In San Francisco, the math placement situation is so bad that voters passed a resolution urging the school board to make Algebra I available to 8th graders.
https://ballotpedia.org/San_Francisco,_California,_Propositi...
Such a low bar, but even in the most recent school year, most 8th graders could only study Algebra I via an online course or summer school, i.e. most had no access to an in-person Algebra I course during the school year.
This at a district with average per-pupil operational spending of over $27k.
This is exactly the kind of obvious mistake that contributes to the complexity of explaining education outcomes. Requiring a "teacher recommendation" to allow a student to take an advanced course introduces bias and consequently is suboptimal to say the least.
That the following had to be done is sadly the state of affairs in the US:
> In 2018, North Carolina passed House Bill 986, Session Law 2018-32, which included Part II: Enrollment in Advanced Mathematics Courses. This legislation established § 115C-81.36, requiring that "any student scoring a level five on the standardized test for the mathematics course in which the student was most recently enrolled shall be enrolled in the advanced course for the next mathematics course in which the student is enrolled."
Edit to add:
This is also the kind of thing that machine learning/"algo" skeptics/detractors skip over or ignore when evaluating automation: humans are often wrong.
I'm not sure why you had that dig about ML skeptics but ML models can often perpetuate human biases if they aren't trained properly. For example, consider the amazon hiring algo that consistently rated female candidates below male candidates.
Who is to say any of this is a mistake and not exactly as intended?
Like, it was not a mistake during red lining laws that you had to go into a bank personally.
Yeah, I would suspect this is intended. The idea being the kids (or parents, really, in communication with teachers) who opt-in to Algebra are more likely to have good study habits, etc. Kids tend to prioritize what the other kids around them prioritize, particularly if there aren't enticing alternatives, so other than raw aptitude the biggest key to success in academia and elsewhere is being surrounded by others invested in the same pursuit.
It's the same rationale more liberal localities use to hold back academically strong students and keep them in classrooms with everyone else. Except you need a critical mass of engaged students and an environment where the less-engaged students are less likely to self-segregate and stick to themselves. I think this is why the liberal policy has roundly failed to achieve the outcomes studies promised. But for the same reason, I would think the risk to the studious kids of adding a minority of bright kids with poor study habits would be minimal. OTOH, the academically successful cohort succeeds precisely because their parents segregate them into higher performing environments; they're not thinking quantitatively or care about averaged group outcomes. What they're doing works for them, so they're gonna fight back tooth-and-nail.
There are parallels here with the rationale many used to justify racial segregation, and that stills echoes today in terms of the distribution of parents who understand how the system works. But by-and-large I think what undergirds the parental hand-wringing and pushback today are more direct heuristics--the failure to choose to opt into Algebra, etc, communicates unsuitability for the higher socio-economic class.
Every system deserves
the bullsh*t it creates.
Educational systems invariably lapse into patterns where autodidacts are rewarded for pretending they received their wisdom from the educational system.
Some cooperate, some refuse...
Damn, before I read this article I would have assumed all grade-level classes with no special facilities requirements were just taught to demand. Crazy to think of a framing that 'advanced' 6th grade math is such a precious resource that your 5th grade teacher can arbitrarily shunt you down an academic path all the way to college. It feels like this exists mostly to create a have and have-nots situation.
Can you meaningfully study advanced math without understanding algebra?
Depends on your definition of both of those terms. Being able to solve a simple equation is generally useful. You probably don't need much more than that to understand Set Theory or much of Logic. You can learn to write proofs without knowing calculus, etc.
Maths is such a wide field that terms like "advanced" have little meaning imo. Or rather, advanced doesn't have to mean complex, and even complex doesn't have to mean inscrutable. But then even simple problems can turn out to be fiendishly hard.
Advanced means you got through the basic quick enough to need more stuff to do. Or move up a year early.
Advanced math builds on algebra, without it, most concepts won’t fully connect.
Yes.
Substitute Algebra with Combinatorics and you will be fine.I do not understand this Algebra worship.Speaking as someone who graduated magna cum laude in in College Math.
I'm struggling to see how this makes sense. What's the evidence that someone can study advanced maths without understanding middle school algebra? It underlies calculus, analytic geometry, even a lot of combinatorics.
Hell, I think you need basic algebra for basic abstract algebra! And you're not convincing me you know anything about upper-level math if you don't know basic like... group theory.
Analytical geometry underlies calculus,not Algebra.And combinatorics is a completely different arm of the two cultures of mathematics.Also Geometry was fine before Rene Descartes messed it up with Algebra and then we christened it Analytical Geometry.The method of exhaustion,amply developed by Archimedes with zero Algebra is the basis of intergration.It is because we start out with differentiation that we think Algebra is super important.Tom Apostol comes close in his calculus textbook when he actually starts with intergration.
A compromise would be to have two streams:The left-brained folks should follow the Algebra ->Geometry->Calculus track;the right-brained folks should have a Combinatorics ->Geometry ->Calculus track.
Algebra seems kind of fundamental to things like physics and chemistry.
Geometry is fundamental to physics and chemistry,not Algebra.Look at the thinking style,not the content.
Still E=mc2, the Schrödinger equation, the Dirac equation, Maxwell's equations... It's hard to understand the equations if you don't understand equations.
Say hello to rings.
The root of this pathology is treating Algebra I as "advanced" math in the first place. This is a uniquely American problem (though it is regrettably spreading to education systems in other English-speaking countries) and something that would be quite unheard of in continental Europe and East Asia. The soft bigotry of low expectations.
No, the issue is if you don't take algebra I by 8th grade then you won't take advanced math. Nobody is considering algebra I tk be advanced, the key is when you take algebra I in order to move on. Turns out, whether you take algebra I before high school has less to do with how good you are at math and more to do with (frankly) segregation. This is an article revealing in data how modern day segregation works.
I'm a product of NC schools. When going to grade school in the 90s I did not realize that those schools desegregated less than 10 years prior. The advanced classes were essentially all white. Those advanced classes in early grade school position you for the slow track, or the fast track.
> Those advanced classes in early grade school position you for the slow track, or the fast track.
So you're agreeing that Algebra I is viewed as an "advanced" class in the context of Junior High math. (Obviously this is not the same sense of "advanced" as pre-calc or calculus. That should go without saying.)
What does K-12 math class even teach until (optionally?) 8th grade then? Surely it's not all just basic arithmetic until kids are 12 years old?
Algebra concepts are taught starting around 6th grade (for most students). The first proper algebra class (actually called that, and not pre-algebra or just math) is 8th or 9th grade.
> Algebra concepts are taught starting around 6th grade (for most students)
That's way too late, BTW. In most of the developed world, loosely "algebraic" thinking is introduced starting from the earliest grades, generally phrased as "here's how you should reason to solve these complex, 'multiple step' word problems". "Single-step" word problems (as we'd call them in the U.S.) are effectively unknown, since they're pointless (except as a curiosity); the whole point of word problems is to introduce complex reasoning about mathematical operations, which then seamlessly motivates formal algebraic reasoning.
(A good review article on this approach: Persson, Ulf and Toom, André: Word Problems in Russian Mathematical Education, available at: https://cs-web.bu.edu/faculty/gacs/toomandre-com-backup/my-a... )
Does this study account for students who are good at math but have no desire to pursue it?
Not that I read, however, that still doesn't explain the discrepancy between non-asian minorities and the other groups
"Non-Asian minority" is really really weird to me. We're just... making that distinction for some reason. Like what they don't count?
One of the most frustrating articles I've read in a while. Is everything in the US just well-off people colluding to keep everyone else down? Most countries don't have this advanced classes thing. Everyone just takes the same classes. It does not make sense to have admins and other parents with vested interests block kids from whatever classes they want to take!
I know you only said "well-off", not rich/entrepreneurial class. But given what I've seen on HN lately I feel this must be emphasized -- this is not another "blame the rich" scenario. This is beaurocract class/college-educated-but-barely-passed education master's degree class. This is a government/administrative bloat problem. This problem is one you're much more likely than not to hear an entrepreneurial class member rail against and maybe even try to fix (to no avail).
The article says that administrators are giving in to the demands of very involved, upper-middle class parents. What other incentives would an administrator have to keep low-income and minority students out of 8th grade algebra?
Just as an example,
"The enrollment process created additional barriers for students and families. When students went online to select their courses, in many school districts they could not see classes that required teacher recommendations and may not have known those courses existed. Students who requested placement in advanced classes were frequently told they could not enroll, even when they had strong academic credentials. Students had no pathway to demonstrate their readiness or earn their way into these courses through their academic performance. They had to be recommended by a teacher."
Maybe this system shouldn't be set up this way? Who set up the system I wonder.
> Most countries don't have this advanced classes thing.
They actually do. They just group the advanced classes in an elite "prep schools" track, whereas everyone else gets the crappy "vocational schools" track. The worst part about this is the pathological incentives it creates among teachers. No one wants to teach bad students, so the "vocational" track gets the worst teachers, and the divergence in outcomes becomes ingrained.
> No one wants to teach bad students
That's not true, but maybe there are too few good teachers who do that...
It's true enough to a first approximation for individual teachers, and what's more relevant, it's systemically true for the educational establishment as a whole. Which means that effective methods for remedial education (such as Direct Instruction) are not taught in Schools of Education and not known among teachers, except for those who opt to go quite deep into "special" education. (And even then, those teachers are not going to teach your average class at a vocational school.)
> It does not make sense to have admins and other parents with vested interests block kids from whatever classes they want to take!
Sure it does. There is a vested interest in some to ensure a desired peer group of the classes their kids take. More generally, to ensure 'space's at the top for those that get the teacher recommendations. Bluntly speaking, it's racist as shit. The data presented is a case study of systemic racism.
Maybe the idea is that limited teaching is better done to people who are more likely to be able to make usage of that knowledge in life?
That is the idea in theory. But in practice, apparently North Carolina teachers, under pressure from rich parents, don't want to teach algebra to talented kids from poor and black families - i.e. don't want to teach precisely those who would be most likely to use and benefit from that knowledge.
Why would rich parents be against this? Also, why are rich kids in same schools as poor ones? That would be unimaginable in "socialist, equitable" EU and makes no sense to me overall.
> This analysis revealed a systematic failure affecting tens of thousands of children across North Carolina alone, wasting human potential on a massive scale.
What? How is this a waste of human potential? Presumably the kids that didn't take HS Algebra took other classes instead, and probably did well at those. Not taking Algebra does not make you a failure at life, it does not waste human potential on a massive scale.
> Presumably the kids that didn't take HS Algebra took other classes instead, and probably did well at those.
The article repeatedly mentions kids who were forced to retake classes/material that they had already achieved mastery on. Moreover the way the system is set up, not taking Algebra in junior high means that you won't be allowed to take the most advanced math classes in the final years of high school. Either of these amounts to a serious waste of potential.
It also seriously impacts college access, since your average college course requires either "College Algebra" (which has a severe weed-out effect on those who didn't already achieve mastery in K-12 math, because you can't really teach the entirety of K-12 in one college semester!) or even calculus.
Damn that's a crazy system. Over here colleges have maths prep courses for those whose maths skills are insufficient (or, like, older folks getting back into learning), and there are typically no admission requirements beyond having graduated HS (with some exceptions like medicine).
> Damn that's a crazy system.
The real craziness is in K-12 education itself. Colleges have just evolved their own "system" to cope with that in the most practicable way while preserving the world-class standards they care about. (Gen-ed college courses is another example. In most of the world, providing 'gen-ed' is the job of high school!)