What happens when even college students can't do math anymore?
theatlantic.com
theatlantic.com
Years ago when I was working in education (Canadian public schools) our school board had a conference ahead of the school year. The keynote was an inclusive-ed researcher / consultant / speaker who told an anecdote of how they had successfully lobbied for a student with a substantive intellectual disability to be registered for the high school physics courses.
Part of the anecdote was pushback from the physics head: "I've known Jake for years. Great kid. But what is he supposed to get out of physics class?"
The consultant's in-anecdote response: "what is anybody supposed to get out of physics class?"
Wild laughter and applause.
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A surprising number of people in education seem to simply not know that there is substantive and consequential content in the curriculum.
Having never really learned math, they've never really used it. Having never used it, they don't recognize its utility.
They seem to earnestly believe that it isn't an actual tool but a gatekeeping mechanism devised by autistic persons to humiliate normies.
it should be that, though.
In time, most figure out people create pet mathematical fictions regardless of background, and while authoritative confident liars often allow people to feel better about uncertainty... it adds little value in the long-term. =3
Well, no fucking shit, Sherlock! You aren't the sort of person to turn to math to solve problems. You're the sort of homesy chuckle-cluck who puts up inspirational posters on your bedroom wall.
OTOH, I've been on my back in an attic with a house builder, and calculated the 3-dimensional length of the bizarre edges of a skylight (where the ceiling opening was completely skew to the roof opening). We absolutely used math to solve the problem.
That grade school teacher? They wouldn't have been asked to check the calculations. The carpenter? Used math IRL.
If only I'd know how important matrix multiplication would turn out to be...
I'm lucky I enjoyed math and science, but I'm not surprised that people who don't enjoy it think it isn't going to be useful to them. It's very much one of the things that if you don't know how to apply it, you won't find the places to apply it, so you end up thinking it has no use.
Other math I use rarely, but I'm still glad I learned, say, geometry or calculus when a situation pops up.
39% got this right:
Round the number 374518 to the nearest 100
Find 13/16 ÷ 2.
If a=-2 and b=-3, evaluate ab² - a/b
For context, "In the 2025 incoming class, this group constitutes roughly one-eighth of our entire entering cohort."
54% of Americans read below a 6th grade level.
We don't need to know how to do these things when we can just have someone/something do it for us.
I think the answer is Boeing
That mindset carried straight into corporate governance. Joint-stock companies inherited a Norman-style hierarchy where a self-defined ruling stratum treats populations as revenue sources, not stakeholders. Legitimacy comes from charter and capital (today: job/founder title and investment), not from any connection to the community affected.
In Norman social architecture you have a ruling stratum that views itself as distinct from and superior to the alien conquered population under it, bound by obligation only to peers and superiors, not to the commons. The joint-stock corporation inherited that same operating philosophy. The “company” wasn’t conceived as part of society; it was a chartered power structure hovering above society. Local populations are revenue sources, not stakeholders. Accountability runs up the hierarchy, not down. Legitimacy comes from charter (now job title/founder title) and capital, not community integration. The company's goal is to be a mini Norman conqueror of it's specific market. The logic of Norman style extraction from a conquered people, rather than participation/obligation/upholding social norms, sits at its core. Norman style extraction first, everything else second.
A key component was the move of corporate HQ and power base from Seattle to Chicago where the execs lived, wrestling it away from the engineers in Seattle. Later they moved their HQ again to Washington DC to be closer to lobbying!
Yet this product is also the cornerstone of our national defense infrastructure.
I unfortunately have to upvote this.
> For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment.
Good grief. No, it's just the pandemic. The kids whose middle school years got disrupted are behind on skills taught in middle school.
Can you squint and blame other things? Sure. But experimental education policies are hardly new ideas, and none of the nonsense from previous decades has shown an effect like this. If you want to show up to the game with a claim that it's some other effect, I want to see a big exposition of why it's not the obvious hypothesis at work.
It's covid, folks. And over the next 3-4 years the scores will bounce back (to much crowing in the media from whichever faction wants to claim credit). Write it down.
Ah, their next article should be about the confidence of fools...
> But the national trend is very clear: America’s students are getting much worse at math. The decline started about a decade ago and sharply accelerated during the coronavirus pandemic.
So I, a "fool", read that and think: Hm... well if the article isn't giving numbers I'm going to take the "sharp acceleration" as a statement about magnitude and clearly infer that the pandemic is at fault.
Again, is the subject complicated? Sure. But education policy doesn't produce effects like this. It never has, probably never will, and the article even doesn't claim it does.
You know what does produce effects like this? Keeping 13-year-olds out of class for two years.
I mean, come on. I repeat: write it down, in 4 years we'll all be reading about the miracle of American education policy. And that will be wrong too.
> How did this happen? One theory is that the attention-shredding influence of phones and social media is to blame. The dip in math scores coincides with the widespread adoption of smartphones; by 2015, nearly three-quarters of high-school-aged kids had access to one. A related possibility is that technology is making students complacent. Emelianenko told me that students “are just not engaged in math classes anymore”; they seem to believe that they don’t need to learn math, because they can use AI instead.
> Or maybe students have stopped achieving in math because schools have stopped demanding it of them. During the George W. Bush administration, federal policy emphasized accountability for public schools. Schools that saw poor performance on standardized tests received increased funding at first, but if scores still didn’t improve, they had their funding pulled. Research suggests that this helped improve math outcomes, particularly for poor Black students. After 2015, however, the federal government backed off from its accountability measures, which had faced bipartisan criticism. (Some teachers’ unions and progressive parents wanted less emphasis on standardized tests, and some conservative politicians wanted the federal government to remove itself from education policy.) Many schools across the country have shifted toward making math engaging for students at the expense of evidence-based teaching practices. And due to funding shortages or misguided efforts to improve equity, many students are held back from taking the hardest math courses.
There was no significant other evidence. And "hand wavy" is missing the point. There is a bleedingly obvious hypothesis for this effect with huge signal in all sorts of other areas of social policy. I mean, really? The pandemic is visible in every measurable segment of society but somehow not a major factor in education results?
In some sense, yes, Occam's Razor is a principle that embraces "hand wavy" understanding by demanding extraordinary evidence for extraordinary claims. And I think it's going to work very well here. Again, for the third time: write it down. In four years this will all bounce back.
What's happening here is actually a different logical fallacy entirely. HN commenters have a distinct ideological bent against new ("woke") ideas in education. And they're willing to ignore things like giant global pandemics to chase their preferred explanations.
Is it though, or is that just what your ideological sense tells you? Like I'm trying to point out, if you take the pandemic shock out of the data set, there really isn't much to argue about here. US aggregate education results have never been great internationally, but haven't ever been moving particularly fast either and seem not to have been before the pandemic either.
There really is a woke-derangement-syndrome at work among the reactionary geek set these days. Teachers have always had funny ideas, and haven't broken kids yet. People need to relax.
> Is it though, or is that just what your ideological sense tells you?
What aside from grade inflation explains why those students in the UCSD report had high grades but had to take remedial math class? The schools I went to had some grade inflation, though perhaps it's not that bad. Heck, Harvard loves grade inflation.
Also, what even is the ideological angle here? I'm the only one talking about grade inflation here (well, one other person mentioned it, but surely not to be "anti-woke").
> but haven't ever been moving particularly fast either
Would it be false that education quality is declining even if it is doing so slowly?
> Teachers have always had funny ideas, and haven't broken kids yet
That "yet" is doing a lot of work, and ignoring the present article. A slow-moving train wreck is still a train wreck.
It's. Not. A. Train. Wreck.
There is a high signal NOW, due (very obviously) to a well-understood and well-characterized effect visible up and down social metrics in all societies where they have been measured.
What I'm saying is that pretending to ignore this very obvious hypothesis in order to push a personal theory about "grade inflation" or whatever and demanding the rest of us freak out about the implied "train wreck" is just bad logic.
Usually that kind of argument is the result of ideological bent, not considered thought.
> > What aside from grade inflation explains why those students in the UCSD report had high grades but had to take remedial math class?
> > Also, what even is the ideological angle here? I'm the only one talking about grade inflation here (well, one other person mentioned it, but surely not to be "anti-woke").
> U.S. students remained relatively steady in science and reading in 2015 compared with 2012, when the exam was last administered, but dropped below the global average in math.
> Of the 35 OECD member countries, the U.S. was among the lowest-performing in math—finishing 31st—continuing a downward trend that started in 2009.
> Outspending all but two countries on education, the U.S. joins countries like Norway and Switzerland that provide significant funding to their school systems yet aren’t seeing the same high performance from their students as other countries that spend less.
It is even more an indictment of the education system if, this long after COVID, so many students are doing so poorly.
If the rest of the system was functioning properly, the COVID-related problems would have been caught early when those kids started failing their high school math classes-- which would have left them with plenty of time to go back and learn what they missed. And if UCSD still required the SAT, it would have been painfully obvious that they were admitting students who don't know basic math.
[1] https://www.theargumentmag.com/p/when-grades-stop-meaning-an...
But since there is a massive profit motive to admit and keep young fools taking on student loans, I doubt that's the answer the industry would adopt
Or as Munger said "show me the incentive and I'll show you the behavior"
If that's the college business model today, it won't survive for long.
Colleges that give you valuable skills for your money should keep doing well though.
we already have "degree-mills" from which you can purchase a degree; doesn't benefit society in any way
It seems we have entered the Find Out phase of FAFO; which FA began with a lack of preparation in US educators in the 1960's for "New Math" which focused on conceptual understanding and abstractions, such as set theory and differential number bases. This lack of preparation, especially among primary educators (who had not themselves encountered mathematical theory in their own education) led to a regression; "Back to Basics" in the mid 1970's. Those missteps; both in educator preparedness, and in systemic regression to a rote memorization approach were substantially aggravated by reduced standards testing in the 1980's to hide the resulting weaknesses resulting from this regression.
First hand experience as a student through these epochs from the late 70's through the 80's and 90's in US academia led to thinking I was 'not good at mathematics.' For me the 'breaking point' of this pattern was the discovery that even with an undergraduate STEM degree from a PAC10 university, including 'advanced' math courses available therein, I was not sufficiently mathematically educated to qualify for enrollment in a post-graduate physics program at a leading scientific institute or to participate in advanced mathematics discourse at an international mathematics symposium.
During COVID lock-down I attempted graduate level bio-molecular studies from several tier-one US and UK online university programs and ran into proctored coursework where the educators opined that "some problems are simply intractable due to scope or complexity" and I was unwilling or unable to accept that there was no approach to solutions for these systems.
The ensuing self-directed relearning from international curricula and classical resources has remedied my misconception of inability; extended my approaches to include concepts such as p-adic bases and complex topological approaches. and shows that current cohorts of US students will need to become self empowered to learn conceptual math beyond what their educators believe achievable.
Those who do not grok math will always be in the position of being taken advantage of by those who do.
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I think bad math teachers (educated in the education department) and bad textbooks are to blame for this collective trauma inflicted on the general populaiton... grown up adults swerving away aggressively at first mention of an formula or algebraic equation.
Chill, y'all. Some of this stuff[1] was know thousands of years ago... it would take you a few months to (re)learn all of high school math and solve all your math phobia issues. You're an adult now, you can totally handle that shit.
[1] https://minireference.com/static/conceptmaps/math_concepts.p...
I'm sure if I walk around in the office and ask people a problem like "Car A starts driving south at time zero, with speed 30km/h. Car B is located 10 km down south and starts driving north 5 minutes later, at speed 45 km/h, at what time do they meet? You have 1 minute. Go." a bunch of them will start to sweat, and many will likely fail - even though they have graduate STEM degrees.
I also did check out the paper, and it does indeed seem like the number of students that are placed into Math 2 (The lowest or second lowest placement if I read it correctly) has 20-fold increased in just 5 years, while most other Math placements have stayed somewhat stable, at least toward the top.
My conclusion is that the students that simply don't have the math knowledge to pursue STEM-degrees, will either not enter them, or finish them, so that might not be a huge problem? They'll purse other majors that don't require math.
My hunch is also that those that are not interested in math, have found shortcuts to get through their math classes the past 5 years (cheating? AI?). But, then again, what are the chances they'll actually end up working with anything math-related after college?
how else do they gauge someone's math ability then?
It’s not a niche ideology, sadly. It’s going mainstream. A core part of Zohran Mamdani’s platform was his goal to phase out gifted education programs, for example.
I think this idea that private schools are no better are even worse is a wishful thinking narrative. Private schools, especially the more expensive ones, naturally select for parents who are more involved. More involved parents are highly correlated with better student outcomes. That alone means private schools are correlated with better outcomes. It honestly doesn’t really matter if it’s cause and effect or correlation, parents send their kids to private schools because they want them in the mix with other students selected into the higher performing environment.
>The average private school mean reading score was 14.7 points higher than the average public school mean reading score, corresponding to an effect size of .41 (the ratio of the absolute value of the estimated difference to the standard deviation of the NAEP fourth-grade reading score distribution). After adjusting for selected student characteristics, the difference in means was near zero and not significant.
For math:
>The average private school mean mathematics score was 7.8 points higher than the average public school mean mathematics score, corresponding to an effect size of .29. After adjusting for selected student characteristics, the difference in means was -4.5 and significantly different from zero. (Note that a negative difference implies that the average school mean was higher for public schools.)
In the context of the specific discussion here, it doesn't really matter that the effect goes away when controling for selected student characteristics. First off this was from 2006, we would have to see if any of that has changed. The 2024 numbers are here[1]. But in any case they are not worse than public schools, although they may be no better or slightly worse than a public school in a rich neighborhood or similar.
[0] https://nces.ed.gov/nationsreportcard/pubs/studies/2006461.a...
[1] https://www.nationsreportcard.gov/dashboards/schools_dashboa...
[0] https://nces.ed.gov/programs/coe/indicator/cmb/public-school...
Your solution is to make the smart kids suffer so maybe they can force the educators to do better? That’s insane. It’s also not going to happen.
Do you know what will happen? Any parent with the means will scrape together cash to pull their students out and go to private schools. Or they’ll hire tutors after school and force their kids to sit down and learn what they should have been learning during the day.
This fantasy where the smart kids rally together to overhaul the system because we banned them from taking advanced classes is a delusion.
I was in a gifted program in grades 5-7, stopped going mainly because I had to travel to another school to attend and it was inconvenient.
I didn't "suffer" being in classes with folks who weren't at my level. The teaching staff did a great job and I never felt like I was being shortchanged. My undiagnosed ADHD means I goofed around a lot, but several of my friends told me after high school that they appreciated me because I helped them see learning from a different angle than their parents or the teachers.
However, please don’t force your experience to be the only allowable experience for others. If some students want to take advanced classes, we should let them.
Refusing to allow students to learn at a faster rate is insanity.
Teachers only really teach the middle third - the top third can be ignored because they can do it for themselves while being bored.
The bottom third can’t be helped because they won’t be helped without a huge amount of energy by the teacher (for little rewards), and so won’t do it for themselves while being bored.
The middle third is all that gets schooled because they can at least be bumped up a little higher towards where the under-achieving top third thus rests.
Gifted education programs for kindergarten. I don't necessarily agree with that either but it's important to be accurate when talking about proposed policies. The man isn't talking about taking away AP algebra. Most kindergarteners still need to be told not to eat their boogers.
Kindergarten is where the phase out starts. That’s how you phase something out. You don’t take it away from everyone all at once because that triggers outrage. You disallow it for new kindergarten students one season, then next year remove it from 1st grade so they can’t go into accelerated programs and so on. He explicitly uses the phrase “phase out” for this reason.
Read more of his platform documents, including the ones before everything got watered down for his website.
The “it’s just for kindergarten” is just positive spin on the first step of the goal of phasing it out in general.
Do you have links?
The phase out starts with kindergarten and “early grades”. In some places he’s said up through second grade which some assume is an upper limit, but really it’s just the natural length of phasing out gifted programs one year at a time over the 4-year course of a mayoral term due to the necessary delays to eliminate the program after his election date (kindergarten next school year, then 1st grade the next, then 2nd grade)
> You disallow it for new kindergarten students one season, then next year remove it from 1st grade so they can’t go into accelerated programs and so on
I don't know how it works in NYC now, but it doesn't have to be like that. When I went to school you could always get into the gifted program at the beginning of any school year if your teacher put you up for it. You didn't have to be in the program since kindergarten.
Sorry, I should have been more clear.
The gifted program for kindergarten will be eliminated in the first year of the phaseout.
The following year it will also be eliminated for first grade.
The following year it will be eliminated for second grade as well.
This is the phase out. Students who start in kindergarten next year won’t have the option of the gifted program because it will be eliminated for the following grade every year.
It doesn’t matter that they didn’t get into it in Kindergarten because it won’t exist in 1st grade when they get there, and so on.
It’s not “ZDS”. It’s literally what he’s said.
Up to what grade though? The article you provided says Mamdani supports gifted programs starting in the 3rd grade. That's different from your original assertion that he's "[phasing out] gifted education programs", implying that they would end completely for everyone.
My original understanding was it was kindergarten only and that was inaccurate. He's following a plan proposed by de Blasio, which I didn't know about, that's phasing it out up to the 2nd grade. Extrapolating from that to "Mamdani will remove all gifted education" is the ZDS I'm referring to.
I agree with you overall about the value of gifted programs. But it's important to not spiral into hyperbole.
you're taking a leap to assume that this will lead to the abolishment of gifted programs in the higher grades (where such programs make more sense)
https://ncrge.uconn.edu/wp-content/uploads/sites/982/2019/04...
Basically, non-gifted kids learn from the gifted ones. It's that whole, "positive influence from peers" thing.
In the long term, having gifted programs results in a handful of accelerated students and a lot more struggling ones (at the end of mandatory education).
In other words, let’s drag the smart students down, disallow them a better education, and instead force them to teach their peers because we don’t think their teachers are doing a good job?
This is a terrible way to solve a problem.
The students won’t get a chance to learn the advanced material by examining it to others because they won’t be allowed to learn the advanced material.
How do people not see the harms in banning advanced classes?
Kids usually don't learn "school" things like math, reading, and science from each other. They learn behaviors. Kindness, cooperation, competition, integrity, working hard, not being disruptive etc. Having a gifted track for part of the day doesn't disrupt that learning.
Allowing advanced students to learn advanced topics should be an easy decision for everyone. It’s so strange that it’s become a contentious topic.
And the variance can happen even in "top level" public schools, for certain definitions of "top level". I went to one of the best high schools in the nation (as rated by college acceptance rates, SAT/ACT scores, etc). There were still teachers people wanted to avoid because they were seen as harsher graders. So you can have grade inflation even at "top level" schools as private schools aren't above selling grades.
It does appear to be reversing a little bit in some places as schools realize they were fooled by people pushing ideology over data and results, but it’s going to take a while.
For those who aren’t in the loop: There’s an ideological push to eliminate testing, aptitude tests, and even to eliminate different educational tracks (accelerated learning programs, AP classes, advanced math tracts) in the name of pursuing equality for everyone. The idea of testing people for aptitude or allowing some students to go into more advanced classes than others is not allowed by some ideologically-driven people who think all students must be given strictly equal education at every grade level.
In America many parents do have resources, though, and they will spend those on private schools, tutoring, or home schooling.
> It is the drive of student and higher standards from parents and teachers that matters.
These proposals restrict the teachers and disallow teaching advanced subjects to students with drive to learn them.
You can’t say it’s up to the students and teachers while also holding back the students and restricting the teachers.
The only other option is for college administrators to be disturbingly stupid.
Someone who knows how the world works! Qui bene --
https://ucsdguardian.org/2025/09/29/uc-regents-greenlight-uc...
> The expansion anticipates 13,600 new students in the next 15 years
https://archive.org/stream/HarrisonBergeron/Harrison%20Berge...
> people pushing ideology
University Education programs and as a result teaching bodies have been taken over by ideology.
I believe it is in part because all the teaching low hanging fruit has been established for centuries. So the only 'novel' things the programs can do is talk about discrimination, disparate outcomes and hand-wavey ideas about improving education. The departments have some of the lowest bars for academic professorship and as a result, the quality of research is similarly bad -> terrible.
The war on phonics is the canonical example.
The fault doesn't lie with 'people'. The above mentioned institutions are squarely at fault for making education ideological, and they should explicitly be blamed for the deterioration in student performance.
It shouldn't be controversial, and in some sense it isn't (in another sense it is, because people confuse themselves), that everyone should be given the opportunity to develop and perform at their full potential. I could name multiple different ideologies that oppose this in some way, though.
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.
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.
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.
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.
But we should keep trying to give more opportunities to the less fortunate. Better education, remedial classes, free school lunches, child credits, etc. We do that by asking the wealthy to contribute more. Not by taking away their advantages.(e.g. Admission tests)
Admissions tests are actually not as big of a driver for the academic advantage of the wealthy. Especially at flagship institutions a lot of it is simply traced back to legacy admissions, athletics, and extra-curricular activities. Those latter two are more gamed by the wealthy than anything.
Removing admission tests and focusing only on the application is actually a huge boon to wealthy families who want to get their children into the best universities because it removes the hard part (having to learn enough to do well in exams) and replaces it with things that are easy to game, like writing essays and getting a track record of doing extra-curriculars.
Standardized tests actually make it easier for lower income families to compete for spots for academically advanced children because they’re measuring academic advancement. Even if it’s not a perfect measure, it’s way better than substituting non-academic things that are so easily gamed by the wealthy.
So whether you include SAT scores in admissions or not, it's still heavily skewed.
Also, the problem with SAT scores is that you end up studying to the test. (This is why Chinese applicants do so well on college entrance exams - they spent most of their high school studying for the specific range/type of questions they will be asked on the test.)
My wife works in private college admissions counseling, so I've been privy to a lot of conversations around these issues over the years.
The article is paywalled, but I feel that in this sentence the author is using all reasons used against standardized testing to criticize the elimination of standardized math testing.
The concerns around racial divides have been mainly in the non-math portion of the SAT's, where it's been found that students with a non-white background don't choose the "right" answer on ambiguous questions because they don't have the same shared experience that would make the "right" answer obvious to someone with a white background. Its inclusion here sounds like the author is trying to inject a little anti-woke hysteria into her argument.
Wealth leading to increased standardized test scores is a very real thing. Many of us have taken multiple choice tests where we've known that the best answer isn't necessarily the "right" answer, and that in order to pass the test we have to select the answer the test is looking for. The SAT and ACT are littered with these questions and there are test prep companies who have decades of industry knowledge that they provide their clients with to get a boost on their scores. No amount of non-profit or public school provided test prep can compete with that.
As someone else commented, someone with an 800 on their SAT math will get admitted 99 percent of the time. Colleges are always very open about their admissions criteria and students are always free to choose to apply or not based on those.
That way, we can defend the study of mathematics as a form of discipline for the human mind that has benefits beyond the knowledge gained.
The meta-process for solving any mathematical problem is the same as any other form of project management.
Or maybe we should first try to teach kids the value of project management & then try to get them to apply those principles to math problems?
In the day job, how many people have to use maths skills beyond arithmetic?
What about trigonometry?
Differential equations?
Integration and calculus?
To be honest, if I am using Boolean Logic then that might as well be 'advanced mathematics', far beyond the comprehension of non-coders. Even simple trigonometry isn't so simple to most people.
Clearly we need some people on the planet able to do more than basic arithmetic, however, what is the point in trying to teach the whole population how to do differential equations given the lack of workplace opportunities to use such knowledge?
The why question isn't explained with maths beyond the theoretical 'yep, you will earn more'. Too many maths textbooks are utterly abstract, you might as well be learning cuneiform for the amount of practical use cases.
It seems to me that the policy makers and journalists that complain about the demise of maths skills aren't doing a lot of maths themselves yet they want to force maths on the masses, as if it was good for you in a 'eat your greens' type of way.
Maths is hard and it really does not suit a lot of people. Fluency in maths is only attainable by a few, the majority that can do maths need a lot of armbands, whether that be calculators, text books or internet crib sheets. Then there is everyone else, not even floundering, just giving it a miss.
Rather than forcing the entire population to be maths geniuses, which will never happen, maths needs to be a specialist subject chosen by those that know what it can be used for, and with ambitions to take a career path where maths happens.
A lot. It's also pretty funny that your examples of useless math are 3 of the most concrete and directly applicable concepts in the entire set of human knowledge. Try, idk, ergodic Ramsey Theory next time.
> What about trigonometry?
Ever heard about FM radio? Or anything that takes a Fourier series? Anything using complex numbers? Game programming? Graphics? Positional encodings in large language models?
> Differential equations?
My brother in christ, literally Newton's second law.
> Integration and calculus?
Ever needed to numerically find the minimum of a function or solve an equation? Newton-Raphson? Literally all of machine learning?
The thing with math is that if you aren't familiar with the concepts then you don't know what you don't know.
However, from what I understand, the only people listening to FM radio are car-dependent commuters and people that have a trade, whether that be building, hospitality and so on. They all know how to find their favourite radio station and get the volume to a level that they can hear. What percentage of these people know how the radio works beyond that? Or are we talking rounding errors here?
As for LLM things, the hundreds of millions that have ChatGPT installed do not need to know any maths whatsoever. They just write prompts. There are some outliers, such as students trying to cheat on their science projects, maybe they should put down ChatGPT and pick up a textbook, but none of them need to know about 'positional encodings in large language models'. They just don't want any of that, the goal is not to do any 'system two' thinking.
This does not mean that a very small amount of programmers need to know such things, but the vast majority of people have better things to bother themselves with.
Game programming, it is the same again. Millions or even billions might spend their lives in front of consoles, but the people writing the games are relatively few in number, and when you take away the people making textures, running tests and whatnot, an even smaller number of people need to know the tricky maths.
I am not sure whether you were just trolling me or not. Where I live, most people have jobs where they definitely don't need to know anything more than basic arithmetic.
My weird take is this: calculus and other sorts of advanced mathematics are cultural artifacts as much as they are tools and people should be exposed to them more or less for the same reasons that we are exposed to Shakespeare or the history of world religions: they are beautiful, and learning them changes us in positive ways.
One thing I've learned after most of a lifetime being smart is that being smart barely matters. It doesn't matter whether people are good at math or bad at it or smart. Most people never achieve fluency in most subjects. But children deserve to be taught math as a matter of basic dignity and eudemonia. The attitude that education is a pragmatic thing meant to achieve some end other than enrichment of the person is why the US is so fucked.
The thing was that I went to a school where I was one of the lucky few to be in the top set for maths. We had a deal with our teacher where he could leave us unattended and we would collaborate amongst ourselves to get all of our assignments done. He would just pop by at the end of the week to see how we all got on and to set the next assignment. Only on rare occasions would he have to actively teach us.
Our class was calm and we brought in home computers (as it was then), board games and cards. We would be betting our lunch money on games of Bridge, since that was (weirdly) the hot game to play. We all passed with A's.
All of the other classes had maximal supervision, maximal homework, additional 'special needs' classes and utter carnage, should the teacher leave the class unattended for a femtosecond. They were taught properly, but none of them were any good at maths and none of them went on to do anything that paid the big bucks.
Arguably, when it came to arithmetic, due to the low-key gambling and games playing, everyone in the top set had an edge over everyone else. They were merely learning by rote. We were learning in a collective self-directed way within a culture of learning that we very much developed by ourselves. We also learned how to collaborate to solve problems, which conventional education considers to be cheating. Our 'client' was the teacher, and we needed to keep him sweet as we didn't want to lose our privileges. So that was the motivation, not the usual nonsense about how you will never get a job unless blah blah'.
Hence, I have another truly epic weird take. With art we also teach the history of art as a separate subject. So why not have 'the history of maths' as a separate subject?
Imagine learning about what was discovered in antiquity, before people had calculators, slide rules, even pens and paper. Why did that Persian mathematician need to devise tools for doing clever things with numbers 2500 years ago? What are these tools useful for in today's world? How do you code up a script to implement such tools to save on the mental arithmetic?
Such an approach could get nearer to your truly weird epic take. We would be introducing the wonders of maths to kids in such a way that they would be learning a little bit about ancient civilisations as well as the applications in the modern context.
Now tell me, without differential equations: * how it deforms at impact? * how much more or less air resistance it has and how it depends on speed? * how quickly solar panels can charge the battery given that charging speed is non-linear?
So you’ll end up building countless prototypes and crash them, run at different speeds and charge with different panels and battery types. 100 years later you find out that its shape is just not good.
In the meantime solving few simple differential equations and optimization problems would tell you the same.
Or something very close to programming. How do you add two empirically measured probability distributions describing how two teams perform?
2. It's not about teaching how to crunch numbers, it's also teaching general problem solving, and using tools to break down complex problems using your various tools to solve it. This translates directly to everyday life.
As a programmer we use calculus and integration all the time in performance testing and stats when we aggregate the data and pull insights. I have started getting into making canopies for events and I have todo a lot of trig to calculate the dimensions of the shapes before I send them to the printer. Hell I even use lots of my high school physics when I go to calculate the load to choose to right type of rope or metal wire and to determine if anchoring points are safe or not. We also use a lot math when calculating generator loads and building power grids for raves & festivals. I also do aerial circus and we use lots of physics when setting up rigging points and determining safety margins. Hell just having a basic physics understanding is really important to figure out if the carabiner you're using is going to kill you or not.
So yea math is really fucking important, and you do use it everyday even if it's just the problem solving it teaches.
Planning a route through an amusement park or mall to reach the most things in the least time...
There's a lot we don't need mathematical perfection on so it never registers as math, but improved intuition can unconsciously help in completely unexpected ways. Like an understanding of latency for why a line at a convention was set up badly.
Electrical items would be plugged in with a slight risk of electrocution or fire, possibly in a pig's shed, in the pouring rain and in the dark. But this was not a worry since the show had to go on and there was the danger of the police turning up in force, with the legal right to steal the whole sound system, which could be big enough to require a semi truck to get it places.
Either the setup worked or it didn't. There was nobody doing advanced maths to get it working, and yes, there would always be a setup problem or two, which happens with kit that is made to work hard. The far more useful skills were the soft skills, so teamwork and coordination, not maths.
In time the rave scene was commercialised to the festival nonsense we have today. A proper rave was a full-on temporary autonomous zone where you could have small children trying to sell you acid tabs or ecstacy. Everything about it was illegal and nobody was sober.
Moving on to festivals and organised mandatory fun events, you have to have an entrance fee, the guys providing the music have to be paid, there has to be a small army of people in high visibility 'security' jackets and you certainly don't have small children trying to sell anyone any drugs.
In this secondary 'professional' context, where the goal is to make money not give people the best party they have ever been to, you really do have to 'calculate generator loads and build power grids' or else you won't get the venue, insurance or the event happening.
Clearly the free party scene is not what it was. Kids today have their five hundred social media friends so they don't need to socialise in real life. However, there was a time, not so long ago, when it all came together wonderfully, with the rave scene, and, part and parcel of that was the complete lack of professionalism. There was fun in taking your life into your own hands.
The aerial circus sounds fun (as does the canopy making). However, across all of the extreme sports where some acrobatics is needed, nobody is doing maths. Engineers behind the scenes, maybe, but the performers? It is all about dedication and practice. To take a relatively modern 'sport', parkour. That dangerous jump from building A to building B, that is done by eye, gut feeling and intuition, after lots of experience doing other jumps. No parkour person is going to whip out the old slide rule to work out the parameters of such a jump.
You mention the carabiner, which is a mountaineering gadget. Again, nobody doing mountaineering is doing fancy maths to select the right carabiner for the job. It comes down to intuition again, and what you and your climbing partner have fielded for the day.
Regarding finance, maths is allegedly useful, but how many bookkeepers are doing any maths beyond addition, subtraction and calculating percentages, mostly for tax paying purposes? In America, where everything is financially engineered and the economy is all about debt payments, maybe more maths is needed for the average citizen, but those hundreds of millions struggling to make their car payments just need a living wage, not added maths skills.
I will stop shouting at the clouds now, however, have you done any of your canopy designs in Blender with the cardboard box plugin that enables you to unwrap a 3D shape into 2D flat surfaces? If that is a no, then give it a go and see if it works for your projects. Note that it enables you to do a render that the client can approve before printing happens.
As it happens, I was working in production AND engineering AND finance all at the same time. I will leave you to guess what roles are in the middle of that Venn Diagram, however, that was a while ago when one of my clients was Lehman Brothers. I had deliberately tried to avoid working in the city, so I was reluctant to work with them, however, they hired my intern for mega bucks. That didn't last long though, as we all know! Ah, the shame...
It is precisely because I do the technical roles that others are scared of that I know most people don't need to know maths beyond basic arithmetic.
One huge advantage of this is that I never treat the maths illiterate with condescension. Unlike some I don't sneer at those that are just trying to get by in life or those that have found there is more to life than maths. Condescension is just plain ugly and there is no need for it.