[sxzygz]

The mathematicians I know wish the were introduced to more material when they were younger so they could spend more time internalizing different concepts before being forced to specialize by the demands of a PhD.

The more scientifically minded people I know wish they were introduced to more mathematical concepts when they were younger so they could feel more able applying more sophisticated models to their problem domain.

Having a pipeline of somewhat mathematically able citizens is crucial to having an advanced economy. I don’t think the preceding statement is remotely controversial.

[Jweb_Guru]

Nobody is saying "don't teach math to high schoolers." My point is that this whole admissions rant appears to be entirely about admission to "elite" schools no longer being fully determined by SAT scores (or whatever--I've never been completely clear on what people are actually arguing for), when anyone good enough at math to get a really high SAT score can easily gain admission to a ton of universities with great math departments. As for the real "gifted" kids, there will always be some middle schoolers taking calculus etc. with or without a structured gifted & talented program. The majority of people in these programs are not so far beyond their peers as you seem to think, and my experience in math departments has been that there's a pretty even mix of kids with precocious math backgrounds and people who developed their skills at a later point.

[sxzygz]

The issue, as I see it, the erosion of the level of mathematical competence seen at university entrance. This inhibits the rate of progress one can make with a student over the period of an undergraduate education, and this reduces the exposure to mathematics of the next generation of educators.

Mathematics education is really, really broken unless your measure is Terry Tao’s are still produced. That’s not the issue. The issue is the breadth of people who can recognize what mathematical proficiency can enable within society, not because some wonk says data shows this, but because they personally have experience as to it has empowered them to perform more capably in their chosen field of endeavour.

[Jweb_Guru]

Okay. A lot of the blame for this has been previously placed directly at the feet of stuff like AP programs that claim to teach, e.g., calculus to a bunch of people who aren't ready for it; it becomes a prestige thing or expected for admittance to college, which results in a bunch of people being taught to the test and not actually gaining the foundational mathematics education they actually need to understand the subject. I don't see how encouraging this sort of thing actually helps with the problem of universities needing to do remedial math education to people who supposedly know the material already, but it appears to be what you're arguing for. If you're arguing for lower education reform in general, great, but that has little to nothing to do with how highly elite colleges weigh the math portion of SAT scores.

I feel compelled to point out that for people who want to learn mathematics, there are more and higher quality resources than there ever have been before. For the most part they are absolutely free, and unlike virtually every other subject on the planet they are generally not the sort of thing where you can be led astray by misleading material. I simply don't see how such people are being suppressed in any way, or why (from the perspective of advancing the state of the art of mathematics) I should care about the "non Terry Taos" in your words, who are merely above average at math but don't actually intend to pursue it as a career. There are plenty of other skills that are actually eroding at a high rate, or have huge startup and lab costs, or are otherwise underappreciated and underpaid relative to their importance to society; I don't think mathematics is one of them.

[sxzygz]

My initial reply to you was to only articulate some nebulous idea that there is desire for mathematical understanding that is being underserved by mathematics education.

If standardized tests statistically “reliably” predict mathematical “ability”, the act of removing their gatekeeper role to higher education in our society (that is structured around prestige colleges resulting in prestige future income) amounts to disincentivizing whatever performative mathematical education students endure.

Some people, as children, are drawn to mathematical concepts and, yes, now is a better time than in all history to be such a person. The ambient possibility of this for a given individual is I assume unchanged through history.

Some people, like me, are able to do performative mathematics in school well enough but didn’t particularly care for it. Then we encounter some remarkable teacher and we feel some fortunate and enriched.

The existence of the remarkable teacher is the product of the possibility of a society producing mathematically proficient educators. That means students must somehow encounter them in their education.

I believe increasing the production of such teachers is important, irrespective of the field. I believe mathematical thinking can address this problem. Above, I have sketched the most meagre possible outline of how such thinking prepares to address further modelling of the problem.

Yes, this is contingent on my assumption that mathematics is generally useful in problem solving.

If you don’t accept this, that’s fine. We simply don’t agree. That said, I want to add that I appreciate the time you took to engage with me. I’m someone who believes that a lot of structures in society are poorly conceived, but that is a much longer discussion. At the present moment in time, standardized tests are a minor stupid in comparison to removing them without a much broader vision of how to address certain shortcomings of society.