An update on the campaign to defend serious math education in California
scottaaronson.blog
scottaaronson.blog
While well-intentioned, we believe that many of the changes proposed by the CMF are deeply misguided and will disproportionately harm under-resourced students. Adopting them would result in a student population that is less prepared to succeed in STEM and other 4-year quantitative degrees in college. The CMF states that 'many students, parents, and teachers encourage acceleration beginning in grade eight (or sooner) because of mistaken beliefs that Calculus is an important high school goal.'
You can have separation of education by ability, and progress, or you can have equality, and everyone being pulled down to the same low level. And suffering for everyone. You can’t have both. Take it from someone who has direct experience with communism, which is the same mentality that drives this.
This seems a little off. What we're talking about (and what it seems like you're defending) is directing more resources towards the most gifted. It's fine to believe that, but it's an argument to give the most to those who have the most. Nobody is pulling anyone down, and communists are as happy to grant power and resources to those with aptitude and connections as capitalists are.
edit: with the constant attacks on teachers, it might be more realistic to stop aiming for calculus in high school. Any kid who manages it within a gutted public system would have gotten there anyway, no matter what situation they found themselves in. They can download calculus books and calculus lectures now; with the internet a feral education is within everyone's reach.
This might mean that there are additional costs for 'gifted' students. But that's no different than there being additional costs for mentally less advanced students: no matter what the students are, providing an education fit to their needs has costs... and a failure to provide it creates inequality when the most privileged families move their children (or relocate entirely) to places that will provide a more suitable education.
Sure, they may not be able to tell you what is a measurable function, but they can explain the way you should feel about a p-value.
It goes without saying this proposed class wouldn’t be based around memorizing unmotivated formulas.
To go back to the car analogy, I know why I need an engine, you might even say I know how to use the engine, but if the engine dies or I want to use the engine for some other purpose, I'm not equipped to do anything.
I don't have "literacy" with engines, I have rote memorization of a series of steps. I don't have enough information to know why the steps are what they are, nor could I know under what conditions the steps should change or what they should change to.
Will it result in students not knowing as many formulas? Of course, but who cares?
Then what? Are they going to incorrectly use anther one, a wrong one, because they understand it better?
(Searching not where one lost the key, but where the light is stronger)
Hmm, I wonder if you studied stats? It sounds as if you studied lots of math.
I did long ago, mostly forgotten, and, hmm, I don't think there's a single real life useful probability function one can understand, without knowing the underlying calculus? Except for understanding in the sense of trusting the teacher.
Which works pretty ok in medicine
Statistics is more complicated philosophically and computationally, as you do in fact need calculus to do statistics, since a fundamental tool of statistics is evaluating the area under a variety of distribution curves.
> Statistics is more complicated philosophically and computationally, as you do in fact need calculus to do statistics
This is just fundamentally false, as there are many statistical concepts and introductory statistics courses (given at some of the most renowned universities in the world) that can be taught without an underpinning of calculus. It's like arguing that you can't teach a programming class until someone understands digital logic design.
And again, you do need calculus to do statistics. Maybe you're saying: "If someone does the calculus part for you, you can use this one equation to solve this one question."
That's akin to calling a spelling test literature. You are confusing practice with knowledge. Anyone can bang on a drum. That does not make them a drummer.
You only need measure theory when working with something that is not easily replaceable by R^n, Z^n, or finite sets to meaningfully define integration, otherwise (in)finite sums and Riemann integration get you very far.
I am a bit rusty on my advanced probability theory, but IIRC the only thing that required* measures was defining conditional probabilities and expected values on zero-probability events.
Of course redoing that class without Lebesgue integration sounds excruciatingly painful.
* Not just to make proofs nicer and theorems more powerful
Discrete distributions can be defined, even infinite discrete distributions (as sequences and series are taught in pre-calc). Continuous distributions can't be formally defined, but a lot of intuition can be given with hand-waving e.g. the area under this curve. Probably most of the class is spent with counting and probability-type problems, but plenty of actual statistics can be done without calculus - we can learn about distributions, what a statistic is, expectation, sampling, counting, probability... the list goes on.
Only in the same sense in which operating a car requires advanced knowledge of mechanical engineering, electrical engineering, aerodynamics, fluid dynamics, thermodynamics, etc. IOW, in no sense related to the everyday, ordinary practice of operating a car.
Sure, statistics requires calculus... and real analysis, and probability, and measure theory, and FSM knows what else - IF you're doing statistics research or trying to break new ground, or do really advanced things. But all of this is light years away from the level of statistics knowledge needed by Joe Q. Public to better understand (and not be misled by) the "statistics" frequently thrown out in news articles, government reports, etc.
Please, for the love of FSM, can we stop this HN "thing" of assuming that every mention of any mathematical topic implies that the goal of the user/learner is to do original research in the field?
As a professional data scientist I've never needed to use calculus unless you consider graphical reasoning on distribution diagrams to be calculus.
Most people who deal with data/statistics in their working lives do not need to know real analysis, do not utilize calculus to draw (correct) conclusions, and do not use linear algebra either. They learned all these things once and forgot them a long time ago, because they did not need them. They utilize statistics an order of a magnitude more often than they do calculus.
They are not statisticians, but people who need to deal with data as part of their job.
I felt I was prepared for 2nd semester calculus when I took that as my first math course in college.
But what I really mean is that, as a person, I just really enjoyed calculus. I found I was very good at it, and that experience helped me understand why some people choose to focus their career on pure mathematics. I am happy I took calculus not as a means of training for the workforce, but because I found it enriching on its own. And I never would have taken all that time if it wasn't offered to me as a class in public school that counted as credits towards graduation.
Where I grew up btw we studied only calculus, integrals and stuff, no stats, in high school. (Stats in uni)
No one does this in the real world. Not even professional statisticians who know calculus. In the old days they used table lookups. Today they use software.
You need to understand the concept of areas under curves. Calculus is just a means to compute the area.
Learn the nuts and bolts in highschool, use the intuition for the rest of your life.
Highschool calculus should be taught with computer algebra software. That's what you'll use in real life as soon as you find an even slightly difficult calculus problem. There's not enough time to teach both the symbol manipulation rules and the intuition.
Unfortunately, I think it comes down to resource constraints: When I attended a relatively wealthy and large suburban school district that offered more courses than most other school system in the state, there were only 18 other students who took AP Calculus BC our senior years (and one anomaly who took it his junior year). There were a couple classes for Calc AB, mostly seniors and a few juniors. That special 18-student course was already pushing the limit on the minimum class size, a couple years prior they hadn't had enough students and didn't offer it at all.
If you'd split the curriculum into discrete math and statistics as well, there wouldn't be enough resources to support those branches. To take a chainsaw to the analogy, you wouldn't have the straight but sturdy tree trunk we have now, you'd have a stump or maybe a shrub.
I give the edge to calculus because it allows students to go right into physics and be able to graduate college with an engineering degree in four years (saving them time and money), but any challenging quantitative material would be good for their development.
The big picture goal is to show them there is this big world of problems that can be approached with specialized knowledge and get them familiar with what it takes to gain that knowledge.
I think this is key. What exactly they study may not be quite as important as whether or not they are actually getting an opportunity to do some form of challenging mathematics.
I think statistical literacy is also important, but more than anything I think students benefit from learning how to think about hard(er) problems. If they learn that in statistics, great.
Generally I would say easy courses is the real problem, not content.
However, many many students enter college engineering programs with 1-2 semesters of calculus, so not having it could be a competitive disadvantage - presumably to your understanding of those first year classes.
But I was a slacker and that experience doesn't necessarily transfer.
And yes, I'd generally favor stats over calculus as an additional HS class; however, I am hesitant about discouraging the opportunity to take either.
I unwittingly had a "low math" high school education, with pre-calculus only introduced spring of my last year. Freshman Engineering was a shock, with Calc, Physics, and Electrical Engineering using concepts I'd never heard of.
There's nothing worse than thinking you're accepted, prepared, and ready, and finding you're totally wrong.
Of course, that's not counting "mathamatical maturity" which is super important or if you're doing some specific thing that needs calculus (hello machine learning.)
- calculus if you want to do engineering
- discrete mathematics if you want to do CS
You can teach these in university, it's not a problem. Calculus doesn't need to be taught in high school to everyone but it should be available and it should be the goal state in terms of curriculum pace for everyone so that you should have no problem taking it by the time you are 17 or 18 (which is what we're talking about).
Anything else propagates back to a regressive dumbing down in an earlier year, from an already dumbed down curriculum by international standards.
> - discrete mathematics if you want to do CS
I'd guess the vast majority of software development jobs are like "gluing one API layer to another" and "writing simple-to-complex CRUD apps". Neither calculus or discrete mathematics really helps if your goal is to simply make a computer read data from database X and display it in webform Y.
I found all of the math required by my undergrad degree to be totally useless in real life programming. Whether you need any math at all will highly depend on the application domain you get in to. The most complex math I needed as a code monkey was vector arithmetic (3D graphics) and trigonometry (ocean and aero mapping navigation).
Just like it is safe to assume that most programmers aren't good at calculus. Or discrete math. Or proofs.
Most programmers will never design new solutions and are objectively terrible at their job.
I don’t think you know anything about professional programming if you think that makes them “objectively terrible at their job”. Sometimes businesses just need a website.
As an aside, those secretarial coding jobs will all go away within 50 years. They are only needed in the transition period where machines still depend on humans to talk to each other.
Many high schools offer mathematics through Calculus. You can typically get to that course at the regular high school pace if you were able to take Algebra 1 in 8th grade. If you were ahead of that pace, then you are typically left with few options outside of taking college courses.
Also, in case anyone is also wondering, 8th grade means 13-14 years old.
There were some other courses that had math involvement, but were more business oriented (finance / accounting type stuff) and I don't recall if they counted towards core math credit requirements.
* Calculus I: limits, derivatives, integrals
* Calculus II: More integration techniques (substitution, by parts, table), infinite series and convergence, basic numerical methods
* Calculus III: multi-variable calculus (partial derivatives, multiple integrals), vector calculus (gradient, divergence, curl, surface and line integrals)
ODEs were a class you could take after Calc II.
Is this uncommon in California schools?
(I think the idea that it's in any means required to be able to do STEM in college is ludicrous, but having the option is great.)
I took Advanced Calc and AP Stats senior year, which in retrospect was a mistake :P
My son is taking high school BC Calculus (one step above "AP" calculus) this year. It includes limits, derivatives, integration (including integration by parts and partial fraction decomposition), ordinary differential equations, infinite series and taylor/mcluarin series.
BC Calculus is the advanced version of AP calculus, not "one step above". Ideally people are moved into AB or BC Calculus based on skill level, but only take one AP course.
1. Blank slate - All humans are of equal ability
2. Any observable differences between humans are merely the result of social factors
3. Any observable differences in outcomes between groups of humans are the result of oppression from the majority group
4. If you observe differences at your org/institution, it's your moral duty to create policies which disfavor groups of humans performing better and to favor groups of humans performing worse, as those performance differences are due to oppression.
If these beliefs undergird your worldview, and your social groups/information environment reinforce and reward these beliefs, it is of no surprise that we'll see a lot of people soberly propose the types of policies we see here. I can empathize that they really do think they are fighting the good fight, and are doing the right thing for society.
The important thing to note here is- if you reduce the bar in high schools, a lot more students will end up in college - more money will spent, more loans will be written out etc.
Or political interest?
I wrote sth about that here:
https://news.ycombinator.com/item?id=31176276
(Namely, foreign state psyops? -- I do not think so, just a thought)
2. This follows from #1, if we rule out nature then it must be nurture. Also, you must not be a parent if you'll accept "some kids are just dumb" as an excuse
3,4. Replace "oppression" with "competition". I think it might sound better to you. But the conclusion is the same.
You want to prevent winners from accumulating an advantage, eliminating all others (which sounds vaguely genocidal in this context), then you have to handicap winners and support the others. And the fact that the wealth distribution in America is so uneven certainly suggests that the initial premise is true (i.e, winning allows you to accumulate and compound advantages with repeated victories).
curious to learn how you arrived at this conclusion?
Is it? Saying "all mean are created equal" has a lot of interpretations, of which many valid ones do not include "all men are born of equal ability in every regard." Given that some people are born to grow up to be 5'4 and weigh 100lbs and others are born to grow up to 6'7 and 320lbs, it should be clear that not everyone is "equal" at least in terms of their physical abilities. I'm pretty sure the Founders were aware of this, making it highly unlikely that their version of "created equal" meant "exactly equal in all terms of ability."
Those compound advantages you're talking about are good things that we want people to have because they help them do more good for society. You seem to want to handicap them in the name of fairness. Where does that thinking end when you realize that the founding assumption (1. above) is false? Disfiguring beautiful people to prevent them accumulating the compounding advantages that come with beauty? Brain damaging intelligent people?
As of now we effectively underwrite anyone who wants to go, often at the expense of the student racking up debt for a useless degree and later the taxpayer who will inevitably have to subsidize them.
Just that they are 'equal' i.e. before God, or before the Law.
That one man is not from some superior lineage, that makes him a superior being.
I would be the founding fathers would have no problem if one man decided to 'discriminate' among others for some arbitrary reason - even if they were landholding men of high status etc..
“ 1. This is kind of a founding principle of the country, so...”
yes those slave owning people really thought their slaves were the same as them, totally dude
Entitlement principles are why the West was the 1st place in the world to abolish slavery and then went about and abolished it throughout the world.
These proposals come from committees and groups of people, and it's just not realistic to write off the entire group of people behind these proposals as having some uniform set of beliefs like that, especially when they give other rationales for the proposals!
The current school system makes decisions in middle school (8th grade and earlier) which determine whether or not each particular student will be able to take calculus in high school. This is, simply put, insane.
Because it's obviously insane, when you introduce questions of race and class into the mix, then it's easy to apply pressure to the department of education to come up with a proposal that changes things. And then you end up with bad proposals... why? Because these proposals are produced by poorly-shepherded committees full of government employees under political pressure, and it's much easier to come up with a bad proposal that responds to political pressure than it is to come up with a good proposal.
There's just no need to try and explain that this proposal is bad because the people who made it have bad beliefs. I'd characterize this as fundamental attribution error here... "the committees made a bad proposal because of wrong beliefs" versus "the committees made bad proposals because it's easier to respond to political pressure than to write a good proposal".
I would never describe someone's beliefs as "circumstantial", and I would also never think of being on a committee as something "intrinsic".
There is however a very broad movement of people who believe that unequal outcomes are a manifestation of racism and so they act accordingly in their roles in government etc..
Many of these people are in the civil service and so this will influence their view.
It would be 'insane' to ignore this movement, it's one of the most powerful social forces in the US right now.
> Many of these people are in the civil service and so this will influence their view.
It influences the political pressures placed on people in the civil service more than anything else. People in the civil service are in the civil service for a long time, typically. Often they are in the civil service for decades. On the other hand, elected officials and political appointees rotate in and out much more quickly.
I know people in the civil service, they have a much more long-term and level-headed view of things, and my impression is that they "weather the storm" of changing political pressures. At least, the ones who survive in the job do. Political appointees and elected officials are much more mercurial. Appointees know that their position is (somewhat) an extension of their own political power to begin with.
watch “the news” or go on twitter
"The news" is dominated by organizations which are trying to maximize their social media engagement metrics so they can get more money from advertisers, so they're subject to the same forces that drive Twitter.
Neither of these sources reliably give you a picture of national affairs. Right now the best I can do is get a picture of local affairs by talking with people that I happen to encounter because I live near them.
Christians are fond if it: "You have an innate, direct relationship with God, in his eyes you are equal to the The King" etc..
But we've only had 'governance' in the broad sense for 100 years.
And we've never really tried to apply such principles into education until the 1960s.
Now we have actually made incredible progress on social issues, we have our 'wars' in Social Media with Holy Anti Racism Fanatics trying to do their best - because 'racism is bad' - which of course it is - and 'systematic racism exists' - which of course it does - but the 'kernel of truth' of these issues drives people into ideological fervour as though it's some giant overwhelming issue, when really it's not. Racism is still pernicious, but it's not fundamental.
And FYI don't think it's all rubbish.
For example - 'Math' is heavily based on prerequisites. If you 'fall back' in Grade 4, you may never be able to 'catch up'. While that's true in general, it's not as acute as in math.
Poor kids might be far more likely to 'fall of the bandwagon' and a lot of poverty might be due to systematic racism, and so the 'Hard Requirements' for certain things may not be ideal.
You could have 'summer school' or 'after school' or 'accelerated catch up' programs.
Those would be 'reasonable' solutions in my view - and FYI these are mostly issues of poverty, not race, they are couched as racial issues because that's what fires people up.
Edit: and yes, I agree 'most people in the civil service' are level-headed. Most people actually are. But some groups have outsized voices, amplified by 'allies' elsewhere.
The 'Anti Racism Agenda' is a 'fundamental pillar', like a religion, of 25% of the US population, and they are pretty active about it. And the actions of the most extreme 5% end up really upsetting other people. Much like a very powerful fool using made up constitutional manoeuvres to try to take over the government would upset a lot of people as well.
Good intentions, surely, but that doesn't make them right.
Systematic racism only exists today to positively discriminate against people belonging to so-called disadvantaged races, at the expense of those belonging to so-called privileged races. That's why White and Asian kids are discriminated against in college admissions.
I assume your example is talking about Prop 58. [1] Is Prop 58 racist? Of course not, the CA Constitution prohibits racist and sexist laws and the courts are very good at enforcing that prohibition.
Prop 58 means a lower property tax bill can be inherited by the children with the property. By your reasoning, isn’t allowing property inheritance at all racist?
To me this is a meaningless injection of “equity” into a discussion on equality. Racism is not a word that means “inequity” - as in - everyone not consuming, producing, contributing, and owning the exact same quanta. That of course is a bizarre fiction.
We are talking about a tax policy which generationally preserves a tax break. It had a meaningful basis in law and policy which does not discriminate based on race, but it certainly provides a significant tax benefit to generational land owners.
Now again, that’s a drop in the bucket compared to the Federal estate tax lifetime exclusion amount, which provides orders of magnitudes greater tax benefits to preserving generational wealth, so Prop 58 is just a bit player in this scheme.
If the argument is that a tax policy which is advantageous to anyone with generational wealth is “systemically racist” then I think the argument has gone off the rails.
There are important justifiable public policy goals to ensuring a certainly level of generational wealth. There is no and never will be an important justifiable public policy goal of being “racist”.
If someone wants to argue for wealth confiscation, redistribution, and equity (e.g. some form of communism) then by all means give it a shot. But I don’t abide calling people racists if they disagree with that as a policy goal. If the argument is “merely” that there should be no tax benefit which preserves generational wealth, you actually immediately end up in exactly the same place.
The answer is of course more likely along the lines of “we do both”. We have policies that provide for protecting and maintaining a certainly level of generational wealth. And we also have policies which provide a massive welfare system for people without any generational wealth.
As to estate tax exemptions, they aren't nearly as egregious. There can certainly be an argument for reparations of ill-gotten gains to level the playing field, but it's at least possible for me to accumulate wealth myself and pass it on to my children. In contrast, it's simply impossible for me to acquire and pass on the same property tax rate that my white neighbors have.
I think saying you can’t go back in time and capitalize on an investment 60 years ago that also comes with an accrued property tax advantage is true, but has nothing to do with race. Anyone can start accruing their own tax advantaged status under the exact same Proposition, and no one can ever try to take it away from them on the basis of a protected trait, right?
I guess what I’m asking is, is there anything specific about this tax policy that accrues benefits to a historical capital investment which makes it “racist” over any other tax policy that accrues benefits based on historical capital investment?
There are so many race neutral policies that provide accrued benefits like this. Even social security benefits accrue based on historical wages. But also things like Roth IRAs which provide compounded tax free growth. You can’t contribute the same dollars today to a Roth IRA and get the same tax advantages as someone who contributed the same amount but over the last 60 years, the benefit can only accrue over time, just like the CA property tax benefit can only accrue over time.
Not everyone pays the same tax rate on their income or their property, nor are they provided the same level of government benefits. In many cases that tax rate or benefit level will be based on historical personal or family wealth. Often times it works out to be a progressive tax, sometimes it’s regressive depending on so many policy goals that are often in conflict with each other.
Simply put, any of your neighbors who have owned their (family) property for several decades have accumulated a several thousand dollar a year tax benefit for being a long-time owner. You too can accrue a several thousand dollar a year tax benefit the longer that you hold your property. You don’t get to buy in and get that benefit on Day 1, and neither did they.
Shitty taxation policies fuck all new home owners and have little to do with race.
This can be trivially demonstrated: ten times more men are arrested and incarcerated than women, yet no one would claim this suggests the US criminal justice system is systemically sexist toward men.
How did you reach this conclusion in the face of 300+ years of verifiable, well-documented federal, state and local racist legislation and policies? If it’s pernicious now then it’s always been pernicious since generations have persevered irregardless of these policies… but that doesn’t make sense to me.
But even conceding that racism is the dominant factor in performance differences, the framework proposed here is plain ridiculous. In essence, what they’re advocating is that because disadvantaged groups underperform in advanced math, advanced math should be scrapped altogether in public schools. The effect of this will be to handicap disadvantaged groups even further, as they’re less likely to attend private school or have access to private tutoring, and thus will be locked out of advanced math entirely while advantages groups continue to receive advanced math instruction in private schools.
Political pressure is a manifestation of the population's problems / beliefs / perceptions. It's wrong to bow completely to political pressure, but it's also wrong to ignore it.
If a political decision-making process concludes "men account for more road traffic deaths than women, but we've decided that gender can't be taken into account when pricing car insurance" that's fine; the facts have remained the facts, and a political decision has been made by a political process.
But if the same process concludes "men and women cause the same number of road traffic deaths" the process has gone off the rails despite the fact the outcome is the same because in one situation the facts have been acknowledged and the decision to act contrary to them made knowingly; while in the second situation that isn't the case.
They ignore the fact that the degree is supposed to be a proof of "This person has X skillsets at minimum". It no longer is. There is basically no job in the United States that cares if you have a high school diploma or GED other than government jobs. They are repeating this process with College right now. The College Diploma is now the new High School Diploma, and pretty soon jobs are gonna want Masters or Doctorates for entry level.
This is a bad belief, they don't (or won't) understand that they are ruining and devaluing a thing by their actions and beliefs.
Yes pretty much every college requires "college algebra". But some schools have "college algebra for stem majors" vs "college algebra for non stem majors". Guess which one is easier, has lots of bonus credit and extra curricular stuff to earn extra credit. (You attended the college showing of "vagely related math movie?! Here's 10 points on your final!") And also grades on a curve. Also you only need 69.5 (and sometimes just a D!) to graduate.
There's also other cheats/hacks. Like lots of state schools will let you transfer from a community college with credit for your "core courses", and some of those have questionable standards. There's also the fact that college algebra usually has some kind of test out or online option. There was a whole sub industry of "pay you to take the online test for me" at colleges for stuff like college algebra. Some of those courses did have some kind "you have to take 1 test in person so we know its you" rule. But they didnt check super heavily that you were actually that person other than a cursory examination of your drivers license name matched who was supposed to take the test. (and oh boy let me tell you about how covid and masks interacted with all of that)
Dont get me started on the "Statistics for Sociology" that was different than actual "Statistics" (but fulfilled the Stats requirement for the degree)
This is also ignoring that taking College Algebra to begin with IN COLLEGE. Was a major sign you were not a Stem Major. Stem Majors took that in high school and were taking at minimum precalculus. (and even that was viewed as the slow lane, you should be talking Calc 1 as a red blooded STEM freshman)
Caltech didn't. In fact, they expect you to know calculus before entering. I didn't, and that nearly capsized my college career before it left the dock.
Sad to hear that. It suggests their admissions process has succumbed. When I attended, it was very rare for the admissions people to admit someone who couldn't do the work. I only knew one who couldn't.
Colleges should only admit those who pledge themselves to the Guild of Software Engineering at 13, so we can keep the noble profession of building CRUD apps in JavaScript free of riffraff.
The calculus requirement was not listed as an admissions requirement. The other students were astonished that I didn't simply assume it was required.
Fortunately, physics prof Ricardo Gomez invited me to his office for some impromptu calculus tutoring, which saved my bacon. I owe him.
This does not in any way imply that those should be the only kind of places to exist.
This does not in any way imply that there's anything wrong with people who started to recently to have relevant background.
We also do split students as early as after the 4th year (end of elementary school) in three different school systems with about 50% of students attending the highest university track tier. The other two tiers might not have calculus or only in a limited form, but also don't qualify for university without further education. Thus setting students on different paths based on ability/performance early on seems very natural to me. Students always can up/downgrade schools based on performance at any year later on.
An acquaintance asked me if she should take "Calculus for Artists" after I suggested she take a calculus course. I laughed, and said that such a course should be named "Pretend to Learn Calculus". She should take a real calculus course, which she did, and did well in it.
If you're in college, stick to the real math classes, not the "math for losers who are forced to take a math class". You'll be with other students who want to learn math, and you'll have a prof that wants to teach math (the loser math course has a prof who doesn't want to be there, either). It'll be a much more pleasant experience.
Hey, if I was running a college, I'd have the two track math system, too. That way the students who want to learn won't be bothered by the ones who don't.
Was that based on actual knowledge of the course content?
It's like "Flight School for Artists". There's no such thing.
dae STEM has got to be one of the most exhausting memes on the internet. Hell, I’m 3/4 of the letters and even I find this aspect of our culture insufferable.
Both have their place.
So, yeah, in the real world, it doesn't work out so good.
I eventually learned to appreciate that Caltech never taught how to use formulas, but instead taught where the formulas came from. I recall a class on jet engines (really, an awesome class!), where the prof spent the entire lecture deriving the formula for a jet engine's performance. It was breathtaking. I knew where every term came from. I finally understood how the damned thing worked. All those other handwavy explanations mystified me.
If I was just handed the formula, it wouldn't have meant much of anything to me.
- get you used to the general feel of the topic
- make you practice proving things
The specific theorems students prove are not really the point.
Right, that's why they should skip the calculus and start students directly on Real analysis. Then they might actually have some use for what they prove in the class.
E.g., there can be a course on compilers that teaches automata theory. There can also be a course that just jumps in and codes a compiler. Both courses teach different, but valuable skills. Now, having a course “Compiler for Artists” where you’re taught such useful gems as “a compiler translates between human-level languages and machine code,” not so much.
For cheating we proctor all of the tests, which are worth by far the highest portion of the grade. I’m sure people have cheated on the proctored tests, but there’s not rampant purchasing of passing grades. This is specifically to rebut your implication that students are cheating or being carried by the grading structure, not necessarily to discount your position in the overall discussion.
It was well known there was a side hustle for some of that. And certain proctors would at times be told to drop it if they pressed. It was notoriously an issue with the non english speaking population. They would show up with an id that was clearly not them, proctors would be told to just let them take the test, same student would still be at classes months later. Though to be fair foreign students and schools chasing that money is probably its own kettle of fish.
That's probably true. But there's just not much that you can do to teach years of junior high and high school math in a single college class, to students who never got the chance to seriously engage with that material because their school replaced actual math courses with this new "data science" thing (or for countless other reasons which would fully apply even today). "Weedout course" might not be the intention, but it's definitely the real-world outcome.
I don't have a specific comment on the policy under discussion, I'm not a californian and I'm not familiar with the specifics - but telling people "You'll be fine without a degree" isn't going to go over well and, honestly, is asking the recipient to accept a large risk regarding their future while you, an employed person, have already passed that hurdle. American colleges definitely have issues with over enrollment but even if wanting that state is a "bad belief", it's certainly an accurate belief.
I don't disagree at all that it's mostly BS, but, much like the stock market, it is functioning primarily on the social valuation - and currently degrees are seen as close to a necessity to enter the job market.
1. The only thing I've seen on this front is some advertising for trades work which can pay equal or better to non-SF software engineers.
The boss of my first internship at Cisco majored in Geology.
[0]: https://www.sfgate.com/bayarea/article/Stanford-professor-Ka...
I have an issue with the parent's gossipy put-down of Professor Boaler.
I think it's important to emphasize that genuine intellectuals who have put serious thought into this proposal support it. I would prefer more serious engagement with it, even if on HN the majority disagree.
A lot of students in the US learn physics without calculus, which is basically useless. It's just a set of magic formulae to plug and chug. We should not go further in that direction but instead go in the other direction.
It's not clear that this is the case. The "current approach" is to offer Algebra I in middle school, which ought to leave plenty of time for students who want to shape up in math and be prepared for HS calculus to do so. Push advanced math later in the curriculum, and you just expose the students to even higher-stakes dilemmas. Lowering standards is no solution, since you'll just end up with lower education quality for all students, that will make it even harder for them to catch up to reasonable levels. This is the broad background of OP's letter.
What is being recommend is that no one take calculus in high school.
Both of these ideas are bad, but only one of them informs the California Math Framework.
It’s very commonly taught in 10th grade in France, Germany, Singapore and Taiwan (where I used to teach). It’s not universal by any means but as far as I can tell, the idea that calculus should be delayed until university is a nearly uniquely American idea.
https://www.mathvalues.org/masterblog/calculus-around-the-wo...
I can’t speak with certainty about other places but this directly contradicts my experience living most of the past 20 years in Taiwan (and speaking with friends who taught mathematics in the public school system).
Many, many people not on a STEM track learn calculus in high school.
Imho, 50% or more of students don’t even need to take algebra.
For that matter, that same number pretty much don’t even need to go to high school (although some sort of voluntary coop with practical skills training might be better than current high school or nothing).
HS is glorified baby sitting for most students. It sometimes is useful for people who want to go to “competitive” schools or enter stem fields in slightly less competitive schools.
As for your solution, learning math starting at algebra or pre-calc in a CC is fine if that is what the person needs for their chosen career path. I think the general idea is that the lack of calculus in high schools prunes the career path tree fairly aggressively in some relatively well-paid fields (esp. STEM).
You don't have to write off entire groups of people - just the few at the top. They got there by sucking up to those who were already at the top. Everyone else just has to keep quiet if they want to keep their job. Worse, they're expected to express visible support for their "superiors" and their ideas if they want to keep their jobs.
It’s an account of how a very diverse group of scholars advising the United Nations ignored research contradicted their ideological views.
One of the scholars even admitted in private some of their recommendations were “wrong.”
The group was chosen for its expertise and diversity.
I’ve served on school boards. They’re heavily susceptible to group think.
Once the culture wars get involved, peoples minds turn off.
In reality it's not quantum computing that we're talking about, it's high school calculus and algebra. You don't have to be a hardcore blank slate proponent to believe that most people can learn it. And that is what these people don't believe.
It's important to consider the goals of this committee. They propose this reform because they oppose the blank slate theory. The current structure really isn't appropriate to most people. Because it relies on a wrong form of the blank slate theory. They offer the wrong solution in my opinion, because they end up going too far the other way.
You have been to a remarkably bad college of education, if that was your experience. Which is saying something, because most of them aren't great, but for very different reasons.
Not that taking calculus takes a genius, as evidenced by more sensible countries.
This is generally true.
People can find extreme examples that “disprove” this but they’re generally wrong. Most things people do aren’t that hard and people have the ability to learn to do them — they either choose a different path, have fewer choices, or just don’t care.
And yes, before you ask, this includes computer programming.
Or, do you really think every 2-year old kid can teach their neighbor kids maths and then explained what groups are when he was 7-year old like Terence Tao did? I tried my own kids. Needless to say, I failed, miserably.
Without pointing to a vague notion of "we're different people", I think there's a few key things that were different, despite everything that was the same:
* She's the second child, I'm the first: there were some things in my education that my mother literally said "we are fixing that for her". (And I should note that I don't resent this: my mother was clearly doing the best she could with the information she had — and because she loved us. But she had more information during Round 2.)
* Education is a finite resource: in my home state, whether I got into a decent school (i.e., a magnet school) was dependent on the literal roll of a dice. (Literally literally. I.e., list of names goes in, gets shuffled, top n go to good school & gets educated, bottom m talent gets wasted.) In the worst case I was 5th? 6th? from the bottom of a several hundred person long wait list. She got in. She got a year in the magnet system that I didn't (I got entry a little over a year later). That missing year was an enormous detriment to my education and growth; it was such a clear detriment my parents were contemplating whether they could afford a Catholic private school (we're not Catholic) or simple home-schooling. Had they had the gift of clairvoyance, I think they would have the moment I was denied.
* Almost certainly the gift of a computer got me interested in CS. She didn't get one, and her interests are different. (She's still STEM, likely due to our parents.)
Education is following as similar course. Things like MITs open courseware, edX, etc. are making it increasingly easy to get the educational content from top teachers regardless of how limited these teachers are.
(Having access to an education is not the same as actually getting a degree, and getting a degree isn't always the same as getting an education.)
But there has probably never been a time in history where more people had free or inexpensive access to the top educational content in the world.
I see where you are coming from on access to labs, chemicals, and equipment. But someone who has fully availed themselves of everything they can learn from free/inexpensive online classes, books, forums, emailing people, etc. is headed on a path where they have a high probability of getting access to those types of things once that is the only thing blocking their continued education.
Not suggesting that, and it's wrong anyways: the point here is that we, as a society, want people to have a basic floor of an education by the time they reach adulthood. Not necessarily MIT, but not nothing either, and the track I was on for a bit in my childhood was closer to "nothing" than it was to "decent", and it was certainly way off course if I were to shoot for MIT.
For the students that never left that track… I cannot imagine that school did much, if anything, to produce a citizen with a high-school education.
In _every_ activity I've ever participated in where I can observe many people's performance and progression - including powerlifting, bodybuilding, various ball sports, mathematics, chess, theoretical CS, software engineering, etc - it is transparently obvious that people's natural abilities vary dramatically.
Although it's not the most common scenario (training and experience do matter), I have seen many situations where someone with, say, 6 months' haphazard and lazy experience will absolutely crush the performance of someone with 3 years of serious and dedicated training.
Talent is real.
Talent is real, but generally speaking, ascribing failure or lack of progress to lack of talent is a mistake.
Not all failures are due to lack of talent, for sure. A blank statement like " ascribing failure or lack of progress to lack of talent is a mistake " in the context of our discussion is nonetheless a mistake as well.
Have you considered that maybe you're just unusually talented? I know most things people do are very hard for me, and the few things I do are very easy. Learning history is an uphill slog even though I love it, but math doesn't warrant effort. For a while I just figured people that failed math were lazy and people that passed history were geniuses, but it turns out people have different amounts of natural talent. It's not the start, it's the slope
Huh. To me it seems more narcissistic for someone to say that they have no special talent and that their success is entirely due to their superior work ethic and years of study and sacrifice.
I’m just like everybody else — can get pretty decent at a lot of things.
That's a very different claim than "innate talent doesn't exist".
Yes! This is why I never said innate talent doesn’t exist.
That's true, but it's the small minority of tasks that require real intelligence that often matter the most. A regular person can probably be trained to 95% the skill of an anesthesiologist just by following instructions, but then they would kill the patient during edge cases.
The same thing applies to programming too. I had an internship at a regular company, and now work at a FAANG. The developers at the regular company are likely better at programming than me, especially when it came to regular tasks, but some of their technical decisions just didn't seem to make any sense.
You’re making the mistake of assuming anesthesiologists are something other than regular people with training.
Can people not have varying degrees of physical and neural plasticity? Perhaps some people are more like blank slates and can adapt more readily than others? Maybe plasticity changes with age?
It's just a 'general set of principles', intuitions, pop culture ideals that lead a large group of people to assumptive believe that 'unequal outcomes are driven mostly by systematic racism' and that's that.
Ergo 'the world is deeply racist' and 'there is racism around every corner' including in your math textbooks and teaching.
Ad nauseum.
Some of it is actually correct.
Some of it is reasonable from an intellectual perspective, but it's hard to take anything from it.
Much of it just ends up being toxic.
Lots of controversies in math education between STEM professors (especially mathematicians) and K-12 math educators/researchers are rooted in this. In the community of math and science education, we educators/researchers always focus on average students who will grow into future citizens, not STEM workers. This is really a different mindset to STEM professors.
“We only cover bad art — we don’t focus on students who go on to be professional artists.”
“We only focus on bad English — we don’t focus on students who go on to be professional writers.”
“We only focus on bad history - we don’t focus on students who go on to study history or social science.”
Each of those has an AP and IB track, competitions to find elites, etc — just as mathematics should for high performers.
If as an educator, you only teach to the lowest common denominator, then you’re failing the children you’re supposed to educate.
To me, your post reads as if you’re bragging about failing at your job.
Middle and high schools start auditioning and training students into “advanced” art, preparing them to go onto competitions and onto serious careers in programs differentiated from the casual art classes.
Learning calculus won’t be enough as a professional in STEM either — but AP Calculus is the equivalent of audition-only advanced art classes. (Which exist all over.)
Both had audition programs in art for “advanced” classes (both music and drawing), where students were matched with more serious training and where their bands went to competitions and drawings were entered in regional shows.
I think you’re confusing “good, on track for professional” with “absolute top tier” — many students from regular schools go on to, eg, be animators at a studio or choir directors.
The same split exists in math:
- advanced classes you have to place into exist at most schools, eg AP calculus
- but to be the “absolute top tier”, you’re talking about STEM schools and private mentoring programs
You need the first for engineers, scientists, etc — even if they’re not going to be Terry Tao.
Depriving college-bound students of calculus, though, is a bad move. A lot of philosophy also involves calculus-related arguments (ie if we cut up space in really small pieces, what do we get?), so it has applications outside the STEM fields.
Germany separates people into vocational school and something closer to what we'd consider high school in the US by 9-10th grade. If you embrace the idea that some people are simply less suited for intensive math - whether it be because of work ethic, inherited IQ, lack of interest, etc. - and give them a path towards jobs that better fit their skillset, I think you'd see a lot less people drowning in college debt because they got a degree in sociology when they got weeded out of Calculus 101.
I've run into it so often by a vocal minority who slander anyone who objects. Fortunately, the popularity is waning.
Not only does the earlier version of the framework explicitly reject this view, it cited specific empirical studies that the broad approach targeted (which I gather had not changed in the revisions which is why the complaints remain despite some revision to details) was better for people across the ability spectrum.
Similar points apply to each of your bad-faith assumptions about the underlying beliefs.
Can you share that explicit rejection of the idea that there are not innate differences in ability, in the CMF? I have not seen it myself, thank you ahead of time.
To share what I've read, and colors my views a bit, is the following, from 'Chapter 1: Mathematics for All' of the Second Field Review [1]:
> An aim of this framework is to respond to the structural barriers put in the place of mathematics success: equity influences all aspects of this document. Some overarching principles that guide work towards equity in mathematics include the following:
> All students deserve powerful mathematics; high-level mathematics achievement is not dependent on rare natural gifts, but rather can be cultivated (Leslie et al., 2015; Boaler, 2019 a, b; Ellenberg, 2014). ...
> All students, regardless of background, language of origin, differences, or foundational knowledge are capable and deserving of depth of understanding and engagement in rich mathematics tasks.
> Hard work and persistence is more important for success in mathematics than natural ability. Actually, I would give this advice to anyone working in any field, but it’s especially important in mathematics and physics where the traditional view was that natural ability was the primary factor in success. —Maria Klawe, Mathematician, Harvey Mudd President (in Williams, 2018)
> Fixed notions about student ability have led to considerable inequities in mathematics education.
Note that my pointing to this doesn't mean I inherently disagree that hard work/education can't help improve outcomes. I show the above citations to show that the CMF is not explicitly denying the Blank slate theory, which is what you are suggesting. If anything, they go out of the way to view ideas of innate ability negatively. I'm happy to also look at the references that you alluded to but did not cite.
[1] https://www.cde.ca.gov/ci/ma/cf/ (it's in the bottom section, the format is .docx, so don't want to directly link to it as that format can sometimes be cause for concern on random links shared on the internet)
I see a lot more stuff that would lead a kid to believe "it's ok that I'm not good in math" rather than "I could be good in math if I wanted to be."
Frankly, I think this is actually worse educationally than what you suggest.
We need to find more ways to reward effort instead of pre-existing ability (regardless of how that pre-existing ability is gained... the kid whose parents got him ahead of the curve through high school math and then bombs out after taking university-level Calculus is similarly harmed by the current system as the one who's shunted away from ever being challenged).
Some observable differences are due to social factors.
Some observable differences by certain groups are the result of past actions by other groups.
You should favor policies to correct for the result of past harms.
One cannot reasonably claim that no groups in the US are still disadvantaged today due to actions taken on a centuries-long timescale. It seems willfully unfair to stick your fingers in your ears and just say "I'm not actively discriminatory, so there's no need to try to mitigate things, everything is peachy."
> Some observable differences are due to social factors.
> Some observable differences by certain groups are the result of past actions by other groups.
Agreed with this as well.
> You should favor policies to correct for the result of past harms.
Mostly disagree. I'm wholly convinced there's never going to be even remote consensus about ancestral oppression and victimhood. I think that if you want to correct harms, you should focus on the current social issues. Not only do I think that has much less shitty side effects (such as exacerbating group identity), but I also think it will be more effective at reaching those that have been mistreated in the past - both directly and their ancestors. The US in particular has, let's say, a decent amount of low-hanging fruit in terms of social issues to address (homelessness, lack of preventative health care, incarceration for victimless crimes etc etc).
> there's no need to try to mitigate things, everything is peachy
This is not the only option. You can recognize that things are fucked but have a vastly different opinion on how to improve.
The alternative would be awful, no?
I really don't think it is. And if it was, it'd be only partly, since apparently lots of this is coming from people inside the US.
But what if there're foreign state controlled FB groups that try to manipulate people in the US, spreading these anti maths ideas? I'd be surprised but not super surprised.
Still, if you were Putin or Xi, why would you not want to damage STEM in the US? And even if you didn't start these ideas in the first place, why not try to amplify them, once they already exist
I wrote sth along those lines here:
https://news.ycombinator.com/item?id=31176276
(Foreign state psyops -- I do not think so, just a thought)
I don’t know anyone who seems to disadvantage high-achieving individuals. Only people who wish to raise the performance of as many as possible to the same level. And yes, I see oppression everywhere, including education.
It would be a net loss to society to deliberately reduce the performance of anyone.
This is laziness of the moral clowns who know the easiest way to remove a difference in success is to eliminate the successful. As they don’t care about anything but the theatrical performance, they naturally take this route of least resistance.
Absolutely no one I have met believes 1 and 2.
As for 3, "average observable differences" in mental ability can largely be explained by socio economic factors. Case in point, East Asian IQs stagnated behind US IQ averages 50 years ago, but are significantly ahead now. I dont think they underwent a general transformation in 50 years time.
4. Is again a strawman. Affirmative action is used for a limited number of historically discriminated populations in very limited contexts.
If you are interested in an actual debate don't invent a caricature of the opposing position.
Admittedly I am a little confused by your comment. You made the above statement, and then follow up with this statement:
> As for 3, "average observable differences" in mental ability can largely be explained by socio economic factors
If we are to assume you are being earnest here in your first statement in that you believe there ARE innate ability differences between humans and social factors don’t explain everything, can you explain how much innate ability differences are a factor in intelligence differences (using it since you brought it up)? And how do you determine it? What methodology are you using for that, and if you aren’t basing it on anything, what methodology should we use?
If you are going to dodge the question and suggest you were talking about averages between groups (for which the question does still apply) and that between groups are a special case, then please share how much of a factor innate ability differences are in intelligence within groups? And how you determined that?
1. If we are to assume you are being earnest
2. If you are going to dodge the question
etc.
I am a statistician and all of your questions have banal answers.
For individual differences you can plot the bell curve and the standard deviation gives you the individual variances.
I was clearly talking about population averages in 3.
> can you explain how much innate ability differences are a factor in intelligence differences (using it since you brought it up)? And how do you determine it?
AFAIK remember, heritable IQ/ height is estimated to be a bigger factor at an individual level. However, there is no existing causal methodology to determine it. Instead we have correlational regression models that make a lot of strong assumptions that are practical. There are various papers but it is clear that IQ is highly heritable like human height.
Also, I am going to replace "innate" ability with "inherited" ability because there is no methodology that can tell you how much of Roger Federer's tennis ability is "innate" and how much is "coached".
> talking about averages between groups
Your wording is ambiguous. But assuming you are talking about intergroup differences. When you sum up IQ or height within a group, the observation from regression models is that individual hereditary differences cancel out, and intergroup height and iq differences are easily explained by socio economic factors in a correlational regression model and heritable height/iq is an insignificant factor. Once again- this is not a causal model. Only correlational.
And this is just common sense. We know from life experiences that different people have differing IQs and heights from an early age. We are also aware of how important it is to have a school system - instead of just letting the kids figure things out on their own. The environment matters because we do have to work to nurture the inherent talents of a kid, otherwise that potential will be lost.
> please share how much of a factor innate ability differences are in intelligence within groups?
I expect the per sample standard deviation to be the same across different ethnic groups. For inherited "ability" i expect the total variance explained by "inheritance" factor to be the same across ethnic groups. I doubt if such an analysis has been conducted, because I don't see the value in this kind of subgroup analysis. Do you have any references to such studies? Have you seen data that contradicts this?
1. Math is a differentiating subject for getting into those competitive colleges, departments, and professions. In the meantime, the progressives simply refuse to believe that some people are just better at studying math. The logical choice, then, is to dumb down math to "level the play ground". It's the same unspoken reason why so many people pushed the magnet schools to use lottery to pick students (I actually think lottery with threshold can be a good solution, but that's another subject).
2. Progressive math educators have been advocating self discovery and that everyone can learn math in their own pace for years. What educators need to do, per the progressive argument, is to protect the fragile passion and creativity of the kids. Jo Boaler even argued that kids should discover all maths by their own. Naturally, we have to dumb down math courses, otherwise we would inevitably hurt the confidence and passion of some kids. As progressives always said: no kid should be left behind and some people got better at math only because they were socially privileged. I disagree with the progressive view of math education based on my personal experience, as so many classmates of mine simply were not interested in STEM, and maths in particular. I'm not sure why we don't accept that most people will hit a wall sooner or later when learning maths. To some it is arithmetic, to some it is calculus, to some it is abstract algebra, etc and etc. To me I definitely lost my drive when taking courses like model logic, and I certainly do not have interest or talent to get good at things like functional analysis or topology or algebraic geometry, but I make peace with it. I really don't understand why the progressives are hell bent on insisting that everyone can learn maths equally.
Bingo. It's well intentioned, but the intentions aren't to ensure that America can keep up with a rising China.
It's shocking to me that people in California aren't more worried about this. About 15 years ago, I was talking to an engineer at Juniper/Cisco. We were joking about how Huawei had copied one of their router designs down to the silk screened assembly instructions (in English!) on the PCBs. Fast forward to today, Huawei is making fully custom equipment down to state of the art switch and router chips, and Chinese companies are white boxing lower end products made by American brands.
There's a big bet out there that the U.S. can survive on software and social media alone. I would think the success of Tik Tok would have blown even that rationalization out of the water.
On the general point of U.S. math education: my cousin who lives in a nice California suburb was complaining that the math education her early high school student is receiving is several grade levels behind what she got--in Bangladesh. My mom, who also went to school in Bangladesh (in the 1960s!) was deeply unhappy about the math education in our affluent Virginia suburb, until I got into a top STEM magnet high school. My own kids go to an expensive private school, but are still getting math tutoring on the side. Math is just a shockingly low priority for Americans.
I'm not trying to suggest that the US is fine and we shouldn't fix anything, but if you look at the world by comparing test scores and grade levels in mathematics, you're going to come to some very warped perceptions about what is important. I'm speaking as someone passionate about STEM education, who got a B.S. in mathematics.
The whole situation is warped. The USA accounts for 4% of the world population, and 40% of the top 100 universities in the world. That's fucking weird. I don't have an explanation for it. I'm just saying that the different signals we use for evaluating how good our education system is functioning are giving us radically different pieces of feedback, and our understanding needs to be correspondingly sophisticated.
There are all these narratives about how China is going to eat our lunch (like Japan in the 1980s, or the USSR in the 1960s) and while I don't feel comfortable betting on long-term US hegemony, and while I do think we should put more work into our mathematics education, I do think that looking at the world through high-school mathematics test scores is going to give you anxiety more than it's going to give you an accurate picture of what are problems really are.
To take another statistic into account, there are actually many STEM graduates in the US. What do we do with this information? How do we change our policies? It's unclear.
that is just inertia, carried over from the time when the US was the only superpower. More and more Chinese universities enter this list every year.
No there aren't, at least if you only count homegrown STEM graduates. USA can be a tech powerhouse thanks to brain drain, not thanks to its STEM education. USA is one of the worst in OECD.
https://i.insider.com/5661f406dd0895ff628b46bb?width=600&for...
What would our STEM university departments look like if the next generation of Indian and Chinese kids with good K-12 math educations decided opportunities were good enough at home that they didn’t need to leave their families behind and immigrate to America?
We lost entire industries of good paying jobs in consumer electronics and appliances to Japan, Taiwan, and Korea. It wasn’t the total eclipse people predicted—in part because our population control evangelists helped derail Japan’s development—but our shift to software and IP didn’t replace the kinds of jobs we lost.
Finance, insurance, social, and professional services will keep our GDP numbers afloat long past the point where the real economy has been surpassed. A better comparison is Britain. Once the real economy moves, most of the ancillary services do too. Banking and insurance keeps Britain going, but it’s actually kinda poor compared to America. (The US is to the UK as the UK is to Hungary or Poland.)
No it isn’t. The best researchers want to go to the best universities and the universities are ranked on research performance. Its a feedback loop.
For those of who were around in that era and watched as the US auto industry and consumer electronics industry were devastated as their Japanese counterparts ran rings around them, Japan did eat America's lunch and with considerable gusto. Sony products were everywhere, as were Toyotas and Hondas.
Japan doesn't support your case. (Neither does China really.)
Yes, because of tariffs. They wouldn’t do it if imported cars weren’t heavily penalized for being manufactured elsewhere.
TJ? :P
Should math be a higher priority in the US? Should working hours in the US be the same as in China? Should the academic pressure on kids be as high in the US as in China?
The US is much smaller population-wise, would we actually need to try five times harder than China?
Is it not enough to compare today's high school overachievers with those of 20 years ago, all still fighting for the same universities but with all similarly-inflated resumes? Do we actually need to push them even further?
Do we instead want to be more like the European countries that currently put themselves under less pressure than the US?
There's a lot of competing / strange interests in school systems that can have well intended but BIZARRE outcomes.
My wife works in early childhood education. At one point it was recognized that the early childhood department should be more involved in helping students with learning disabilities as soon as possible. There was lots of outreach to parents to get them into free classes and education, and most importantly screening so they could get free services if they qualified / needed them.
However, it was noticed at some point by some very vocal parents that some students with specific backgrounds were refereed to these services more than others. These services were provided in and out of school, the kids weren't moved to another school or anything like that, but despite all their efforts... The result was deemed to be some sort of bias, or outright racism.
Therefore it was made very clear that they could not disproportionately "single out" students of some backgrounds for these services, that are free, to help them learn.
They are optimizing towards "High School Graduates" and "College Graduates". And if they need to destroy the value of being any kind of graduate to get there. So be it.
Another way is to lower the standard to make the outcome easier to attain. It’s gross and racist.
https://en.wikipedia.org/wiki/Bayes%27_theorem
Yes, it is ultimately founded on calculus. But we don't teach numbers to kindergarteners starting from Peano's axioms, and we don't need to gate the essentials of conditional probability behind calculus. In fact, doing so is positively harmful to society at large.
[1] - I take it as a fact that different people have different talent levels for different things, but not everyone agrees with that, and disagreement on this point is a big driver (but not the only driver) in the "everyone gets exactly the same" approach that is trending now.
In the year 2081, the 211th, 212th, and 213th amendments to the Constitution dictate that all Americans are fully equal and not allowed to be smarter, better-looking, or more physically able than anyone else
I'm glad for it. I would never want to bring anyone else down to meet me at my level on any metric.
I don’t want everyone to be the same, but unbridled disparity seems equally as bad to me… especially considering how arbitrary it can be.
Firstly, evidentially, people do care about disparity: increasing disparity seems to adversely affect people physiologically, independently from wealth. That is, having someone else be significantly richer than you, independently of your own health, seems to create stress effects in a population. By the metrics of national health and well-being, it seems like wealth disparity is a bad thing in its own right.
Secondly, the problem with billionaires is not that they simply have so much money, it's that one's ability to influence society, including making and breaking the rules of society, is intrinsically tied to money. For example, consider the recent news about Bezos buying a new boat, and having to take down and rebuild a bridge to get it to sea. On the one hand, it doesn't really matter to me how much he spends on that boat - it's his money, and he can use it as he likes. However, the people of Rotterdam were promised that the bridge would remain put, yet Bezos' money (presumably via the shipyard that organised this) was enough to override the democratic process, presumably alongside adding a significant inconvenience to the people living there.
Or consider the recent trend of billionaires buying media companies. On the one hand, it's kind of irrelevant how they want to invest their money, but on the other hand, these media companies afford significant impact on the views and perspectives seen by society. If we really want to claim that we live in a democracy, it seems dangerous to also accept that one person can, essentially on a whim, buy one of the largest social media platforms with only vague hints as to what he plans to do with it. That sort of power is absolutely not something that you (I assume) or I personally can wield, yet it could well have a significant impact in shaping public opinion.
As long as money can be roughly equated to power, then wealth disparity will remain a very important thing to be concerned about.
People going hungry, especially children, is a travesty.
What is your solution to it? We already have food stamps, welfare, fully subsidized healthcare, child tax credits, social security disability, free school breakfasts and lunches, Section 8 Housing, SNAP, WIC, CHIP, Medicaid, churches, charities, social security death benefit and so much more. People are still hungry.
Should we do more? The lesson of Africa says we shouldn’t. Decades of food aid to Africa did little more than make the continent dependent on food aid and drive all the farmers out of business because they couldn’t compete against free.
https://www.nytimes.com/2007/08/14/world/americas/14iht-food...
And I haven’t even brought up lthat there simply aren’t enough billionaires to tax to make even a tiny difference in any of this. Even if you took literally their entire net worth, converted it to cash (which is literally impossible) and spent it on the poor it wouldn’t make any difference.
THe child tax credit cut child hunger by 26%. We let it end. Giving people food isn't an especially hard problem in the US, yet we're not able to do it.
https://www.thebalance.com/new-child-tax-credit-cut-hunger-s....
Doling that out in smaller increments and making the purpose specific (child credit, instead of tax refund) seems like a good nudge into better spending habits... especially when the amount is known ahead of time.
For many people that get the child tax credit, a bonus is exactly what it is.
The word you should have put in quotes is “refund”. My sister, for example, used to pay about $1,500 in tax throughout the year yet get a $7,500 “refund”.
Isn’t that something? Pay x and get 5x as a “refund”.
When I was in school in the U.K. we did the first and second things, including eg multiplying matrices, eigenstuff, diagonalising them, inverting small matrices, some determinant/cross product stuff, and we maybe did the thing where you solve a first order linear ODE system by converting to matrix exponentiation, though I don’t quite remember. I think we just called it vectors and matrices.
There was some useful stuff there. The problem is that it was at a course so close to the leaves of the ‘x allowed to depend on material from y’ tree that we didn’t get to apply that much (related example: we had to waste a bunch of time on silly equations in physics because they couldn’t depend on us knowing about the y’ = kx ODE)
At university we did some courses in vectors and matrices / vector calculus that went down the practical route towards physics things and useful tools, and we had a course called ‘linear algebra’ that covered the abstract algebra side of things, where everything was lemmas/theorems/proofs beginning with e.g. suppose e1, e2, …, en is a basis for a vector space V over F, …. However it is certainly possible that the US terminology (linear algebra for everything) was more common outside of the courses I took.
It wasn't until I'd dropped out of college and taught myself math, because of the interviews in this industry, that I learned to enjoy math again. My point is that you're really fucking with the social firmware of kids when you do that. Also, reading between the lines of my life, not being in that upper level math class clearly had no impact on the latter parts of my life.
I'm trying to figure out how this relates. It sounds like you had a bad experience with tracking, and there is a fundamental issue with tracking where some amount of people will have bad experiences, but ultimately you were able to achieve your potential anyway, so why make the experience bad with tracking if people will eventually get to the right level over time - is that a fair interpretation of your comment?
Edit:
To make what I'm saying a bit more clear: There's a ton of people in these threads assuming that not everybody is born with math skills (or variants of that attitude). That is exactly what these teachers thought and how different my life would've been had I agreed.
It sounds like that was implemented very poorly in your case. You yourself said "I was immediately bored in our lower maths class". I don't see how the solution to this is to make everyone take the lower math class. Certainly there is some middle ground between the California plan and what you experienced.
It’s hard to see that as undermining tracking as a concept, since the problem is actually the absence of oversight and termination of bad teachers. No one teacher should have the power to doom a student, but a school needs to be able to recognize and cultivate talent.
It sounds like the implementation of levels was especially bad in the OP's case though, so I agree it isn't really a good anecdote to argue against leveling entirely like California is doing. It's throwing out the baby with the bathwater.
Edit: in the new version it has been changed to "high-level mathematics achievement is not dependent on rare natural gifts, but rather can be cultivated"
I mean, I would hope this is true.
I'm not "naturally" gifted at mathematics, but like reading, writing, and other things, I can learn them in school and got quite good at them.
Public education is like mass transit. Not everyone gets their own Lamborghini. Most have to take the bus. Its goal should be providing the best general education it can for all people and making as many people as possible productive.
If you looked at society 500 years ago you could assume that only certain people were smart enough to read and write.
It seems like any other guided/misguided attempt to improve the school system that has already taken feedback into account.
This entire HN thread is filled with "back in my days" and "wokism" but no one actually is disputing the content of the framework itself with actual evidence.
Holding kids back is really the opposite of cultivating mathematical achievement. To use the reading analogy, do you think a kid that can read at 4th grade level should be forced to only read 1st grade books anyway because that's what their age is? I'm not sure what that accomplishes.
It'd be one thing to make a resource allocation argument but that's not even what this is. This curriculum is clearly a philosophical statement and personally I don't get it.
Certainly some people are better at things than others - but so what? I know plenty of people that excelled in math in grade school and struggled in high school, also many more that excelled in high school and struggled in college. Some, like myself, struggled in grade school and excelled in high school. The difference was motivation.
> Holding kids back is really the opposite of cultivating mathematical achievement. To use the reading analogy, do you think a kid that can read at 4th grade level should be forced to only read 1st grade books anyway because that's what their age is? I'm not sure what that accomplishes.
And how many brilliant kids moved just a bit too fast and lost interest? The thing is you only view things one way. You forget that a fast ramp-up in difficulty can turn away many students who could've turned out to be brilliant scientists and engineers.
> It'd be one thing to make a resource allocation argument but that's not even what this is. This curriculum is clearly a philosophical statement and personally I don't get it.
I don't agree that it is a philosophical statement, having read it, it seems pretty straightforward. The alarmism about the woke mob is overstated.
The people that wrote said publicly available draft are still involved with this plan, and have not personally nor explicitly backed down from the statement. It's a good sign that some moderation has been introduced to the text, but it seems clear to me there are still some pretty extreme beliefs amongst those leading this thing.
Whether the "woke alarmism" is over the top or not, I don't think it should be controversial to say that a philosophical statement is at the root of this plan. I wouldn't be surprised if the Equitable Math folks would agree with that assessment even.
I also don't think that criticism of a specific model of leveled courses should be used to dismiss all leveled courses. You talk about kids that are rushed ahead or that perform differently at different points in their math "career" - which could certainly be problematic if levels are rigid throughout the educational timeline and leave little choice to students.
Yes sometimes it is implemented that way. But it is not impossible nor even particularly impractical to implement a more flexible levels system that would mitigate those concerns. There are schools that have done this well, California school system was not one of them. This proposal is throwing out the baby with the bathwater.
> I also don't think that criticism of a specific model of leveled courses should be used to dismiss all leveled courses. You talk about kids that are rushed ahead or that perform differently at different points in their math "career" - which could certainly be problematic if levels are rigid throughout the educational timeline and leave little choice to students.
But arguing for a gifted track IS rigid - it basically says "you must decide now if you're good at math, or not." That is deeply flawed. You can't add flexibility - you need algebra and geometry to do calculus. If you decide or become motivated too late (even if naturally gifted!), you have no recourse, as the "gifted track" starts before you can even know. The current system and system you advocate for could be removing huge numbers of potential STEM graduates from the mix.
> Yes sometimes it is implemented that way. But it is not impossible nor even particularly impractical to implement a more flexible levels system that would mitigate those concerns. There are schools that have done this well, California school system was not one of them. This proposal is throwing out the baby with the bathwater.
Not really - as is said in the framework, most foreign nations that outperform the US have a standard curriculum. So the problem isn't flexibility.
"The framework builds on the strategies used in a number of high-achieving jurisdictions (e.g., Estonia, Finland, Japan, and Korea) that pursue an integrated curriculum—connecting the domains of mathematics with one another as students collaborate in using data to solve real-world problems. These countries pursue a common curriculum in elementary and middle school, supporting more students in reaching higher level mathematics. The framework illustrates how this integrated approach with many different kinds of supports can be used to expand the number of students excelling in mathematics and heading for science, technology, engineering, and mathematics (STEM) careers."
Schools spend a lot of time reviewing things over the course of the academic year, including things from prior years - I disagree that it is not possible for students to move tracks with a well thought out curriculum plan. But regardless the proposed curriculum eliminates material that would be covered in upper track courses, and explicitly states it does not aim to have students prepared to take calculus during high school. This is like putting all students on the lower track, which is a hell of a solution to the problem of students getting stuck on the lower track.
Japan's model is much more like putting every student in the high track, it is not comparable to what is being proposed here. Japanese high schoolers are able to take intro analysis in 11th grade, here is a translated textbook that would be extremely rare to see a US 11th grader cover the same material (even with standard tracks you'd be lucky to cover it all in 12th): https://bookstore.ams.org/mawrld-11
Putting everyone together in the high track has its own obvious issues. ~70% of students go to "cram school" after school in Japan to be able to handle the curriculum: http://www.oecd.org/pisa/keyfindings/PISA-2012-results-japan...
I'm not familiar with math education in those other countries mentioned, but I imagine it is more similar to Japan than the US. Hilariously there have been some recent pushes in Japan to be more like the US education system as far as flexibility is concerned, in order to take some of the pressure off of students.
On the other side of the argument you have people from the Department of Education who specialize in Mathematics Education who seem happy to lower the bar as far as possible in the name of equality.
When I was in University the Department of Education was the most woke department on campus, except for perhaps the Department of Gender Studies. We are now seeing policies that favour wokeness ahead of the best interests of the students affected by the policies.
They should rename the Department of Education the Department of Equity. By pushing frameworks like this, they show that they are less interested in education and more interested in achieving equity. They'll even privilege equity at the expense of actual education.
Do we need to mail copies of Stand and Deliver to the entire California school board? Or am I the only one that recalls that movie... based on something that actually happened... in California.
When you're highly privileged it's extremely easy to imagine that most things are positive sum and not zero sum competition because when you're wrong and your cooperation was actually a disadvantage it's still no big deal for you.
Instead, I think it's just cheap feel good measures, virtue signaling, and not wanting to take the costs/risks of bucking a fad. If you don't know whats good or bad, well cheer for the popular change and pat yourself on the back. If you do know that the initiative is bad, speaking against it may get you called a racist-- better to say nothing and relocate to where your kids will get a good education.
Someone sufficiently wealthy never has to worry about a known bad policy resulting in a poor education for their kids-- they can always apply money to the problem, one way or another.
Is it about budgets? Is it because some people might think these classes "aren't that important?". The open letter seems to suggest that it's about closing gaps between privileged and less privileged - is that it? Honest question - I'm not trying to stir the pot.
> The framework would not forbid districts from accelerating students in middle school. It does, however, recommend that middle-school students all take the same sequence of “integrated” math classes that blend concepts from arithmetic, algebra and other subjects with the goal of cultivating a foundation and comfort level with numbers.
> On top of that, the framework recommends that schools postpone offering students Algebra 1 until 9th grade or later, when it says more students are likely to be able to master the material.
> “When kids struggle, they immediately say ‘I don’t have a math brain,’” Boaler said. “That changes how the brain operates.”
https://calmatters.org/education/k-12-education/2021/11/cali...
I am sympathetic to the idea that we don't want to send the message that some kids are just bad at math, but it does seem to be a bit of throwing the baby out with the bathwater by holding back the other kids who are doing well. Even if you keep the advanced kids in the same class, the kids are are struggling are going to be well aware that some of the kids are getting it really quickly.
You are right that this is a lot of nonsense. Specifically, 'you aren't good at math/math is hard' is the nonsense meme that gets hammered into student heads so frequently during school that most of them actually start to believe it.
It's not some kind of novel woke nonsense, though, it's how math instruction on this continent has been happening over the past X decades.
The wokies are pushing back on this nonsense.
I feel too often the people who play the 'woke nonsense' card think that we should just allow the current failings to continue, and any work to help struggling groups is wrong.
The cited issue was that higher level math courses were making other students feel like they weren't cut out for math. So it seems more like the issue is a mindset one. They shouldn't be looking at better performing kids and think "I can never do that". We should be instilling a better growth mindset to these kids, so they understand that they can overcome their inabilities.
The "woke" solution of removing high level courses actually achieves the opposite. It reinforces the idea that such a level is inachievable for some people so it should be cut out for all people.
If you think a high-achieving student won't get a good education in an curriculum where they are 'dragged down' by the low-level course... Why on earth do you think that a non-high-achieving student isn't going to get 'dragged down' by being pigeonholed into the low-level course?
If your goal is to just write those people off as lost causes, then sure, by all means, bifurcate the coursework. But then the criticism of this approach starts to sound rather on point.
If you can run a < 5 minute mile, you are not going to benefit from jogging at a pace set by the slowest pace. If you're that slowest kid, being forced to jog will be hugely beneficial.
If you think the bar is too low for the non-advanced classes, that's fine. You should be advocating for more rigour and mathematics across the board, not less. The stratification of classes is orthogonal to math education not being rigorous enough in general.
I don't know how it works in CA, but where I grew up the regular math classes were perfectly good math classes. But if you excelled in math, and wanted to focus on it, you could take the honors and AP level classes. Most of the kids in the regular math wanted to instead focus their time and energy on AP history, or literature. I found the system to work quite well. Nobody was "pigeonholed" and everyone got the fundamental education in all subjects that they needed.
I am advocating for more across the board.
People all over this thread are making the assumption that the non-advanced math class is equivalent to no math class at all. That doesn't make any sense to me, and does not match my experience of regular, honors, and AP classes in high school.
Accepting your premise, the issue in your case is that the PE class needs to run more. Pulling all the talented athletes into that shitty class without changing the curriculum at all will strictly cause harm.
Why do you assume it is a zero sum game? We can have high level math courses and improve the quality of lower level ones (if you think they are problem). Or if you are saying that students shouldn't be forced into lower levels just because they aren't getting good grades, then yeah sure, let people join high level courses based on passion and not achievement. I think that's an entirely separate debate though.
Huh? Are you suggesting that removing upper level maths classes helps kids achieve their potential?
If the current system is untenable, then I would force all students to have one "tutor" period. Everyone has to take a tutor period, so the social stigmatization you're worried about it not a factor. This way, kids gets extra help in their "worst" subject (decided by some combination of grades / introspection/ parental involvement).
This way, the kids who need more help in math can get it, without pulling down the kids who belong in more advanced classes.
That is the purpose, but I agree that I don’t think it will work. I am saying we need to keep trying, and not dismiss any attempt to fix the issue as woke nonsense.
No, the nonsense is the idea that we are all cut out for math. That's the fundamental underpinning behind the "wokies" push for equity, a silent conflation of equality of opportunity with equality of outcome based on the totally untrue premise that we are all equally capable given identical environments.
The only possible resolution to this goal, given the obvious uneven distribution of innate human ability, is the handicapping of those who are capable, because there fundamentally is no way to boost those at the bottom to match the middle and top.
And I don't think people understand how dangerously pervasive this mindset has become, as it is also the foundation for diversity and inclusion in the workplace, the equally misguided idea that given equal opportunity all demographics would see equal representation in a true meritocracy.
I think the nonsense is making a decision about who is and isn't cut-out for math at such a young age, and keeping them hemmed into that path for the duration of their education. That's not merely recognizing the top, middle, and bottom - it's creating it.
I see that as a worthy thing to try to avoid. I also think we should strive to avoid falsely concluding that all persons are equally capable.
But every decision is one that creates tradeoffs. I don't know what should be done. I'm an observer on this topic, and I think there's a lot of hubris in this thread from others oh so certain they know what's best.
This means an informed discussion needs to be had about the costs of lowering the bar against the costs of early streaming. I think people are rather strongly against lowering the bar to the point of effectively removing calculus from high school based on the general reaction in this thread.
If over twelve years of math instruction you can't figure out how to teach the average child algebra, trigonometry, logarithms, and the very basics of calculus, I would advise the educators to look into why their peers in other countries are managing to accomplish these feats.
But, of course, it's easier to just throw your hands up into the air, and just bifurcate people at Grade 7 into 'good math' and 'bad math' tracks.
You think they're doing it with "Common Core" and "ethnic" rainforest math, let alone this new "data science" insanity? You couldn't be more mistaken on that. Take a look at the popular Russian and Singapore Math. Not even the smallest trace of the failing "progressive education" thinking, just a lot of solid, high-quality, direct, rigorous, focused teaching.
Their peers in other countries are working with culturally and genetically different populations. Intelligence is 70%+ heritable, you do the math, as taboo as it may be. Then add in the difference between a culture that prizes academic achievement versus one that is ambivalent or worse, prioritizes sports or music over education, and you have more than enough to explain the divergence between nations, as well as demographic groups in the US.
This is where the goalposts generally get shifted toward teacher resources and/or pay. That's fine to discuss as well, but likely not a significant factor for the above suggestions.
This simply isn't true. There are things that can be done to improve the outcome for students, and we should continue to work to try to improve the success of all students. This doesn't mean that you expect everyone to achieve equally, just that you can help people achieve more than they would have without the help.
I also find this argument a bit paradoxical; if you truly believe that innate ability is the only determining factor for how well students do, then why do you worry about handicapping those who are capable? It shouldn't matter if we force them into classes they are too advanced for, since how we educate them doesn't matter and only natural talent matters.
It seems that you believe schooling does affect achievement, since you want to make sure we aren't holding back the high achievers, yet you are saying at the same time we shouldn't worry about how we educate the low achievers because they are stuck where they are no matter what. You can't argue that it matters for high achievers but not for low achievers, that doesn't make any sense.
How would you suggest we do this?
Without a dramatic reinvention of our education system, you have to fill a room with N students and 1 teacher. If you want that teacher to be maximally effective at "improving outcomes" - how do we do that?
The proposal here is to group the kids strictly by age. Every kid in grade X gets the same math class. This will inevitably lead to the math class being irrelevant to some portion of the class. Some kids will be so far behind the teacher may as well be speaking a foreign language, and some kids will be bored out of their mind because the material is moving too slow.
By being a little more intelligent in choosing our groups of N student, we can maximize the relevance of what the teacher is teaching and therefore better improve the success of all students.
'you can be good at math/math is easy' may be an equal nonsense.
This seems to be a symmetrical situation to me. You can absolutely underrate or overrate a person's abilities to do X. I don't see how one is preferable to the other. Both are pretty destructive when taken to their extreme logical conclusions. For example, from the relative underrepresentation of blacks in advanced math classes, you can draw a conclusion that math as a science is inherently racist/white supremacist. Such sentiments can be sometimes seen in discussions and I consider them dangerous, toxic nonsense.
Because it seems to me that if you have experience with any sampling of children where N>1, you'll see that's simply not true.
I'm not, there are always extreme outliers and exceptions, but I do believe that the vast majority of children can meet the incredibly low bar for mathematics education that is considered normal in North American schools.
I also believe that teaching them to be afraid of math, (and having their teachers be afraid of math) is a major contributing factor for why so many of them struggle so much to meet that bar.
This is a huge part of the issue I feel. I know way too many elementary school teachers who are afraid of math themselves and struggle to understand it. Is it any wonder the kids they teach don't? It causes big problems when they get to me for mathematics in high school.
This is a big one. I was in sixth grade when my science teacher told me that the boiling point of water was 132F, because she thought you added 32 to convert from Celsius to Fahrenheit.
This problem runs all the way down, from teachers colleges to the kinds of people who apply to be K-12 teachers. That fearing math is okay and normal is pervasive in the culture and it’s not clear to me you can even do anything about it other than implement gating math credentials for teachers that would exclude a huge fraction of teaching school graduates.
Speaking of teachers... my own grade-school math development, decades ago, was stunted by the fact that my teacher didn't know anything about linear algebra. I asked her for help deciphering my "Amiga 3-D Graphics Programming" book, and she concluded that the vector and matrix notation must be a bunch of typos. Arrgh!
In my case I got a letter about summer school at a local university. So I pre-calced over summer school to get moved into calculus in high school. It honestly changed my path. I get having tiers, but once placed into one its hard to move. If I wasn't self motivated, and had the opportunity to try I would be in a different place.
Had I gone into college without that work ethic, I almost certainly would have failed out early.
My school supported me in taking trig as an independent study over the summer (with a textbook and slides from one of the teachers plus a few meetings as needed.) This let me take AP Calc senior year; otherwise I would have missed that opportunity due to being placed in the wrong math class freshman year.
And sometimes the kids talk with each other about the maths problems. But that won't work so well if they're in different books.
Simpler for both the teacher and students, if those in a class are at roughly the same level.
But I do think that what you say, would work in a group where everyone is pretty good at maths, enjoy it so much so "yes I got a new book" they think (when they get the next book). And dive into it, no matter if there's a teacher there or not.
That's not generally the case though is it
I didn’t think our understanding of the brain was that advanced yet. AFAIK we run some experiments and observe results, but we can’t explain why those results were observed.
Which is useful and awesome from a learning perspective, but extremely worrying we use it to craft public policy.
Downsides are that kids develop at different times, have different educational needs, have home life issues that can temporarily derail progress, etc and if those happen around the time kids are getting tracked, they may not reach their full potential.
A good education system would offer students a way to rise up whenever they're ready to rise up, let them learn at their pace, focus on mastery, build upon knowledge gained rather than schedule followed, etc. There's a lot of edtech out there that incorporate these concepts but school models struggle to integrate it into the (literally) old school way they operate. It's quite difficult to reorient school around these new concepts at scale, it has to be done school-by-school, leader-by-leader, school board by school board.
Agree its complex, as it may be the 'best of the worst' option for certain contexts. Anything involving balancing equity/access/etc is like that.
1) A lot of K-8 education is babysitting. If you let kids do their own thing they'll just watch YouTube and play Roblox instead. Most kids are not _that_ self motivated at this point in life. It's hard for teachers to manage a classroom if everyone is working on different things.
2) Staring at a computer screen is not a great learning experience. A classroom is an interactive, social experience with active feedback. It's hard to socialize when the kid next to you is not working on the same activity or problems you are.
3) Personalizing education diminishes the importance of teachers in the classroom, which teachers unions obviously oppose. Teachers can't teach if every kid is learning something different, and online education strongly promotes winner-take-all dynamics where the best teacher and content can scale up infinitely and dominate.
Out of all these I think 2) and 3) are the hardest problems to solve and whoever solves them is going to meaningfully advance education. But I'm not very convinced by the startups I'm seeing in this space that anyone has solved it yet.
That said some of these programs have solid learning science foundations and good outcomes. Teachers roles necessarily change to ‘guide on the side’ and motivator, there’s a lot more there to go into but basically it’ll take time.
I was not seriously challenged and felt like math classes wasted my time.
But some kids are just bad at math. Some kids are bad at sports, music, dance, etc. Some kids are good at some things and kids are good at different things.
Let's use your example of sports, for example. Yes, no matter how much I train and practice running, I will never be as fast as Usain Bolt... but I sure will be faster than if I didn't practice at all.
The lower level math class is exactly where you belong to train up your math ability. You wouldn't expect to practice running with the same routine that marathon runners use.
This really jumped out at me.
I didn't read any context, but students CAN and SHOULD learn to struggle. Productively. Without thinking they are failing.
Imagine you thought everything should come easily? That's not my experience in the world.
The fact that students (are reported to) shut down when faced with difficulty is a failing of the educational system and something that should be worked against.
Unproductive struggling with math is the natural consequence of substandard math education, such as is encouraged by the unscientific and arguably insane notion (which is however common throughout the Education field) that all students can simply be expected to "learn their math by themselves", and therefore have no need for actual, focused and direct teaching of that subject.
Black and Latino students are overrepresented in underperforming math classes, while White and Asian students are overrepresented in the high-performing math class. That's literally the only reason there's any controversy, and if said disparity didn't exist, or if the races were reversed, then we wouldn't be having this discussion whatsoever.
If you approached athletics with the same strategy, you'd end up with a similarly wonky outcome. Consider that Asian students have always been highly underrepresented in high school football.
> “When kids struggle, they immediately say ‘I don’t have a football body,’” Boaler said. “That changes how the body operates.”
Is the equitable conclusion to change the rules of football so Asian students perform better? Surely not, right?
It’s sad that the state is proposing these changes. I remember in school there were kids who argued “algebra is stupid, who needs it, why waste time” and there were one or two sympathetic teachers who would respond “well, I rarely have to use algebra to balance my checkbook” or something silly. It seems like those kids have grown up, gained power, and are literally pushing the argument that this math isn’t important.
I'm not saying I agree with the proposed California Framework. As a formerly gifted maths student, I hate it. But let's not dismiss the rigorous work of an academic who is attempting to improve education for a public education body for a state with 40 million people as "bonehead" (or "woke nonsense" as another commenter did).
90% of the reasons why kids say "<subject> is stupid, who needs it" it's because they are not enjoying it or struggling with it and using this as a defense mechanism. Noone who is doing WELL at a school subject dismisses it as useless.
So maybe, just maybe, it's worth evaluating the education process to make it easier to teach kids to give them the foundations that then the more gifted ones can invest and build on top of, and everyone comes out with baseline math competency.
When the Mathematicians and Scientists are screaming that the policy is nonsense, I'm not convinced by an advocacy researcher saying it's rigorous work.
Can you make specific arguments instead of devolving to shorthand dogwhistles that are completely up to the interpretation of the reader.
The term 'woke' has no meaning, depending on the context it's anything between "We should shame all white people for the crimes of their ancestors" to "We should make a movie with a female lead".
By using it, you leave it ambiguous as to where on the spectrum you fall.
It’s mainly a qualitative analysis that wouldn’t pass for rigorous in any real scientific or engineering field.
Engaging with their current, relevant work would be more appropriate.
This is exactly what the GP is saying - many of us don't like the conclusions, but just blowing off a whole body of work in a sentence is pretty arrogant.
Stop it with the accusations of “arrogance” and naked credentialism. Any of the millions of people with an undergraduate STEM degree (mine is in aerospace engineering) learns enough about the scientific method to distinguish “rigorous” work from non-rigorous work. It’s actually kind of an important thing they try to teach.
Scientists and engineers who don’t call out non-rigorous work that claims the mantle of “expertise” are shirking their moral obligations and helping to erode the credibility of science as a larger discipline.
It's not an original arrogance - it's pretty common amongst the STEM educated to basically consider all humanities, philosophy, social sciences to be not "serious" fields.
Just because it's common, doesn't make it not arrogant.
Individual humans are not free body diagrams. And societies even more so.
The study of people and groups of people and the way to understand them, engage them, and influence them (which is what "education" is) is not going to be familiar to an aerospace engineer. That doesn't mean it isn't built on the work and research of thousands of people over centuries.
What a flimsy and transparent effort to insulate non-rigorous fields from criticism.
Ironically, one of the things I do for a living these days, as an attorney, is attack the credibility of credentialed experts: https://en.wikipedia.org/wiki/Daubert_standard. There is a whole process where attorneys and judges without specific expertise in a field evaluate the reliability of assertions by expert by reference to accepted scientific principles. Because that’s a thing you can do! You don’t need to be an expert in a field to know whether they applied reliable methodologies.
More importantly, people will do it. If you tell them to trust stuff that doesn’t seem trustworthy based on what they learned about the scientific method in high school, then it erodes your credibility and the credibility of all authorities. There’s a lot of work out there that’s not rigorous, and we have a moral obligation to call it out: https://en.wikipedia.org/wiki/Cargo_cult_science
> It's not an original arrogance - it's pretty common amongst the STEM educated to basically consider all humanities, philosophy, social sciences to be not "serious" fields.
Theology, film, German literature, European history, etc., are all “serious fields.” They’re the product of work by thousands of people over decades or centuries. That doesn’t mean they’re rigorous. Their ability to provide truth value is fundamentally limited by the nature of the discipline.
And yes, maybe engineers have a big head about it. I suspect that’s because they don’t have to brow beat anyone into recognizing the seriousness of their field or the authority of the expertise it generates. You can go up to a random yokel in a Bangladeshi village and he’ll be impressed at your STEM degree. I’ll posit to you that there is a basis for that.
In methodology, the field of education is akin to something like the field of business. It’s based on observation and case studies. It’s not wholly without value, but holding it up as a rigorous discipline that commands deference is disingenuous.
Are you saying that all the "serious but not rigorous" fields that do so are A) all doing it wrong, and that you know a better way, B) That there is a better way and noone has tried, Or C) that it is impossible and we shouldn't bother trying.
Because if it's A or B, you can see why someone would call you arrogant. And if it's C, is that not defeatist? Seems like trying to understand our fellow humans and the societies we create is a task worth pursuing?
I think it is incumbent on all fields to be exceptionally clear about which of their results are rigorous, and which are outside the realm of rigorous knowledge. For example, as someone with expertise in CS, I can give you very reliable information about computability theory, and pretty reliable information about what is technically feasible to implement using current technology, but my opinion on fair moderation policies for social media are not really buttressed by my CS expertise. I wish public health officials (as just one example) were similarly clear about what they have expertise about (how disease spreads and what interventions will have what outcomes) and what is their personal opinion (cost/benefit analysis of different options, who should get vaccines first, etc).
Q1: "What is the worst-case runtime complexity of quick sort" is a question that has a rigorous answer that can be proven with fundamental scientific concepts.
Q2: "What is the programming language/framework we should use for this next project" is one that absolutely cannot.
Any answer to Q2 will invariably involve some personal opinion and bias, AND YET serious professionals with decades of experience - ones perfectly capable of answering Q1 would also be expected to weigh in on Q2, incorporating their knowledge, context, the skills of the rest of the team, the existing architecture, the requirements, etc, etc.
It would be absolutely arrogant to push back against the qualitative analysis of a senior software developer making a recommendation to Q2 with "That's just your own opinion and bias" - ESPECIALLY by someone outside the field who doesn't understand all the considerations being weighed.
I sympathize with your desire for health officials, but my theory is that everything about epidemiology, public health, disease spread, etc are all mostly Q2-category questions. You still need a PhD and rigorous understanding of all the Q1 questions but shaping public policy in a pandemic is all Q2.
Education is much the same way. Education of mathematics at scale is less about mathematics and more about people.
Q3: "Should the US regulate Bitcoin?"
CS expertise will give a person much greater understanding about the details of how Bitcoin works. But any layperson can learn enough about how Bitcoin works to form an opinion on the question of whether the US should regulate it. I would never tell a non-CS person that they don't get to weigh in on this issue because they are not in the field. Would you?
Ultimately what we are talking about here is policy, which affects everybody, and value judgments, which everyone is entitled to make.
That's as complex of a question as "How should the US regulate Bitcoin (if it were to)". And while it's true that laypeople do have lots and lots of opinions on financial regulations, if there's one thing that HackerNews can agree on is that most lay opinions on financial regulations are not rigorous or serious, and come with unexpected side effects and consequences. (Whether it's taxing billionaires on stock grants or restricting crypto).
So in that sense I do still this requires people with expertise. And gifted math nerds (which I were) that benefited from a dramatically accellerated program have as much knowledge about the subject as a stereotypical redneck saying "We don't need math out on the tobacco farm".
> And gifted math nerds (which I were) that benefited from a dramatically accellerated program have as much knowledge about the subject as a stereotypical redneck saying "We don't need math out on the tobacco farm".
I think the "nerds" would know enough to understand that they benefitted from the accelerated program and would have not achieved as much if it were taken away.
That is not to say we can't seek to understand these things. To the contrary, humans have myriad ways to understand and respond to these things, including religion, tradition, culture, convention, etc. Academic inquiry that has the veneer of rigor--through credentials, peer review, conferences, etc.--but isn't actually rigorous improperly displaces those other ways of knowing, and cedes social power to a narrow class of elites.
The education and socialization of children, for example, is one of the fundamental pillars of society. People around the world have their own ideas of how best to socialize their kids. Unless you can bring real science to the table--unless you can create reproducible results that speak for themselves--you shouldn't be so arrogant as to act like your work can substitute for those other ways of knowing.
The current system pushes 50% of the kids into calculus and 50% into 'I hate math.' Of the 50% that go into calculus, 50% go into STEM.
That leads to (hyperbole) 25% A's / 25% B's / 50% F's.
The intent of the new rule is to maybe be more like 25% A's / 10% B's / 50% C's / 15% F's.
The key questions are 1) Is that actually better (I certainly think bringing up the floor is a good idea, but at what cost)? 2) Is this policy even going to get us there?
I guess there is a societal discussion to be had if we should trade off losing As to reduce Fs.
But I think that first there’s not a dichotomy between approaches so the only way to get fewer Fs is to reduce the number of As. I think there are ways to improve education that doesn’t remove the opportunity to excel. And framing it as the California proposal or failing math is unfair.
I think what surprises me so is that they continue to propose these solutions that seem to reduce the overall math capabilities being produced.
The draft Mathematics Framework includes calculus in the possible high school pathways, and also suggests ways to enable more students to get access to calculus. It notes that many high schools currently organize their coursework in a manner that requires eighth grade acceleration in order to reach calculus or other advanced mathematics courses by senior year. While some students succeed with this approach, acceleration has proved a problematic option for other students who could reach higher level math courses but would benefit from a stronger foundation in middle school mathematics.
There is nothing in this about actually removing calculus for high achievers, and this there’s an argument against it, it’s what I laid out: “is it better to push more kids into calculus at all costs or should we focus on raising the floor?”
It’s honestly a very similar argument to the (popular on HN) argument of “not everyone needs college”
And to be quite frank, this isn’t coming from nowhere, this is modeled on the success of other western countries with higher math scores across the board.
> "Since achieving a solid foundation in mathematics is more important for long-term success than rushing through courses with a superficial understanding, it would be desirable to consider how students who do not accelerate in eighth grade can reach higher level courses, potentially including Calculus, by twelfth grade. One possibility could involve reducing the repetition of content in high school, so that students do not need four courses before Calculus. Algebra 2 repeats a significant amount of the content of Algebra 1 and Pre-calculus repeats content from Algebra 2. While recognizing that some repetition of content has value, further analysis should be conducted to evaluate how high school course pathways may be redesigned to create a more streamlined three-year pathway to pre-calculus / calculus or statistics or data science, allowing students to take three years of middle school foundations and still reach advanced mathematics courses."
At face value, that suggests that the root problem is that students reaching middle school Algebra 1 aren't ready and need more remedial math instruction. As an Electrical Engineering professor, I can definitely attest to the fact that students reaching higher level classes with a precarious foundation are rarely as successful as those whose foundation is more solid. I suspect Scott would also agree that barely passing calculus in high school is not an adequate preparation for a career in data science. As a parent of a kindergartner and a second grader, I can also see that there is opportunity to push more math further down, but even at that age there are kids who have a huge variability in how they view their math.
With regard to resources, I thought this statement in the CMF was particularly insightful:
> “While early tracking of students into low-level courses has been problematic, there is evidence that thoughtful grouping of students to ensure they receive high-quality instruction geared to their needs at a moment in time can be helpful. This includes students who need to fill in gaps in their prior learning and high-achieving students who are ready to be more intensely challenged. It is also true that teaching heterogeneous classes requires greater skill for differentiating supports than teaching in classes where the range of performance may be narrower, and should be accompanied by high-quality professional development to enable success.”
I agree with that!
I can understand how an electrical engineering professor like yourself is rightly concerned about your incoming students having less calculus proficiency. On the other hand, there many (possibly far more numerous than EE) education and career paths that would benefit from better general numeracy but not necessary calculus.
The terrible thing here is that these goals should be set against one another due to resource limitations. The blame for that lies with the broader societal inequities and their reflection on the educational funding system.
I had multiple high school teachers that were checked out. Would watch movies and do worksheets. We learned nothing in their class other than how bad they thought students were now days. Yet they were never fired. Some lasted another 10 years before retiring.
I also had multiple professors that would start terms by saying if you have conservative views and you express them in class I will fail you. Had another professor joke about how she found out a student was part of a club she didn't like so she failed him. Often times these were not GE classes but CS specific. Politics have nothing to do with a class on OOP or AI. That is not teaching IMO. I have a ton of friends that feel the same way. Until this issue is actually recognized and addressed I do not believe you see anything change.
Or that 50% of total K-12 school funding comes from federal and state sources, which is directed mainly at lower-income districts? And that, when including those funds, only a few states (ironically blue ones) have more than a 5% gap between rich and poor districts: https://edtrust.org/wp-content/uploads/2018/02/Gaps-in-State.... Meanwhile about 20 states (including many red ones like Utah and Georgia) direct over 5% or more funding to poor school districts than rich ones?
Yes, and I'm also aware that in the US we expect the public school system to be a primary treatment center for the disadvantages and traumas associated with poverty and unequal opportunity.
It's more expensive (and harder) to educate hungry, ignored, and traumatized children than it is to educate children who are well take care of. They need more support staff, more psychologists, more free lunch programs, after-school care that their parents can never afford. And it's hard to attract good teachers to teach academics in those circumstances.
The major problems with primary education in the US are largely faced disadvantaged communities, not prosperous ones. If we decide to remove educational funding from disadvantaged communities, we have to be prepared to either put it into those communities in other ways, otherwise we'll face even greater problems in schools.
None of that is to say that there doesn't need to be more accountability in school systems - there is a lot that needs to be done to re-examine how education is delivered. But just looking at the situation by comparing $ spent on primary education between countries is oversimplifying things.
That’s true in virtually every country, because the school system is always the government’s primary point of contact with poor families.
> It's more expensive (and harder) to educate hungry, ignored, and traumatized children than it is to educate children who are well take care of. They need more support staff, more psychologists, more free lunch programs, after-school care that their parents can never afford.
Agreed on school lunch. Large school districts already offer after school and summer programs.
Disagree on more staff and psychologists. That’s the kind of waste that detracts from money for instruction. Countries like Japan and Singapore went from being desperately poor (at a level unimaginable even to an inner city American) to developed in a couple of generations in the 20th century. I’m pretty sure they didn’t (and still don’t) have a bunch of school psychologists on staff.
Those countries did so by making absolutely massive infrastructure and human development investments in their poor populations during their industrializing phase, very similar to what the US did for its previously poor white population after the 2nd world war.
The people who face the greatest educational obstacles in the US today are disproportionately people who were also largely excluded from the huge post-WW2 investments and ensuing economic miracle, and have since faced the economic brunt of de-industrialization.
> I’m pretty sure they didn’t (and still don’t) have a bunch of school psychologists on staff.
They have far less crime and trauma to deal with, are not awash with weapons, and had very strong communal support systems. They were/are also quite authoritarian. Those are very different societies with very different circumstances. You can't directly compare the situation in post war Japan and Singapore with inner city America. By dint of our own history, issues of education and equity actually quite a bit harder here.
Japan and Singapore aren’t Nordic social welfare states. They invested heavily in development but not particularly targeted at the poor.
> The people who face the greatest educational obstacles in the US today are disproportionately people who were also largely excluded from the huge post-WW2 investments and ensuing economic miracle, and have since faced the economic brunt of de-industrialization.
Only if you pretend that white people in Appalachia are the same group as white people in Massachusetts.
> They have far less crime and trauma to deal with, are not awash with weapons, and had very strong communal support systems. They were/are also quite authoritarian. Those are very different societies with very different circumstances.
That indicates that America’s problem is culture, not the availability of school psychologists.
Nor are they comparable to American inner cities.
My own anecdote about Singapore is an old friend who grew up very poor in Singapore (themself a child of impoverished rural immigrants laborers from India), but whose family received subsidized housing, transportation, and most of all, stability and security. If their family had arrived in Singapore as slaves, their outcome might have differed.
> Only if you pretend that white people in Appalachia are the same group as white people in Massachusetts.
Who is pretending that? Not me. I agree that they also have born the brunt of disinvestment and de-industrialization, and we are seeing the effects of that in the opioid and methamphetamine epidemics in those areas. It's interesting that we don't usually call it a culture problem with them though, like we do with black inner city communities facing similar challenges.
> That indicates that America’s problem is culture, not the availability of school psychologists.
It indicates a problem of economics and disinvestment. The psychologists are only there to manage the impacts of that disinvestment on society, not solve the original problem of lack of economic opportunity.
I'm also happy to reduce the number of school psychologists when teachers no longer have to deal with traumatized children disrupting and endangering their classes. Until then someone has to manage those issues, and as you stated, that's what we expect public schools to do.
Want to know the one resource that schools can never give students? Parental involvement. It also happens to be the #1 variable in success for students.
If parents aren't checking their children's grades on a daily basis, asking what they're studying, staying in frequent communication with teachers and the school, there is nothing that is going to replace that.
My oldest son was on a robotics team during high school in which we were a minority. All the other parents, their kids were studying calculus by the end of high school. I asked every one of them how their kid was able to do that and each one of them shrugged and said, "nothing".
To them, "nothing" was their child spending 2 hours per day at Kumon after school and a few hours on the weekend in addition to their constant checking of their work and insistence on academic excellence.
The teachers expect a lot because of this. Good luck if you can't afford such help.
This concept is strange to me; when I was growing up, a "tutor" was someone who helped kids who were behind. Nowadays the word seems to also refer to an outside coach who helps kids get ahead.
It's saying that it is impossible to get the bulk of students (with the teachers we have) to complete the standard mathematics curriculum by the end of high school. This has always been true, in all countries, hence "streaming". But now they're saying let's do away with the advanced stream, therefore students can't complete the last part of the US mathematics curriculum (which is called "Calculus"). Rather than justify that move in terms of cost or fairness, we're going to say "because Calculus isn't important now".
This is obviously completely bogus. If their assertion that Leibnitz-style calculus isn't important now, they could replace it with Linear Algebra, Number Theory, or some other "important now" subject.
Add to that, the fact that in the US the names of high school mathematics classes are by convention. "Geometry" isn't all geometry, for example. And "Calculus" isn't all calculus. The classes are really : Math 1, Math 2, Math 3, Math 4, AP Math.
For example, it is really important to understand that 1 / 3 chance is the same thing as 3 / 9 chance. It is obvious to you now since you have done so much arithmetic's, but to someone who never properly learned it they wouldn't be able to properly compare those two and could think that one is a very different number than the other. Without basic understanding about quantities all other quantitative skills become worthless.
I'd be surprised if there were any countries where multiplication was formally taught to pre-K students as part of the standard curriculum, but i'd love to be proven wrong.
> What's the point ... ?
Paraphrasing what I said a comment above, you drill addition and subtraction until everyone is good at it, then you drill multiplication, then you do basic division, then you start introducing basic one variable algebra with "move plus to the other side to get minus" etc. The application is using algebra for word problems; formalism can come later.
Though empirically, I don't know about age 4 but kindergarten is definitely not too young for learning up to 12*12. And once you figure out multiplication and eventually mental division, it's not too big of a leap to have one variable algebra with "move a plus to the other side to become minus" etc. The formalism can come later but it's fantastic to have some exposure to moving numbers and symbols around from an early age.
So I'm not saying it can't be done by any 5 year olds, but it seems young to teach this to the majority of 5 year olds.
But don't ask me about division, my siblings/parents/whoever tried to explain it as "the opposite of multiplication", which was complete nonsensical gibberish and I didn't learn division until years later.
I think establishing a foundation of addition and subtraction takes far longer for children to master than you're considering, especially since there is evidence that children of this age appear to intuitively view numbers logarithmically rather than linearly [0].
I suppose you could take advantage of this by somehow prioritizing multiplication and division over addition and subtraction, but I think there's too much value in comprehension of linear numbers and addition/subtraction since that is the lion's share of interactions they will experience at that age.
On the other hand, if you're merely talking about abstracting multiplication and division into patterns, then I wholeheartedly agree with you, and there is evidence supporting this [1]. Although pattern identification is already part of kindergarten/1st grade curriculum here.
Ultimately, IMO the most important aspect of education in general is covered in the open letter linked to the OP:
> There cannot be a “one size fits all” approach to K-12 mathematical education.
My children have thrived with their current math curriculum, and I know some of their classmates have struggled in contrast. One size does not fit all in education, nor in many aspects of life.
0: https://news.mit.edu/2012/thinking-logarithmically-1005 1: https://www.tandfonline.com/doi/abs/10.1080/15248372.2012.68...
And you'll start seeing beauty in patters and sequences of numbers. The sooner the better.
She had (has?) a solid grasp on numeracy. I recall asking her why, around 7th grade, "0.999..." is equal to 1. I was prepared to show some fancy algebra and she one upped me when she said "well, 1/9 is 0.111... so 9/9 is one and 0.999...".
She never liked math though. She spurned calculus.
I get the sense that such rote methods are no longer encouraged and a lot of the "new math" in Common Core is aimed at approximation and reckoning so that students won't rely on memorization.
Facility with those methods is then necessary to be able to adequately follow important proofs and gain understanding of more advanced concepts.
I don't know how you would teach people important results in their fields (physics, computer science etc., I'm not talking about actual mathematicians) without those skills.
I'm only good at _arithmetic_ because of making Warhammer 40k armies (true story bro).
I'm good at _algebra_ because I was taught well, on top of a knack.
Speed with basic algebraic operations was very helpful in many places but speed with arithmetic operations has only been helpful in board games.
I don't think anyone here would disagree with your point about algebra, but I think a lot of people such as myself would disagree that pre-K memorization of arithmetic helps with algebra later.
As I stated in another post, I don't know when it is neurologically ideal to learn arithmetics, it seems something that would be important to study carefully (personally I learnt before grade school, when I was 3-4 years old, but I didn't learn to read until I was 6, something that is often taught earlier).
10x+7 = -2x+31
Move 7 to the other side (picking up a minus sign)
10x = -2x + 31 - 7 = -2x + 24
Move -2x to the other side (flipping sign)
12x = 24
Recover 12*2 = 24 via memorization, quick division (though not long division), or whatever method
Therefore, x = 2. Then I drew a square and was done.
I don't get this part.
You mean to highlight the end result? In that case, it would, most of the time, be a rectangle (or try to be).
A cursory web search yielded nothing.
"∎"
I wasn't familiar with this, despite being a graduate. Its use might depend wildly on where.
Edit: thanks to the reply; HN ate my superscript 2. Apparently it doesn't like the unicode multiplication x, either: × ² ?
...but the only time I ever saw significant numbers when actually doing math was in toy problems that deliberately chose weird, big coefficients, where the arithmetic part was by far the least significant.
This aspect of the Common Core was about recognizing deficits in conceptual understanding resulting from rote methods of drilling arithmetic.
The empirical evidence is the opposite of OP's assertion, but the end point of giving students a better intuitive foundation for higher level math is indeed the goal!
Signed,
An elementary school math teacher who has studied the 60 years of math reform in America, internationally, and worked very hard to ensure all students have a foundation to succeed in higher level mathematics
On a similar note, I have a friend who majored in math at Harvard. He once told me that he came into Harvard being arrogant because in high school he was always at the top of his class in math. He enrolls in his first college level math course thinking he's got this, but he soon realizes that "higher math", which is largely proof-based, is a completely different subject than what he learned in high school. A month in he bombs the first exam. He went to the professor, who is originally from Italy, and explained his situation and how he was a star in high school. He responds in a thick Italian accent "that was not math, that was computation. In this course I teach math".
The math you typically learn in high school is very important, but I wish that we did a better job of explaining to high school students that what they are learning is completely different from what "real mathematicians" study (although I do think that computation is quite important in engineering, for example).
To be fair to your friend, 90 years ago they probably could've had a productive career in applied math as an expert computer. There was a point when calc tricks could get you a PhD, but those days are gone.
1. Make it possible for HS students who are interested in Calculus to take the course under the instruction from a college profess on the high school campus. That way it would be set up for students to get college credit for the class and they would not need to travel to a college campus or deal with the AP exam system.
2. Make it possible for HS students who are not interested (Yet) or at all to graduate with out taking the class. Lots of student are ready for Calculus until college anyway. No need to force them on a single path IMO.
https://www.khanacademy.org/math/ap-calculus-ab
When we focus narrowly on what brick and mortar Public HS should and should not be teaching in regards to math curium we sideline all the pathways for learning available outside of this bureaucratic model.
Folks in most places in the United States a least can check out a Chromebook from a local library and use their free internet to access this information.
Highschoolers fork over swaths of their day to the public education system already. Let's try to not waste any more of their time.
Especially for kids from poorer backgrounds it is not easy to just sit on Khan Academy after school. If they can't teach leveled classes they should let kids test out of certain classes, and spend time in a semi-supervised study hall with those free resources instead.
But it's not about resources here, or at least that isn't the main argument they're giving. The mere existence of students that can test out of math is apparently detrimental to others. This seems like over the top sheltering to me.
> 5,972 Math Professors in USA [2]
1. There are simply not enough college math professors for this to work.
[1] https://www.zippia.com/high-school-mathematics-teacher-jobs/...
[2] https://www.zippia.com/math-professor-jobs/demographics/
Students could also take additional ge's at college outside of school hours, and I entered University with about 80 credits
Which country do you mean? As far as I'm aware, it's the opposite: countries like China and South Korea have math as a required subject on their college entrance exams for all students. The non-STEM students may have fewer requirements, but I'm fairly sure they've still learned more than the average American high school student.
https://en.wikipedia.org/wiki/Gaokao#Reform_of_the_National_...
https://en.wikipedia.org/wiki/College_Scholastic_Ability_Tes...
https://medium.com/@yujia_jo/2016-jiangsu-gaokao-national-hi...
I do know there are countries which allow specialization at the high school level (India, Italy, Romania I believe).
I found this interesting list, which is more complete than I can be on this. I don't think it proves that countries with great mathematical cultures always allow specialization in high school, but it does have some examples of this.
https://en.wikipedia.org/wiki/List_of_secondary_education_sy...
I think you are right that we need more flexibility on the high school level though, at least for juniors/seniors that have safely passed the earlier requirements. I like that we have a chance to dabble in various subjects in college here before committing to something, but it would be a lot more efficient if some of that could be done in late high school.
I thought about this for a bit. Suppose we kept the number of teachers (or courses) fixed, but eliminated the gen-ed math requirement. You would end up with a better teacher : student ratio, and I believe this would benefit the serious math learners. And so by not doing this, I believe we may be implicitly impeding them.
My guess is there are lots of ways wasted resources (and I do believe any class which could be perceived as "rocks for jocks"-type is wasted resources, and may actually be a damaging use of resources - I say this as a TA for the pre-major courses*, where the students are constantly and overwhelmingly negative about the whole thing) are implicitly impeding the serious students.
(And, as a positive note, I think the students not characterized as "serious students" for the above discussion could have a chance at meaningful and valuable contribution elsewhere, if we weren't putting so much effort into wasting their time.)
Edit: Changed "lower level courses" to "pre-major courses"
I came to that realization a decade after college when I was digesting 3Blue1Brown's series on Calculus for fun and had it finally click. Before then I was basically a Chinese Room that was able to solve calculus problems via pattern matching (i.e. "oh, this problem fits the shape of these rules, etc.") without really understanding how calculus works.
I think this is the key. No, calculus isn't incredibly applicable in day to day life. But understanding how it works builds critical thinking skills that absolutely are. Math should be about critical thinking, not memorizing. Common core seems to be moving us in the right direction.
One side (Equitable Math) is engaged in a discussion of white supremacy in Californian math pedagogy. The other side (Moses Charikar, Scott Aaronson, et al) is arguing against a weakening of math standards.
There were three factions in WW2 and the Cold War. It was about preventing the assault of extremists on both sides.
It's a lot easier to just move the goal post than to actually achieve the goal.
The first is The Dawn of Everything, by David Graeber. I’m left with the notion that what we now call science and mathematics emerged from tinkering, persistent experimentation done mostly by women, and that what we have now disciplined into mathematics emerges from the systematic study and production of pattern (basket making, the organization of communal structures), and Graeber seems to argue against the hierarchical gender divides when viewed across the broad stretch of human history.
Rachel Thomas https://www.fast.ai/2022/03/15/math-person/ also makes a case that math is something that all people do.
I think that the larger point both are making is that disciplines don’t have to be the way they are constructed now.
My only “political”’statement would be the hope that states (particularly the u.s.) would invest as deeply in mathematics education at the primary and secondary level, for all of its communities, at the level of investment in big science and big military projects.
How do I know that? I was one of such students. I made it because my teachers pushed me. They used carefully designed homework to show me that I didn't really have the deep understanding of math as I thought. They used homework to show me that my understanding of Newton physics was inadequate. They used midterms to show me that I didn't really intuitively grasp algorithm analysis (I didn't know how to rigorously and succinctly argue that two pivots and one pivot are really the same in quicksort). I grew to enjoy STEM and CS precisely because I was lucky to have tough yet encouraging schools. Dumbing down courses would have taken away the push I needed, and I would likely have a lot more failures in my life.
How we got to this point is perhaps a lot more complicated and politically fraught, but it has to be dealt with. Administrators and state education leadership are often simply responding to the incentives and avoiding dire outcomes suggested by the data. They have to craft palatable excuses for it, and it's ultimately a waste of time to engage those excuses on face.
There's also a strong racial/class component to who gets into Hauptschule/Realschule/Gymnasium, surprise surprise.
I mean... e.g. in Philosophy the teacher was absent for most of those two years resulting in us having to entertain ourselves for those "lessons". When we finally entered Gymnasium at 7th grade we received a culture shock when we had to learn the "Zauberlehrling" by Goethe in 1,5-2 weeks for recital in the first weeks.
Realschule felt more like Kindergarten from the treatment by teachers like their attitude while teaching and them not being interested in bullying unless it turned really physical, then protected the bullies when the bullied hit back. What I'm saying is, as the slightly fat kid who also didn't get all the shiny new things from his parents I was bullied by a group of other students surrounding and harassing me almost every single day during breaks those incompetent "teachers" only had the "advice" to basically let the bullies tire themselves out from bullying but heaven forbid once trying to break out of the encirclement i tried to hit one of those bullying lowlives, the teachers descended like vultures isolating me in a room for the rest of the break questioning why I did that instead of "just ignoring the bullies". Those bullies never received any kind of discipline/punishment.
Later in Gymnasium, I once had a very heated verbal altercation with a classmate within earshot of a teacher, we were taken aside, our parents called in for an evening sitdown that same week, there we resolved our differences with some guidance from a teacher and remain friends even now.
Both schools were only staffed by older teachers with the youngest being late-40s/early-50s and several teachers retiring during my stay at the Gymnasium, so probably little to no influence from education during newer eras of teaching.
Honestly I wish I could smack that idiot Brodkorb for all the stupid shit he did as education minister.
¹: no split after 4th grade, instead have everyone go through Realschule for 5th and 6th grade, only starting the split at grade 7.
> our parents called in
should be
our parents were called in
I don't think university is appropriate for everyone and I dearly wish skilled trades had a higher position in society, and generally don't believe in the idea of "unskilled labor". But the German system is ultimately as cruel as the American one.
One path could be partnerships with local community/technical colleges. My high school participated in a program called "Middle College" where high school students took classes at a local community college (can't remember if it was all or just some) and that seemed to work well.
We previously ran a split system, with exams splitting pupils at 11 into academic ('grammar') and non-academic ('secondary modern') schools. Many grammar schools were good; most sec mods were awful. The exams also famously had pretty poor predictive power for underlying academic ability as an adult, so pathways had to be developed to allow bright pupils to go to higher education despite being mis-sorted in the original exam - which somewhat undermines the point of the system. Comprehensivisation has never been nationally mandated, but nearly all areas have now done away with academic selection at 11. The remaining holdouts are mostly suburban Conservative areas where political power is in the hands of the well-heeled upper middle classes who are strongly in favour of grammars (and expect their own children to go there). Interestingly, Margaret Thatcher (as Education Secretary under Heath) was responsible for more grammar school closures than Labour was.
Vocational/academic choices are now being made at age 14 and 16 either within the secondary schools or by moving to local further education colleges (similar to US community colleges and trade schools). Vocational classes are low status. Britain no longer has a strong industrial sector to use such skills, and although both parties advocate for better vocational education essentially everyone who matters would be most unhappy if their darling children were diverted from a university track in the direction of trades. That's something they want other (poorer) people's children to do, not their own. We've never developed good vocational training for offices/services jobs, and although such courses do exist they're not taken particularly seriously by employers, despite several rounds of national reforms.
There are clearly decision makers detached from reality involved here.
Obviously indirect social stratification is still at work in the process.
For those not familiar, he is the founder of BioNTech, the German researchers who developed Pfizer's SARS-COV2 mRNA vaccine.
Uğur moved from Turkey to Germany at age 4. At the end of primary school his teacher had assigned him to 'hauptschule'. It was only because of a neighbour's intervention that he was later put through 'Gymnasium' i.e. on track to study 'higher' studies.
The rest is history, after med school he did a doctorate in Imunotherapy, he founded a 18billion revenue biotech company and saved countless lives with what we now call the Pfizer mRNA covid vaccine.
Had that primary teacher's decision been held it really would have been a 'butterfly effect' of catastrophic proportions for Humanity.
This one example just stuck with me when I read it because of how serindipitous his mRNA research turned out to be during an all out worldwide pandemic.
For every unit of societal productivity created by a late bloomer that is saved by a common-stream system, I would personally argue that there is an order of magnitude more societal productivity lost by holding back the more typical high performers.
Late blooming intellectuals aren't the norm. Most highly intelligent people begin performing as such from a young age.
If you look at people that are not academically inclined and call them under performers then maybe that’s part of the issue. I think everyone has strengths and weaknesses, and if someone is more inclined to do vocational training rather than the standard track I think their strengths and interests should be developed / encouraged. An educator teaching someone that is actually interested in what they are being taught sounds like a more rewarding experience than lecturing a class where maybe 5 of 40 (not an actual stat) students are actually engaged.
It's not me doing that, it's education schools telling prospective teachers that their students will just be "learning their math by themselves", and the teachers can simply be facilitators. It must be a comfy job teaching math class to little Carl Friedrich Gauss and the like, but what about the remaining 99% of students - who will need actual teaching?
I didn't really find my academic ability, and programming until I was in my twenties.
Is there something you wish they had done differently?
That problem is hard to fix, whereas the curriculum is soft and malleable. You also have an entire industry of education PHDs who have never taught class for any appreciable amount of time who have a neoliberal fetish for minor policy tweaks as the path to heaven.
Teachers have the same problems as police, random societal functions have fallen to them by default because there's no alternative. They're surrogate parents, social workers, mental health counselors, etc. and there's barely any time to do any teaching afterwards.
And they're paid dick all on top of it
Likewise, the minority parents and schools simply see upper-class white schools in this country as we do the Chinese schools. I'm not saying that this is the best solution to the problem but I can at least understand where these parents are coming from.
You can pass and pass and pass people, but eventually an employer is going to need someone to do the job, and they will make sure they get that someone. So there will be a hard standard sooner or later. The only choice is whether we give all students a chance to meet that standard.
I remember the huge blowups over “Common Core” years ago, which included new ways of teaching math concepts. I got to see some of it in action during COVID as I sat in on elementary Zoom school with my kid. I have to say I was impressed; they used techniques I did not recognize, but they seemed to work well.
If we are going to get anywhere with math education, it can’t be based on pandering to parent’s expectations.
I think you are touching on theory I have that Americans are becoming increasingly resentful that technical skills are becoming more necessary for middle class living. This is a huge driver of the pervading sense of precariousness. For some reason there’s a huge math phobia in this country
Unfortunately, maybe where they come from now? India, China, and other immigration.
I think an interesting part of 20th century American industrial/scientific history is that many of the prominent figures were European immigrants (many Jewish) or children of immigrants.
Maybe there is something exceptional about the environment itself. But the talented and privileged native citizens rarely aspire to be an innovator; they dream of being a leader or strategic thinker or mover of capital.
That’s why I think hard math is so marginalized even in elite circles (“I’ve never been good at math”). Technical work is essentially blue collar to the upper middle class. Many of my peers are in this group, and the only time they were ever interested in math or programming, was due to its possibility as a conduit to a more prestigious position.
This attitude is directly ingrained in undergrad institutions. They focus on general knowledge to serve as a justification to skip over front line work to become a leader (military officer, factory manager, investment banker).
There are excellent American technicians no doubt but most of them don’t fit the typical WASP mold or are predisposed to obsessing over systemic topics (which describes myself, being ADHD, although I can only strive to be excellent).
And the upper class? They have never aspired to much of anything really other than hedonism and protecting their position of status. At least in other countries, the upper class ideal is a renaissance man.
Edit: some of these assertions are sweeping and maybe a little mean. But I do think the thesis is directionally correct. America will need to change the culture around education to succeed in the 21st century. Immigration has and will continue to be a boon; but we have to accept the possibility that America could become a less desirable immigration target
Sadly, I don't think that is very true in many (most?) places.
Well-trained people showing up by themselves is a huge advantage.
The unfortunate part is we don't educate enough of our own citizens for these well paid jobs.
Why is this a rational fear? It seems shocking to me that students can't perform at the same prior standards given their parents are more educated than the prior generation's parents.
Speaking for myself, I had to worry very little about computers until late in high school (Senior year, specifically). There were no spreadsheet or word processing classes, and the typing classes were only for the girls. There was Algebra (up through Calculus as an optional course), but many others that my niece has that I didn't.
Unfortunately I don't expect these changes to impact that. It will likely take more rich kids out of public schools and further widen the gap.
The achievement gap is growing. Part of this is explained by union dynamics [1]. Part by California's elites caring less about addressing the gap than talking about it.
[1] https://journals.sagepub.com/doi/abs/10.3102/0013189X2110063...
> Altogether, this study provides some evidence that contract changes are associated with the educational opportunities of school districts’ diverse and economically disadvantaged students.
Essentially, if you want to prioritize your child's education above all else, get them into the richest school district you can manage.
How many folks are really willing to do that? The problem is that actually discussing the perceived root causes of this issue will get you shunned out of polite society.
Those are the only topics I am seeing being outright banned from being discussed or taught.
I don't think the previous standards of rigor were ever so high for most students.
When I was growing up in the 80s and 90s in the suburban working class Midwest, the vast majority of the students in my high school didn't advance beyond algebra. This was in a well resourced school district.
But that was a time when it was felt that most people didn't even need to know anything past basic math to be employable. Times have changed of course, but the vast majority of educational paths, even STEM paths, don't require calculus.
However a great many do require basic data analysis abilities, so it's reasonable to emphasize those.
This shouldn't be done at the cost of offering calculus as an option for students who are prepared for and motivated to do it, though. Of course in the end this is about cost. Assuming the same resources, to teach a broader set of students data science will require reducing the availability teaching resources for something else.
I also recall that in the 1980s in some places there were programs that taught calculus at public community colleges for students who were on an accelerated academic path in high school. That is another option to consider.
It's a warning to any parents of younger children: Unless something has changed radically in the past 8 years, your child will be put into a math track in 6th grade: Separated into standard, accelerated and advanced classes. Which track you're in is determined by grades, standardized tests and teacher input after 5th grade.
This track determines which classes you can take in 7th and 8th. If you were in the advanced class, you will have finished Algebra 1 by the end of 8th grade. This allows the student to begin 9th grade taking Algebra 2, and then extending from there so that by their senior year they can take AP Calculus.
If you want little Suzy to be in more advanced classes, you better be prepared to be the most vocal Tiger Mom Karen you can imagine, because you'll have plenty of competition. As a result, almost no child moves between tracks. And in fact, in my opinion, the difference between normal and accelerated is so little, I'm pretty sure it's there just to give those children somewhere to go.
In other words, if your child doesn't demonstrate math skills as an 11yo, they will unlikely be able to take AP calculus 7 years later without doing something extra like taking summer classes, redoing an entire school year (an option a fellow parent I know took), or extraordinary effort like that.
Even if the MVLA education system isn't exactly the same now, or you live in a district that does something totally different, or even if you're in another state, I suspect this sort of thing is happening everywhere.
I personally was happy my son was in accelerated classes, right up until 9th grade when I realized how this circumscribed his future options for classes. In the end he would never have wanted to take AP Calculus, so it was fine. But I personally felt like I had fucked up as a parent because I simply wasn't paying attention. Planning out your kid's future math classes in detail in the 5th grade never crossed my mind, or if it had, I would have dismissed it as ludicrous overparenting! Had I known, I might have sent him to a math camp or something if I had realized how important the difference between a B+ and an A in math was at that moment. And he my have really gotten into mathematics as a subject. I really don't know.
So anyways, that's my experience. California is such a massive change from where I grew up in rural NH, I honestly can't imagine where to begin to fix a system with so many millions of children from such a varied socioeconomic and cultural backgrounds. I barely got my one kid through the system unscathed, and I live in one of the wealthiest districts in the country.
And then the home school quality goes down and that hurts everyone else who isn't among the small group at the magnet.
Boston proper and surrounding areas have begun to suffer from the same epidemic of anti-gifted mania that plagues California and is beginning to affect New York City, especially with regards to the exam schools (i.e. Boston Latin et al).
I absolutely loved learning Calculus in high school in Math and 1st and 2nd year of University. I consistently got 97+% on my grades.
And I've never had to use it in my Computer Science degree or my 20 year Software Engineer career since.
Am in a bubble because I don't spend much time in the Machine Learning domain?
On the other hand, I feel psychology and stats are the biggest missing pieces in K12 education. We need to build greater awareness of human needs and fallibilities, and awareness of how to make decisions in uncertain environments by understanding probabilities. Both are about developing a nuanced perspective on life and making better, more sober decisions, and they build a great deal of empathy to boot.
Finally, psych & stats are inherently relatable - everyone deals with people and has to make decisions. So much of the K12 experience isn't relatable, which is why students often hate school.
Ergo, it’s best to a) not to have college expectations be built around most/everyone having it before college and punishing those who don’t, b) focus on teaching it where it’s needed (eg when in college for those majors), and of course c) if a kid knows their path involves it earlier, make it available to learn when they want to.
One way to see how curriculum has changed over the last 70 years is in Sheldon Glashow's autobiography. He graduated from the Bronx High School of Science in 1950. Quoting https://www.nobelprize.org/prizes/physics/1979/glashow/biogr... , "High-school mathematics then terminated with solid geometry."
If you take the position that calculus is the concept of limit and all its consequences, then things like exp() and log() are calculus and it's hard to get anything done in CS without those. In this view, saying that quicksort is O(n log n) is a statement of calculus.
If you say that calculus is derivatives and integrals, then I'd say that calculus is not that important in a digital world, and that discrete math is much more useful. However, discrete math is harder than calculus, but you can use calculus as an approximation to the discrete answer (i.e., compute the integral if you don't know how to compute a sum, or use a derivative to approximate a difference). Ironically, this is the opposite of the old attitude that the continuous answer was the true one and the discrete answer was a poor man's approximation to the true one.
I got to the point of writing my own toy neural network from scratch, seeing backpropegation, figuring that I'd have to use the chain rule myself on my forward pass, understanding what "automatic differentiation" was and why it's important, and decided "screw that I'm not putting myself through this hell again" and decided to look into https://en.wikipedia.org/wiki/Derivative-free_optimization
You can literally just find your own hetrodox subset of scholars in your field who are like "calculus? pfft!"
I agree with this problem statement.
It's a MS Word document. How am I supposed to find lines 1226-1239? They might want to actually quote it.
https://www.groovypost.com/howto/quickly-go-to-a-certain-pag...
> We write to emphasize that for students to be prepared for STEM and other quantitative majors in 4-year colleges, [...], learning the Algebra II curriculum [...] in high school is essential.
Problems with math are one of the most common reasons why students encounter difficulties in STEM education and careers. The most common problem is difficulty with high-school level algebra.
I agree, fundamentally, with the relevant premise of the CA effort here (and agree with Aaronson's criticism of its implementation). That premise is that you shouldn't have to be on an accelerated track in middle school in order to take calculus in high school. And yet... the fact is, we get a lot of adults in college or graduate school pursuing STEM degrees, who have shaky foundations in high-school algebra.
Just looking at the "typical" math track in US high schools it does seem a bit arbitrary. Algebra I, Geometry, Algebra II, Pre-Calculus, Calculus--this is the most common math track I see, with accelerated students starting Geometry in 9th grade, Calculus in 12th grade.
The thing is... individual performance is highly variable in math classes, and to make sure that everyone gets good foundations in mathematics, we see high-school mathematics curricula that repeat the core algebra concepts in different classes. This repetition and focus on fundamentals is why the division between classes seems so arbitrary--what is presented as a sequence of classes is really more of a unified curriculum spread across multiple years. When you combine these two factors (variable performance, repetition in the curriculum), you end up with a population of high-school students who develop good foundations in algebra early on and are bored by the repetition, and a population of students who really benefit from the time spent mastering algebra, and it's hard to serve both.
I think we can figure out a way to let high-school students take AP calculus in 12th grade without expecting them to take Algebra I in 8th grade, and we don't need to push everyone into calculus faster in order to do it. And yet, my experience with high-school education in the US has left me very cynical about it. Letting students progress through the high-school math curriculum at the right rate requires a kind of "personal touch" that seems to only happen to individual students when their parents are involved, but not pushy. It's rare. The school system would rather do the easy thing (everybody moves in lockstep to the next class in the sequence), and parents are largely either uninvolved or overinvolved.
(This is more or less what the article says, I'm agreeing with the article.)
I feel as though there is too much focus on giving everyone more or less the same type of mathematical education in high school. This is probably due to limited resources (ie teacher availability and class sizes), but ideally there would be room for a more varied approach wherein students don’t need to have every year build on the next if the aren’t STEM tracked. Too many students fall behind and never are able to recover. Math class just becomes dead time, and those that do make it to college end up retaking the same subjects over again.
It sounds like we agree 100% on that point.
I'm mostly thinking about the students who are going into STEM degrees later in life, who will (hopefully) come from varied backgrounds in high school and middle school. If you decide in high-school that you're interested in STEM, then it makes sense to develop solid foundations in algebra during high-school. Just like it doesn't make sense for all people to take math like a STEM major, it doesn't make sense to fast-track all future STEM majors to take calculus in high-school, and it doesn't make sense to make decisions in middle school that lock students out of high-school calculus.
The thing that confounds this is that people overvalue high-school calculus as the ticket to a STEM degree, when (like the article says) many people would be better served by developing stronger foundations in algebra. And public schools are generally not good at educating students at their own rate & level.
This sounds contradictory to me.
Moreover, how does IQ differ in this respect from "capacity and willingness to do hard work"?
The essense of materialistic nihilism.
Also assuming that "capacity and willingness to do hard work" is a personality trait, that is also largely random. So no matter which way you slice it, you gotta get lucky on either the intelligence or industriousness axes (or both) to be successful.
Yes exactly my point! At some level, success can only possibly be seen as a product of chance.
In a excellent school district in a suburb of Chicago a district goal was adopted to reach equitable outcomes in higher Math. In a nutshell since black students scored statistically lower on AP Calculus this was seen as a failure in the school district. Despite increasing the number of black students able to pass AP Calculus the school district looked to cancel offering the course since Asian and affluent white students still scored statistically higher.
The idea that all races, genders, or whatever categorization you can come up with must have the same equitable outcome is a flawed goal. Education used to be about taking a student where they are and showing improved learning outcomes.
Equality used to be about striving for equal opportunity. The shift to conflating equality with equalized outcomes simply doesn't work.
Note that to the extent there was a shift, it took place in the 70s.
This really has ramped up in the last 2-3 years.
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