California tries to close the gap in math, but sets off a backlash(nytimes.com)
nytimes.com
California tries to close the gap in math, but sets off a backlash
https://www.nytimes.com/2021/11/04/us/california-math-curriculum-guidelines.html
180 comments
This topic has shown up in enough threads and I've held my tongue but want to add on
I was a student in largely remedial classes at my initial kindergarten/elementary school, regularly suspended and sent to detention for misbehavior, usually being distracted in class, and for years the school pressured my parents to apply heavy medication.
just before middle school I was finally kicked out, but this ended up being the single best thing to happen to me, as I ended up at a school that had a gifted program.
Within the first few weeks my math teacher had contacted my parents about it (entertainingly, this was her response to my being distracted in her class rather than just suspending me, I'm forever grateful to her for this.) and I was rapidly moved into a different track.
It is not exaggeration to say this likely saved my life. I was bullied HEAVILY as the new and nerdy kid who was literally always reading a book, and had a ton of trouble fitting in, and this gave me something that I felt competent at, a place away from the normal class behavior that involved far more fights than learning, as well as friends and a path forward. I say this final part not to brag but to be clear about where this ended up: I graduated a national merit finalist and went to an ivy and then into research.
The efforts to gut gifted programs makes the pit of my stomach drop, and I have no skin in the game. It makes me think of where I'd have been without that outlet, and what students in the future will not have access to, and it makes me truly sad.
I was a student in largely remedial classes at my initial kindergarten/elementary school, regularly suspended and sent to detention for misbehavior, usually being distracted in class, and for years the school pressured my parents to apply heavy medication.
just before middle school I was finally kicked out, but this ended up being the single best thing to happen to me, as I ended up at a school that had a gifted program.
Within the first few weeks my math teacher had contacted my parents about it (entertainingly, this was her response to my being distracted in her class rather than just suspending me, I'm forever grateful to her for this.) and I was rapidly moved into a different track.
It is not exaggeration to say this likely saved my life. I was bullied HEAVILY as the new and nerdy kid who was literally always reading a book, and had a ton of trouble fitting in, and this gave me something that I felt competent at, a place away from the normal class behavior that involved far more fights than learning, as well as friends and a path forward. I say this final part not to brag but to be clear about where this ended up: I graduated a national merit finalist and went to an ivy and then into research.
The efforts to gut gifted programs makes the pit of my stomach drop, and I have no skin in the game. It makes me think of where I'd have been without that outlet, and what students in the future will not have access to, and it makes me truly sad.
Same, but I just dropped out and did my GED at 16. Worthless to waste my time in a place I did not want to be, had to wake up at 5AM and had to play along. Best decision I made.
I would never put my children to any USA public school, private or entirely outside the USA.
I would never put my children to any USA public school, private or entirely outside the USA.
As the father of a gifted kid I feel the same.
But i have 0 experience with private school because I grew up in Canada where they are extremely rare.
How do you suggest I proceed to find which private school are actually better and not just religion oriented?
How do you suggest I proceed to find which private school are actually better and not just religion oriented?
It's a hard question, I was lucky to have some private school but for my high school years it was public and a complete waste.
Religion for the schools I went too weren't that enforced, but I would say ask other parents, there should be a good tour of the school included, and then check out the clubs they offer.
"Better" though, is hard. I would just review how they teach STEM - interview the teachers with open ended questions and see how they respond.
One big PLUS though is the networking, private school, the peers/kids are usually from "better*" (for lack of a better word.) off families so that could mean better success, even if religious.
It's hard to quantify it, but the friends I made from my private school days helped me tremendously learn so many different things - how life is different for the truly well off, to community, and "success".
It sounds odd writing it like this, but in the USA many kids in school are there because it is compulsory and it is not a profit center, it is a cost center, bigger classrooms per teacher, smaller campuses, food not healthy, and draconian rules like no water bottles in class or other.
Of course it does depend per school, but those pain points about public school, can be taken to see if you can find a proper private school.
And if you do, I would get the most of your dollar and do the parent events too - meet the other parents and strike bonds that may really last your childs lifetime.
Religion for the schools I went too weren't that enforced, but I would say ask other parents, there should be a good tour of the school included, and then check out the clubs they offer.
"Better" though, is hard. I would just review how they teach STEM - interview the teachers with open ended questions and see how they respond.
One big PLUS though is the networking, private school, the peers/kids are usually from "better*" (for lack of a better word.) off families so that could mean better success, even if religious.
It's hard to quantify it, but the friends I made from my private school days helped me tremendously learn so many different things - how life is different for the truly well off, to community, and "success".
It sounds odd writing it like this, but in the USA many kids in school are there because it is compulsory and it is not a profit center, it is a cost center, bigger classrooms per teacher, smaller campuses, food not healthy, and draconian rules like no water bottles in class or other.
Of course it does depend per school, but those pain points about public school, can be taken to see if you can find a proper private school.
And if you do, I would get the most of your dollar and do the parent events too - meet the other parents and strike bonds that may really last your childs lifetime.
Most of them should offer tours and the like. One of the biggest things to pay attention to is teacher to student ratios. Most of my classes had 6 or so students in elementary school.
Education is another one. Private school teachers are usually very well qualified. I would ask what kind of professionals they have on site. I.e. there should be at least one person specifically versed in childhood development, preferably several. It's not uncommon for them to have dual degrees in childhood development, and teaching in some specific field.
Education is another one. Private school teachers are usually very well qualified. I would ask what kind of professionals they have on site. I.e. there should be at least one person specifically versed in childhood development, preferably several. It's not uncommon for them to have dual degrees in childhood development, and teaching in some specific field.
100% agree with you.
Gifted student should not be ignored!
Gifted student when put in normal class will be so bored they will start getting awful grade.
Ironically such a document frames Black / Latino students as 1 monolith, frames them all as too stupid to get math, frames them all as poor, frames them all as caring about their community of color (ie have no friends outside their own race), cannot be gifted or excel at math naturally.
It does all this by pretending math needs to change, when there are a million other things we could fix in bad schools to make all students perform better at math.
If you expect less from people, they will meet that mark. If you expect more from people they will rise to the challenge
150 years ago most people in America were not literate. Now it's expected so they are
It does all this by pretending math needs to change, when there are a million other things we could fix in bad schools to make all students perform better at math.
If you expect less from people, they will meet that mark. If you expect more from people they will rise to the challenge
150 years ago most people in America were not literate. Now it's expected so they are
There is nothing ironic about it. This document is a fruit of an entire mental framework that divides people into monoliths according to racial characteristics and, at the same time, drips with soft bigotry of low expectations towards half of humanity.
It is a tragedy to see such fundamentally inhuman philosophy take root. This approach cannot remedy anything at all.
It is a tragedy to see such fundamentally inhuman philosophy take root. This approach cannot remedy anything at all.
> Tracking is part of a larger debate about access to college. Under the current system, students who are not placed in accelerated courses by middle school may never get the opportunity to take calculus, which has long been an informal gatekeeper for acceptance to selective schools.
>
> According to data from the Education Department, calculus is not even offered in most schools that serve a large number of Black and Latino students. Expecting but then not providing opportunity to learn isn’t a great model.
And, this problem is not universal for all people attending those schools. The fact that Black and Latino folks are statistically more impacted is important, yet not necessary for wishing to improve.
>
> According to data from the Education Department, calculus is not even offered in most schools that serve a large number of Black and Latino students. Expecting but then not providing opportunity to learn isn’t a great model.
And, this problem is not universal for all people attending those schools. The fact that Black and Latino folks are statistically more impacted is important, yet not necessary for wishing to improve.
why make it about race?
Those school also have student that are not black and latino.
There are 2 distinct problems:
1- School in poor neighborhood don’t offer calculus
2- Poor neighborhood have more Black and latino.
Changing math for everyone or reserving spot for black and latino in university is not the solution it will just make the USA less educated compared to other country.
there is only one real solution are:
1- Make sure school in poor neighborhood have enough funding to offer calculus
2- Stop telling minorities they are not smart enough and couldn’t succeed if they tried.
Asian parent know kids are smart enough to learn math and just need to work hard! that’s why they send kid to tutoring school. And that’s why asian are good at school even if they are a minority
Those school also have student that are not black and latino.
There are 2 distinct problems:
1- School in poor neighborhood don’t offer calculus
2- Poor neighborhood have more Black and latino.
Changing math for everyone or reserving spot for black and latino in university is not the solution it will just make the USA less educated compared to other country.
there is only one real solution are:
1- Make sure school in poor neighborhood have enough funding to offer calculus
2- Stop telling minorities they are not smart enough and couldn’t succeed if they tried.
Asian parent know kids are smart enough to learn math and just need to work hard! that’s why they send kid to tutoring school. And that’s why asian are good at school even if they are a minority
That’s my main problem with it, it’s basically segregating these kids based solely on race. It’s literally enforcing racial stereotypes onto them “for their own good”, telling them to accept it as fact.
It’s frankly ridiculous
It’s frankly ridiculous
Why is calculus more important than statistics or data science? Frankly, I think that it’s far more valuable for people to learn stars and data science as they provide far more real world benefits over calculus.
Also, who is telling minorities that they aren’t smart enough? The argument made is that, despite their aptitude, they are not given the opportunities.
And again, this is indeed relevant regardless of race and should be a concern even if the schools disproportionately impacted weren’t minority majority.
All that said, I think your point about funding is the bigger issue. Even if this change happens, how will these schools suddenly be able to offer stats when they couldn’t offer calc?
Also, who is telling minorities that they aren’t smart enough? The argument made is that, despite their aptitude, they are not given the opportunities.
And again, this is indeed relevant regardless of race and should be a concern even if the schools disproportionately impacted weren’t minority majority.
All that said, I think your point about funding is the bigger issue. Even if this change happens, how will these schools suddenly be able to offer stats when they couldn’t offer calc?
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The assumption is that math teacher at poor school are not as good because poor school can’t afford better teacher!
if student have bad teacher in algebra class they can’t reach the level needed for calculus. And if not enough student are good enough to take calculus the school simply decide to cut it.
if student have bad teacher in algebra class they can’t reach the level needed for calculus. And if not enough student are good enough to take calculus the school simply decide to cut it.
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It's well-established that radical leftists, the people who scream "Racist!" at anyone they can find, are ironically some of the most racist people in existence. Their whole ideology demands that they infantalize, disempower and rob of agency the very people they claim to fight for, so they can be more effective victims. And of course, anyone who doesn't fit their narrative (like Asians) gets kicked to the curb.
The people who preach the loudest often do so to overshout their own past. It’s no coincidence that the loudest proponents of cancel culture have a history of bigotry, racism and bullying. Today, this the most effective way to bully someone.
Most recently this was seen with the organizer of the Netflix walkout, who has a history of racist tweets, primarily anti Asian: https://www.youtube.com/watch?v=i7wMZ_R_anw
Most recently this was seen with the organizer of the Netflix walkout, who has a history of racist tweets, primarily anti Asian: https://www.youtube.com/watch?v=i7wMZ_R_anw
An ex of mine is as radical and as left as it’s possible to get, in that she self-identifies as a “revolutionary Marxist”. She goes on marches, she wants to defund the police, to ban the existence of billionaires, and the world to be a series of anarcho-communist collectives.
For all the flaws and wishful thinking that I can see in her politics, infantilising and disempowering those she goes on protest marches to help is not among them. She absolutely keeps quiet and listens to anyone having a bad time — proper active listening — even though when she does speak up for them her voice is exactly the stereotype of extreme volume and energy the rest of the world has for Americans in general.
For all the flaws and wishful thinking that I can see in her politics, infantilising and disempowering those she goes on protest marches to help is not among them. She absolutely keeps quiet and listens to anyone having a bad time — proper active listening — even though when she does speak up for them her voice is exactly the stereotype of extreme volume and energy the rest of the world has for Americans in general.
So true.
Here is a link to the Equitable Math proposal which is in the process of being finalized.
https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
I found it notable that in a lengthy multi-part document about white supremacy in math, there is zero mention of the word "Asian" despite that Asians are about 15% of California's population.
https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
I found it notable that in a lengthy multi-part document about white supremacy in math, there is zero mention of the word "Asian" despite that Asians are about 15% of California's population.
In 2050, the contemporary struggle against white supremacy that is purportedly found in pretty much everything will be listed among great examples of moral panics.
And the society will be morally panicking about something else, because this seems to be a generic weakness in human nature, not amenable to learning.
And the society will be morally panicking about something else, because this seems to be a generic weakness in human nature, not amenable to learning.
Actually if you read the document and remove the phrase "white supremacy" I tend to agree with some of the conclusions. For example the section about procedural knowledge vs. conceptual is spot on. You don't need to be a human calculator to be good at math. Schools emphasize surface level understandings and almost never allow you to go deep on a topic.
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Asians of course don't fit the narrative of balming underperformance of some racial groups on racism, being of a different racial group themselves but probably out performing whites on average.
I heard this talk at Microsoft about outlier success, and while somewhat of a throwaway comment, the speaker mentioned that the vast majority of the low American standing in those international math score comparison is due to motivation. Summarized, he said when taking the PISA math exam used to benchmark countries on their academic rankings, we always hear how the US is nearly last among developed countries, but if you compare how far different county’s students get on the 120 question end-of-assessment question (with nothing to do with math), THAT ranking almost perfectly lined up with the math assessment ranking.
Overall, if true, the weak showing of the US seems to be in large part a matter of motivation and persistence than what we’d traditionally call math ability (so maybe we need to change our thinking to include grit to stick it out as part of the math curriculum).
Paper on the topic: https://www.nber.org/system/files/working_papers/w24004/w240...
Overall, if true, the weak showing of the US seems to be in large part a matter of motivation and persistence than what we’d traditionally call math ability (so maybe we need to change our thinking to include grit to stick it out as part of the math curriculum).
Paper on the topic: https://www.nber.org/system/files/working_papers/w24004/w240...
>Overall, if true, the weak showing of the US seems to be in large part a matter of motivation and persistence than what we’d traditionally call math ability (so maybe we need to change our thinking to include grit to stick it out as part of the math curriculum).
Yes, but that motivation (or lack thereof) is symptom of more fundamental differences.
Americans do well on PISA compared to their ethnic relatives (<https://www.unz.com/isteve/the-new-2018-pisa-school-test-sco...>) Asian Americans do better than Asians; whites do better than Europeans; Latinos do better than Latin Americans; and blacks do better than Africans.
Hispanics and especially blacks' scores drag the US average down. Both white and Asian Americans score higher than Canada (and white+Asian is essentially Canada's racial makeup), and higher than New Zealand, Australia, the Netherlands, Belgium, Germany, France, Norway, and the UK; Estonia is below US Asians but above white Americans. Norway is by far the wealthiest Nordic state but its average is only two points higher than the US national average, despite not having a demographic that is 13% of the population and scores 85 points below the white American average.
Yes, but that motivation (or lack thereof) is symptom of more fundamental differences.
Americans do well on PISA compared to their ethnic relatives (<https://www.unz.com/isteve/the-new-2018-pisa-school-test-sco...>) Asian Americans do better than Asians; whites do better than Europeans; Latinos do better than Latin Americans; and blacks do better than Africans.
Hispanics and especially blacks' scores drag the US average down. Both white and Asian Americans score higher than Canada (and white+Asian is essentially Canada's racial makeup), and higher than New Zealand, Australia, the Netherlands, Belgium, Germany, France, Norway, and the UK; Estonia is below US Asians but above white Americans. Norway is by far the wealthiest Nordic state but its average is only two points higher than the US national average, despite not having a demographic that is 13% of the population and scores 85 points below the white American average.
> Overall, if true, the weak showing of the US seems to be in large part a matter of motivation and persistence than what we’d traditionally call math ability (so maybe we need to change our thinking to include grit to stick it out as part of the math curriculum).
Emphasis on persistence in drudgery is already deeply ingrained in our educational system, because it fits well with our cultural predisposition and moral framework, and is a big part of why our educational system ranks where it does, because it doesn't actually work.
You don't motivate students by training them to endure nonmotivating instructional methods.
Its funny how people think evidence that motivation matters means we should try to change students to be motivated rather than change instructional approach to be motivating.
Emphasis on persistence in drudgery is already deeply ingrained in our educational system, because it fits well with our cultural predisposition and moral framework, and is a big part of why our educational system ranks where it does, because it doesn't actually work.
You don't motivate students by training them to endure nonmotivating instructional methods.
Its funny how people think evidence that motivation matters means we should try to change students to be motivated rather than change instructional approach to be motivating.
That's a fair point, and one I'm just as prepared to agree with as the one I made if it is a more viable path.
I remember visiting Sri Lanka a while back and seeing in massive letters on the side of a school: 'Education is the only path to success'. I asked myself why I never, ever saw this kind of simple reinforcement during my schooling in the UK. The conspiracy theorist in me would say it suits them to deny the riff raff the tools to see through the diet of bullshit they serve us on a daily basis.
Saying that education is the only path to success would make students with bad grades feel bad. That is the reason. The goal is to shield students from real world pressure so that it all comes down on them like a hammer when they get out of school and can't get a job, at that point they are no longer the teachers problem so it doesn't matter.
As an American my first thought is “That’s not true in general.” There are many paths to success, many of which require a great deal of formal education, some which would at least benefit from it, but also some which are more or less orthogonal to education.
Perhaps what rubs me the wrong way about that phrase in particular is it seems to imply that education is not only necessary but sufficient for success. A common anti-pattern I’ve seen in young adults is finishing 20 years of schooling, entering the real world, and saying “Wait, now what?”
Perhaps what rubs me the wrong way about that phrase in particular is it seems to imply that education is not only necessary but sufficient for success. A common anti-pattern I’ve seen in young adults is finishing 20 years of schooling, entering the real world, and saying “Wait, now what?”
Also because in countries with low social mobility, the only path to success is inheritance.
I think in the UK that would quickly get graffitied with "except being born royal or landed" or similar.
> so maybe we need to change our thinking to include grit to stick it out as part of the math curriculum
What makes you think students don't have a good idea of their own situation? They know best what they want, they know best how miserable it actually makes them to keep grinding though failure vs. the potential payoffs.
Which isn't to say that they're right about it, individually. But on average they probably make better decisions in their circumstances, than someone else would make for them.
You can't teach grit. You can at best preach it.
What makes you think students don't have a good idea of their own situation? They know best what they want, they know best how miserable it actually makes them to keep grinding though failure vs. the potential payoffs.
Which isn't to say that they're right about it, individually. But on average they probably make better decisions in their circumstances, than someone else would make for them.
You can't teach grit. You can at best preach it.
One of the major purposes of K-12 school is to prepare kids for their future life. For the vast majority of people, life is nonstop grinding through things you don't like: Grinding a job you don't like so you can survive, grinding through traffic/commute, filling out forms, waiting in lines, paying bills. I'd almost argue the grit and persistence to keep grinding is the primary skill you need to be a baseline functional member of society and not end up broke or in prison. Even video games teach people to grind boring tasks for skill points and experience. For better or worse, it's ingrained in the fabric of society.
But I don't think it's a skill. Anyone will grind, if they feel the goal is worth it, something they really want - don't computer games prove that?
It's about values, not skill. Maybe it's possible to value persistence as a good in itself, even if you're less than idealistic about the goal. But then that is not something to be taught as a skill, but something to be preached as a value, by someone who believes it and lives it.
It's about values, not skill. Maybe it's possible to value persistence as a good in itself, even if you're less than idealistic about the goal. But then that is not something to be taught as a skill, but something to be preached as a value, by someone who believes it and lives it.
This guy gets it. And life is easier when it doesn’t bother you to get shit done so much you feel like it’s a revolt.
I wasn't trying to make a controversial statement here. Whatever needs to be done to best prepare students for success is the goal, whether that's teaching them different things or simply changing the way we teach entirely.
It's not controversial. I'm the one making controversial statements, I admit, and I'm genuinely thankful that you don't just dismiss it.
I just think, we can't be agnostic about what success is, what the goal is.
I don't think "grit" really is a thing - if we both believed in the same things, shared the same ideas about what's important and valuable, I think we would be equally capable of the "sticking to it" part of it.
But changing the way we teach won't help, because bringing people around to your set of values - whether it's convincing them that math has inherent beauty, or merely that mastering it is a great way to a lot of awesome material comforts - that isn't really teaching. It's preaching. It has to come from someone who believes it, and lives it - and is sufficiently similar to his students (or congregation!) that they can imagine themselves living it too.
I just think, we can't be agnostic about what success is, what the goal is.
I don't think "grit" really is a thing - if we both believed in the same things, shared the same ideas about what's important and valuable, I think we would be equally capable of the "sticking to it" part of it.
But changing the way we teach won't help, because bringing people around to your set of values - whether it's convincing them that math has inherent beauty, or merely that mastering it is a great way to a lot of awesome material comforts - that isn't really teaching. It's preaching. It has to come from someone who believes it, and lives it - and is sufficiently similar to his students (or congregation!) that they can imagine themselves living it too.
From abstract:
> Offering incentives to U.S. students, who generally perform poorly on assessments, improved performance substantially. In contrast, Shanghai students, who are top performers on assessments, were not affected by incentives.
That's pretty interesting. What's with US students and motivation?
> Offering incentives to U.S. students, who generally perform poorly on assessments, improved performance substantially. In contrast, Shanghai students, who are top performers on assessments, were not affected by incentives.
That's pretty interesting. What's with US students and motivation?
China cherry-picked higher performing, higher socioeconomic regions for their PISA testing, where poorer students don't have access to HS & tests. US PISA scores would be very different if Cambridge and Minnesota and a few other regions were tested.
Worth considering before social factors come into play, as large countries have a lot of variance. Not saying motivation isn't also an issue, but there are lots of motivated kids and great schools in the US if you know where to look.
https://www.the74million.org/article/schneider-the-strange-c...
Worth considering before social factors come into play, as large countries have a lot of variance. Not saying motivation isn't also an issue, but there are lots of motivated kids and great schools in the US if you know where to look.
https://www.the74million.org/article/schneider-the-strange-c...
Well ability and motivation can also have a causation relation in both ways...
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reject the idea that some children are naturally gifted
I could see an argument that there aren't significantly high numbers of genetically gifted children. However, I don't think you can make that argument without recognizing the fact that children's home lives and home cultures have enormous impact on their potential, effects you can't undue with special teacher guidelines. The child who goes home and spends four hours studying quietly is going to demolish in every academic way the child who goes home and listens to his parents cursing at each other and the child who goes home and watches TV for four hours.
I could see an argument that there aren't significantly high numbers of genetically gifted children. However, I don't think you can make that argument without recognizing the fact that children's home lives and home cultures have enormous impact on their potential, effects you can't undue with special teacher guidelines. The child who goes home and spends four hours studying quietly is going to demolish in every academic way the child who goes home and listens to his parents cursing at each other and the child who goes home and watches TV for four hours.
OTOH, when I was a kid, I never did homework at home and I always got straight As in math and science. I was just naturally good at those subjects and was able to not only listen to the lecture in class and learn, but also do my homework for that same day in that same time period. And I retained the knowledge for the quizzes and tests, too.
If that isn't "naturally gifted" I don't know what is. I definitely watched other students struggle to maintain a B average with lots of studying and effort.
I suffered in other subjects, and others excelled at them with little effort. They were the naturally gifted ones there.
It was a constant source of stress to me that they would treat everyone the same when it came to those subjects, to the point that in 6th grade, when reviewing multiplication tables that I'd learned years before, I refused to do my homework. I ended up with an F that semester in math because I was so good at it. Luckily they moved on to harder subjects in the next semester and my grades returned.
If that isn't "naturally gifted" I don't know what is. I definitely watched other students struggle to maintain a B average with lots of studying and effort.
I suffered in other subjects, and others excelled at them with little effort. They were the naturally gifted ones there.
It was a constant source of stress to me that they would treat everyone the same when it came to those subjects, to the point that in 6th grade, when reviewing multiplication tables that I'd learned years before, I refused to do my homework. I ended up with an F that semester in math because I was so good at it. Luckily they moved on to harder subjects in the next semester and my grades returned.
I had a healthy and stable home life, but also parents who pretty much left me to my own devices when it came to school work. In elementary school, I mostly did my homework and never, ever studied for a test. In high school, I did about 50% of my homework and probably studied for a grand total of 3-4 tests over that four years. All the while, I aced tests with nearly straight As.
In school (elementary school especially), I'd finish tests and other work well before other students, would be bored as they asked questions with "easy" answers, etc.
When I got to college, I had zero healthy study habits, and got a good six months of getting my ass kicked until I sorted things out. It wasn't until then that I actually felt challenged and engaged. Until then, I expected to get As and didn't have to work for it. Once in college, where I was challenged, EARNING As was so satisfying. I still remember the feeling of accomplishment of getting As in two chemistry classes, which was a subject I didn't like and I had to work HARD for those grades.
In school (elementary school especially), I'd finish tests and other work well before other students, would be bored as they asked questions with "easy" answers, etc.
When I got to college, I had zero healthy study habits, and got a good six months of getting my ass kicked until I sorted things out. It wasn't until then that I actually felt challenged and engaged. Until then, I expected to get As and didn't have to work for it. Once in college, where I was challenged, EARNING As was so satisfying. I still remember the feeling of accomplishment of getting As in two chemistry classes, which was a subject I didn't like and I had to work HARD for those grades.
rejecting natural aptitude is ridiculous for sure. It needs to be recognized but it also does not necessarily need to be segregated. People learn from being around smart peers. The important thing imo is to hold _all_ students to a higher bar so that concepts like multiplication tables are drilled in the same year they are taught, not being reviewed in 6th grade
The slower students slow down the faster students, the disruptive students disrupt the less disruptive students. This is why there are accelerated classes, to allow each student to reach their potential, as well as why disruptive students need to be removed from the classroom.
If you are morally outraged by accelerated classes because they don't have your preferred racial mix, then that's fine, but understand it means that the faster students have their potential held back. If that's an acceptable price for equality of outcomes, then at least say that and don't pretend that somehow you can have your cake and eat it -- that faster students benefit from being taught slower paced material, and that well-behaved students benefit from being in a class with disruptive students, or that math education is improved when calculus and other challenging topics are removed. That's just doublespeak. Have whatever values you want to have, but don't fool yourself into thinking there isn't a price, and that faster or well-behaved students aren't the ones paying the price.
What will happen is that wealthy students will pay for extra tutors or private school, and we will be back to a less meritocratic system in which you need to be both rich and smart in order to get the good education, as the state is now focused on making sure the best students don't learn too much to upset the ideals of "equality".
This the logical endgame for a state that believes Harrison Bergeron is a utopian work.
If you are morally outraged by accelerated classes because they don't have your preferred racial mix, then that's fine, but understand it means that the faster students have their potential held back. If that's an acceptable price for equality of outcomes, then at least say that and don't pretend that somehow you can have your cake and eat it -- that faster students benefit from being taught slower paced material, and that well-behaved students benefit from being in a class with disruptive students, or that math education is improved when calculus and other challenging topics are removed. That's just doublespeak. Have whatever values you want to have, but don't fool yourself into thinking there isn't a price, and that faster or well-behaved students aren't the ones paying the price.
What will happen is that wealthy students will pay for extra tutors or private school, and we will be back to a less meritocratic system in which you need to be both rich and smart in order to get the good education, as the state is now focused on making sure the best students don't learn too much to upset the ideals of "equality".
This the logical endgame for a state that believes Harrison Bergeron is a utopian work.
I believed what you said for a long time and still kind of do. But this is how our system has operated for a long time and we see today the effects on our society. Some high performers, but many many people who lack even basic principles of mathematics. Do you think this is okay, or should things change? Is it okay to "sacrifice" some potential to raise the floor for everyone else? (I don't even think that a "sacrifice" is necessarily involved, and there's always self-study - the route all the _truly_ gifted prodigies of history take - but let's operate under that assumption)
I think dismissing the whole concept out of hand is just as dogmatic as the caricatured liberal views you seem to have assumed I hold. There are education systems in the world, like in East Asia, that follow these principles, so I think they are worth exploring. This is a weakly held position for me.
I think dismissing the whole concept out of hand is just as dogmatic as the caricatured liberal views you seem to have assumed I hold. There are education systems in the world, like in East Asia, that follow these principles, so I think they are worth exploring. This is a weakly held position for me.
> Do you think this is okay, or should things change?
This is not the result of accelerated classes, it's the lack of accelerated classes. Really it's the result of insufficient sorting. If we had good sorting, we'd be routing half our kids into trade schools where they learn useful skills, and route the other half of our kids into real college prep high schools where the slow track would do calculus and the fast track would do differential equations.
But instead, we send everyone to the same school, pretend that everyone should go to college, and then slow things down so that the slowest student in the room sets the pace. Then we don't remove disruptive students, hire social crusading teachers who themselves don't have a passion for the subjects they teach, and end up with our current outcomes. Most US high school teachers wouldn't even be qualified to teach at a gymnasium in Europe because even our standards for teachers are so low.
Yes, you have to do heroics to learn anything in a U.S. school. The solution to that is not to do more of the same that got us here. The U.S. used to have high schools with college-preparatory ("prep") emphasis that existed side by side with vocational high schools where you could learn a useful trade. High schools even used to have entrance exams. We've fallen a long way in the name of pretending everyone is equal - just in the last 60 years - and the end result is that we have a shortage of both skilled tradesmen and skilled engineers - now we need to import both, and immigrants come from all over the world and earn much higher salaries than the native born because they got a better education.
For example many systems in Europe still do good sorting, managing to give a good education to both fast and slow students by sending one to a gymnasium and the other to a vocational school, and the result is high paying careers for both.
So what's happening in California is merely the continuation of dumbing things down in the name of equality, an ideological process that has been happening for many decades, but taking it to such a level of absurdity and doublespeak that more people are starting to recognize how foolish it all is.
This is not the result of accelerated classes, it's the lack of accelerated classes. Really it's the result of insufficient sorting. If we had good sorting, we'd be routing half our kids into trade schools where they learn useful skills, and route the other half of our kids into real college prep high schools where the slow track would do calculus and the fast track would do differential equations.
But instead, we send everyone to the same school, pretend that everyone should go to college, and then slow things down so that the slowest student in the room sets the pace. Then we don't remove disruptive students, hire social crusading teachers who themselves don't have a passion for the subjects they teach, and end up with our current outcomes. Most US high school teachers wouldn't even be qualified to teach at a gymnasium in Europe because even our standards for teachers are so low.
Yes, you have to do heroics to learn anything in a U.S. school. The solution to that is not to do more of the same that got us here. The U.S. used to have high schools with college-preparatory ("prep") emphasis that existed side by side with vocational high schools where you could learn a useful trade. High schools even used to have entrance exams. We've fallen a long way in the name of pretending everyone is equal - just in the last 60 years - and the end result is that we have a shortage of both skilled tradesmen and skilled engineers - now we need to import both, and immigrants come from all over the world and earn much higher salaries than the native born because they got a better education.
For example many systems in Europe still do good sorting, managing to give a good education to both fast and slow students by sending one to a gymnasium and the other to a vocational school, and the result is high paying careers for both.
So what's happening in California is merely the continuation of dumbing things down in the name of equality, an ideological process that has been happening for many decades, but taking it to such a level of absurdity and doublespeak that more people are starting to recognize how foolish it all is.
If we had good sorting, we'd be routing half our kids into trade schools where they learn useful skills, and route the other half of our kids into real college prep high schools where the slow track would do calculus and the fast track would do differential equations.
I mean that's also a world in which the humanities don't seem to exist at all.
I mean that's also a world in which the humanities don't seem to exist at all.
> But this is how our system has operated for a long time and we see today the effects on our society. Some high performers, but many many people who lack even basic principles of mathematics. Do you think this is okay, or should things change?
I would pin this on widening income/wealth gaps, family problems at home, cultural differences, and other non advanced class related reasons. I dismiss the concept because I think trying to attack a problem not at the root is a waste of time, and in this case, actually harmful.
The big elephant in the room with all these problems is wealth and power redistribution, but that is untouchable so efforts are redirected to things like this.
I would pin this on widening income/wealth gaps, family problems at home, cultural differences, and other non advanced class related reasons. I dismiss the concept because I think trying to attack a problem not at the root is a waste of time, and in this case, actually harmful.
The big elephant in the room with all these problems is wealth and power redistribution, but that is untouchable so efforts are redirected to things like this.
Not to mention the converse-racism. If I as a child was raised racist or otherwise-inclined to be racist toward black students, that perception might be challenged by seeing them alongside me in a gifted course. If I as that child believe the reason there is no gifted class for me to attend because it would hurt the black students' feelings, then that will heavily reinforce my racism.
But in the pedagogical literature, children who are ahead in math don't substantially benefit in the reverse direction.
In this case, holding everyone to a higher standard specifically means disallowing children from taking Calculus even if they are ready, and de-emphasizing Algebra in middle school.
In this case, holding everyone to a higher standard specifically means disallowing children from taking Calculus even if they are ready, and de-emphasizing Algebra in middle school.
Is "naturally gifted" the new "self-made man"?
It seems so obviously self-refuting that I can't believe people use it without irony.
Can anyone name anyone who is naturally gifted at anything that didn't get taught and learn a million different things (not all of which they were good at) in order to get to the point where they could display their "natural gift"?
I say we take anyone's kid who they claim is naturally gifted and dump them on a deserted island shortly after birth and we'll see exactly how well they get on with their natural gifts. Maybe we'll come back in 16 years and they'll be doing calculus, speaking three languages fluently and playing the saxophone, but I doubt it.
After all, we wouldn't want them held back by the decades of parental care and schooling that we give to the normies who need to like, learn stuff from books and be fed for years and other such crutches for the feeble-minded lesser beings.
It seems so obviously self-refuting that I can't believe people use it without irony.
Can anyone name anyone who is naturally gifted at anything that didn't get taught and learn a million different things (not all of which they were good at) in order to get to the point where they could display their "natural gift"?
I say we take anyone's kid who they claim is naturally gifted and dump them on a deserted island shortly after birth and we'll see exactly how well they get on with their natural gifts. Maybe we'll come back in 16 years and they'll be doing calculus, speaking three languages fluently and playing the saxophone, but I doubt it.
After all, we wouldn't want them held back by the decades of parental care and schooling that we give to the normies who need to like, learn stuff from books and be fed for years and other such crutches for the feeble-minded lesser beings.
It makes almost as much sense as saying: "Do fish live in water? Nonsense! Throw a fish into boiling water and watch how it dies."
If you throw a naturally gifted child into a volcano, or abandon it on a deserted island, sure, it will die. Therefore, no gifted kids, QED. But the standard assumption is that the gifted kids grow up in normal environment (and the fish swim in non-boiling water), and then do better in math that average kids growing up in the same kind of normal environment.
The argument is "different outputs for the same input", not "excellent output for any kind of input".
School definitely can (and should) be improved, including math education. But instead of making everyone equally good at math, the optimal kind of math education would make everyone better at math, and the gifted kids even more better.
If you throw a naturally gifted child into a volcano, or abandon it on a deserted island, sure, it will die. Therefore, no gifted kids, QED. But the standard assumption is that the gifted kids grow up in normal environment (and the fish swim in non-boiling water), and then do better in math that average kids growing up in the same kind of normal environment.
The argument is "different outputs for the same input", not "excellent output for any kind of input".
School definitely can (and should) be improved, including math education. But instead of making everyone equally good at math, the optimal kind of math education would make everyone better at math, and the gifted kids even more better.
Yes, this is all fine, until the parent of the fish who gets sent to the ocean says to the parent of the fish sent to the volcanic geyser, "well my kid is just naturally gifted, that's why we put them in the cool ocean water, all you volcano fish were holding him back, I mean just look at your test scores".
And then a fish says, maybe they're not naturally gifted, but just not poached, and everyone suddenly starts talking very specifically about fish in some alternate world that all share the same water. "What, are you saying there's no biological differences between fish, what kind of nonsense is this? If we explicitly assume there's no other factor involved then what is left but raw natural intelligence?" as if they're trying to miss the point intentionally.
And then a fish says, maybe they're not naturally gifted, but just not poached, and everyone suddenly starts talking very specifically about fish in some alternate world that all share the same water. "What, are you saying there's no biological differences between fish, what kind of nonsense is this? If we explicitly assume there's no other factor involved then what is left but raw natural intelligence?" as if they're trying to miss the point intentionally.
> Can anyone name anyone who is naturally gifted at anything that didn't get taught and learn a million different things.
Dude it's high school math not spring boot.
Some kids have some types of intelligence better than others.
If some part of intelligence was not intrinsic, we could be teaching calculus to rabbits.
Dude it's high school math not spring boot.
Some kids have some types of intelligence better than others.
If some part of intelligence was not intrinsic, we could be teaching calculus to rabbits.
What on earth are you talking about?
Yes, obviously in order to make an apple pie you must first create the universe. In order to be gifted you must first be born, have a basic level of food and shelter, be mostly free of disease and so on. That's not a relevant point of discussion here. We're discussing a case where all things are equal.
"But all things aren't equal!" You scream. "Those evil white people grew up in the lap of luxury while the poor, repressed minorities had a life of scraping, miserable poverty!"
First, this isn't always true. There are poor white people and middle-class (or even rich) minorities, and to suggest that every minority is hopelessly disadvantaged because they all grew up in the ghetto is its own kind of racism. But second, this is a separate discussion. To answer the question "Are some people naturally gifted?" you have to adjust the other variables to equal first in order to tease out the answer to that specific question. Having discovered that yes, indeed they are, you can then conclude that this CONTINUES TO BE THE CASE in situations where "privilege" is not equal. The fact that some people are handicapped or helped by their economic or racial background does not magically erase the fact that they are ALSO helped or held back by their innate intelligence, and tendency to understand or not understand specific concepts.
Some people are smarter than other people, in a way that has nothing to do with economics or racism, but is purely biological luck. In direct contradiction to your assertion, THIS is self-evident, in the same way that "Things fall to the earth when dropped". and "Eventually, everyone dies" are. To deny this is to deny basic, readily-observable and reproducible reality, in a way that suggests either disingenuousness or mental illness.
Everyone is not equal, never has been, and never will be. It is an inherent property of the randomness of nature that some members of a species end up with abilities superior to others, completely independent of economics, race, social class, or any other human construction. Stop pushing this inane Harrison Bergeron gibberish.
Yes, obviously in order to make an apple pie you must first create the universe. In order to be gifted you must first be born, have a basic level of food and shelter, be mostly free of disease and so on. That's not a relevant point of discussion here. We're discussing a case where all things are equal.
"But all things aren't equal!" You scream. "Those evil white people grew up in the lap of luxury while the poor, repressed minorities had a life of scraping, miserable poverty!"
First, this isn't always true. There are poor white people and middle-class (or even rich) minorities, and to suggest that every minority is hopelessly disadvantaged because they all grew up in the ghetto is its own kind of racism. But second, this is a separate discussion. To answer the question "Are some people naturally gifted?" you have to adjust the other variables to equal first in order to tease out the answer to that specific question. Having discovered that yes, indeed they are, you can then conclude that this CONTINUES TO BE THE CASE in situations where "privilege" is not equal. The fact that some people are handicapped or helped by their economic or racial background does not magically erase the fact that they are ALSO helped or held back by their innate intelligence, and tendency to understand or not understand specific concepts.
Some people are smarter than other people, in a way that has nothing to do with economics or racism, but is purely biological luck. In direct contradiction to your assertion, THIS is self-evident, in the same way that "Things fall to the earth when dropped". and "Eventually, everyone dies" are. To deny this is to deny basic, readily-observable and reproducible reality, in a way that suggests either disingenuousness or mental illness.
Everyone is not equal, never has been, and never will be. It is an inherent property of the randomness of nature that some members of a species end up with abilities superior to others, completely independent of economics, race, social class, or any other human construction. Stop pushing this inane Harrison Bergeron gibberish.
> We're discussing a case where all things are equal.
No, we're not.
No, we're not.
I don’t know how math education has evolved since the late 90s - early 2000s when I experienced it, but it was far more damaging to my self esteem and my relationship with math than anything else.
I learned from a pretty early age that solving long equations with a pencil and paper is simply something my mind is never going to be good at. I hated every minute of it, and it was a huge source of anxiety for me and my parents. My mom, a house cleaner at the time, managed to muster the money to get me a tutor, which got me through high school and into college.
Fast forward 15 years and my relationship with math couldn’t be any different. In the context of my career where math has a practical purpose and I no longer have an artificially imposed requirement to memorize, I actually have quite a bit of use for and natural curiosity around math.
I’m not saying that my experience means that math education should change dramatically for everyone, but it certainly fails a wide swath of people like me. Their math education is traumatic, that they are “bad at math” is reinforced into their brains by the educational system, and they live the rest of their lives avoiding it. (I’m married to someone like this!)
I’m just glad that I was able to see how math as it is experienced in the classroom is pretty dramatically different from the way it is used in the professional world, and that I’m only bad at the former, not the latter.
I learned from a pretty early age that solving long equations with a pencil and paper is simply something my mind is never going to be good at. I hated every minute of it, and it was a huge source of anxiety for me and my parents. My mom, a house cleaner at the time, managed to muster the money to get me a tutor, which got me through high school and into college.
Fast forward 15 years and my relationship with math couldn’t be any different. In the context of my career where math has a practical purpose and I no longer have an artificially imposed requirement to memorize, I actually have quite a bit of use for and natural curiosity around math.
I’m not saying that my experience means that math education should change dramatically for everyone, but it certainly fails a wide swath of people like me. Their math education is traumatic, that they are “bad at math” is reinforced into their brains by the educational system, and they live the rest of their lives avoiding it. (I’m married to someone like this!)
I’m just glad that I was able to see how math as it is experienced in the classroom is pretty dramatically different from the way it is used in the professional world, and that I’m only bad at the former, not the latter.
I hear this "let's change math education" often. But how do you propose to do it?
A lot of the attempts at teaching Common Core math that I looked at were far superior to my experience in the 80s/90s. I was taught math wrongly. Like the GP, I didn't grow to appreciate it like I do today until years after the fact... and I got a math minor!
But really what I'd like to see is math taught in a far more granular way. Weekly chunks that were pass/no-pass. If you didn't get it, repeat the week. If you got it, progress to the next week.
If you have _n_ weeks of math done, great, you get a HS diploma. If you have _m_, you have a minor, etc.
And I'm saying "math", but that could be broken down into subspecialities. You don't qualify for precalc week 1 until you've reached Trig Week 12 and Geometry Week 8, or whatever.
Weeks could be "challenged", as well, if you were able to skip ahead.
And there'd be no need for a gifted program. (Such programs--I was in one--always sat the wrong way with me. Like it was an artifact of bad structural design of the education system.)
Anyway, that's what I'd do if I were king. In fact, I'd change every subject to use this model. (HT Kahn Academy and their flipped-classroom work.)
But really what I'd like to see is math taught in a far more granular way. Weekly chunks that were pass/no-pass. If you didn't get it, repeat the week. If you got it, progress to the next week.
If you have _n_ weeks of math done, great, you get a HS diploma. If you have _m_, you have a minor, etc.
And I'm saying "math", but that could be broken down into subspecialities. You don't qualify for precalc week 1 until you've reached Trig Week 12 and Geometry Week 8, or whatever.
Weeks could be "challenged", as well, if you were able to skip ahead.
And there'd be no need for a gifted program. (Such programs--I was in one--always sat the wrong way with me. Like it was an artifact of bad structural design of the education system.)
Anyway, that's what I'd do if I were king. In fact, I'd change every subject to use this model. (HT Kahn Academy and their flipped-classroom work.)
> But really what I'd like to see is math taught in a far more granular way.
I really like your proposal! (And not just for math; any subject could be taught this way.) Problem is, if everyone advances in a different way, it is no longer possible to have 20-30 kids in the classroom listening to the same lecture. Because one of them is today at week 1, another at week 2, etc. So now you need to learn from books or computer.
> And there'd be no need for a gifted program.
We would need some bonus "weeks" that are not meant for the average student, but the matematically gifted students could take them.
First, students should be able to take "weeks" typically meant for older students, even if that meant that gifted kids at elementary school would take lessons meant for high school students. Second, there could be alternative lessons exploring the topic in greater depth, or exploring connections between various topics. Third, there could be optional lessons with topics that are normally not taught at all.
All three of these should be available, not just the first one (although even that would be way better than nothing, which is what we have now). To give an example of a deeper lesson, while average students learn e.g. that binary numbers exist, and maybe learn to convert from decimal to binary and vice versa, gifted students could also learn to do addition and multiplication directly in binary. An example of a topic typically not taught could be set theory, or game theory.
I really like your proposal! (And not just for math; any subject could be taught this way.) Problem is, if everyone advances in a different way, it is no longer possible to have 20-30 kids in the classroom listening to the same lecture. Because one of them is today at week 1, another at week 2, etc. So now you need to learn from books or computer.
> And there'd be no need for a gifted program.
We would need some bonus "weeks" that are not meant for the average student, but the matematically gifted students could take them.
First, students should be able to take "weeks" typically meant for older students, even if that meant that gifted kids at elementary school would take lessons meant for high school students. Second, there could be alternative lessons exploring the topic in greater depth, or exploring connections between various topics. Third, there could be optional lessons with topics that are normally not taught at all.
All three of these should be available, not just the first one (although even that would be way better than nothing, which is what we have now). To give an example of a deeper lesson, while average students learn e.g. that binary numbers exist, and maybe learn to convert from decimal to binary and vice versa, gifted students could also learn to do addition and multiplication directly in binary. An example of a topic typically not taught could be set theory, or game theory.
> So now you need to learn from books or computer.
Or, since I'm King, I propose we hire enough well-paid teachers to cover our needs.
But actually in the inverted classroom model, you have video lesson "homework" (what we think of as the lecture) and then the students come to class to do exercises. The teacher becomes more of a tutor. So one teacher could still cover students within a few weeks of each other.
And I definitely like the idea of a week having the minimum work and a pile of bonus work for the over achievers.
Or, since I'm King, I propose we hire enough well-paid teachers to cover our needs.
But actually in the inverted classroom model, you have video lesson "homework" (what we think of as the lecture) and then the students come to class to do exercises. The teacher becomes more of a tutor. So one teacher could still cover students within a few weeks of each other.
And I definitely like the idea of a week having the minimum work and a pile of bonus work for the over achievers.
California largely does not have the same kind of gifted and talented program as NYC, which was recently discussed. Rather, students have multiple chances to move forward based on their performance on standardized tests.
what do you mean by flipped-classroom work?
I'm assuming you don't know what the term means in general, not specific to beej71's comment
Flipped classroom = instructional approach in which "lectures" are pre-recorded and watched by students and home, while class time is used for discussions and solving problems (individually or in groups).
The term flipped is used because what you do "homework" in class, and watch "class lectures" at home.
See https://en.wikipedia.org/wiki/Flipped_classroom
Flipped classroom = instructional approach in which "lectures" are pre-recorded and watched by students and home, while class time is used for discussions and solving problems (individually or in groups).
The term flipped is used because what you do "homework" in class, and watch "class lectures" at home.
See https://en.wikipedia.org/wiki/Flipped_classroom
Thanks a lot for the explanation. This make a lot of sense now.
A question for the mathematically inclined / advanced: Where do you feel your interest in math was mostly developed?
For me it's clearly at home. My dad loved math and statistics, taught me concepts from a young age and a generation on I try to pass that on to my children. Given their aptitude and results it seems to work. I don't much believe that "some people just can't grok math" other than a basic correlation with IQ. I think we don't lay the foundation right for kids struggling with math since they have to follow or be dragged along a median path.
If mathematical enthousiasm is mostly developed at home, do American parents have or take less time to give kids that enthousiasm?
My kids get extra schooling in math in school (K-12 is the US equivalent), a few hours a week with a dedicated teacher for those hours. Okay, that teacher doesn't really grok math (gives the answers to the really hard questions, with 9 years olds ;), but the extra sessions with the peers combined with attention at home give good results on standardized tests plus exactly that enthousiasm that I'm hoping for.
For me it's clearly at home. My dad loved math and statistics, taught me concepts from a young age and a generation on I try to pass that on to my children. Given their aptitude and results it seems to work. I don't much believe that "some people just can't grok math" other than a basic correlation with IQ. I think we don't lay the foundation right for kids struggling with math since they have to follow or be dragged along a median path.
If mathematical enthousiasm is mostly developed at home, do American parents have or take less time to give kids that enthousiasm?
My kids get extra schooling in math in school (K-12 is the US equivalent), a few hours a week with a dedicated teacher for those hours. Okay, that teacher doesn't really grok math (gives the answers to the really hard questions, with 9 years olds ;), but the extra sessions with the peers combined with attention at home give good results on standardized tests plus exactly that enthousiasm that I'm hoping for.
> If mathematical enthousiasm is mostly developed at home, do American parents have or take less time to give kids that enthousiasm?
I am going to say something controversial when we see the the success of former soviet countries in Maths and the lack of success in central Europe and North America, despite the resources, to me, there appears to be a difference in how schooling handles suffering/frustration in those cultures.
What I mean is that often the process of learning maths needs frustration and sometimes feeling overwhelmed and you have to stay with it, until your brain re-organizes and things click.
In most western cultures there is a general sense that all learning should be fun and interesting and that children should be sheltered from frustration. I agree with it for the most part as a general principle, but I don't believe that works with the re-wiring needed to _understand_ topics in mathematics.
I am going to say something controversial when we see the the success of former soviet countries in Maths and the lack of success in central Europe and North America, despite the resources, to me, there appears to be a difference in how schooling handles suffering/frustration in those cultures.
What I mean is that often the process of learning maths needs frustration and sometimes feeling overwhelmed and you have to stay with it, until your brain re-organizes and things click.
In most western cultures there is a general sense that all learning should be fun and interesting and that children should be sheltered from frustration. I agree with it for the most part as a general principle, but I don't believe that works with the re-wiring needed to _understand_ topics in mathematics.
> success of former soviet countries in Maths [...] there appears to be a difference in how schooling handles suffering/frustration in those cultures
I agree with what you wrote, but there is yet another part of the puzzle, various extracurricular educational activities. Things like the International Mathematical Olympiad, which during its first two decades was mostly an Eastern Bloc thing; or the Russian popular-science magazine for kids, Kvant.
I suspect that these extracurricular activities were more responsible for the peak math performance in former Soviet Union and Eastern Europe that whatever was happening at schools. Mere school knowledge was never enough to win the math olympiad.
Going further, the reason why so much energy was spent in this direction, was that mathematics and physics were the only sciences that you could do in former soviet countries without risk of accidentally saying something politically incorrect and bringing doom on yourself and your family. (As far as I know, there was nothing in math comparable to e.g. Lysenkoism in biology. And humanities were pure ideology.) The smart people couldn't become entrepreneurs anyway, so many of them enjoyed teaching math and physics; it provided them a parallel universe they could escape to.
I agree with what you wrote, but there is yet another part of the puzzle, various extracurricular educational activities. Things like the International Mathematical Olympiad, which during its first two decades was mostly an Eastern Bloc thing; or the Russian popular-science magazine for kids, Kvant.
I suspect that these extracurricular activities were more responsible for the peak math performance in former Soviet Union and Eastern Europe that whatever was happening at schools. Mere school knowledge was never enough to win the math olympiad.
Going further, the reason why so much energy was spent in this direction, was that mathematics and physics were the only sciences that you could do in former soviet countries without risk of accidentally saying something politically incorrect and bringing doom on yourself and your family. (As far as I know, there was nothing in math comparable to e.g. Lysenkoism in biology. And humanities were pure ideology.) The smart people couldn't become entrepreneurs anyway, so many of them enjoyed teaching math and physics; it provided them a parallel universe they could escape to.
This is especially puzzling in presence of advanced athletics in the West and especially US. People have no problem saying "no pain, no gain" or admitting some have great genetics for sports. But as soon as it comes to mental prowess there's no aptitude, no training and nobody can fail. If a student doesn't understand something it's the teacher's fault. Oh, and rich and white kids succeed in school because their parents apparently do their homework. Parents in the USSR, with few exceptions, would laugh at their children if they asked them to do homework. Ones that did had been neurotic types who believed their child is a misunderstood genius who is being picked on by teachers.
> A question for the mathematically inclined / advanced: Where do you feel your interest in math was mostly developed?
I liked math because it was easy. And then I continued to like math because it continued to be easy. Then at a phd level and you had to write papers and do other tedious things etc, I realized I didn't care that much and learned programming instead.
I liked math because it was easy. And then I continued to like math because it continued to be easy. Then at a phd level and you had to write papers and do other tedious things etc, I realized I didn't care that much and learned programming instead.
My dad barely passed college algebra and my mom studied early childhood education. I had literally zero home enrichment in math. But I was put in "Gifted & Talented" in 4th grade. Ended with Ph.D. in Applied Math.
Did you have stimulating parents, or a teacher, or was it purely on grit? I’m interested!
Good teachers. But mostly interest. I wouldn't even call it grit because it wasn't hard for me.
> mathematically inclined / advanced: Where do you feel your interest in math was mostly developed?
I did pretty bad in primary school, mostly because I never did/turned in any of the homework. Whenever we took tests, I did well, but enough of my grade depended on homework assignments that my test scores didn't make up the difference. I always did well on the standardized aptitude tests (back then it was the CTBS tests) - well enough that they had to place me in the "gifted" program. That didn't actually mean anything at my school - you didn't go to different classes and weren't separated from everybody else; it was just a label applied to everybody who scored above a certain percentage on the standardized tests.
And man, did I hate math. I hated doing the never-ending worksheets of long division and thought math meant miserable drudgery. About halfway through 8th grade, I had the opportunity to start taking joint-enrollment classes at a community college. They taught me algebra there and that was when I started to enjoy math. I think a lot of that had to do with being able to move at a reasonable pace through the material rather than spending an entire year on long division.
I did pretty bad in primary school, mostly because I never did/turned in any of the homework. Whenever we took tests, I did well, but enough of my grade depended on homework assignments that my test scores didn't make up the difference. I always did well on the standardized aptitude tests (back then it was the CTBS tests) - well enough that they had to place me in the "gifted" program. That didn't actually mean anything at my school - you didn't go to different classes and weren't separated from everybody else; it was just a label applied to everybody who scored above a certain percentage on the standardized tests.
And man, did I hate math. I hated doing the never-ending worksheets of long division and thought math meant miserable drudgery. About halfway through 8th grade, I had the opportunity to start taking joint-enrollment classes at a community college. They taught me algebra there and that was when I started to enjoy math. I think a lot of that had to do with being able to move at a reasonable pace through the material rather than spending an entire year on long division.
> Where do you feel your interest in math was mostly developed?
First at home. I remember doing division by 7 and being fascinated by how the decimals repeat, before I started elementary school. Later: math books, math competitions, and math camps where university students explained advanced math concept to small kids using simple words.
I also learned a few interesting math things at high school, but it was a small part of the whole, maybe 10% or 20%.
In my opinion, to be good at math requires a combination of IQ + motivation + good learning resources. With low IQ, some things are simply too difficult or too abstract. Without motivation, you will not spend the necessary time and effort. Good learning resources (books, tutors, videos, whatever) will remind you of things you haven't considered yet, and will help you solve difficult problems by giving you easier problems first.
In perfect case, educational system should provide as good learning resources as possible, and perhaps also some motivation. It can do nothing about IQ. There is a possibility that kids with average IQ would do much better than now; but kids with high IQ would do even better.
First at home. I remember doing division by 7 and being fascinated by how the decimals repeat, before I started elementary school. Later: math books, math competitions, and math camps where university students explained advanced math concept to small kids using simple words.
I also learned a few interesting math things at high school, but it was a small part of the whole, maybe 10% or 20%.
In my opinion, to be good at math requires a combination of IQ + motivation + good learning resources. With low IQ, some things are simply too difficult or too abstract. Without motivation, you will not spend the necessary time and effort. Good learning resources (books, tutors, videos, whatever) will remind you of things you haven't considered yet, and will help you solve difficult problems by giving you easier problems first.
In perfect case, educational system should provide as good learning resources as possible, and perhaps also some motivation. It can do nothing about IQ. There is a possibility that kids with average IQ would do much better than now; but kids with high IQ would do even better.
Government school.
In home I had no one to teach me maths (parents had elementary school education and doing farming work).
But here in India government schooling is pretty good if you have interest to learn. Everything from textbooks was free.
What we were told was, until 10th grade, to learn English and Mathematics properly. Then I got into CS and that's a different story.
Government school teachers were pretty good, I learned a lot of English, science and mathematics from books in libraries and borrowed by other people as well.
Still not comparable to those who could crack olympiads and high level exams, but it doesn't take spoon feeding from 5 years of age, to grow an interest in math.
In home I had no one to teach me maths (parents had elementary school education and doing farming work).
But here in India government schooling is pretty good if you have interest to learn. Everything from textbooks was free.
What we were told was, until 10th grade, to learn English and Mathematics properly. Then I got into CS and that's a different story.
Government school teachers were pretty good, I learned a lot of English, science and mathematics from books in libraries and borrowed by other people as well.
Still not comparable to those who could crack olympiads and high level exams, but it doesn't take spoon feeding from 5 years of age, to grow an interest in math.
Wait, so the idea to close the gap is to lower the standards so you need less effort to score better?
Well the problem that we're trying to address here is inequality of outcomes. Grading people against how intelligent we would expect them to be tends to be too obvious, and going out of our way to cognitively impair some of the them would be too controversial, so our only option for the time being is to redefine what attainment is.
> Wait, so the idea to close the gap is to lower the standards so you need less effort to score better?
No, its not.
No, its not.
Yes it is, as you will now be unable to jump ahead in math. Also, algebra is going to be de-emphasized as the soft goal of junior high.
> Yes it is
No, it is not.
> as you will now be unable to jump ahead in math. Also, algebra is going to be de-emphasized as the soft goal of junior high.
Changing how performance above the standards is responded to is not lowering the standards.
No, it is not.
> as you will now be unable to jump ahead in math. Also, algebra is going to be de-emphasized as the soft goal of junior high.
Changing how performance above the standards is responded to is not lowering the standards.
> No, it is not.
> No, its not.
There's no point in having a conversation if you think explaining yourself is a step too far.
> No, its not.
There's no point in having a conversation if you think explaining yourself is a step too far.
> There's no point in having a conversation if you think explaining yourself is a step too far.
Er, I did explain myself in the part you didn't quote.
But, there is no conversation if reading beyond the first three words of a post is a step too far...
Er, I did explain myself in the part you didn't quote.
But, there is no conversation if reading beyond the first three words of a post is a step too far...
is that the idea, or is that how it's being framed? It could also be to raise the standards so that low-performing students in the class are held to a higher bar.
Getting rid of calculus is lowering standards.
>The draft rejected the idea of naturally gifted children, recommended against shifting certain students into accelerated courses in middle school and tried to promote high-level math courses that could serve as alternatives to calculus, like data science or statistics.
>The draft rejected the idea of naturally gifted children, recommended against shifting certain students into accelerated courses in middle school and tried to promote high-level math courses that could serve as alternatives to calculus, like data science or statistics.
okay that is true, and I will absolutely die on the "calculus is a crucial part of math education" hill
I do think there could be a benefit to reducing "gifted"/"accelerated" classes before high school, though, which is something that 1. could be framed as either raising or lowering standards and 2. the general public seems to have a visceral reaction to. that's more what I was addressing
I do think there could be a benefit to reducing "gifted"/"accelerated" classes before high school, though, which is something that 1. could be framed as either raising or lowering standards and 2. the general public seems to have a visceral reaction to. that's more what I was addressing
I think it is understandable for people to have a visceral reaction to even the idea of limiting their kids' potential. I do not see how reducing gifted/accelerated classes can be framed as raising standards though. The standards are the standards, they do not have anything to do with a child's age.
i mean it in the sense of not being okay with underperforming students year after year such that they drag their peers down. have higher standards for the whole class from the start, otherwise problems compound. This is what we have now, where every year basic concepts that should already be understood need to be rehashed for half the year before moving on to actual new material
there are bound to be truly exceptional students that far outpace everyone else, but in those cases i dont think its entirely fair to expect schools to fully accommodate such outliers. historically such prodigies resort to self-study
there are bound to be truly exceptional students that far outpace everyone else, but in those cases i dont think its entirely fair to expect schools to fully accommodate such outliers. historically such prodigies resort to self-study
> but in those cases i dont think its entirely fair to expect schools to fully accommodate such outliers
This sentiment would equally support removing special education programs for students with learning disabilities, yet those are not being called into question.
This sentiment would equally support removing special education programs for students with learning disabilities, yet those are not being called into question.
100% this. Why aren’t we doing full inclusion then? (Another thing they want but can’t have because of all of the spedbux they get from the Feds.)
I agree with your first paragraph, but I think there are significant political and logistic headwinds to being able to solve that problem in the classroom. Namely, I think it is a sociopolitical problem starting at home that is far greater in scope than a school can provide a solution for.
So while schools have to keep passing kids that should be failing for reasons outside of their control, I think the next best option is to keep giving those who can advance quicker an option to keep advancing quicker.
So while schools have to keep passing kids that should be failing for reasons outside of their control, I think the next best option is to keep giving those who can advance quicker an option to keep advancing quicker.
For schools already offering Calculus, offering support to outliers simply means moving them to the Calculus class when they are ready. For other schools it means allowing students to get high school credit from college courses.
In the case of some Californian schools, over half their math faculty may already be Calculus teachers, and in the incoming junior high, over half the students may be on track to take Calculus. We should not think of students with the potential to reach Calculus as outliers.
In the case of some Californian schools, over half their math faculty may already be Calculus teachers, and in the incoming junior high, over half the students may be on track to take Calculus. We should not think of students with the potential to reach Calculus as outliers.
Why would you say reducing accelerated classes could be a good thing?
I had no such thing in school, but being bored had a huge part in school being hell for me. I read about schools for gifted children and dreamed about how cool it would be to be on such a school (not that I would necessarily have qualified, mind you).
I am personally in favor of teachers having high expectations from pupils, that they can rise to meet.
I had no such thing in school, but being bored had a huge part in school being hell for me. I read about schools for gifted children and dreamed about how cool it would be to be on such a school (not that I would necessarily have qualified, mind you).
I am personally in favor of teachers having high expectations from pupils, that they can rise to meet.
"Gifted" is potentially misleading, as California largely does not have the same system as the one being removed in NYC. In many Californian schools under the common core, you are allowed to jump forward in math depending on your performance on standardized tests.
But jumping ahead in math does not mean you are now part of a gifted & talented program.
But jumping ahead in math does not mean you are now part of a gifted & talented program.
But how far does that definition of calculus go, on your hill? Is it being able to perform single-digit additions in your head? Rote memorization of the 1-10 multiplication tables? Remembering the squares of 1 through 25? Performing division of 7-digit numbers in your head?
I don't think that any of that is crucial to math education by itself, but having an affinity with numbers (rather, an intuitive sense of magnitude) is very beneficial to understanding the more advanced concepts. The open question (at least to me) is whether that understanding is nurtured best by calculus, geometry or Cartesian graphs.
I don't think that any of that is crucial to math education by itself, but having an affinity with numbers (rather, an intuitive sense of magnitude) is very beneficial to understanding the more advanced concepts. The open question (at least to me) is whether that understanding is nurtured best by calculus, geometry or Cartesian graphs.
You described arithmetic, not calculus [1].
https://en.wikipedia.org/wiki/Calculus
https://en.wikipedia.org/wiki/Calculus
Ah, thanks!
[deleted]
Honestly, at a high school level, I wish a lot of calculus concepts (and non-calculus concepts) got cut in favor of delving deeper into algebraic concepts. So many things only get taught at a surface level that I ended up just needing them retaught in college anyway.
> I will absolutely die on "calculus is a crucial part of math education"
Pro tip: your life is more important than that.
Pro tip: your life is more important than that.
Not teaching calculus in secondary schooling is not lowering standards if it replaced with something equally or more important.
Math isn't political. Math is Math.
All this abstraction is just excuses and bandages for why the USA is falling behind compared to China, Japan, Russia, Philippines and more.
It's just sad. 1+1=2. It shouldn't equal 11 or whatever political current events of the day are.
All this abstraction is just excuses and bandages for why the USA is falling behind compared to China, Japan, Russia, Philippines and more.
It's just sad. 1+1=2. It shouldn't equal 11 or whatever political current events of the day are.
The USA is not falling behind those countries. It’s in healthier shape than all of them.
This is what a dying country looks like. The ship is sinking, and we're arguing about whether the scrollwork above the bar is cultural appropriation.
100% Agree.
Knowing what I know of math now, having the high level high school math class be statistics or data science instead of calculus would have changed my life.
"data science" is not a field of math. lord knows the term does not need to be watered down further. is "statistics" not adequate (in a high school context)? (I'm not singling you out - they have a "Data Science" section in the proposed California mathematics education framework)
while I do agree that statistics education should be much more heavily emphasized, I still believe it and calculus should both be taught. Understanding the basic ideas of calculus opens a lot of doors in other fields of study. Hell, "data science" math would necessarily involve understanding calculus and optimization
while I do agree that statistics education should be much more heavily emphasized, I still believe it and calculus should both be taught. Understanding the basic ideas of calculus opens a lot of doors in other fields of study. Hell, "data science" math would necessarily involve understanding calculus and optimization
I think you can decompose a calculus course into three key components; principle/concepts, proofs, and procedurally solvable math problems.
All three have value but clearly the math problem aspect of it has depreciated in value due to calculators, wolfram alpha, etc yet it tends to remain the focus of many math curriculums. Calculus by its nature is more computationally intensive, meaning that it has experienced the greatest decline. If you really think about it, that curriculum was designed for an era when we called human "computers". There is probably opportunity to make calculus a more broadly valuable class by deemphasizing the mechanics and focusing on the principles and proofs.
All three have value but clearly the math problem aspect of it has depreciated in value due to calculators, wolfram alpha, etc yet it tends to remain the focus of many math curriculums. Calculus by its nature is more computationally intensive, meaning that it has experienced the greatest decline. If you really think about it, that curriculum was designed for an era when we called human "computers". There is probably opportunity to make calculus a more broadly valuable class by deemphasizing the mechanics and focusing on the principles and proofs.
What calculus class did you take? I don't think that there are many calculus classes where computation is a significant part. Rather you learn how to work with and translate equations, but there is little about methods for manually calculating integrals or derivatives by hand with different approximation methods etc. Basically nobody learns that properly today. And the tiny part of the course is the part where you learn and get intuition for the "Area under curve" concept, which is extremely important for basically everything.
How far can you get in statistics without any calculus? Or do you just take the normal distribution as given?
Depends on how much handwaving you're willing to tolerate. There's definitely some useful statistics you can do without showing the integral sign.
One could similarly say "How far can you get in statistics without measure theory? Or do you just take the definition of random variable as given?". It's still hand-waving, just at a different level.
One could similarly say "How far can you get in statistics without measure theory? Or do you just take the definition of random variable as given?". It's still hand-waving, just at a different level.
The statistics I took in college just had Intermediate algebra, and trig. as a prerequisite.
Huge agreement. Calculus is one branch on the tree of mathematics and one of the more useless ones in modern society (that can be taught to HS students).
How can you understand statistics without understanding basic calculus? e.g. Central Limit Theorem, probability density functions, etc.
>How can you understand statistics without understanding basic calculus?
Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?"
And yet some college degree requirements (e.g. Business Admin) do let students take Calc I without Real Analysis.
Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas.
We can expose people to many statistics topics such as Bayesian reasoning without calculus.
There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea.
Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?"
And yet some college degree requirements (e.g. Business Admin) do let students take Calc I without Real Analysis.
Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas.
We can expose people to many statistics topics such as Bayesian reasoning without calculus.
There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea.
> Because "understand" has different levels. Your question can be reworded for Calculus itself: "How can one one understand calculus without understanding Real Analysis?"
I agree, but I think with the tools and technology we have today, I think more can be expected of kids. There are countries where every high school graduate is expected to have some experience with calculus.
Maybe in 50 years, real analysis will be in the purview of high schoolers, just like 50 years ago, and programming was not.
> Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas.
I probably do have that bias, but I think a lot of things taught in school are automated away, yet they are still taught to teach “how to think”. There is software that spits out areas of circles and spheres and regression models and p values, but I would think the goal is still to provide as much background as possible to build as accurate of a model of the world as possible.
> There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea.
I can see Linear Algebra being useful too, but I would actually hope high schoolers are graduating with introductions to both Calculus and Linear Algebra.
I agree, but I think with the tools and technology we have today, I think more can be expected of kids. There are countries where every high school graduate is expected to have some experience with calculus.
Maybe in 50 years, real analysis will be in the purview of high schoolers, just like 50 years ago, and programming was not.
> Your question has the following bias because you happen to know both <X> and <Y>, so you then believe <Y> can't be taught without <X>. But we do that all the time at all ages. E.g. we teach kids how to find area of circles and spheres -- without teaching them calculus methods to derive those formulas.
I probably do have that bias, but I think a lot of things taught in school are automated away, yet they are still taught to teach “how to think”. There is software that spits out areas of circles and spheres and regression models and p values, but I would think the goal is still to provide as much background as possible to build as accurate of a model of the world as possible.
> There are several college professors of Calculus that also agree that substituting Statistics or Linear Algebra for Calculus at the high school level is not a bad idea.
I can see Linear Algebra being useful too, but I would actually hope high schoolers are graduating with introductions to both Calculus and Linear Algebra.
>the goal is still to provide as much background as possible
Sure, we can say that as an ideal but we still have to convert the "as much background as possible" into an actionable concrete curriculum.
The issue is a finite amount of time to teach a list of topics and the bias in 99% of recommendations is to always say "kids should be taught X" but we never frame it in the opposite way to reveal the inherent tradeoffs : "kids should be denied being taught Y so that time is used to teach X":
In other words, any recommendation that kids "must learn topic X" means we're silently omitting Y. It's an inherent optimization problem of what to do with limited time window in classrooms. That's why some college Calculus professors recommend switching out Calc I for a Statistics/LinearAlgebra. They're not saying calculus is unimportant. Instead, they're treating it as optimizing the best bang-for-the-buck math topics for 17-year olds.
We can do a lot of radical thinking regarding optimization of high school curriculums. E.g. I've always thought that a semester of dissecting advertisements in newspapers and tv commercials and how they manipulate you would be an excellent class for teenagers. But devoting time to that comes at the expense of something else. Therefore, I'd recommend substituting Shakespeare's plays Romeo & Juliet and Julius Caesar with "Media Manipulation Studies" but of course, some people would complain "how can you possibly understand Western Civilization and humanities without studying Shakespeare?!?". Maybe true but making kids study Shakespeare also means we're denying them <Other_Really_Important_Topics> because there's always a constraint of finite time.
Sure, we can say that as an ideal but we still have to convert the "as much background as possible" into an actionable concrete curriculum.
The issue is a finite amount of time to teach a list of topics and the bias in 99% of recommendations is to always say "kids should be taught X" but we never frame it in the opposite way to reveal the inherent tradeoffs : "kids should be denied being taught Y so that time is used to teach X":
In other words, any recommendation that kids "must learn topic X" means we're silently omitting Y. It's an inherent optimization problem of what to do with limited time window in classrooms. That's why some college Calculus professors recommend switching out Calc I for a Statistics/LinearAlgebra. They're not saying calculus is unimportant. Instead, they're treating it as optimizing the best bang-for-the-buck math topics for 17-year olds.
We can do a lot of radical thinking regarding optimization of high school curriculums. E.g. I've always thought that a semester of dissecting advertisements in newspapers and tv commercials and how they manipulate you would be an excellent class for teenagers. But devoting time to that comes at the expense of something else. Therefore, I'd recommend substituting Shakespeare's plays Romeo & Juliet and Julius Caesar with "Media Manipulation Studies" but of course, some people would complain "how can you possibly understand Western Civilization and humanities without studying Shakespeare?!?". Maybe true but making kids study Shakespeare also means we're denying them <Other_Really_Important_Topics> because there's always a constraint of finite time.
I agree with what you are saying, especially your last paragraph. I guess I would have to modify my point to say that whatever is being replaced needs to be for the purposes of making the students’ model of the world more accurate.
But if it is being done because a subject is too hard and making the population look bad (since other countries seem to manage just find with the same topic), then I would have a problem with that. Which is what it seems like in the California proposal.
But if it is being done because a subject is too hard and making the population look bad (since other countries seem to manage just find with the same topic), then I would have a problem with that. Which is what it seems like in the California proposal.
In my limited experience, it's natural to learn things by looking at a problem I want to solve, looking at solutions, and then looking at how to adapt solutions. That's pretty much a high-level to low-level progression. Once you reach a low-level understanding (calculus in this example) that opens a lot of doors, but it's hard for me to imagine starting there. That said I've never been good at schools and this experience is from learning on my own. I think there are people who have found ways to make "low to high-level" learning work well for them.
You don't need to take an entire year or semester of calculus to understand statistics.
You don't need to take an entire year or semester of statistics to understand statistics either if you put the bar that low. Basic statistics is already taught to most kids and there isn't much value in teaching them more complex formulas without also teaching them the needed background to properly understand those formulas.
> there isn't much value in teaching them more complex formulas without also teaching them the needed background to properly understand those formulas.
We'll just have to agree to disagree. I believe with a strong background in algebra and simply knowing how to take an integral and derivative you can go far in stats. Will you be an expert? Obviously not, but high school level stats knowledge can easily be attained.
We'll just have to agree to disagree. I believe with a strong background in algebra and simply knowing how to take an integral and derivative you can go far in stats. Will you be an expert? Obviously not, but high school level stats knowledge can easily be attained.
But what is the point? Formulas get forgotten, the class needs to teach them a concept or it wont stick. Calculus at least teaches people how to think about rate of change and slopes, what would a statistics class teach? Probabilities and event chains is already in the base curriculum before calculus, so it isn't that, and I don't see how learning about the normal distribution and the formulas for different statistical tests would help them at all in life.
The people who need it already takes statistics, and nobody else needs to learn those formulas, and just learning those formulas doesn't teach you to understand statistics (as we can see how they get heavily abused in every non-quantitative field).
Edit: Now from this discussion, I just realized that the fields that abuse statistics a lot are also the fields that doesn't require you to learn calculus. So maybe calculus is needed to understand statistics after all?
The people who need it already takes statistics, and nobody else needs to learn those formulas, and just learning those formulas doesn't teach you to understand statistics (as we can see how they get heavily abused in every non-quantitative field).
Edit: Now from this discussion, I just realized that the fields that abuse statistics a lot are also the fields that doesn't require you to learn calculus. So maybe calculus is needed to understand statistics after all?
A bit misinformed. Differential equations form the backbone of much of the following: simulations, animations, fluid dynamics, FEA, financial modeling etc. A lot of computing is numerical methods and needs significant calculus knowledge.
Sure, but you don't need to spend 32 weeks learning 10 different ways to do integrals which is what our calculuses classes would teach. Learn the concepts of derivatives and integrals and then move on to the actually interesting stuff you just mentioned here.
You can't skip those steps without overwhelming your students. Advanced classes are already seen as hard even when students have practiced all this math a lot, remove the practice and you'll make the class impossible to pass for almost everyone.
I'll just continue to disagree, I guess. I was able to learn algebra just fine even though I didn't know my multiplication tables, while the rest of the class spent a year memorizing them. Our methods of deciding when someone "knows" something so they can "pass" needs to be radically rethought. We spend all our time practicing how to integrate by parts when in reality a computer will do that for you, and youre needed for higher level thinking and abstractions that the math classes don't bother to get to until graduate school. Sad imo.
There have been countless experiments along your lines of thinking, none of them has actually worked well at scale. If you think that educators love math, then think again, almost every teacher hated math when they were a student just like you do. And even though they hate it we still have it in its current form, that really tells you a lot about its merits.
Competitive high schools already offer statistics and data science. The question is not whether schools ought to offer statistics, but whether the state ought to require that children cannot jump forward into statistics or Calculus (or any class whatsoever) regardless of their readiness.
Hindsight is 20/20. As an undergrad in the 90s I distinctly remember the
stats major had fewer than fifty students, and I went to a big university.
> statistics instead of calculus would have changed my life.
This sounds really extreme, what makes you think a statistics class would have changed your life?
This sounds really extreme, what makes you think a statistics class would have changed your life?
Please explain me how you can have maximum likelihood estimator or cumulative distribution function without calculus.
In what way?
“ reject the idea that some children are naturally gifted”
as a father of a gifted kid this make me angry!
Why is it ok to say some kid are one standard deviation below the curve and need special class and teacher.
But it’s not ok to say some student are also one standard deviation above the curve and also bold special class and teachers?
as a father of a gifted kid this make me angry!
Why is it ok to say some kid are one standard deviation below the curve and need special class and teacher.
But it’s not ok to say some student are also one standard deviation above the curve and also bold special class and teachers?
If you reject the idea that anybody is "naturally gifted", you must also reject the idea that anybody is smarter than anybody else, unless you want to waste everybody's time on meaningless semantics and pretend that the word "smart" doesn't mean what everybody uses it to mean… but wasting time on meaningless semantics is a popular pastime these days! I can understand why some people hate to face the fact that some people are smarter than some other people (maybe even themselves!) and I'm honestly surprised that this has only become a societal problem recently.
> Why is it ok to say some kid are one standard deviation below the curve and need special class and teacher.
Because it doesn't offend the families of the average children, who make most of the population.
Because it doesn't offend the families of the average children, who make most of the population.
Look at that misleading headline, and then continue to trust the NYT.
What is misleading about the headline?
It's not about the "Gap in Math", it is about ideology with regard to social justice, withdrawing support from gifted children, removing difficult topics. They don't want to help kids catch up, they want to make sure nobody can get ahead. The Backlash is not against helping out "poor" kids, it is against hampering the progress of talented kids.
I think we are nearing the point where "liberals" or "the left" would have to meet reality.
"reject the idea that some children are naturally gifted"
That's simply not true, empirically not true. Clearly some children are naturally gifted in math, ability to play music, drawing, computer programming, sport, learning foreign languages and so on.
Obviously we can ignore reality, in the same way as not-so-long dead communistic block ignored reality of economy, but this always end up in the same way - reality wins, soon or later, but the price of learning this is typically rather high.
The tragic part here is that obviously rich kids will go to private schools that will let them develop their skills and talents. Those who will be hurt are gifted kids from poor families.
"reject the idea that some children are naturally gifted"
That's simply not true, empirically not true. Clearly some children are naturally gifted in math, ability to play music, drawing, computer programming, sport, learning foreign languages and so on.
Obviously we can ignore reality, in the same way as not-so-long dead communistic block ignored reality of economy, but this always end up in the same way - reality wins, soon or later, but the price of learning this is typically rather high.
The tragic part here is that obviously rich kids will go to private schools that will let them develop their skills and talents. Those who will be hurt are gifted kids from poor families.
Math is racist because thinking is hard
> According to data from the Education Department, calculus is not even offered in most schools that serve a large number of Black and Latino students.
The data mentioned does not show if the problem is in the schools or the Black/Latino students picking such schools.
The data mentioned does not show if the problem is in the schools or the Black/Latino students picking such schools.
Students don't typically pick their high schools. They're sorted into one based on their address. Transfers are possible, within enrollment limits, and subject to a parent's willingness to go through the paperwork, but they're certainly not the norm.
I'm going to guess you just have no idea how schooling works in the US. Otherwise I'd be super interested in your theory that the poorest parents are spending resources to take their kids out of their way to shittier schools.
I'm not an American, so can you tell me? Don't you have some sort of state or national standards every school has to cover?
No. Every state is different, and even within states, every county/city can be different, and even within county/city, different school districts can be different. My city of 200k people has two different school districts led by different people. I am assuming there are some standards tied to federal government funding, or maybe standards at the state level.
Generally though, you want to live in the more expensive parts of town because those schools will be better managed (and obviously have a more capable cohort of students due to them being kids of richer parents). When buying a house, the basic question all couples with kids face is "what is the least expensive house in the most expensive neighborhood" in order for their kids to attend the better schools (assuming the parents are not rich enough to send them to $20k+ per year private schools).
It is one of the reasons the SAT and Advanced Placement test scores is (or was back in my day) so prominent in determining admittance to college. They are optional tests that kids take to show their proficiency.
Generally though, you want to live in the more expensive parts of town because those schools will be better managed (and obviously have a more capable cohort of students due to them being kids of richer parents). When buying a house, the basic question all couples with kids face is "what is the least expensive house in the most expensive neighborhood" in order for their kids to attend the better schools (assuming the parents are not rich enough to send them to $20k+ per year private schools).
It is one of the reasons the SAT and Advanced Placement test scores is (or was back in my day) so prominent in determining admittance to college. They are optional tests that kids take to show their proficiency.
Sort of, it's complicated, but that's also not related to what GGP said? They were claiming parents could choose schools, which is not true (at least, in most of the US). Whether schools are pf consistent quality (they aren't really) is a separate issue.
Don't students get to pick even in high school? High school is when education between kids starts to diverge so you need a way to select where to go at that stage, USA doesn't let you do that unless you pay for private school?
It depends -- in some areas there's schools called "magnet schools" that are public, free schools that you can test into. I went to a high school like that. In New York there's a lottery system for magnet schools instead of tests, I believe. However, magnet schools still have a "feeder area" like regular schools, just a larger one -- I drove ~45 minutes to my high school, whereas my regular high school was 10 minutes away.
A lot of this is due to how US schools are funded, which is primarily by property taxes. That plays into the strict location requirements, since you could imagine a small school funded by a small property tax base being overwhelmed by students from outside the school's tax base choosing to go there and not having funding to support them. It also plays into the quality discrepancies: wealthy areas have nicer houses and therefore pay higher property-tax-per-capita (sort of, there's also racial discrimination dynamics here), so schools in wealthy areas have more money per student and can hire better teachers, have better teacher:student ratios, nicer equipment, etc. There's some state/federal funding of schools I think, but most funding is from property taxes, at least in the places I've lived.
In general, I think most confusion non-Americans have about the US stems from confusion about how our government works: in a very real way schools are run by counties and towns, not federal or state governments. School boards are elected, and schools are mainly run on a local level. Asking why a student can't choose to go to a different school is a bit like asking why a German student can't choose to go to a French high school -- there's an administrative barrier between them.
A lot of this is due to how US schools are funded, which is primarily by property taxes. That plays into the strict location requirements, since you could imagine a small school funded by a small property tax base being overwhelmed by students from outside the school's tax base choosing to go there and not having funding to support them. It also plays into the quality discrepancies: wealthy areas have nicer houses and therefore pay higher property-tax-per-capita (sort of, there's also racial discrimination dynamics here), so schools in wealthy areas have more money per student and can hire better teachers, have better teacher:student ratios, nicer equipment, etc. There's some state/federal funding of schools I think, but most funding is from property taxes, at least in the places I've lived.
In general, I think most confusion non-Americans have about the US stems from confusion about how our government works: in a very real way schools are run by counties and towns, not federal or state governments. School boards are elected, and schools are mainly run on a local level. Asking why a student can't choose to go to a different school is a bit like asking why a German student can't choose to go to a French high school -- there's an administrative barrier between them.
Nope. You can choose classes within your school, but if you go to a shitty school you're out of luck. This is why initiatives like this are so important. And comments like the original one that started this thread are ignorant at best, and when made into a political viewpoint, oppressive.
Well, to me and probably many others it is unthinkable that students wouldn't be able to pick their high school. But thanks for explaining, now I think I understand better why American college is structured as it is. I always wondered why American colleges offered high school courses, but if students cannot reliably take high school courses then colleges needs to offer those to all the students who couldn't take them in high school.
This is also, in similar theme to my other comment, because high schools aren't standardized and have often wildly different curricula, even between high-quality high schools. Colleges do a ton of work to smooth this out, from offering high-school courses for freshmen to re-normalizing GPAs to account for different grading scales between schools.
It depends on the city and how they have setup admissions to the government high schools. Some cities allow people to apply to high schools not in their neighborhood. But for the vast, vast majority, your high school will be based on the address you live.
It is relatively common to use the address of a relative or friend in a richer part of town to get your kid in the nicer high school that you cannot afford to buy a house or rent an apartment in. My immigrant parents did that for me on multiple occasions.
It is relatively common to use the address of a relative or friend in a richer part of town to get your kid in the nicer high school that you cannot afford to buy a house or rent an apartment in. My immigrant parents did that for me on multiple occasions.
"The data mentioned does not show if the problem is in the schools or the Black/Latino students picking such schools"
This wording is so wrong. You can't say that the Black/Latino Students are the problem in any context. You can't say Race-People-problem. Can't.
This wording is so wrong. You can't say that the Black/Latino Students are the problem in any context. You can't say Race-People-problem. Can't.
Maybe emphasis on conceptual understanding vs. calculation is what we need to be driving at. Higher level math is not focused on getting exact answers. I always thought that starting out with set theory would be a better as it is the historical precursor calculus anyway. Most calculus courses seemed to be focused on the memorization of techniques that don't make much sense until you take an analysis course. Atleast set theory gives you a foundation for understanding probability which gives you a foundation for stats.
The problem is closed book exams, not calculus itself, right?
Have we ever considered the idea that teachers are to blame for the disparity?
As long as I've been alive and even further back, teaching has been peoples' "backup". It's not attracting the best and brightest, and now it attracts all these angry woke virgins who deliberately want to force communism into their classes.
I think it might be time to figure out some hard questions for the union to answer
As long as I've been alive and even further back, teaching has been peoples' "backup". It's not attracting the best and brightest, and now it attracts all these angry woke virgins who deliberately want to force communism into their classes.
I think it might be time to figure out some hard questions for the union to answer
[deleted]
More accurate title: "California seeks to turn Math education into anti-white, anti-intelligence propaganda devoid of any connection to reality. Few remaining sane people in state protest fruitlessly."
These people are monsters. They're literally tearing apart civilization (education of children is foundational) for the sake of their doomed ideology. If you can't see the parallels to the Soviet Union, you're either already drinking the kool-aide or incomprehensibly dense.
These people are monsters. They're literally tearing apart civilization (education of children is foundational) for the sake of their doomed ideology. If you can't see the parallels to the Soviet Union, you're either already drinking the kool-aide or incomprehensibly dense.
To be fair to Soviet Union (I'm from USSR/Russia), they were actually the reverse in that area, there were gifted programs, gifted schools where you would be tracked if you were good, competitions for school kids in many subjects (from history to physics) that would also track you to gifted schools or could earn an automatic college admission, etc. AFAIK even the classes in regular run-of-the-mill schools would sometimes be "semi-tracked", with most of the smarter/better behaved kids ending up in some classes and the less smart/worse behaved kids in others for the same age group, without any other differences (i.e. lessons would be more or less the same). Soviet Union was an evil empire, but it was not entirely dumb.
The modern progressives, on the other hand, are evil AND dumb.
The modern progressives, on the other hand, are evil AND dumb.
I feel bad for kids that will be the subjects of these social experiments. And if (when) the results aren't good, can you trust ideologically driven administrators to change their methods? [[it would be great if it ended up working well for the kids, but it's a huge risk especially at a public, state level]]
I was lucky enough to grow up in a system where gifted math kids could take classes at the local university, and from what I've heard this is common in various CA school districts as well. Hopefully, that won't be discouraged as I found it to be a huge positive being both much more interesting and good prep for university. It seems like the resources are widely available (in semi-rural/urban areas, and now online) to support kids with different learning speeds, styles, and interests. Holding back individuals, purely for the sake of raising the average, if that is their intention, is sick- learning isn't a zero-sum game, but should be the opposite.
I was lucky enough to grow up in a system where gifted math kids could take classes at the local university, and from what I've heard this is common in various CA school districts as well. Hopefully, that won't be discouraged as I found it to be a huge positive being both much more interesting and good prep for university. It seems like the resources are widely available (in semi-rural/urban areas, and now online) to support kids with different learning speeds, styles, and interests. Holding back individuals, purely for the sake of raising the average, if that is their intention, is sick- learning isn't a zero-sum game, but should be the opposite.
i agree with your new title, but also agree with the commentator below. Soviet Russia excelled in STEM which makes California public school education a tragic joke.
Russian School of Mathematics is very popular in Bay Area.I think there are branches all over the states(not sure). They exist solely for 'math enrichment of K-12 students'. The after school programs are tough and come highly recommended.
There is also 'Singapore Math' that I am not very familiar with but its supposed to be based on the very challenging Singapore Math curriculum.
Russian School of Mathematics is very popular in Bay Area.I think there are branches all over the states(not sure). They exist solely for 'math enrichment of K-12 students'. The after school programs are tough and come highly recommended.
There is also 'Singapore Math' that I am not very familiar with but its supposed to be based on the very challenging Singapore Math curriculum.
What does this have to do with Soviet Union? Soviet Union always had gifted student programs.
Lysenkoism, usually, when people refer to denial of reality in connection with the Soviet Union.
Also, there was a weird period when cybernetics was considered bourgeoise pseudo-science.
https://en.wikipedia.org/wiki/Bourgeois_pseudoscience
Late Stalinism is worth studying, if only to learn how twisted can an entire country become out of fear.
https://en.wikipedia.org/wiki/Bourgeois_pseudoscience
Late Stalinism is worth studying, if only to learn how twisted can an entire country become out of fear.
Yeah imagine a country getting freaked out over a few dozens of millions of dead and going crazy and passing a bunch of insane laws and having its politics go insane. It’s not like that doesn’t describe post 9/11 America.
The timing was a bit different though: first the country got crazy, then it passed a bunch of insane laws, then a few dozens of millions died, then they started WW2 (Molotov–Ribbentrop pact), and then a few more millions died.
I don't think denial of reality is something that would be strongly associated with SU, and not because it was not prevalent there, but because of its prevalence everywhere else.
No, Soviet Union only got these programs in 1960s, when it started to suffer fully from its sciences being based on the "scientific Marxism-Leninism" and unable to catch up with advances in the West.
In short, they’re Commies.
I am pretty sure I would have become a delinquent without it. I still flunked out of high school when I was 17 but I kept going as long as I did because the teachers were interesting and the coursework challenging (even if I never did much of it). Not all intelligent kids are studious by nature.