I would like to quote Bernard Dimanche on MCMaths, the only YouTube channel on which I heard “someone from the inside” talk about the difficulties encountered by “those on the outside”, pointing out real problems and outlining possible solutions. He lists several factors that contribute to making maths arid, unpopular and abstruse:
Selection Tool
Using maths as a selection tool automatically means not making them universally accessible. Of course, otherwise there would be no selection. So out goes any manipulation, any connection with reality, practice, the tangible, the observable, and in comes the concept, abstraction, a purely intellectual mechanism which, in addition to running on idle and in circles (at least at the beginning), is not necessarily suitable for everyone. All of this goes against the meaning and the basis of education in a republic: making knowledge accessible to as many people as possible while shaping capable and responsible citizens.
Another infernal side effect is all these “well-trained” young people, those who have passed the bottleneck, will head for the most lucrative or powerful careers, certainly not primary education, for example. So Mr. Villani may well regret that 30% of school teachers do not like teaching maths, that 80% of them come from literature departments, which are or have long been considered dumping grounds. In other words, it included people who were motivated by literature as well as those who had been rejected from scientific courses and the slackers who had nowhere else left to go. But my dear Mr. Villani, it was entirely predictable. I don't know what it's called in maths, the systemic ad libitum renewal of a distressing and, personally as well as nationally, disabling situation. You are also mistaken in your observation. I quote: “The issue is not the way we teach, but the educational ecosystem.” There is of course much to be said about this ecosystem, of which I was a part for a time, but I think, like many others, to have witnessed the flaws in the teaching of mathematics.
Mister V. points to another problem:
When we think about it, the most fundamental threat to Western science is neither budgetary nor structural: it is the lack of motivation of young people. Cédric Villani on Les Echos.fr
But Cédric... Why don't you go and motivate them! What are you waiting for? Well, I'll stop picking on Villani. At least he asks himself questions, although. . . not the right ones. None that question the teaching and vision of his subject that have served him so well. And yes, it is Mr. Villani, among others, that I mentioned at the beginning of this story.
Not connected to reality
One of the consequences of point 1 is the failure to link them to concrete experimentation, staying in the abstract. The concept of a recursive loop, for example, was only understandable from my window by observing how PHP scripts worked; it was the only place where I could “understand” what it was for and what it looked like. The failure to use practical examples reinforces, from the outside, the ungrounded, useless and closed aspect of maths, whereas, on the contrary, the emphasis should be placed on their practical side, anchored in reality, showing their usefulness in the most diverse fields in order to interest the maximum number of pupils and to have the most diverse approaches possible.
The pretension to train the mind
Well, um... as far as I'm concerned, there's more of a mindfuck there ;-). What can you say about a discipline that triggers Melting Brain Syndrom or other conditioned reflex as soon as it is even mentioned? I think the way maths was taught to me damaged my mind, negatively conditioned it. Thank you to all those Pavlovian-like teachers!
Aside from my personal case, however, it seems to me that it is more a question of mind formatting than education.
Learn → Apply → Don't ask too many questions, you will understand later.
The subtext is: you will understand if you have started by learning and applying stupidly, otherwise... So there is indeed a formatting, a shaping of the mind. As with a hard disk, the support is prepared before the system can be fully installed so that it can be used and perfected at a later stage (higher education).
Problem, it has become THE mandatory port of call for all those aiming for excellence or who want to join the nation's elite. So we end up with an elite fed from the same source, identically molded and, for the most part, unable to think differently from each other, except on rare occasions. Conform.
Random terms
The use of several different terms to refer to one and same thing. Did you say clarity? Rigor? Paradoxical, isn't it? This is a point that I could not have identified on my own given my abysmal level, but which does not really surprise me. Gibberish when you got us...
Make time to listen to it (in french); it's instructive whether you're inside or outside.
