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.
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.
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?
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.
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.
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.
'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.
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 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 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.
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.
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.
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.
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.
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!
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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?
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.
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.
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.