other words, one can only really learn other languages if one knows one's own language well."

Of course, the content of one’s is in some cases problematic. For example, in a survey of pupils, when asked 'what is your mother tongue', the child replied 'my mother tongue is French and Arabic'. That says it all. This child is fully bi-plurilingual, i.e. the two languages function in his brain as two registers of the same language.

It is not necessary to be a highly well-versed in grammar to learn a foreign language, especially since, as Goethe said, learning modern languages contributes to the knowledge of one's own language. So do other forms of learning, especially artistic ones. But we must not reverse the priorities.

The centrality of language

This is not a speculative statement. Education, even informal education, and language, even oral and sign languages, are strategic in the development of individuals and societies, and their importance has only increased in modern times with the widespread use of the written word.

Language is not only primary, it is central.

The idea of the centrality of language, i.e. the ability to give sense to the things in the world, goes back to ancient times. In the beginning was the word", says the Old Testament, and the Greek word "poetic", at the source of language and languages, expresses the creative function of language. But from Heraclitus to Aristotle and right up to the present day, very few philosophers have actually dealt with this postulate, which has a certain form of self-evidence: namely, that no human being can do without language when he or she wants to communicate, and more than that, when he or she wants to elaborate and express a thought, when he or she wants to talk about the world. Language is a medium, not a tool. This is the centrality of language, without succumbing to any form of essentialization.

The great Italian linguist, Tullio de Mauro, devotes the first article of his famous essay Lezioni di linguistica teorica⁹ to the question of the centrality of verbal language:

"Verbal language is of fundamental importance in social and individual life because, through both receptive (ability to understand) and productive mastery of words and formulations, we can understand others and make ourselves understood (communicative uses); order and subject experience to analysis (heuristic and cognitive uses); and intervene to transform experience itself (emotional, argumentative uses, etc.).

This does not limit the importance of verbal language, but places it more clearly, emphasising that in general and in human beings in particular, it is one of the forms assumed by the capacity to communicate, which has been variously called the fundamental symbolic capacity or the semiological (or semiotic) capacity. And, again, both in general and in theory, and in the concrete and specific development of human organisms, verbal language has very close relations with the other expressive and symbolic capacities and activities."

This is why today, in France and not only, there is a fight for language and mathematics and it is the same, or almost!