This idea is fascinating to me - my kid has described calculus to me like this, and that is not how I see it at all. But maybe that is the difference between someone who is a true math person and one who is not. AP Stats may be one day of studying for some (kiddo described it as “just vocabulary, not math”), but for others like me the unifying simplicity escapes them. There may be nothing wrong with muscling through math in the early years to get to calculus if you are not a math person, but what’s the point? And what’s the point of keeping someone in a class for those who muscle it out if their intuitive math sense is so qualitatively different?
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Probably comes down to numbers. Many schools have enough students who want to take honors or AP courses (calculus in the case of +1 math students) that they can move a teacher from the regular level courses that the teacher would otherwise teach and the students would otherwise sign up for into honors or AP courses that the students actually want.
But when you get to uncommon outliers like +2 or +3 math students in many schools, it may not be realistic to reallocate a teacher from a regular (or common level of honors or AP) course to teach a course for (for example) 2 or 3 students who need some math beyond calculus BC. That is why some school districts have special magnet schools and the like (and sometimes in other subjects like arts in addition to of math) so that there can be enough students in the school to make efficient use of a given number of teachers. But where that does not exist, and there are not other good options for the highly advanced student(s) (e.g. nearby college with suitable courses), the student(s) in question may be accelerated more just to run out of courses earlier (though gaining a free elective in high school may be a minor advantage).
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Speaking generally and not about you personally, my impression is that oftentimes the supposed “intuitive” math sense is more a product of circumstance, access, learning style, opportunity, educational quality, personality, etc. Many give up on and/or are driven away from math before they ever get much of a chance to understand and explore the fundamental concepts. That to me is a much more important failing of math education, compared to the lack of access to high school courses on differential equations and linear algebra. (Although the ever-present push for the latter might well exacerbate the former, especially in schools with limited resources.)
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I don’t disagree with anything you say, though I am a firm believer in the existence of natural math ability. I think it is found in equal measure in privileged and marginalized communities- probably distributed on a bell curve. To me the true educational and societal tragedy are those with that talent who don’t have it nurtured and are never discovered.
I don’t think advanced math education should be sacrificed for anyone. It should be available to all who can manage it. Why isn’t it? That’s the true issue, it shouldn’t be about rationing educational resources and pitting advanced students against marginalized students for insufficient resources. We need both.
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I am too, to a degree. But the system we currently have isn’t necessarily geared to identifying and developing such ability, and I am generally dubious of any approach to math that drives away a substantial portion of the student population without identifying and cultivating their ability.
Believe it or not I am not only talking about marginalized communities. I am talking about something more fundamental. For example, girls across the socioeconomic spectrum are disproportionately driven away from math and stem starting in early grade school, despite that there is no difference in innate math ability. It doesn’t seem they are well served by the check-the-box, math-as-a-race culture of “advanced” math education. The “done, done, on to the next one” mentality doesn’t suit everyone. Yet even those trying to take a balanced view in this conversation seem to be assuming that if a student has not gone as far as possible and checked as many boxes as are offered, this is some sort of a knock on their math ability. People really seem to believe that kids who take summer classes to get onto Multivariable Calculus track (for beyond) are necessarily more talented, but I don’t buy it. There are plenty of extremely talented kids being boxed out or discouraged by the process itself.
I somewhat agree with the sentiment, but that’s not the world we live in. The money has to come from somewhere else in the budget if districts want to pay for programs allowing “gifted” kids to take mid-level college courses while still in high school.
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First, I totally relate to your comment about girls and stem. Competitive math is a bizarre concept to me. My brothers are hot shot stem people and I wanted nothing to do with it. If I were to do it again, I think I would go into engineering. But at the time for those kinds of choices in my life there was no way I would have considered it. It is getting a little better but there is a lot of work to do.
As for the above quote - a girl can dream, can’t she? The quote brings to mind a common complaint I hear about how much of a public school budget gets diverted to special ed and how that is supposedly an illogical priority when schools can’t afford basic level educational goals. But those unfunded federal mandates are (thankfully) met at much higher cost than an advanced math class, because it is the law. Where there is a will there is a way. I fundamentally bristle at the notion that it is ok not to meet the academic needs of advanced students - whether they are male, female, privileged or marginalized. It hurts us all and is bad policy.
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When most of our high schools and middle schools don’t even have high quality math and science teachers, how can they offer quality college-level courses in these subjects? Sure, students can take them at local colleges or online, but in most such cases (with a few exceptions), their qualities are suspect too, for supposedly mathematically advanced students. If these students are passionate about math, there’re plenty of other math subjects they can study that aren’t in the regular school curriculum, which will not only broaden their math knowledge but also hone their math and critical thinking skills better than the few standard freshman college math courses often mentioned and recommended on CC.
I know this thread is about math acceleration (and math is obviously a basic skill needed for other STEM disciplines), but there’re other STEM subjects that are just as critical and challenging for advanced students. Take physics, for example. Being mathematically advanced is far from sufficient to truly understand it. The math helps formulate it, but if a student relies on math to understand it, s/he is missing what is critical and fundamental about physics. The 3-volume set of “The Feynman Lectures on Physics”, which I still consider to be the best introduction to physics, has barely any math in it.
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You answered your own question. It isn’t done because despite that we may wish it otherwise, societal resources, generally, and educational resources, specifically, are finite.
“I support providing +3 math education” isn’t a serious policy argument. “I support re-allocating resources from x to y”, or “accelerated math is worth my school taxes going up 3%” are, though, so go ahead and make one of them!
Done.
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You just need to get the people whose kids won’t be in accelerated math so support those higher taxes too. 
Add to that the fact that the ability to teach math is very different than understanding it yourself. The worst math teacher at our HS is a MIT grad and another lackluster teacher went to Dartmouth.
This is often the argument for hiring non math people as math teachers, but I think this kind of hiring has been a bad idea for a long time. They should expand teach for america where fresh STEM grads come and teach math for 2 years before moving on to other things.
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I like the way you think. I am happy to not pay taxes at all in our town at this rate because I don’t send the kids to the local school.
Good luck with that. LOL Does your state constitution have a right to an education?
I am from NJ. I googled and found this:
“the State is obligated to provide a “system” of free public schools .”
OK, let’s move on from taxes and states’ responsibility for education.
I should be more clear in my statement. I support a substantial increase in taxes (I don’t have a precise percentage) to support math education across the board. And better stem education overall.
But I agree with the mod - this is far afield from the topic at hand.
Tying it back to the topic - the goal shouldn’t be accelerating for acceleration’s sake, but quality public education that is suitable for the challenges our kids will be facing, meeting the kids at their level, and pushing them to meet their potential. My kid’s public middle school did none of those things.
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I think people with a strong math background should teach math. I’ve just noticed that a strong math background,alone, won’t do the trick.
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I think a big problem with math education in the US (and it is true with respect to other aspects of education as well but this thread is about math) is a lack of priority. And not necessarily on the side of educators (though that is often a problem) but on the side of students/families. My kids got a fantastic public school education (particularly in math/science but in the humanities as well – though my daughter may be the worst speller on the planet). One that ran circles around the private school one I got 40+ years ago. They were very well prepared for college, did very well in college and are doing well beyond college. But I looked at many of their classmates and they got amazingly mediocre educations. Same schools; same teachers; same opportunities. Just different priorities.
Won’t be popular for many on this site I know but I think if we put the same energy, drive and focus into math/science as we do youth sports, we would be a lot better at math and science. Its crazy to me how obsessed so many people are with youth sports. My brother has made a very successful career out of running/managing youth sports programs for the parentally obsessed.
So I don’t think that putting together the perfect educational programs (with broad, deep, quality math programs at different levels based on abilities/capacities or just at one level – seems to me though the latter is a mistake in terms of telling the kids ready for more at younger ages to wait until everyone else catches up) will in an of themselves move the needle much if at all in terms of math education. Kids/parents actually have to make it a priority and I just see too many people who have no interest in doing that.
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I completely agree with you. As a family we are personally interested in math/science and throw an enormous amount of stuff at the kids early on hoping that they catch an interest. Once they catch some interest, you need to do much less. Even this throwing stuff at them is not in a way to pressure them. No different than throwing a ball at a kid that is 5 years old. In my case, if the kid is 5, I sit down with him and starting solving a puzzle, and he is curious and comes and sits next to me. I tell him what I am doing. He also tries to solve it. Then I leave it to him. 2 years ago, I started doing Project Euler with one of my kids to give him company. When one of my kids was in 1st grade, I wanted him to read Harry Potter. So I brought all 7 books home and I started reading them myself, and he caught on to it and finished them in 3 months. And we talked about the books after that. Kids often show interest in whatever the parents show interest in. As they get older, you change the content. I am forwarding articles from quantamagazine.com at this point, and they are forwarding articles they see as well. When my son calls me from college, some of the call is often about some cool math stuff he came across (and it is way beyond me at this point), and I ask him to explain to me in language that I can understand. And to send me links that I can read and understand … You need to nurture interest. The courses in the high school don’t matter. By the time they are done with high school, they will be way ahead of the high school class anyway if they catch an interest.
Anyway conversations are not confined to math/science – they are often about politics, public policy, econ, markets, education policy, tech policy, geo politics, religion, careers, and whatever else. The more you engage critically, the more their critical thinking develops.
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