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I was in the "middle" tier math program in high school. But around sophomore year I wanted to get more into science/engineering but you can't switch tiers or catch up to those ahead of you, no matter if you're making extra effort and doing well. It was frustrating.

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.

Many public schools take local college credits. There is always a path.

My understanding is that CA law requires public schools to accept any class that would receive credit by the UCs. They don't always, and I believe some bay area schools have been (successfully) sued over their non-compliance.

Yes, but these alternatives are much harder to find for students who already aren’t the best at navigating the school system. Requiring students to figure all of this out is going to reduce the number of students who benefit by quite a bit.

My school allowed changing tiers, and I am very grateful that it did. I had a bad year in my early teens with some mental health stuff, and spent my first year in high school with kids who needed much more time and practice to get a handle on concepts than I did. If I had been forced to stay in those tracks, my life would have taken a drastically different course, as I didn't really need to work to learn. Getting bumped into a higher tier challenged me, and that challenge is what prepared me for college.

Had I gone into college without that work ethic, I almost certainly would have failed out early.

Nice work. However you say you couldn't switch tiers but in the next paragraph you did find a way. So, it sounds like you can.

I read it as an unspoken "within the school system." It seems reasonable to expect schools to include a path for changing tiers if they put such a system in place, rather than leaving it up to students to find a workaround.

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.

If he was only able to get on this track due to interventions from outside the school system which many students could not afford or otherwise could not access, then that's a failure of the public school system.

I know it's considered good form on HN to beat around the bush a bit when it comes to sensitive culture war topics, but I think it's worth pointing for the non-Americans here that the only reason this discussion is even happening is because of the demographics which are observed after the "split" occurs.

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?

Yep, tracking students into systems like high/low early on makes it very hard to ever escape that track, as they're a sort of self-perpetuating system. That has downstream effects for one's entire life. It's a crude method of personalizing education within the context of factory education.

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.

From what I've seen there are three major problems with edtech that gives a personalized education:

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.

Yeah we’re early on in really nailing the formula. Butts in seats staring at screens doing single player activities isn’t a particularly compelling education environment nor one children are accustomed to biologically. We need more embodied, social, psychologically safe, and intrinsically motivating learning environments, and I don’t think the enabling technologies and designs have yet emerged to fully satisfy these needs.

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.

Another non-obvious problem is that you can get mis-tracked too low even on the highest track. It happened to me. There was an assessment test on entering middle school for how many classes up you got shifted, I went into the highest bucket with 4 other kids. Last year of middle school we had to get bussed into the local high school for math education and back for everything else.

I was not seriously challenged and felt like math classes wasted my time.

> “When kids struggle, they immediately say ‘I don’t have a math brain,’” Boaler said. “That changes how the brain operates.”

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.

> I didn't read any context, but students CAN and SHOULD learn to struggle. Productively. Without thinking they are failing.

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.

Sounds like more woke nonsense. Sounds nice and easy to a layman from a super high level but not practical or put through any kind of rigorous rational thought.

> Sounds like more woke nonsense

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.

Like I said, sounds good to a layman in general terms (just how you explained it). But the actual implementation is half-baked, short-sighted, and favors a weak/easy solution rather than something more well thought out and complex.

Ok, so what would your approach be to address the issue of huge groups of kids underperforming what they are actually capable of?

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.

Wouldn't cutting out high level math courses make even more kids underperform below what they are capable of?

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.

It would be most equitable and inclusive for everyone to be equally destitute. Let's drag everyone down to the lowest common denominator...

So, the solution is to instead decide at ~grade 6 or 7 that some people are going to get dragged down, instead?

Why would adding higher level courses drag anybody down? They aren't removing low level courses

The problem is that these higher level courses aren't 'extras', they are table stakes for getting an education.

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 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 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.

If you can't run a five-minute mile, and are therefore put into a PE class where you never run, do you think you'll ever get into a shape where you can?

I am advocating for more across the board.

> If you can't run a five-minute mile, and are therefore put into a PE class where you never run, do you think you'll ever get into a shape where you can?

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.

> 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?

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.

> what would your approach be to address the issue of huge groups of kids underperforming what they are actually capable of?

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.

> Huh? Are you suggesting that removing upper level maths classes helps kids achieve their potential?

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.

>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.

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.

> No, the nonsense is the idea that we are all cut out for math.

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.

What's the longest we can go without streaming and still meet reasonable targets? The people designing this curriculum seem to say they can't get rid of streaming without dramatically lowering the bar.

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.

> The people designing this curriculum seem to say they can't get rid of streaming without dramatically lowering the bar.

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.

> 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.

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.

>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

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.

And what institutions are responsible for spending half of the waking hours of a child teaching culture?

Parents and peers/communities. If the US is any indication, teachers are incapable of instilling appreciation for learning once scholastic achievement is branded "uncool".

You underestimate the impact that schooling has on culture. As a school-age child, you spend more time being socialized and educated by your teachers, than by your parents.

Perhaps a simple solution is worth a try: publicly praise/acknowledge those who excel, while also teaching that it's okay to not be at that level [yet]. Encourage peer mentorship, so that the more advanced ones can help someone who struggles. For the outliers who are absolutely stuck in the "I don't care" mindset, apply additional resources to find alternate ways to make the material matter to that individual (practical examples, scenarios, hands-on application, etc.). Ask other students who are interested what real world uses they can think of for the material/topic/equation/concept. If something works, consider implementing that method for the entire class earlier on for the next class.

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.

Can't we agree that both extremes are wrong? While I agree that it is wrong to assume there is no such thing as innate human ability, and it is wrong to assume everyone can achieve equally, you seem to be arguing the opposite; that there is nothing that can be done to improve achievement for those who are struggling.

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.

> 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.

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.

I don’t know how we do it, I am not an education expert. I am simply saying we should keep trying new ways to try to help lower performing student improve until we find one that works. We shouldn’t just give up and write them off as being unable to improve.

'you aren't good at math/math is hard' may be nonsense, no doubt.

'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.

I don't understand if you're saying that every kid is equally good at math. Or, similarly, that every kid that the same capacity for it or ability to pickup math concepts.

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 don't understand if you're saying that every kid is equally good at math.

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.

> (and having their teachers be afraid of math)

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.

> (and having their teachers be afraid of math)

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.

I would agree with this. The standards aren't super high -- from my POV as someone who always excelled in math. But it's clear (to me, at least) that even the "incredibly low bar" is actually quite challenging, at every grade level, for very many students.

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!

> That changes how the brain operates.

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.

> we don't want to send the message that some kids are just bad at math

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.

Yes, some kids are bad at math... but they could be better than they are.

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.

Yes, that's correct. So you (and I) should be taking remedial running and Usain should be taking AP running.

You're making a straw man that non-advanced math class == no math class.

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.

Why wouldn't you just let everyone take the same class and the same exams, but let the kids who have interest do extra work? Want to do calculus a year early? Here's the book, here's the exercises, why would I stop you?

What you suggest is already the case. The book and exercises are "here" for you to do, nobody to stop you. It's called the internet. The calculus police doesn't come get you if you're reading a calc book in 10th grade. It's just that you don't have any way of getting instruction or school credit - so you are very unlikely to be successful, and not very likely to have your university credit you as having mastered the material without taking a college class.

Any high schooler can take the AP calculus test and earn credit, no?

Because that's inefficient. A class geared towards the bottom 50% of kids is going to waste a lot of time for the top 50% of kids. Simply giving the gifted kids more homework just wastes more time, and hardly encourages them to reach their potential.

I think the teacher sometimes says and explains things to the whole class, and if what the teacher says, or homework s/he has prepared, applies only to 5 out of 25 kids, the others can get bored and unmotivated, sometimes even start disturbing the others.

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