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You are arguing for rigor, not for its didactics. Those are different.

> had you, you would have instantly known how to do numerical differentiation and understand the limits, pitfalls, and other subjects like FEM

No, you wouldn't. You would also learn things out of order. You would be exposed to things without understanding why you are learning them. People who argue this usually learn things the intuitive way (whether from rigorous material or not - what goes on in their mind isn't rigorous), and then they go back and reassess the rigor in the light of that. Then they pretend that they learned from the rigorous exposition. No, they didn't.

It is totally fine to iterate. Learn non-rigorously. Go back to it and iterate on rigor later. As it becomes necessary, and if it ever becomes necessary for your field.

> Unless you're Ramanujan, every mathematician has spent hours banging their head against a literal or metaphorical wall

Particularly if you are learning from "rigorous" material. But then you go watch some YouTube videos to make up for the absence of didactics in your textbook.

I mean, why don't we just throw Bourbaki books at freshmen and let them sort it out without classes? They are maximally rigorous, therefore maximally great to learn from, right?

1 comments

  > I mean, why don't we just throw Bourbaki books at freshmen and let them sort it out without classes?

The Bourbaki group was quite famous for wanting to restructure math education. Teaching many things that are considered advanced to children. Despite not sticking around we see elements of resurgence and effectiveness.

So I'm not sure your argument of "out of order" is accurate. The order is what we make. There's no clear optimal way to teach math. Your argument hinges on that. You might argue that the current status quo is working, so why disrupt it, and I'll point around asking if you really think it's so effective when many demonstrate a lack of understanding all around us. That so many struggle with calculus is evidence itself. We need not even acknowledge that there are many children who learn this (and let's certainly not admit that it's far more common for them to learn it in unconventional ways).

  > let them sort it out without classes?

To suggest I'm arguing for the elimination of educators is beyond silly. I'd hope the caliber of your arguments would match that of your diction.

The Bourbaki group was reponsible for the Mathématiques modernes movement which intended to reform basic education on rigorous math. This may be the world's best documented educational failure in history. It was tried in several countries, so the sample size isn't one. All evidence points at rigor as a terrible educational tool.

The point of Math education isn't to create a clone army of the most pedantic pure Mathematicians in Academia.

> if you really think it's so effective when many demonstrate a lack of understanding all around us. That so many struggle with calculus is evidence itself

Because the first attempt went so well.

New Maths often called a failure but there's not real clear evidence that's the case. This is especially true in America where criticism was quite high as parents were quite vocal and struggled to help their kids (remind you of a different movement?).

There is a certain irony with that too. The major criticisms were about the de-emphasis of arithmetic, arguing that this is the skill people need more. Here we are today though, where everyone has a calculator in their pocket. Plus, people still struggle with extremely basic arithmetic such as calculating a 10% tip... SAT scores are commonly pointed to as evidence, but in the same period of time Verbal skills fell even more[0]! Would you suggest that New Maths was so bad that it made people worse at English? Or maybe there's another explanation like how the number of SAT takers dramatically increased, especially from those in the bottom percentile of high school[1,2].

If you explore the NAEP data[2] there's no decline and there's been progress the entire time for math scores for ages 9, 13, and 17 (the ages that participated).

The Russians famously did very well too.

It would be even a greater irony if we concluded something was a failure because we made mathematical errors in analyzing...

[0] https://www.reddit.com/r/dataisbeautiful/comments/xg6gsz/his...

[1] The Sandia Report and U.S. Achievement: An Assessment: https://www.jstor.org/stable/pdf/27541911.pdf

[2] https://www.nationsreportcard.gov/ndecore/xplore/ltt [2] https://www.reddit.com/r/dataisbeautiful/comments/qz3the/us_...