A lot of trig. Trig identities is my bête noire, though I would save off one day for them, after Taylor polynomials, to derive a few through practice that way. But I remember grinding on them for quite a while; I would just have one day and use them as Taylor fodder. (Taylor polynomials are not practically useful for most people but they are extremely important as "the simplest thing that converts transcendental functions into the world of the elementary arithmetic functions"; it is good to demystify how one might compute sine or cosine "from scratch".) But I wouldn't nuke trig out entirely as classical geometry is an almost unparalleled place to learn basic proof techniques and mathematical thinking in a playground where you are not distracted by a lot of arithmetic. I think I still like that better than graph theory, and simple trig/geometry is in fact practically useful for a chunk of the students we're pushing through these courses. It would just get toned down.

I would cut out a lot of integration grinding. The concept of integration is extremely important, and I want the students introduced to the ideas of doing it symbolically, but the details of all of the manipulations are much less important than the concepts. I would retain only things that are of mathematical interest, like integration by parts (useful as an exercise in how much fluidity you have in doing math and a good check you understand the concept).

Symbolic differential equations I'd cut down a lot. I think there's a sense in which they are useful but the utility is not revealed until a couple of semesters in. Even my college semester was frankly not that useful, you really need to dedicate yourself to them to get the value out of them. I'd put in some more work on numeric integration, and working with computers to get them done. The concepts of differential equations are super, super, super important; the exact knowledge of how to solve this super precise form of this exact differential equation is not. More practical experience to teach intuition, less grinding on symbolic details. The net time spent on them if I were writing the curriculum might even go up, because I'd tip in some (very) basic chaos mathematics here instead of all that grinding.

Matrices I'd have a hard think about. HN is at the epicenter of their utility so it might be hard to see that for most people it's not all that useful in any sense. I might like to move them on to a very explicitly STEM-focused track.

If that sounds horrible, remember that my whole point here is that there's a lot of stuff that should be in the curriculum that currently isn't, or is just glossed over very briefly. Like, I'd like more work spent on basic financial math, both for personal finances and doing things like a bit of running stochastic financial scenarios (integrate this into the stats curriculum, for instance). Which also brings up the idea of doing more simulations of somewhat larger statistical scenarios than you can solve as a closed form by doing Monte Carlo simulations; statistics and probability is very important but for most people it spins off into the symbolic weeds when in fact most problems people will have in real life are not cleanly amenable to such things. (This might also help erase the implicit belief that stats tends to teach that everything is uniformly distributed.)

The curriculum as it is is also structured as an unmotived series of solutions to problems the students don't have. I would try to give them the problems before the solutions; e.g., if I'm building a stats curriculum around simulations that go into symbolic math rather than just handing them symbolic math from the beginning, imagine covering the Central Limit Theorem from the point of view of me giving out a couple of different simulation assignments that all "happen" to converge to it despite very different scenarios, and we can discuss & teach why the seemingly totally different scenarios produced such a similar outcome, rather than just handing it down from On High as a Solution to a problem none of them have.

You can't have things like that if you aren't willing to cut something else because we are full up right now. There's a lot of room now for people to get more intuitive grasps of these things by virtue of working with them through practical numeric integration, Monte Carlo simulations, maybe we'll do a brief section on enough 3D geometry to do a useful introduction to 3D modelling/CAD/CNC/3D printing/the whole complex of modern tools available that use some form of 3D modelling, there's so much useful stuff that's just aching to be let in that the culling of the old needs to be a bit aggressive after a century.

To be honest I'd not cover this dimensionality stuff, except perhaps as a special-interest side day or something. It's not bad to do a few of those, just to expose students to the diversity in math. I got graph theory like that in my own high school, and it can stay that way; I wouldn't amp it up any. Dimensionality does pivot nicely into fractals and fractals have notoriously pretty pictures associated with them, so maybe I'd sneak it in with that.

I doubt it. Local math programs tried to jam those things down sooner, but it doesn't do much good and may do harm. While I understand Piaget is not necessarily the last word in human development, using his terminology, real mathematical education can't really proceed until the formal operational stage is attained. Prior to that all you can really expect is extremely concrete things (in the aptly-named concrete operational stage) like arithmetic. Only single-digit percentages can handle simply moving that stuff earlier into the curriculum. The local conversation on that is distorted by HN having a lot of those single-digit percentages in question, but it's not the normal case.

While I didn't lay it out in my curriculum discussion, I also extremely, extremely strongly support using computers to provide personalized curricula to students designed to probe them for when they are ready to start more advanced math, leading to the complete destruction of the unbelievable awful cohort system in use today, and giving those single-digit percentages the ability to proceed onwards at their own pace, however much faster or slower it may be than anyone else's. But if my curriculum is goring a sacred cow, this idea is goring an entire herd of them at once. The field of education's resistance to computerization has been incredibly effective, to their personal benefit but to all our children's detriment.

Where the heck are they teaching algebra in 9th grade? Here in California that's 6th-7th grade curriculum.

Huh, Australia had (many years ago when I did it) algebra in year 7, and if you were in any kind of accelerated/gifted-and-talented class you'd see it even earlier.

But choosing not to discuss the obvious answer to a rhetorical question is a typical device of useless engagement bait posts on social media, hidden and made worse by the somewhat difficult subject. Ignorance is a much more charitable assumption than malicious waste of time.

I’d suggest it’s a problem with your browser that it respects the zoom restrictions, regardless of the page’s choices. Browsers are meant to be user agents – agents for the user – not agents for the page.

Firefox > Settings > Accesibility > Zoom on all websites.

Many browsers have similar settings.

I'm on mobile (iOS Safari) and seem to be able to zoom fine.

I'm not criticising Minkowski, I'm criticising the author of the article. He starts out by talking about one dimensional lines, then suddenly jumps to curves as if they could be mistaken for the same thing. And in my humble opinion, it goes downhill from there. He even manage to talk about one dimensional squiggles which is an oxymoron. In one dimension, nothing is squiggly - that is an effect of higher dimensions.

That being said, I don't care much for Einstein's relativity or the derived works either. I think Maxwell was on to something and that quantum mechanics more or less agrees with him.