95% eeeech….

A question on the French public radio, France Inter, in a weekly high school students quizz:

If a lamp bulb factory has a constant failure rate of 5%, how many bulbs should it at least produce to deliver 1900 operational bulbs?

To which the pair taking part in the quizz, in their final year of high school and hence entering university next year (!), could not answer… Another illustration of the cataclysmic collapse of maths skills in French schools.

la remise en cause des mathématiques comme outil exclusif de reproduction de la bourgeoisie

A tribune that was published by Le Monde a few days ago celebrates the end of the “dominance of mathematics [in high school programs] as the unique reproduction medium of the bourgeoisie”, in  connection with a recent reformation of French high school programs where students have to specialise in only three topics in their final years. This change has led to a major drop both in the number of students studying maths and in the contents of the maths curriculum. As a result, there will less students entering university with a basic maths background and an overall regression in their level. At a time when international scores show French pupils are on average the worst ones in Europe and when the French government has huge ambitions to develop national AI companies,  this drift should be most concerning… But not for the author of the tribune, a high school professor of history and geography, who is most happy in the rise of students specialising in his subject, with a caricaturesque opinion on the inegalitarian role of mathematics:

“[la réforme] devait dès lors permettre, par le jeu des nouvelles spécialités, l’expression d’aptitudes plus diverses et d’en finir avec la prééminence systématique des mathématiques comme instrument de sélection scolaire et sociale.” [the reformation should then allow through new specialties to account for a wider range of abilities and to end the systemic preeminence of mathematics as a tool for school and social selection]

“[les mathématiques] demeurent le choix privilégié des mâles CSP + soucieux de préserver leur rang social” [mathematics still are the favoured option of higher class males afraid to loose their social position]

“[la spécialité histoire-géographie-sciences politiques] doit contribuer à la promotion sociale des plus défavorisés et à la remise en cause des mathématiques comme outil exclusif de reproduction de la bourgeoisie.” [the history, geography and political science specialty must contribute to the social promotion of the least favoured and to the demotion of mathematics as the unique instrument of preservation of the bourgeoisie]

If it was not so sadly representative of a general perception of mathematics within the global population and among the high administration of the Education Ministry, the outdated ideological tone of the tribune would have been quite hilarious.

Le Monde puzzle [#1063] and le bac’

As pointed out by Jean-Louis Foulley in his comment on the recent Le Monde puzzle [#1063] post, the questions are heavily inspired by the 2018 high school final exam (known as Le Baccalauréat or Le Bac’) in mathematics in France, as can be checked from the above. Including the denomination of powerful number! In Part A, the students had to study the Diophantine equation x²-8y²=1 (E) and show it had an infinite number of (integer) solutions. While these students did not have access to computing facilities, question 1 was solved by sheer enumeration, providing 8=2³ and 9=3² as an answer. While (2) and (3) are rather straightforward, using the prime number decomposition of a and b for (2), the fact that x² and 8y² are powerful for (3). Brute force search leading to x=99,y=35 for the final question.

(mis)selection at French universities

There was an most relevant article in the weekend edition of Le Monde about the absurd posture of French laws, governments and universities about prohibiting any selection at the entrance to university. Under the current regulation, anyone with the baccalauréat degree can apply to any first year program and expect to be accepted. Since this is impossible, universities have to discriminate based on the current address and, if there still are too many applicants, resort to random sampling. To avoid selecting based on high school records or even the final grades at the State level baccalauréat. Or the same universities have to invent some local degrees that are not recognised as national (State) degrees. This is more than absurd, obviously, as it drives most of the best students away from the university system into private schools or abroad. (Paris-Dauphine chose a few years ago to opt out from being a national university, in order to select its students and is thus private in this respect if public in its funding.)

One extreme [and personal] example of this Kafkaian (dis)organisation is provided by medical studies. Anyone with a baccalauréat with any major (science, humanities, carpentry, …) can on principle enter a medical school! Obviously, there must be some selection before too many patients die or too many doctors graduate and the way it operates is as follows: a huge number of students enter the first year of medical studies where they follow mass teaching, with courses mostly on video and tutoring from second year students. They take two one-day exams in December and May with only multiple answer questions. And about 10% of those students are accepted in second year… Among the 90% who fail, about 40% are allowed to try again. Once. [Our daughter thus spent two years of intense bachotage to enter the second year. Congrats to her for her dedication and success!] In the end, French doctors are certainly not worse than others, but this remains a waste of time, energy and money for a huge number of people, with no other argument than an ideological call to égalité. Which translates in practice into a huge inequality between students who can afford private tuition and massive family logistic support [as we found out!] and those who cannot. Furthermore, some universities are bursting at the seams with the number of first year medical students, in constant augmentation despite the 10% success rate. And are thus considering introducing random sampling as well! Using the (costly) baccalauréat to restrict the number of accepted first years students would seem reasonable and rational, as would a more directive orientation of high school students as advocated by Le Monde. An unlikely move, given the potential political impact of the measure.

philosophy at the 2015 Baccalauréat

[Here is the pre-Bayesian quote from Hume that students had to analyse this year for the Baccalauréat:]

The maxim, by which we commonly conduct ourselves in our reasonings, is, that the objects, of which we have no experience, resembles those, of which we have; that what we have found to be most usual is always most probable; and that where there is an opposition of arguments, we ought to give the preference to such as are founded on the greatest number of past observations. But though, in proceeding by this rule, we readily reject any fact which is unusual and incredible in an ordinary degree; yet in advancing farther, the mind observes not always the same rule; but when anything is affirmed utterly absurd and miraculous, it rather the more readily admits of such a fact, upon account of that very circumstance, which ought to destroy all its authority. The passion of surprise and wonder, arising from miracles, being an agreeable emotion, gives a sensible tendency towards the belief of those events, from which it is derived.” David Hume, An Enquiry Concerning Human Understanding,