Where we do a little "flash-bac"...
Yep! When I was 18, I took the Ecole Normale d'Auteuil entrance exam, and came 43rd out of 700. They accepted 90 of us, so I was right in the middle, which wasn't too bad considering my poor maths. I should point out that I took the exam at the time because I was attracted to this profession. It took the National Education system 20 years to discourage me from it, but that's another story, which is just as sad.
I was part of the last two-year program. I quickly realized how “out of touch” the teaching was. Basically, only “observation” or “situational” stays in classes at schools close to EN d'Auteuil or at the Decroly school in Vincennes, the aptly named “application schools”, taught us valid and usable things. The education we received at Auteuil was intellectual wank. For example, we didn't take any tests that would have enabled us to identify our shortcomings, with a subsequent remedial program. Nothing! You'd passed the concours, you were supposed to master everything.
We babbled on about linguistics and psycho-pedagogy, in an infantilizing and above all theoretical, even ethico-psycho-logorrheic atmosphere. We avoided at all costs venturing into their practical use. Most of these teachers had never taught in kindergarten, primary or secondary school. They'd just been appointed, God knows how.
I particularly remember the psychopedagogy teacher, who could have been drawn by Goossens (a french cartoonist) in his heyday. He was the archetypal self-conscious, vaguely hostile Catholic fundamentalist, wearing short-length pants with the hem 10 cm from the shoe. For him, a schoolteacher could only be a man, with a well-designed beard, prescription glasses, blouse, small leather satchel, street shoes that would never know the soft touch of the pants and, if possible, an incipient baldness. One day, the guy finally admitted that, in his eyes, we were all dressed “like beggars”. Nice, huh? Since I had nothing to expect from such narrow-minded, pitiful individuals, I embarked on a personal remedial program that lasted two years (79/80), because fortunately, if the EN teachers weren't any good, the teachers at the training schools were sometimes very helpful.
For french, especially grammar, I found a copy of the Berthoux/Gremaux/Voegelé Cours Moyen, 1951 edition, aged for 30 years in an oak bookcase, with an exemplary rigor and clarity that finally enabled me to clearly understand the mechanics of object complements, to review and refine logical analysis and to revisit what I'd learned. I eventually found one copy, which I still have. Of course, I supplemented it with the Bled series, dictionaries, synonyms, etymology and so on. In short, for French, it was no problem at all - I just needed to refresh some knowledge and fill in a few gaps.
As for maths, my “personal hollowness” being matched only by the intellectual indigence of our teaching staff (at Auteuil, I mean), the programs and, consequently, the math textbooks were much harder to grasp for a neophyte like me. As I explained earlier, I had no difficulty with arithmetic, mental arithmetic, the metric system, problem-type reasoning, etc. So I reviewed basic geometry, practising making exact if not pretty geometrical drawings, then doing the same on a blackboard with chalk and the famous yellow, wooden, ugly and fragile compasses, protractors, squares and T-rulers.
Somewhere during those two years, I came across a book that finally made me realize that the letters in equations were numbers, and it was “there and only there” that I learned how to solve ultra-simple tricks, enough to ensure elementary school level, but not much more, which is to say that my general mathematical culture was still on the same level. I shouldn't have been discussing equations with a 6th grader. I still don't.
I think I was as good a teacher as many others, and my pupils have confirmed this, even decades later, but I've always wished I'd been sharper in maths, for them.
On the basis of my experience as a “bad pupil”, I nevertheless tried other, more practical approaches, with the metric system for example. Visual or tactile experience of a meter, a centimeter or a decimeter is easy, a millimeter is manageable, but what about a decameter? Or a hectometer? Fortunately, I found five land surveyor's chains in the school cellar. These are 10m-long metal chains made up of 20cm segments with a handle at each end. And we spent the afternoon at Montsouris Park, with 5 teams measuring around the lake. Now I can tell you that the decameter became tangible - we had it right in front of us, it was no longer just a notion. Later, with the help of my students, I did set up exercises.free.fr, which hasn't been maintained for over 15 years and has attracted over five and a half million visitors. For the more advanced maths and geometry, I asked some teachers for permission to use some of their exercises online. We had a lot of fun putting this site together and, at the same time, we even won the first national Net Challenges competition in the primary school category.
Another episode in my life where I dragged math, well part of math, like a millstone. That's why math teachers and math education have ruined my life. Math seems (at least it seems) super efficient, it can indeed be applied in many different sectors, including some of the ones I care about the most. So, once again, why was no teacher able, throughout my secondary education, to show me any of these applications? Why show me, demonstrate to me that it was a boring to the bone, borderline totalitarian subject (admit it, learn it, you'll understand later) that you didn't need if you weren't planning to build cars, planes or rockets? You bastards!
