French & German’s Secondary School Maths Comparison

A French math teacher’s insight in math classes in Germany (15 years old = Secondary 3) and France (16/17 years old in Sec 4 & Pre-U / JC 1):

The French Math is more theoretical while the German Math (like English Math) is applied. So the result is Germany produces excellent precision engineers with Applied Math, while France produces 1/3 of the World’s Fields Medalists in theoretical Pure Math.

Many English GCE A-level top Math students from Singapore studying in French Universities face the same dilemma: while their French Math professors think they are “weak” in Math (i.e. French abstract Pure Math), yet they beat the French classmates in Applied Math.

The ideal Math Education is to have the best of both worlds: the Applied Math used in science & engineering, and the theoretical Pure Math in its powerful generalisation capability for higher research & development.

French Prépas ‘Colle’

Colle = Oral Interrogation

In French, ‘coller’ (the verb of colle) is to ‘glue’ (on the blackboard) i.e. get stuck by the Oral Interrogation.

This tradition started from Napoleon time, even Victor Hugo (author of Les Misérables) got ‘colle’ in Lycée Louis Le Grand’s Classe Préparation (or Prépas in short, equivalent to 1st and 2nd year of undergraduate course, for French Top 10% Baccalaureat students, who aspire to enter the elite Grandes Ecoles after many competitive Concours Entrance Exams).

Every week in the 2 years of Prépas there are 2 of the 4 colles: Math & Physics, or, Chemistry & Second Language (English / Spanish / Russian / German).

This video is the session of a Math colle. The students are grouped in 3 (Trinôme), take the oral test after 6 pm by a professor from internal or external university.

It is a nightmare for Math colle. Not so much for Physics or Chemistry. English colle for Singaporean student is easy except the translation from English to French.

300 years ago till today the Colles are still the same. The French like tradition but this Prépas and the Colles are horrible to kill the young French like Evariste Galois and many more young talents.

French Taupe: 3/2 & 5/2

French elite Grandes Écoles (Engineering College), established since Napoleon with the first Military College (1794) École Polytechnique (nickname X because the College logo shows two crossed swords like X), entry only through very competitive ‘Concours’ Entrance Exams – to gauge its difficulty, Évariste Galois failed in two consecutive years.

Before taking Concours, there are two years of Prépas, or Classe Préparatoire (Preparatory class) housed in a Lycée (High school) to prepare the top Math / Science post-Baccalaureat students. These two undergraduate years are so torturous that French call these students Taupes (Moles) – they don’t see sunlight because most of the time they are studying 24×7, minus sleeping and meal time.

Most students take 2 years to prepare (Year 1: Mathématiques Supérieures, Year 2: Mathématiques Spéciales) for the Concours in order to enter X. These students are nicknamed 3/2 (Trois-Demi), so called playfully by the integration of X:

\displaystyle\int_{1}^{2} xdx= \frac{1}{2}x^{2}\Bigr|_{1}^{2}=\frac{3}{2}

If by the end of second year some students fail the Concours, they can repeat the second year, then these repeat students are called 5/2 (Cinq-Demi) – integrating X from Year 2 to Year 3:

\displaystyle\int_{2}^{3} x dx=\frac{1}{2}x^{2}\Bigr\vert_{2}^{3}=\frac{5}{2}

Évariste Galois was 5/2 yet he still failed X, not because of his intelligence but the incompetent X Examiner at whom the angry Galois threw the chalk duster. (Well done !)

Another famous 5/2 is René Thom (Fields medal 1958) who discovered ‘Chaos Theory’.

There are few rare cases of 7/2 (Sept-Demi):
\displaystyle\int_{3}^{4} x dx=\frac{1}{2}x^{2}\Bigr\vert_{3}^{4}=\frac{7}{2}
for those who insist on attempting 3 times to enter X or other elite Grandes Écoles. Equally good – if not better – is École Normale Supérieure (ENS) where Galois finally entered after having failed X twice. The tragic Galois was expelled by ENS for his involvement in the Revolution.

Note: Only 200 years later that ENS officially apologized in recent year, during the Évariste Galois Anniversary ceremony, for wrongfully expelled the greatest Math genius of France and mankind.

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One of the top Classe Préparatoire “Lycée Pierre de Fermat” named after the 17th century great Mathematician of the “Last Theorem of Fermat”, in his hometown Toulouse, Southern France.

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