[HN Gopher] The Algebra Gatekeepers
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The Algebra Gatekeepers
Author : domofutu
Score : 44 points
Date : 2025-08-03 04:02 UTC (18 hours ago)
(HTM) web link (www.educationprogress.org)
(TXT) w3m dump (www.educationprogress.org)
| vorgol wrote:
| Can you meaningfully study advanced math without understanding
| algebra?
| elric wrote:
| 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.
| bravesoul2 wrote:
| Advanced means you got through the basic quick enough to need
| more stuff to do. Or move up a year early.
| Lesterrr wrote:
| Advanced math builds on algebra, without it, most concepts
| won't fully connect.
| ekm2 wrote:
| 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.
| griffzhowl wrote:
| 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.
| ekm2 wrote:
| 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.
| anthk wrote:
| Say hello to rings.
| tim333 wrote:
| Algebra seems kind of fundamental to things like physics and
| chemistry.
| zozbot234 wrote:
| 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.
| ginko wrote:
| 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?
| Jtsummers wrote:
| 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.
| zozbot234 wrote:
| > 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, Andre: _Word Problems in Russian Mathematical
| Education_ , available at: https://cs-
| web.bu.edu/faculty/gacs/toomandre-com-backup/my-a... )
| seadan83 wrote:
| 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.
| zozbot234 wrote:
| > 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.)
| elric wrote:
| > 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.
| zozbot234 wrote:
| > 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.
| elric wrote:
| 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).
| zozbot234 wrote:
| > 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!)
| anovikov wrote:
| 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?
| tetromino_ wrote:
| 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.
| anovikov wrote:
| 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.
| djoldman wrote:
| 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 SS 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.
| seadan83 wrote:
| 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.
| wahern wrote:
| 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.
| thevillagechief wrote:
| 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!
| zozbot234 wrote:
| > 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.
| avmich wrote:
| > No one wants to teach bad students
|
| That's not true, but maybe there are too few good teachers
| who do that...
| zozbot234 wrote:
| 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.)
| chermi wrote:
| 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).
| desertrider12 wrote:
| 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?
| chermi wrote:
| 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.
| seadan83 wrote:
| > 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.
| chriscrisby wrote:
| Does this study account for students who are good at math but
| have no desire to pursue it?
| readthenotes1 wrote:
| Not that I read, however, that still doesn't explain the
| discrepancy between non-asian minorities and the other groups
| rahimnathwani wrote:
| 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.
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