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The Algebra Gatekeepers

• vorgol 1y ago
  Can you meaningfully study advanced math without understanding algebra?
  • elric 1y ago
    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 1y ago
      Advanced means you got through the basic quick enough to need more stuff to do. Or move up a year early.
  • Lesterrr 1y ago
    Advanced math builds on algebra, without it, most concepts won’t fully connect.
    • Lesterrr 1y ago
      [dead]
  • ekm2 1y ago
    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 1y ago
      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 1y ago
        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.
      • briangriffinfan 1y ago
        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.
        • ekm2 1y ago
          Are you saying that because they end with "Algebra"?You can get an A+ in basic Algebra and have no clue about Abstract Algebra.It is the chain of reasoning rather than the mindless manipulation present in baby Algebra.
          • briangriffinfan 1y ago
            No, I am obviously not saying math ends with algebra.
    • anthk 1y ago
• zozbot234 1y ago
  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 1y ago
    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?
    • deleted 1y ago
      [deleted]
    • Jtsummers 1y ago
      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 1y ago
        > 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-articles/swedish/ULFENG.PDF https://cs-web.bu.edu/faculty/gacs/toomandre-com-backup/my-a... )
  • seadan83 1y ago
• elric 1y ago
  > 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 1y ago
    > 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 1y ago
      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 1y ago
        > 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 1y ago
  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_ 1y ago
    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.
    • deleted 1y ago
      [deleted]
    • anovikov 1y ago
      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.
      • DrillShopper 1y ago
        Because Racism
• djoldman 1y ago
  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.
  • seadan83 1y ago
    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 1y ago
      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 1y ago
  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 1y ago
    > 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 1y ago
      > No one wants to teach bad students That's not true, but maybe there are too few good teachers who do that...
      • zozbot234 1y ago
        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 1y ago
    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).
• chriscrisby 1y ago
  Does this study account for students who are good at math but have no desire to pursue it?
  • readthenotes1 1y ago
    Not that I read, however, that still doesn't explain the discrepancy between non-asian minorities and the other groups
    • briangriffinfan 1y ago
      "Non-Asian minority" is really really weird to me. We're just... making that distinction for some reason. Like what they don't count?
      • aaplok 1y ago
        From the article: > Research in the 1990s found that in California, Latino students scoring above the 90th percentile on standardized tests had only about a 50% chance of being placed in college preparatory classes, while Asian and white students with similar scores had more than a 90% chance. The data is split by community ( Black, Latino, White, ...). Whites and Asians fare the best (see also their fig. 6.1). Kids from other communities are prevented from getting the same opportunities as kids from these two communities performing equivalently. So it is not that Asian kids don't matter, it is that the data indicates that Asian kids already seem to be treated reasonably well.
        • briangriffinfan 1y ago
          It just seems arbitrary to me. Split the groups of people into "good results" and "bad results" and then treating everyone in both groups the same seems so reductive as to not just be useless but convince me there's some kind of background reason for doing so.
          • aaplok 1y ago
• rahimnathwani 1y ago
  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,_Proposition_G,_Declaration_of_Policy_Urging_San_Francisco_Unified_School_District_to_Offer_Algebra_1_to_Students_by_Eighth_Grade_Measure_(March_2024) 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.
  • mathattack 1y ago
    It's a problem everywhere in California. In Palo Alto they're getting rid of honors classes in STEM subjects like Biology.
• recursivecaveat 1y ago
  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.
• lunaticlabs 1y ago
  Holy shit! I ran into this growing up in California. Would have been early 1990s. I have long been bitter that I had taken algebra in 8th grade, and starting high school in 9th grade they made me take algebra again because I was told I couldn’t skip ahead that far. I was too young to be in the class. For the record, I’m white snd middle class, so don’t fit that pattern, but I am neuro diverse. Anyhow, everyone has excused it at the time with shit like it must have been a technicality, or that the algebra was more advanced, or something along those lines. Anyhow, it’s nice to be validated sometimes, and this is one of those times so I thought I’d share.