California moves to recommend delaying algebra to 9th grade statewide
sfstandard.com
sfstandard.com
applies social justice principles to math lessons
The inmates aren't running the asylum anymore; they're running the government. All I hope is that this cancerous ideology (I'll resist the prop65 joke...) doesn't grow any further than it already has. The decline is certainly sad to see and already rather visible.
1 - American school teach the alphabet before grade 1, and push kids to read early. German schools don’t even teach the alphabet until grade 1' yet by the end of that year the reading level of the kids is the same as US kids at the end of grade 1, or better. German Pädagogin justify this by saying there is some neural development issue — I think that is likely bull. But what I do recognize is that instead of being pushed to read before the kids are ready, the kids instead learn other valuable life skills. I happened to learn to read at age 5 (not in Germany nor USA) but that didn’t make me “better” than other kids; they did other things.
2 - kids who have parents who can afford tutors and such can push the kids through the prescribed steps sooner. Kids whose parents each have two jobs to get food on the table, well, they simply can’t. So the former define “higher standards” because they chose their parents well?
3 - To combine the two: if we can open up opportunities for all the kids aren’t we likely to end up with a larger pool of well educated people who will end up being the inventors, leaders, poets etc of the future? How many ramanujans are we leaving behind?
I’m not saying “throw out all the standards” but rather quite the opposite. I think your unidimensional absolutism is narrow and inadequate.
Instead of opening up opportunities for all the kids, this will ensure that no poor student can compete because the courses won't even be available.
After retaking calculus at Berkeley (which I admit is not exactly a local college), IMO they teach it here more rigorously (e.g. they introduce epsilon-delta fairly early, and they are precise about details like domains of functions, etc.)
The real place where Exeter shines is for competition math and for second/third year college math courses. But most of the people who seriously study competition math there have a strong math background to begin with, so I find it unlikely that someone who is inexperienced in math would actually pick up competition math as the culture is intimidating.
Also, very few students take second/third year college math. When I was there, they offered one term of topology and one term of real analysis. Each of these classes had one section of ~10 people. But in all honestly, only a few students in the class actually were mature enough to understand most of that material. Even though I was on the stronger side of students, I don't think I internalized the material at all.
I'm honestly really skeptical of pushing students to learn more and more "advanced" material because getting good at math isn't about being able to memorize mechanical rules for derivatives or integrals. Learning math should be about learning the process of discovery -- playing around with problems until you are able to tease out some insight or a solution. The skill of "distilling" a problem to its essence is one that has served me much more usefully than being able to find an integral.
The way I'd put it is the kids all need to learn things close to the pace that they can go. If there are kids who can go really fast, let them do that, find a teacher who teaches real analysis or whatever and let them get on with it.
On the other end of the scale, kids with difficulties need help too. Dyslexia needs to be discovered early, and anxieties related to learning need to be resolved.
Whether you think algebra is coming in too late or too early is not really the issue IMO, the idea of one-speed-fits-all is the real problem. I always wondered why education wasn't just a bunch of ladder steps. Pass a given course, get put on the next one asap. For all subjects, without cross-restrictions. For instance I'm still a relative beginner in creative writing, and I'll likely stay there, but I should be able to take some advanced math and coding courses.
I'll probably end up implementing this myself for my older kid via tutors, since he's interested in a lot of things above his year, but I think everyone would benefit if the system worked this way.
As you mention, poorer students are denied the opportunity to take more advanced classes. But even those who do are faced with a massive disadvantage.
See, top tier private schools shamelessly pass students unwilling to actually learn [1]. These same schools and parents subsequently leverage connections, wealth, etc. to insert their students into prestigious schools...where they continue to not learn math (and ultimately are hand-held to high-paying, white collar jobs, but that's another story)
Net result is unfilled higher math seats filled, and with that less math competence across society. Fewer thinkers advancing our perspective, etc.
Opportunities to access these materials is key, but providing consistent standards is just as important. If we can't do that with math, where?
[1] prior work with NE boarding schools, witnessed the contortions these institutions would go through to pass / give top marks to obviously unqualified students.
I multiple times heard from exchange students that the standard of the English curses they had in the US hand been below the standard of the English cursed they had Germany...
Which yes you could argue is somewhat out of context as the original discussion is for children around age 7.
To think ramanujans of this world would benefit from lower standards is also having no idea or never knowing one in real life.
Also even before you had schools which covered multiple of this schools and allow students to "move" between them, sometimes in a per-course level.
There also always had been ways to get the same degree as from a gymnasium even if you initially ended up on a hauptshule, through it was a often shitty path and potentially took you a bit longer. While a few people which state out in a realschole doing it was the norm, for people on a hauptschule it was very very very unlikely.
Don't get me wrong the German school system is a mess, especially if composed to some of the Nordic states but it still beats the US.
The system is quite fluid if you put in some effort.
Some snark: it is mostly intelectuals that dread at the thought and possible implication that not all people are meant to get an university degree.To achieve that goal they are willing to degrade all standards so that anyone can have a pretty paper in wooden frame.
These jobs are going away in the near future. Nowadays the only people who work in factories are highly skilled engineers with complex e.g. CNC skills and a heavy math background.
I have a personal corollary to the Dunning-Kruger effect: If you don't understand why something is difficult, you are completely clueless about it. And most things are difficult in some way.
Totally different. You just cant compare a phonetic language to one like English.
My daughter is now learning how to read in the best school in my city and its taking her over year compared to me. We started at roughly the same age, but she and her classmates are struggling through hours of practice.
“Thats a sharp e honey”
“That letter is silent, baby”
“You’ll never sound that out, that words just messed up”
EDIT - punctuation and mistypes
My story is just anecdote, not science, of course, as is yours.
I noticed that a number of the German parents had the same concerns as you, because they expected the spelling to be more phonetic. German orthography, like Spanish’s has changed over time to match pronunciation shifts. English does not. As a result English words often hold their roots. The trade off is that you may not knownthe pronunciation of an unfamiliar word but may be able to figure out its meaning. As with all languages, in the end none is “harder” than the other despite folklore: sharp corners are always being knocked off because the tool is so important and in continuous use.
In the most recent German spelling reform, the authors were concerned about this trade off.
Another way to describe it: you can’t approach writing c++ as if it were Java, and vice versa. Quite similar, yet quite different.
Likewise, I could mostly read English when I arrived in the new country despite not being able to say or understand a single word. This is because English is, maybe, 75% phonetic and I had already figured reading out.
Reading is not just memorizing characters and phonemes, but being able to join everything into a fluid mental motion. In english, practice of their fluidity is constantly being interrupted by an adult having to tell the kid which sound variation a vowel has
Why would that be bull? Kids brains develops over time.
I mean there isn’t a sharp delineation that magically happens; there are n factors (some large, unknown number) each of which develop at a slightly different rate in each child; there’s nothing magic about reaching 6. My opinion might reflect an accidentally rigid expression of this when my own kid was 6.
Thanks for your comment!
The thing is that you have to adjust curriculum to the developmental stage of the INDIVIDUAL child. Teaching someone too early only wastes the time, resources and money of that teaching. Too late and you lose future options.
I didn't learn to read until 1st grade but many of my peers learned in kindergarten. Individuals do NOT all reach the same learning readiness phase at the same time or same age (two different things).
BTW this "teacher's credential 101".
Systems like Montessori focus on this dynamic and thus have fairly open-ended schedules for things. Falling behind is defined by not meeting ANY learning goals but being on schedule is meeting enough learning goals.
Naturally customization of education like this does not fit well into a "School as a Factory; Child as a manufactured Part" model or the efficiency metrics that factories typically have that are similarly applied to public schools in the US (standardized testing is akin to process control; you do want some type of testing but it has to be structured with more nuance because children are not factory parts with narrow distributions of variance).
At this point, home schooling probably can't be worse. But more focus on customization of education is pretty essential. US Schools are 80%-90% focused on the bottom 10%-20% of IQ based on actual school budgets and funding. And for those not in that bottom group, it's all 100% uniformity and low budgets. One size can never fit all.
On the other hand getting as many people as possible especially those with developmental issues to a minimum standard allows them to function in society. That pays real long term dividends and is worth significant investment.
In your very own example, you went to a private school and did well. That's great, that's what's supposed to happen. What's currently happening in public schools is that too many resources are being allocated to the over achievers and not enough to the under achievers. There's not enough money to fund all programs, so you have to ensure you fund the most needy first.
But even if we have unlimited funding for lower education, what's the purpose? The vast majority of society isn't fit for a traditional university education. And even if they are, the vast majority of university students go on to achieve what, exactly?
Sure, some kids might not be able to achieve their dreams, welcome to the club. Is the dream of a life being a scientist or some such any better than the dream of being a professional skier or race car driver? We're not robots, we're people. The obsession with academic excellence has to end.
The fact that my parents had to pay for both the public school and some tuition for private school (I had financial aid) left a really bad taste in my mouth. On top of that, full tuition at the private school was less than the per-student cost of public school! To me, that is ridiculous.
Let's also mention that education is one of the best ways to climb the socioeconomic ladder. Advanced and higher education shouldn't only be available to those that are wealthy and/or have time to send their kids to extra schooling. Ensuring a high quality education in disenfranchised neighborhoods is one of the best tools we have for helping those people.
No matter how you frame it, I want children getting the best education that they can get. So if they're ready to achieve more, give it to them. We all, as a society, benefit.
Again, the funding is not unlimited. We're sacrificing some less than average students' learning for the sake of the small minority of above average students.
> Let's also mention that education is one of the best ways to climb the socioeconomic ladder.
Currently, that is true. But, does it have to be true? Should the only way to leave poverty be an above average education? There used to be plenty of blue collar jobs that paid a comfortable middle class wage, now there's not. You know the guy that started KFC? Did he go to college? No, he dropped out in the 7th grade. You used to be able to work hard and be successful.
> No matter how you frame it, I want children getting the best education that they can get. So if they're ready to achieve more, give it to them. We all, as a society, benefit.
Not every kid wants or needs more education.
And that’s a bad thing because? You where receiving exactly the kind of minimum education that was seemingly enough even if your grades where poor.
Remember life doesn’t hold your hand, self motivation is just as important for long term success as innate intelligence. Hand holding the academically gifted to cram as much as possible into young minds has been traded before it doesn’t actually seem to accomplish anything of note beyond excelling in artificial milestones like the Putnam.
Considering how many of todays highly effective knowledge workers where demoralized and demotivated in public school, you are talking about a short term effect. Personally I and many people at know greatly befitted from an easy public school education that enabled me plenty of free time to dive extremely deep into various personal projects. In comparison I took plenty of difficult electives in collage like Differential Equations for the fun of it, but thinking back I would have been better served with more free time.
I still remember coming up with the equivalent of the Bit Torrent algorithm in collage before BT was a thing, and thinking I just don’t have time to build it. In the wider context not a big deal, but don’t assume you can simply ramp things up without any cost.
While I agree with this, I suspect the social winds that led to this change, wouldn't put us on the path of creating individualized curriculum like you wanted. As gp mentioned, this change was motivated by social justice, and the same movement has called for getting rid of AP or other advanced material classes on the basis they're discriminatory (blacks/hispanics are underrepresented in them). I remembered a school district doing this sort of thing, but I can't find the link right now. That said, I did find a link of an entire province (!) dropping advanced classes under similar justifications: https://www.theglobeandmail.com/canada/article-ontario-to-en...
When considering the issue of individual variability in math ambition and readiness, it's more plausible to have a student who is ready for Geometry to move into a classroom where a teacher has already been polishing a year-long discourse on Geometry, as opposed to expecting any teacher to be ready for a discussion on Geometry.
Under Equitable Math this will not be possible. Instead, all students must always be at the same level up until the last year.
That is the largest problem with American schooling, is we try to keep all kids in a chronological age based system, instead of a skills based system.
> Sooner doesn’t necessarily imply “higher standard”
To be clear: I don't know enough detail about the proposal in California to judge it, but the idea that most children might be better off learning certain subjects at a later age, when they are more mature, cannot be dismissed a priori, without facts, based on ideological arguments.
Your comment reminds me of this passage from an old article about Finland's educational system, widely considered to be one of the best in the world:
> Children [in Finland] spend far more time playing outside, even in the depths of winter. Homework is minimal. Compulsory schooling does not begin until age 7. “We have no hurry,” said Louhivuori [a Finnish teacher]. “Children learn better when they are ready. Why stress them out?”
Text in brackets is mine. I highly recommend reading the whole article:
https://www.smithsonianmag.com/innovation/why-are-finlands-s...
Neither should it be accepted a priori. It would be a compelling reason to delay math instruction, if supported by evidence - but is there any evidence to support it?
And if improving education by delaying instruction until students are mature enough to handle the material is truly the goal, why delay instruction for students who are already mature enough to handle it sooner? Holding back students who are ready doesn't improve education for anyone.
But maybe what should be changed is the expectation. If the vast bulk of 8th graders aren't ready to handle algebra, don't create an expectation that "the smart kids" are taking algebra in 8th grade, because parents are going to be pushing their kids to be one of the smart kids (as measured by when they take algebra), and you're going to get a bunch of kids who aren't ready.
But this brings up a problem. Who decides if a kid is ready? The parents? The teachers? The school bureaucracy? On what basis do they decide?
Teachers seems like the best bet (they observe kids in the classroom all day), but they also have biases, blind spots, laziness, and so on. I don't know that it's possible to build a system where it happens "as it should" all the time.
>> Sooner doesn’t necessarily imply “higher standard”
Thanks! The critical word in my comment was necessarily. Seems like most of the comments have been polar.
> To be clear: I don't know enough detail about the proposal in California to judge it
It is available online as are interviews with some of the people who wrote them, which include mathematics professors and other educators. Seems like most of the objections are from people who are reading the headlines and drawing immediate conclusions based on their preconceptions.
I have a nagging suspicion that the only way to reach broad agreement on whether the plan will work (or not) is... by trying it. Perhaps it can be tried on a small number of schools at first, and then gradually expanded to more schools if the results are promising, or nix the whole plan and revert to the old ways otherwise. I would propose starting with the schools that enroll children closely related to the authors of the plan.
Whether this indeed is the case, need to be discussed separately for each topic.
> Finland's educational system, widely considered to be one of the best in the world
Finland achieves good education of the average student by sacrificing the potential of the best. For example, look at their results at international mathematical olympiad: the last (and only) time they had a gold medal was in 1981. They are below-average not just compared to the developed countries, but globally. This is intentional; Finnish students who are "too good" at math are strongly advised to focus on other subjects instead.
https://www.imo-official.org/country_team_r.aspx?code=FIN
Now, we can discuss whether it is better to focus on the average students, or on the best student. (In my imaginary utopia, we would provide the best individually tailored opportunity for both. In reality, no country seems able to achieve both.) An argument in favor of the best students is that we need people to invent new things.
My experience is the opposite. Because I learned to read early, I was able to absorb a huge amount of information previously inaccessible to me. There was simply no comparison - I was far better in every subject that required either knowing some information or processing it. The only exceptions were the subjects where body skill was important (art, PE, etc.) - in these areas I had some competition, I others there was nobody. I believe our chances balanced more or less in the second year of high school.
Personally I was lucky my dad was running a computer repair business from the 80's onward. Growing up with a computer and a mountain of pirated educational software prepped me more than anything else my parents could have done. They lucked out that I particularly enjoyed learning.
Well, maybe, but you're hiding a lot in that "if we can". You're assuming that this possibility is brought to fruition, and using the shiny abstract potential of that optimization to argue against real-world actual practices, and this is apples versus oranges.
In fact, I have approximately zero confidence that your "if we can" could ever come to pass. Consider the crazy levels of funding that's already pumped into education with no discernible benefit, and the extremely powerful lobbies that work night and day to maintain the status quo (modulo the increases in funding).
In a perfect world without competition for scarce resources we might be able to do what you envision. But starting the project from the current political realities, it's not in the realm of possibility. So let's not let the pipe dream interfere with some way to prevent the status quo from sliding down into even worse territory.
Yes. Kids born in rich families will do better, kids born to better parents will do better and that is a good thing. A lot of scientific research in early years did not come from government funded labs but rich people working on their passions. Note that privileged people will define "higher standards" always no matter what laws you pass and how you twist the public education system. But these sort of social justice solutions damage the very poor people who cant afford kumon.
2. Children are quite literally extensions of their parents. Their intelligence, beliefs, genetics, et cetera are a product of their nature (100% parental) and nurture (varies, but usually significantly attributed to their parents). Giving your child tutoring is no more cheating than when you pick up a book for yourself. Your children are you.
3. userbinator was in no way criticizing the opening up of opportunities to achieve equality by elevating all people to genius status. He, and most people here, are critical of handicapping the gifted/lucky/affluent/whatever in order to achieve parity at a lower level. The fact is it doesn't matter if you learn AI programming because you're so gifted the knowledge just flows into you easily, or if your parents spent $1mm a year teaching it to you. We need AI programmers, and having none because you thought it was unfair for people to get that education when others can't is nuts.
Luckily, our teachers made it clear that math was about effort, not skills, talents, or parents.
We were all expected to practice a lot of math, including algebra, until we figured it out.
And it worked - the ‘gifted’ students needed less practice, everyone else needed more practice. But by 6th grade, everybody passed algebra and figured out the basics. By 9th grade, when we were doing pre-Calc, it was unthinkable that someone in our class couldn’t do algebra.
Applying ‘Social Justice’ to math is simply the continued dumbing down of California. To what end, I can’t figure out.
Sometimes children benefit from a delay, and other children benefit by moving ahead; but all children deserve the opportunity to advance according to their individual math ambition and ability. Under Equitable Math, all children must be at the same level up until the last year.
This is a huge win for private schools and after-school programs such as RSM.
Besides everyone knows what the real problem is: teachers not having decent levels at a bunch of subjects themselves, and not willing to improve. This is about saving money on the back of children, not about being equitable. Whilst there should be some allowance for high achievers and (very) low achievers that no teacher has much influence over, the average achievement of students is very much a property of the teacher, not so much of the students.
This is about cheaper and less capable (not just in subject knowledge either) teachers, at any cost to children.
It is not abnormal for Californian high schools, including in some of the prestigious areas mentioned in other posts, to have math classroom sizes of 40 children, with classroom size penalties ending in middle school. When classroom sizes get that big, the problem becomes one of classroom management (are children even listening now?) and targeting average performance.
And then there is the matter of teacher pay. To have the credibility to convince the math faculty that you are ready to teach Calculus, you likely have a Masters in education and a Bachelors in math. Such a technical person may just have well earned a CS degree instead.
Lastly, the students. The schools which are severely underperforming are those schools where absenteeism may be enormous... in all classes. This is not a matter of math teachers not being engaging or ambitious enough. One might merely volunteer at some schools in East Palo Alto to see some of this. These are problems which extend well beyond the school.
I would also ask, if learning were just a matter of quality instruction, then what's wrong with Khan Academy? Khan Academy is a world class resource and it is delivering pedagogical wins. But something is missing.
No. "they" are going to lead fine lives, revered as warriors against social injustice, and living in the most exclusive corners of the state. As is typical, the next generation will pay the price.
For what it's worth, it drives me crazy too. The only reason we live such comfortable lives, that we can dedicate so much effort and money to such considerations, is due to the giants on whose shoulders we stand.
My daughter in grade 4 (Israel) is currently learning basic algebra tenets, notably associative, commutative, and distributive properties in basic equations, in addition to basic solve for variable questions. SIN, COSIGN, TANGENT and friends start in grade 6.
It's spelled "SINE, COSINE, and TANGENT".
I dont think minimum standards or curriculum moving accross grades have all that much to do with what competitive higher top does. The higher top require way more knowledge then what standards require. And more importantly, it requires more depth and speed.
High achievers are expected to know so much more then standards and to apply it in much higher variety of situations to compete.
Almost by definition, school (and everything else) is designed for the top of the bell curve.
Now, maybe school plan design can move the median ability up or down, and I don't have an opinion on if this change here does that, and if so, in what direction. I do think it doesn't affect the high end much either way.
If black kids aren't being served by the current curriculum, then I think it's reasonable to assume that some white kids aren't either.
I suggest that certain kids are being served poorly by the current system. If those kids were served better we could lift the floor, which would enable the high achievers to reach even further.
If you have 100 high achievers it's much more likely that one of them will produce a breakthrough than if you have 10.
1) HIDE the difference from the weaker students (whether black, or poor, or ... we can abstract about which exact group you think is less capable here)
2) take away the opportunity these classes give children to work to compensate
In IQ studies it is reported diligent work can increase your aptitude by slightly above 2 standard deviations, if you start young enough. That would imply that with enough support some mentally retarded people (which starts at IQ ~85) can be taught up to above normal intelligence (IQ ~105)
Both factors of course increase whatever innate differences exist. I find it very hard to believe these people working for California, who have studied pedagogy, would not be aware of this. So you can be very sure they are purposefully working to hide the difference. Well, until these kids try university, or to find a job. Then it can't be hidden anymore. Also, then it'll be much more difficult for them to do anything about it.
So this is very much about denying kids opportunities, for the personal gain of the people implementing these policies.
Give me one reason why you think your hope is valid. Everywhere I look this attitude seems to grow stronger and even discussing it becomes socially awkward, at least in some circles.
Don't be like Argentina.
However, regarding math, if there are cognitive research studies that justify delaying some topics, I don't consider that as negative.
Having said that as a priviledged parent I merely chuckle at this social justice wanking as my kid goes to a private school and is tutored by me. She will be more successful than the "equity" kids from California if eveyrthing else remains the same.
I don’t think social justice or equality should play a part of the argument, but it’s always hard to tell where the legislation ends and the propaganda begins these days, and I’m honestly no interested enough to read the 800 page document this article is about.
I will say, however, that I think we’re going to have problems teaching math until we reform the school system to be suited for the modern world instead of the early 1900’s “assembly line” society. It makes no sense to place children in classes based on their age, and certainly not for all subjects.
The result is always going to be that both slow and brilliant students get fucked over, in a myriad of ways, especially if they are a mix of good and bad at different subjects.
Why exactly is it that you aren’t taught courses like math, or history or language according to your ability instead of your age?
It would be great though. I loved going to school for the first 4 years when we were ~30 people in the whole school (spread over 1-4th graders) - the teachers were able to address individual needs. Then I went to fifth grade where were were 35 people in the class. It just went downhill from there.
I once took a computer-repair class at a local school district adult school. It was self paced, and despite being bored as hell during high school, I crushed the repair course at like 4x the normal speed. Because I could. There was literally no one to stop me.
The more evaluation and feedback are in the process, the more individualized it gets, the more burdensome and expensive it gets, generally. That's not to say we can't improve our teaching methods to automate some mechanisms for feedback and pace adjustment in the future, though...
Education is due for a genuine upset. I think there are a bunch of ways technology could make general education significantly more effective, given the technology was designed for that. (Current device / OS / app design norms are mostly in service of consumerism, which assumes no one ever wants to learn anything unless someone paid for them to hear it. So, not that stuff.)
Take a multimedia corpus, arrange the material for delivery via Spaced Repetition Learning (SRS) coupled with an active reinforcement learning system to gradually introduce and deepen understanding of topics that expand the learner’s challenge boundary.
Instead of teachers and fixed class sizes, allow students to self select into rooms based on noise level. Include a range of furniture from desks to couches. Any adults are only present to monitor for fighting or harassment and need no special training — they are certainly not to be responsible for lecturing or grading. Leave that to the machines. Perhaps direct students that have mastered material help students that have not.
Naturally and smoothly steer learners into vocational or academic studies based on their performance without social discontinuities like the German method.
One challenge with this approach would be how to organize appraisals of essays or long-form written content. Peer review might be one answer. There are, no doubt, many other challenges and criticisms. This scheme would dramatically upend the economics of education and make a large number of positions redundant.
That's exactly the question. Under Equitable Math, all children must always be at the same level up until the senior year, and Algebra will not be offered in middle school. Some children are ready for Algebra in middle school, and some aren't.
This is the most critical point of contention, and why the debate is not over whether the Common Core, which already emphasizes "deep" comprehension over rote memorization, ought be reformed to go even "deeper".
> I’m honestly no interested enough to read the 800 page document this article is about.
It's notable that the entire Common Core specification for math can be read in a single day. It is meant to be a coordinating document for many parties, and not just metaphorical lawyers.
Are they really advocating putting all kids in the same math class regardless of ability? That seems completely insane to me. For some fraction of the class, literally handing them a textbook and telling them to go nuts would be better in every way. At the other end, some of those kids feel awful for holding the class back.
Could someone help me understand what the big picture is here? How does this actually help the under-privileged students in any way? Are they expecting that this will level the playing field for college admissions and the job market?
It allows them to become teachers and school social workers and school admins and ... without requiring knowledge or capabilities they don't have?
School standards are about teachers and school management, not about students. Or, more to the point, they're about letting schools hire cheaper teachers, having simpler schedules, less hours, ... It massively simplifies the business that is a school.
At great cost to the kids and society as a whole, yes, but hey, savings! (goes on tv) "This is NOT about savings, this is about FAIRNESS. What are you, racist?"
Or do I confuse this with something else?
> Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
The result was that, despite lacking 6 years of formal math education, the students in that district were only one year behind the other students when they went to junior high. That is, they were able to recover all six years of missed elementary school math education in one year of junior high. And in the superintendent’s opinion, those students were better at critical thinking and were able to solve some problems their better-educated counterparts were not. I can find the link if anyone is interested.
Basically, it seems like kid’s brains are just not able to efficiently learn math. I know I could learn math concepts now that would have taken me much longer in highschool. I kind of wish we would just let kids be kids for more of their lives
(Additional references at the end of the article.)
Good to see someone trying it.
If you spent the math classes on getting the basics right, the rest could be formalized and then deepened in college. The saved time could be used to go to college earlier.
If it is anything like German math education back when I was in school a lot of the early things are simplified to an insane extreme and either have to be revisited later or are completely replaced with a better approach. I think we went through half a dozen ways on how to multiply and divide numbers when only one mattered in the end. If you learned the basics from your parents you could even expect to be penalized since you had to use the useless methods described in the curriculum for the first few years and could get penalized for correctly identifying an equation with a negative result.
> Basically, it seems like kid’s brains are just not able to efficiently learn math
Or it may be related to a really bad curriculum that tries to be "age appropriate" by teaching mostly useless crap.
https://www.webmatematik.dk/lektioner/7-9-klasse/algebra
https://matematik.gyldendal.dk/til_laeren/01-om-portalen/06-...
We’re not the best inspiration for how to run your school system though, we have had several huge reforms since the 1995, and the most recent major reform is failing miserably compared to what they are doing in other Scandinavian countries. Which is ironic because the reform was created to catch up, and then ended up failing more than what we had before.
Most it has to due with how our government isn’t willing to commit the necessary resources to run it. We actually have major, major, issues with that in all parts of our public sector right now. So bad with nurses that we’re cancelling operations and seeing delays on our emergency service phone lines on a national scale which are outside of what is legally required.
I think Finland has the best recipe for a modern school system for the west. They did the opposite of us, where instead of making children go to school for longer hours (thus needing more resources), they make children go to school less hours, but focus the resources better.
The Finnish idea of less hours, but more concentrated effort sounds like it could work. I have five children from medical school age to elementary school, and I have seen the hours of homework go up, but not the time to properly teach, or at least the lecture/lab model in university.
Passion to learn, curiosity, and finally, need drive successful learners.
The second link appears to be a curriculum by grade. I'll try again later, thanks!
The particular reason people struggle with algebra is because it is one of the first fundamentally abstractionist topics taught in schools. There is a huge cognitive development and experiential component.
Delaying teaching algebra makes cognitive developmental sense, but it is also inherently intertwined with with race, class, and gender for a bunch of reasons that get a lot of people really angry.
The only defense I hear is that kids don't really benefit from advanced classes and they'll be fine anyway. But gifted children will not necessarily be fine. Most of the smartest people I know struggled in school just, but most were fortunately saved by advanced placement classes that put them in classes where they can learn at a faster pace than the rest of the children. Were they forced to stay in what to them amounted to remedial classes, they would grow to resent education and actually underperform.
The utter disregard the people pushing these policies have for children is appalling. Hopefully this is just a weird time in our countries history where that we'll look back on and think how absurd the policies were.
They're replacing advanced placement classes ... with straightjackets.
So the only way to even the playing field is to eliminate difficult subjects in high school, so that everyone gets near-perfect grades.
Like another poster already mentioned, reminds me of the Harrison Bergeron story by Vonnegut - seems like we are rapidly approaching that point.
x + 3 = 7
Instead, they will get questions such as
__ + 3 = 7
They might not formally learn it, but they'll learn the patterns that they will eventually apply in algebra.
"Solving linear equations with multiple variables", "solving quadratic equations", "solving polynomials", etc. Those are things you really need to teach as a distinct concept. Algebra is just the language, introduced in a pedagogically sound way you wouldn't even realize you were learning it.
Even "new math" is too rote/heavy on memorization of process. And not enough patterns/puzzles/games/etc.
We need to find a way that the math content can be interesting for 80% of the room, and provide competition where there's multiple axes of success and multiple ways to stand out. Then you get everyone in the room really trying.
Instead, what happens is this: we start with curriculum that is very algorithm-heavy, taught by elementary teachers who generally do not love math. Half of the kids struggle with the rote-heavy workload and fall behind, and it becomes a frantic effort to try and drill steps into kids' heads who just hate it more and more. For a lot of the class, this is very painful and zero-sum, and it's only fear of what the teacher will say to parents that generates any effort.
[Note, I do think there is a point around 3rd grade developmentally where it makes sense to drill some arithmetic processes, and around 8th-9th grade to drill some algebraic process... but algebraic ideas can come in well before that time and hopefully be taught in a way that makes them interesting].
Ideally everything would be taught this way, like actually doing interesting things rather than just remembering things from textbooks.
Fast forward a few years in school when the teacher introduced algebra in class (maybe sixth grade?), everything suddenly clicked, and I pretty much got the highest grade for several months straight because I learned this material before, albeit not well, but still way ahead of everyone else.
I think this could be a middle ground: introduce the material earlier, but with no expectation that the pupil must grasp it immediately; then review or reintroduce the material again at a later date.
In my experience, kids whose parents help teach concepts and don't just leave things up to school generally end up with an advantage. Kids love learning from their parents and other loved ones, but school is generally regarded as sort of a chore even if it does bring friends and playtime. A great many parents simply don't have the time or energy left after their day job to support their children the same way others can. Kids whose parents often read to (and with) have a noticeable advantage in many school settings, and you can't substitute that for all students by just cramming in more reading time in their busy school schedules.
Kids have a finite time they spend in school. You can shuffle the time they spend around all you want, but in the end every kid requires a certain amount of time to grasp a certain context. That time may differ when kids get older or younger, but the required time spent on learning won't suddenly change.
Everything builds on other concepts and people's misunderstandings generally came from not truly understanding the basics. Its hard to personalize education at scale though.
Now, over a decade later, I am a professional software engineer. Sitting next to that guy in my 7th grade algebra class set my life on a course that turned out to be great. It makes me sad to know that future students won't be able to have such opportunities to be surrounded by similarly smart people. In the rest of my middle school classes the disrespect, distracting behavior, bullying, etc. were totally out of control - now I guess students won't know anything different.
I think this is a TERRIBLE decision, pushed by radical leftists that are completely out of touch with regular people. I wonder how much farther California and its cities will fall before people wake up.
After what we have learned the last 30-50 years from cognitive sciences one has to wonder what schools are actually for, nowadays. There are most certainly not optimized for "learning" by any means. Imho to put it blatantly schools are reduced to be a effective stronghold for indoctrination. They justify their power by using "science, technology, art, literature, history, social community, cultural exchange ...". Of course sheer by its power and scope we certainly "learn" something there. And you also happen to find great teachers in that system but its certainly not its main purpose.
Going back historically, schools still remain inherently (and shockingly so) medieval institutions. Interestingly "school" originally stems from the greek word of σχολή (/skʰo.lɛ̌ː/) which simply means "free time, leisure" which got hijacked by the church with "monastic schools" and today "school" means quite the opposite.
Throughout its (western) history with changing society they were succesful adaptions made (Prussian system, Humboldt's Ideal, Montessori pedagogy) skyrocketing literacy, expolding number of scientists etc.
But today the educational system is massively outpaced by the societal changes and by failing simply regresses to its medieval core of indoctrination ("preparation for the labor market").
No scientific literacy (aka critical thinking, controversial debates), no "learning" grounded on cognitive sciences, no hearing and tending to the needs of our young which they can perfectly articulate.
They're daycare so their parents can be productive members of society. Learning is incidental.
They're daycares and increasingly being used to spread propaganda.
This idea that ANYONE will be helped by giving them a free pass needs to stop. No minority will have an improved life by saying they are too mentally deficient to learn hard things. This is a political game where politicians refuse to recognize that fixing this is not an easy slap a bill in place an everything will be better. I think what they're hoping is that they can "fix" the numbers to show higher achievement by lowering standards and get voted back into office. We'll certainly be feeling the negative effects of these sorts of policies in a few decades if this bullshit continues.
Resources were so scarce communities could only afford to send a select few to learn to read and write and spend time on the highest levels of human thought, i.e. questions of the meaning of existence and epistemology.
When I am doing homework with my son or check is lessons I always wonder what is happening with students that parents don't have the time or the skill to do math,physics,programming together with the child. Some will hire private tutors but to few.
Seems to me that either you get fewer students to a teacher, or have less dense material to work with so the teacher can have the time to check each student and figure-out what exactly is unclear. And you ofcourse you need good teachers,
It's not obvious to the authors of the California Math Framework, who believe that:
- we should sort kids into classes purely by age, and that any other method of sorting is inequitable
- every child should be taught grade-level material (no matter how far behind, or far ahead, they may be)
- teachers are capable of successfully teaching mixed ability classes (irrespective of how the min/max) using 'differentiated instruction'
It's just "strange" that this is only done for academics, but never for athletics.
The fact that academic results can be thought of in "equitable" terms, but not athletic results (aka, you must be able to run 100m in X seconds), points to some systemic, cultural bias in thinking that everyone is just as smart, and that genetics don't play a role in intelligence.
The question is: are differences in overall (say median) academic performance of broad racial groupings (black, white, asian, hispanic, other) mostly the result of differences in genetics?
Many (most?) people would say the differences are mostly genetic for sports, but not for academics.
Lol what?
So uh are white people more genetically suited for lacrosse like 80% of the PLL is white, and us black people are somehow genetically suited for basketball because the NBA is like 70% black?
We should really look into these... lacrosse genes. And those basketball genes. Or not? https://scholarworks.wmich.edu/cgi/viewcontent.cgi?article=1..., https://pubmed.ncbi.nlm.nih.gov/18317378/
Your perceived difference in athletic difference is just showing the difference in opportunity just like the difference in education is. Of course this is the part where we start bringing in IQ results that show this same difference right?: https://repositorio.uchile.cl/bitstream/handle/2250/124054/I...?
A) The differences are mostly genetic for sports, but not for academics.
B) Many (most?) people would say the differences are mostly genetic for sports, but not for academics.
You seem to be arguing against A (about which I expressed no opinion).
Like what bizarre circles are you stewing in that you hear "They're great because they inherited the right genes for VO2 max!" more than you hear "They're great because they put in the hard work and effort! That's dedication right there!"
And even if we focus on this truly fringe group that you seem to run with, the genetic factors like height are also readily overriden by inequality in the "broad racial groupings" you mentioned earlier... https://pubmed.ncbi.nlm.nih.gov/34065650/
Inequality is the great genetic equalizer...
- the paper didn't claim that nutrition could fully override genetic factors, and
- they acknowledged that adult height is correlated with ethnicity (hence the need to adjust for ethnicity before calculating correlations)
Like did you need a paper to realize that environment doesn't *fully( override genetic factors? That we're not born as some blob that morphs into shape based on the current lon,lat?
This isn't about height... this is about the notion that people associate athletic excellence with genetics over environment and personal effort... maybe in Nazi Germany?
And then to top it off, the point you're using as a "gotcha" still shuts down your line of reasoning but you fail to realize that... The study needs to adjust for ethnicity not just because of genes, but because of socioeconomic factors associated with ethnicity!
The point of science is to examine what you set out to examine. You have one study that shows the tie between nutrition and height survives adjusting for ethnicity. Here, have a study showing how socioeconomics are tied to nutrition: https://academic.oup.com/ajcn/article/87/5/1107/4650128
And then from there go ahead and put two and two together. Nutrition is a statistically important factor even when adjusting for race, socioeconomics affects nutrition... and how do socioeconomics tie back into race?
Because we don't teach athletics at all. PE is not even trying.
Especially in teams sports, if you want the kid to learn soccer/basketball/whatever and the kid is not a talent meant to win competition, coaches wont spend much time teaching the kid. You may pay private lessons or something.
Can you maybe explain to a non US person why a system merit based is not used(or if it was used in the past was dropped) , I understand there are limitation with this system, I will describe next:
1 there is national/state level exam with super strong security to prevent cheating
2 highschool/universities will be placed on a list with all the classes they offer
3 candidates will fill an ordered list with their preferences. In practice this means you put on the top the "good" high schools and the classes/profiles that interest you , like if you hate Math you will avoid science/math stuff and go to art/literature/languages profiles. How I personally ordered the schools was by checking the results of their students at the national exams.
The result is that students that are very smart or that are OK smart but worked hard are concentrated on 3 hghschools in my region. This seems OK sincee the kid that is a really jerk, never liked school or failed the exam will be at a different highschool and not drag down the working hard students.
1. Using only these scores would boost the proportion of elite university places awarded to Asians, who are already 'overrepresented' relative to their share of the population. Propel state various reasons why this is undesirable (equity/diversity, don't want everyone on campus to be 'the same') and unstated reasons (racism against Asians).
2. Blacks and Hispanics are 'underrepresented' at elite colleges relative to their respective shares of the population. The argument here is that these outcomes are prima facie due to 'systemic racism', i.e. not necessarily overt racist acts, but things in the system that together result in worse outcomes for certain ethnic groups.
If you want to read more about these topics, a few starting points:
1. Recent news (and Twitter discussions) about the University of California dropping the SAT.
2. Recent news about Lowell High School switching from partially-merit-based admission, to lottery-based admission. (And the court order from a few days ago, declaring this switch null and void.)
3. Thomas Sowell's books 'Economic facts and fallacies' and 'Charter schools and their enemies'. One of the points in these books (which include data) is that, when you adjust for things like parental educational level, number of parents in home, differences in outcomes between ethnic groups' career success often lessen or disappear altogether.
Asians having high scores and taking the sits of rich white kids feels to me as a more plausible reasons politicians are addressing the problem like this and not fixing the actual cause of poverty and racism. A solution would be to make all school good enough, so even if you have to go to a middle level school it will still be enough t get your dream job.
https://admission.universityofcalifornia.edu/how-to-apply/ap...
This will allow them to achieve any desired demographic/ethnic mix.
> and just leads to your entire high school being devoted to test cramming.
This is a better measure on how competent you are then some lottery or interview.
To prepare for tests like mathematics implies you actually need to learn and solve problems, it is not an exam that measures your instincts or if you are gifted.
I am from Romania btw, and when IO was a child there was no national exam, I had to chose 1 highschool then go there and take an exam with the other kids that chose the same highschool , if I overestimated my abilities then I would have been screwed for at least 1 semester or year. In present with a national exams the kids have it much better
- it is clear exactly what areas are covered by the exam so you can ignore stuff that is not needed
- models of subject exams are published and you can try and evaluate your level
- you can check the previous years subjects, grades, admision numbers and you can have a good idea what grade you need to get at your proffered high school.
Also as I mentioned high schools here are specialized, so you have 2 that are specialized in math, physics ad informatics , 1 that is art , 1 focused on economics, 1 focused in pedagogy,literature and languages , 1 focused in chemistry and we have professional school that are for kids that hate books and just want a job, here they can learn to be a car mechanic, construction, cooks etc. So you could not randomly distribute children around and ignore their preferences, you could put a child that hates math in the math highscool and a child that hates art in the art school.
I believe SJ activists care only about class conflict and don't have any respect for individual choice. Like feminists criticising women who choose to be housewives. They know what's better for everyone.
The pejorative used for structuring curriculum and resources based on this observation is "tracking" and aside from special needs and other narrow exceptions it is thought to be a great historical injustice that has largely been eliminated from public schooling in the US. Now we look forward to ending the injustice unequal funding due to differential tax bases among communities has created. Doubtless ending this remaining vestige of inequity will herald a new age of public education excellence in the US.
Or something.
But there still is the children learn at different speed or some are left behind, at least in my son case I feel in Math they move too fast, there was the same when I was in high school too.
Sure, some students will not be able to handle algebra as early as others. That doesn't mean you hold back the students who can. That's disastrous public policy, at the very least.
While I personally agree with your point, I think your statement makes the case for the folks who developed this policy.
The “problem” that these policymakers see is that students, when stratified, are not stratified across certain groups in a proportion that is similar to the population.
For folks who focus on equality of outcome, this is a problem.
For folks who focus on equality of opportunity, it is not a problem.
I believe what's likely to be best for everyone is:
* Keep everyone on the same track through early elementary, but we need to work hard on making the classrooms encourage everyone to be curious and stretch themselves. Games and puzzles are the answer here.
* In upper elementary, start to offer differentiated instruction within a classroom.
* In middle school and beyond, have true stratified tracks (which this article recommends not doing).
"A key sticking point in the approval process has been the framework’s recommendation that teachers refrain from labeling students as “naturally talented” in math."
My overall recommendations are here: https://news.ycombinator.com/item?id=29326295
I'd recommend that we try in elementary to make the current math curriculum reach a broader set of students through games, puzzles, and in-classroom competition that doesn't absolutely favor the strongest students. Maybe Tom is farthest in math and wins a lot, and maybe Amy has a natural talent for computation that makes her strong, but there's also some randomness and the ability for gambits in the game to let others have a chance of winning. The result is that everyone tries hard. Sorting students by level prematurely has been shown to be bad, so I think having levels before late upper elementary or early middle school is bad.
I think the link's recommendation of not sorting students based on level in middle school is bad-- my 7th grader is doing precalc now. But he was on the normal math path through elementary with some enrichment and diversions.
Gifted kids are hard to deal with in math in elementary, because they may have a good intuitive understanding of math, but they generally are not so developmentally ahead in focus, accuracy, etc. So while you may have some 9 year olds that can understand work intended for 14 year old students, they generally cannot do difficult problems with any degree of accuracy. They make too many mistakes, swapping coefficients and signs.
> The below is un-acceptable.
> "A key sticking point in the approval process has been the framework’s recommendation that teachers refrain from labeling students as “naturally talented” in math."
Gotta disagree with you on this one point. Labelling someone as having a natural talent helps no one. Label them as ahead, or having worked hard.
"Natural talent" may be the truth, but as a label is toxic for everyone. It's toxic for everyone else, because it's not something they can hope to have: why try? And it's toxic for the labelled-- anything that is hard can be threatening that this label of natural talent could be stripped away if they try and don't do well-- so why try.
Studies show that praising kids for "talent" or "intelligence" is actually demotivating.
Let's not rush to apply labels, but instead try to create environments where everyone can be motivated to try hard, excel, and grow. In middle school and up this can be through tracks. In late elementary this can be through differentiated instruction. And throughout elementary, we need to just focus on keeping it engaging and interesting and speaking to curiosity of everyone in the room, instead of drilling the poor kid who's struggling on arithmetic facts incessantly.
Another issue is that the labels are not overwhelmingly predictive. The students who are considered weakest in elementary school can improve a lot. And many of those who continue struggling may do so because they've internalized a message of being weak at math-- or internalized short term coping strategies imposed by teachers (e.g. given up on understanding and instead are trying to learn the correct sequence of juggling symbols by rote to pass this next class).
They may not be able to have the attention span and accuracy to factor some 6th degree polynomial in 2 variables with mixed signs.
But the idea of an equation; of invertible operations; of doing things to both sides of an equation... If you word the questions right and make it interesting, most 7-8 year olds can do this stuff no problem.
I think a whole lot of the math whizs who post on HN grew up around people who loved math and figured out how to share interesting tidbits with them very young.
E.g. why are my kids all terrifically accelerated at mathematics? Is it because of some magical genetic thing (maybe a small part of it is)? Or is it because we, as parents, value and enjoy it?
I want to figure out how to bring more of that magic to ordinary classrooms.
Doesn't this get at the root of the problem though? Some students have the mathematical maturity for it. Others don't. The arguments seem to be between "we should present these concepts early for the benefit of the students who are ready for it" vs "we should delay these concepts until all students are ready."
But different students have different levels of mathematical maturity. the problem seems to stem from working in a paradigm where everyone at a particular age has to learn the same thing. It seems we should be moving in the direction of more personalization rather than less.
Yes, I'm saying that the argument should be quite a bit broader than that. There's much that could be improved in how we expose students to more advanced math in early grades, and there's also much to learn from these well-established teaching approaches. If you do it badly, it's less likely to work.
I think part of the problem here is definitional.
* My oldest son's a few years ahead in mathematical understanding. He understood algebraic concepts very early, as presented in Singapore math and then through enrichment and bantering about various problems with his mathematically-inclined parents. Kids can absolutely get algebra and learn the rules early.
* But even if your 4th grader understands all the rules of symbolic manipulation, and the general concepts behind them... that's only part of what is taught in an algebra class aimed to 13 year olds. There's an emphasis on systematic process, checking for mistakes, carefully matching terms that is likely to be unnecessarily frustrating to younger kids.
* Many programs for gifted youth go in exactly the wrong direction: emphasizing more rigor for the gifted youth, harder problem sets, etc. He took Algebra I with CTY and the number of opportunities for sign mistakes or mismatching coefficients per problem were dizzying.
I believe we should be:
* Throwing ideas at primary kids, with small numbers of degrees of freedom to make the problems manageable for a population that developmentally has less discipline. The complexity of the ideas involved can scale based on what the kid knows so far.
* Throwing deep process and carefulness at older kids. The complexity of the ideas involved can scale based on what the kid knows so far, but the process and accuracy expectations can scale mostly with age.
> 5 + $basketEmoji = 7
> What number is hiding in the basket?
They have no idea they’re doing algebra or what algebra even is but they’re doing it. And they understand the concept on a fundamental level.
I don’t remember anyone explaining a variable to me so explicitly. I just remember showing up one day and having to deal with random letters mixed into my math homework.
Not everyone took algebra in 7th grade; those who did not, took it in 8th grade.
All it takes is a little one-on-one time and some interest.
Kids are way smarter that you realize.
I use the concept of a derivative often, and I'm glad it enriches my understanding of the world even if I calculate derivatives almost never. But there are so many other useful math concepts which might be better to communicate than just doing exercises around techniques (e.g. can you apply the quotient rule correctly).
Concepts I wish we emphasized instead:
- stats: uncertainty, confidence intervals. (In)dependence of variables. Correlation.
- discrete math: enough to communicate the concept of structure being preserved. Enough combinatorics to understand why some families of structures might be huge. Basic concepts around graphs.
These ideas don't necessarily need to be sequenced. You can deal with plenty of integrals while learning stats, but you don't have to.
What if our concept of woke math involved introducing posets and relations and cases where comparison isn't possible? What if we stopped talking about high school math as a single ladder and consider it more as a landscape to explore? By desequentualizing topics, maybe upper class hs students can actually catch up by taking more than one math class at a time?
http://mcb.berkeley.edu/undergrad/major/major-requirements/r...
Edit: You hardly contradicted me. My claim was that the math requirements of non-engineering science majors were 0-2 semesters of calculus and a course on statistical methods. You added combinatorics, which I usually just see taught as part of that applied methods course, rather than a stand-alone semester of mathematical combinatorics (I welcome correction). This is exactly what the current secondary math curriculum leads up to: calculus.
> my claim was..
No, it wasn't, but nice try.
I mean we should definitely teach basic probability and combinatorics early on, but my recollection was that is the case.
Instead, the central question is whether all students ought be in the same class up until the senior year, regardless of their individual ambitions or abilities in math.
For context, Californian math classrooms may have ratios of 1 teacher to 40 students, and classroom sizes are not penalized past middle school. This is the context under which teachers must somehow address cohort variability, the same context under which we might somehow expect an Algebra teacher have units planned for those who are ready for Geometry. This is not a realistic assumption of teacher competency.
Equitable Math would be a huge win for private schools and after-school programs such as RSM.
It's Harrison Bergeron Math.
"In the year 2081, the 211th, 212th, and 213th amendments to the Constitution dictate that all Americans are fully equal and not allowed to be smarter, better-looking, or more physically able than anyone else. The Handicapper General's agents enforce the equality laws, forcing citizens to wear "handicaps": masks for those who are too beautiful, loud radios that disrupt thoughts inside the ears of intelligent people, and heavy weights for the strong or athletic."
3 + ? = 10
10 - ? = 3
Diversity is supposed to only extend as far as categories one mustn't use to discriminate (age, race, sex, religion, etc.). If it occurs in other areas (achievement level, ability in particular subjects) ... oooh that's bad. Must make it stop.
So it benefits a minority (those who care) and differentiates them from the rest -- that's what they don't like. Because those who care come from "privileged" backgrounds more often than not, thus perpetuating the gap between privileged and non-privileged.
They seek to accomplish this by pulling down those who would otherwise excel, not by solving the real problems that are preventing people from excelling in the first place.
Part of the problem is that outcomes can never be equalized. It's a fallacy to try to force everyone into the same educational mold. A statistical normal distribution will always occur.
Better to remove impediments that are keeping people from excelling -- things like poverty, crime, etc. would be a great place to start.
If all (e.g.) 7th graders must have the same knowledge of math, that knowledge of math cannot exceed the knowledge attainable by the dumbest (read: any) 7th grader. This is tautologically true.
What is your solution to enable high quality curriculum and ensuring uniform success?
What did you mean by equalize life outcomes then?
again, what is your position and proposal?
The only noteworthy difference is defining acceptable failure rate, which neither of you did.
2) Can no student advance until everyone has mastered the material?
When most kids can’t do algebra, the teacher invests most of their time into helping those students catch up. Because most of the teachers time is now going to students who don’t understand algebra, algebra gets dropped all together. Minority high achievers who were capable of understanding algebra now feel that they are held back by low achievers.
High achievers should probably check out Khan Academy or similar…
Please stop parroting this talking point. It's just not true. California schools are funded at record levels--$18k p.a. per pupil[0].
My third grader does these (in an Oregon public school), so I think you've read too much into one article and a lot of uninformed commenters.
Most third graders cannot consistently do the following:
10 - ? = 3
10 - ? (- 10) = 3 (- 10)
- ? = - 7
(-) ? = (-) 7
? = 7
This is absolute voodoo magic to most third graders. They may be able to memorize specific patterns, but they won’t be able to manipulate equations consistently and accurately.
Fwiw, at 3rd grade, some of the smarter kids might be able to understand and manipulate these abstractions, but those kids aren’t the norm.
https://dragonbox.com/products/algebra-5
My kid tore through almost the whole set of problems in the app at about the recommended age (5yo).
The question with the software that I have is how much is actually understood. Specially, how much of what was done can be applied in a different context. Ideally consistently, accurately, and without any scaffolding. I’m guessing the answer might be “a lot” for a typical HNer’s child (or maybe not), but it rounds to zero for the average or lower 5yo.
I would also be curious about how much success can be had with just rapid trial and error rather than learning and applying. 5 year olds can be great at the trial and error part while not actually developing and retaining much understanding. I could be very off the mark with this speculation, but a lot of my experience in this area makes me think I’m not.
Basic understanding is a lower bar, and I'd suggest that most students leave Algebra 1 with just basic understanding. Hopefully a little better than Dragon Box.
Edit:
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-ad...
He's never completely gotten over it. He's still mad about it to this day.
The thing you wrote here does not count as teaching algebra. It is just one preparatory step and has nothing to do with delaying algebra or not.
It's effectively impossible to get someone with an IQ of 130 to have empathy for someone with an IQ of 95. They just need to work harder, they just need to have better teachers, they just need to stop watching so much television, they just need to get better nutrition, ad nauseum.
Imagine the ego crush that would occur if a 130 IQ true-believer in human equality is faced with the prospect that their intellectual success is due to winning a genetic lottery, not due to their hard work and proper life choices.
Of course they're going to deny the reality of hardwired cognitive horsepower.
To do otherwise is to deny how much better they are than you.
That is when multiplication tables are actually taught. Multiplication itself starts to be taught before, but 4th grade is when the full tables are expected to be learned.
So, you have met kids that struggle to learn multiplication tables when they are first introduced to them. Which is actually fine, it is ok to struggle at first before getting it.
In his consumption of publicly-funded universal education? Or...something completely irrelevant?
50 + x = 100 ↔ x = 100 - 50 = 50. I definitely linked to something that has word problems that can be converted to algebraic equations in 1 unknown.
Sparky the dragon was born with 28 spikes. He grew several more spikes as he got older. Now Sparky has 80 spikes. How many new spikes did Sparky grow?
Sure, this could be expressed as an algebra problem, 28 + X = 80, but the intention here is quite clearly for the student to see it as a subtraction problem.
https://www.khanacademy.org/math/cc-2nd-grade-math/cc-2nd-ad...
It's entirely disingenuous, then, to refer to these word problems being solved by Russian students in 2nd grade, as though it has any relevance on whether it's appropriate to teach Algebra 1 in 9th grade. 2nd graders in the US are also expected to be able to solve these types of problems and it's not because they are taught any actual algebraic concepts.
When the virus leaked from the Wuhan laboratory and spread across the globe in a matter of months, we knew even then that children are not really at risk of dying from sars-cov-2.
Seems like the correct course of action for the times is to take education out of the hands of government.
I do not believe children should be left behind, but the dumbing down of society isn't going to work. Seems like a segment ripe for complete market disruption.
My 5th grader is learning algebra and we support him at home.
Naturally we will continue to look for resources for him outside of public indoctrination. Perhaps we will see countless real schools being formed across the nation.
I learned almost all I know from the Internet over my 36 years. If more injection mandates occur, especially for children in my region, I will pull my children out of government school.
In 2020 we did distance learning and my children thrived while so many another's back tracked regarding test scores.
Our children thrived because my wife and I work from home. They thrived because life at home, while not structured like school, is an on going homeschool-like experience.
I'm so grateful to have been able to see my children thrive in these times.
We have had a lot of set backs as a society but we will continue to rebuild, repair, and grow!
My oldest is a freshman in high-school and he is very happy to be back in school, even with a mask all day and 6 feet apart in class and lunch, if it means seeing his friends and not being isolated (teachers treated the final wave of children doing distance learning last year horribly). I think he is relieved from being discriminated.
Sounds like prison to me, but he wakes himself up and gets ready, and goes. Over all he appears happier. <3
My 5th grader wants to be homeschooled after going back.
If this is what gets "taught" around the dinner table at home ... then in such a house, all STEM education will be moot.
The NIH has been caught funding gain of function there.
So, sure go ahead and dismiss it as conspiracy but at this point you're the one sounding more like a conspiracy theorist by denying the ever growing evidence.
In the same sense that to a Creationist, "all indications point to" the fact that Homo Sapiens first appeared on earth around 6,000 BCE and could not have evolved from other species. And that "evolution" in general is basically a myth fostered by an atheistic academic elite.
If it's what you're determined to believe, then hey, it's what you're gonna believe.
In this example you're the creationist denying the ever growing evidence. You'd be the one out there calling Darwin a scam artist.
There's one of two things going on here:
1. You're ignorant of what's actually going on. 2. You're malicious
You can be forgiven for #1 but you really need to take your blinders off and maybe consider some different news sources.
I've heard a good argument that algebra specifically should be moved the other way: teach it in elementary school, when kids are first exposed to arithmetic. There's a really natural progression from addition/subtraction/zero and multiplication/division/one to inverses and identities, and from addition/multiplication to distribution and associativity. My 3-year-old understands that if he has 5 raspberries on his fingers and he takes away one, he has 4, and then if he grabs another one and puts it on his finger, he has 5 again. Not a huge leap from there to the concept of equations, inverse operations, and solving for unknowns.
Unfortunately, for a child it typically is a huge leap.
There are certain abstractions that young children simply cannot do. The ability to do certain abstractions is distributed along a bell curve (edit: of age), and maybe your child is on the very far left of that curve, but most kids won’t be able to handle the abstractions you speak of until at least a little later.
To be fair, that “later” is definitely not 8th or 9th grade (much earlier), but it’s also not immediately after learning basic arithmetic.
When you have a system set up to force one adult to teach 30+ children you will never be able to spend the time required to ensure everyone gets the concept, but that neglect comes at the cost of compressing the learning in later years which still only benefits those who have high aptitude. Which is exactly why they are pushing it back further, not because it will help kids learn more, but because more children will have the ability to learn it without much interaction from an instructor.
Many decades of cognitive science disagree with you.
See Piaget for one of the earlier researchers on this topic. Even though his original ideas have been refuted or refined, the basic premises of his ideas are still prominent among the large group of modern researchers that some people dub neo-Piagetians.
Even here in America, tutoring schools such as Russian Math or Kumon are successfully teaching advanced topics to children at much younger ages than the public schools. I know the temptation is to just say its its high aptitude kids that are being sent to these after school programs, but it's not. It is just rich kids whose parents want to give their children a leg up. Almost all children could learn the topics, but we won't put in the effort
Based on your reply, I’m fairly certain that you are not familiar with the research and your not familiar with what is actually happening in Eastern Europe, Kumon, etc. in relation to that research. As a professional in this area of research, I feel fairly qualified to say that I am.
I am happy to agree to disagree about what the problem is here, but I strongly encourage you to look deeper into what is actually happening in the research and the learning environments you are praising/promoting before you propagate a loose collection of anecdotes as data that points to a clear solution.
Just because I completely reject the ideas you may be involved with researching doesn't mean I am ignorant of them, I just haven't been convinced that they are based in reality.
Interestingly, on this we agree. That’s why throwing more bodies at the problem (your initial suggestion) is not a solution that I think would work. When a typical educator is asked why a certain teaching or learning method works, their answers tend to be both incorrect/incomplete and remarkably shallow (e.g., it worked for them when they were in school).
The research available points at multiple tried and true ways of learning, but getting these ways of learning implemented in households and in the public school system in the US is a Sisyphean task.
Most of the broader ideas that he espoused and is famous for were refined in a way that made them accurately generalizable. Typical research timeline where an idea is introduced and is refined over time.
Some of the specific ideas he stated (and typically backed with data) was not generalizable to broader populations and was therefore refuted as an absolute. The data and conclusions were not necessarily wrong for the sample of the population studied, but they were not found to be as broadly true as initially believed.
This additional research led to the refinement of his theories, to great effect, imho.
I could believe that the ability to abstract develops at different times in different kids. But I'd caution about taking Western research and generalizing it across all cultures, or generally assuming that kids are less adaptable than they are. There are existence proofs for kids learning algebra at much younger ages than most American schools do (3rd and 4th graders do in eastern Europe, as do Americans who participate in RSM).
Part of the success is most certainly the student culture, which pushes far harder than the faculty. It's one thing for a school to offer opportunity for advanced math (and in that sense Khan Academy already offers this); it's quite another for peer pressure to demand it.
What does this mean? Is there some special qualification or licence to be allowed to teach calculus?
* Concrete example: our district had a shortage of high school qualified teachers. Middle school teachers were invited to apply with the understanding that they’d teach only general math, pre-Algebra, Algebra I, and Geometry.
Observations:
* Wow-- the brighter half of MS students can do nearly as well as bright undergraduates on this material if you go a little slower and make some allowances for attention span. The neuroplasticity, recent memory of learning arithmetic, and lack of fear of the material really helps.
* Holy crap-- I had no idea before trying to teach this how much number theory that I take for granted. Like, I forgot to cover how many possibilities there are for n-digit numbers in different bases and some early lessons on number systems took this for granted. Figuring out what you need to cover, and how, for something to make sense later is hard.
It is hard to teach something. Being able to do it is isn't anywhere near the level of expertise needed to:
* Do it up on a board at a moderately quick but consistent cadence, with engagement and narrating the whole part through.
* Not be taken off track by inevitable distractions.
* Understand the stack of necessary knowledge in the ways needed to figure out what a student is missing.
* Completely reinvent your lesson plan when you find the students unexpectedly lost, providing whatever the missing bit of knowledge is to get your class back on track.
* Handle unexpected diversions and requests for deeper knowledge on the fly.
In the UK a mathematics teacher is just a mathematics teacher. They all have to teach calculus because that's part of the curriculum. If you couldn't teach calculus then you couldn't be a mathematics teacher.
(That's not a boast - we're poorer and less effective at maths than you are.)
What do you do if you're a mathematics teacher but can't do the calculus part? Handover to someone else for just that part of the year? Must be a bit professionally embarrassing?
This is hugely variable within the US.
> In the UK a mathematics teacher is just a mathematics teacher. They all have to teach calculus because that's part of the curriculum. If you couldn't teach calculus then you couldn't be a mathematics teacher.
I think there's a lot of math teachers who would be a bit iffy teaching Calculus that have department chairs that schedule them to teach earlier math instead.
> (That's not a boast - we're poorer and less effective at maths than you are.)
I don't feel like our mathematics system is very good at all.
Maybe they're terrible at half of it? I don't know.
Really? That's very interesting.
I had a different math teacher every year / level. I'm at a smaller independent school, where you may have the same math teacher a couple times but people definitely specialize-- we have the teacher who teaches mostly 6th grade math and pre-algebra, and a teacher who mostly teaches algebra I and geometry, and so on.
On the one hand, you lose continuity. But you also get a fresh start each year, with a new teacher who probably teaches the things you had trouble with in a different way...
Further, at that point in time, calculus was only part of the A’ level curriculum, and most people would never encounter it unless electing to do that course.
Other parents likely believe that further math isn't necessary because they have done well without it and think their children will as well. They do not understand that a large portion of the world that was impoverished when they were growing up now have functioning education systems and are now able to compete for the same cushy jobs.
In this case, it's design. Increasing social injustice is the whole point, because that ensures increased political power for those who campaign on social justice.
I think the core problem here is trying to teach all kids math in the same way. Not all kids are equally capable of learning math.
Some smart kids can learn algebra in elementary school. There are plenty of students capable of going through the standard curriculum and finishing calculus by the time they are 13 or 14. For these students, the faster the better. Go into even a "good" second-grade math class and you will find some of these students, acing tests and completely bored with everything taught in class.
On the other hand, some students will never be able to have a good understanding of pre-calculus. It doesn't matter if they take it when they are 17 or in college, they will never really get it. Or at least, there is no known teaching method capable of doing it.
How can you possibly design an education program that takes this into account? You just can't teach all 15-year-olds the same math curriculum without wasting the time of many of the students, either it's too hard or too easy.
E.g. "Find the missing number: _ + 1 = 5". Same thing with subtraction.
Based upon my experience with my 6 year old (in a public California elementary school), they actually seem to teach math in a huge variety of ways in 1st grade. Word problems, number problems, relationships between plus and minus, and boatloads of ways to solve any given problem.
I think they introduced it in Kindergarten too. But it was way beyond her at the time.
The reason many minorities and POC lag behind has nothing to do with race. Like many issues in the US there are effective ways to address this, none of which survive the compromises and competing desires of bureaucracy.
I think that we can agree that the whatever they are doing in the United States isn't working very well. According to the scores on the PSIA math test given internationally to 15 year olds, the US ranks behind 21 other nations [1], well below the international average. Why not pick, say, the top four countries, (recently South Korea, Japan, Switzerland, and the Netherlands) and adopt their methods that are working? Instead of dreaming up new approaches that have no quality research justification, just teach math in a manner that is already known to be significantly better.
[1] https://www.nsf.gov/nsb/sei/edTool/data/highschool-08.html
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.
The critically important part of their method is funding of schools being independent from wealth of the kids’ parents.
I’m not sure US can adopt that; American voters view that method as communism.
[0]: https://apps.urban.org/features/school-funding-do-poor-kids-...
The constitution makes clear (to me, but I'm not a constitutional scholar) that the federal government has specific enumerated responsibilities, everything else is up to the states and local governments. The benefit of this is it allows competition of ideas for governance between the states, which occasionally reveals alternatives that aren't always apparent. (For example, the disparate state wide regulations put in place to mitigate the impact of Covid. Why are the states doing things so differently?)
Unfortunately, there are big differences between schools across the country and the federal government has tried to get involved, despite the constitution. To work around the constitution the feds use now commonly employed methods like spreading federal tax money around to fund federally regulated programs in state and local school programs. It might be better if the country didn't have to be so indirect about it and could simply impose a uniform educational system, but this would require a titanic effort to overcome state's rights types of constitutional challenges.
Is it really just a money problem for schools? I don't think so. Baltimore public schools are notoriously bad, but spend well over the national average per pupil.
The Leander Independent School District is nearby to me. It is ranked 12th among 1,018 Texas school districts. It's an excellent school district. It has a 97% graduation rate and an average SAT score of 1230 while the Texas wide average is 1022. This school district spends $11,496 per pupil, which is below the national average of $12,239, see [1].
It seems that without spending more we could do much better by emulating the Leander Independent School District and ensuring that instead of $12,239 being the national average spending make it the national minimum spending per pupil. Parents willing to spend even more could still move those districts that spend twice as much per pupil, but we should strive to give all students the benefits of a school district like the Leander Independent School District.
[1] https://www.niche.com/k12/d/leander-independent-school-distr...
No, the inconvenient truth of the matter is that american blacks (and Hispanics? Not sure) drag down the scores. This score, and every score that we have yet devised. Every measure of intelligence that we can think of, every control for income and parents, every statistical trick to attempt some socially acceptable explanation, it all comes up the same way: they're just not as smart. The natural attempt to handwave this as some kind of systemic racism is thwarted by the existence of those poor Asians who perform better than whites; this is another inconvenience and is why Asians are being quietly dropped from "PoC" initiatives and measurements. Californian education reform is all a song and dance to desperately ignore this fact. When you have a group of people who are less smart, and the goal is that they achieve the same level as everyone else, what can you do? Well, you can give them more class time and free tutoring, but no one will support an initiative where some students take extra classes. There simply is no solution apart from lowering the ceiling. And since the governing bodies refuse to stop measuring everything by race, they also refuse to simply segregate based on ability, since this would show too many blacks in the lower performing classes.
This problem will literally never be solved under the current mode of thinking. It can't be, because those in charge are adamant about rejecting reality. No solution can be had if the problem cannot be identified. They will continue lowering the ceiling, and they may eventually lower it enough to get an equitable result. But those pesky private schools and tutors will still be around ruining their plans, and if there ever still exists a high educational standard out there somewhere, it's the tutored and the private schooled who will pass that bar. And at that point then it actually will be because of privilege.
Program goals includes the de-emphasis of Algebra for middle school and Calculus for high school. Under Equitable Math, all students must take the same level of courses up until the senior year.
[1]: https://equitablemath.org
[2]: https://en.wikipedia.org/wiki/Asian_Americans_in_California
> "There is a greater focus on getting the "right" answer than understanding concepts and reasoning."
Probably most people would be on-board with the idea that concepts/reasoning are more important than blindly getting to the right answer, but "right" in quotes seems like a tell that some math-is-objective nonsense is on the way. Reading further, though, it turns out it's just talking about how word problems can be imprecise!
> "Math is taught in a linear fashion and skills are taught sequentially without true understanding of prerequisite knowledge."
This seems like the flexibility the other commenters are gunning for, even if California isn't on board with it.
> "Rigor is expressed only in difficulty."
I immediately thought, ugh, they're just trying to dumb everything down! But if we read further:
> "Too often in math, we limit the definition of rigor to difficulty, rather than its full complexity including thoroughness; exhaustiveness; interdisciplinary; and balancing conceptual understanding, procedural skills and fluency, and application. This allows math teachers to shy away from complex problems and tasks and instead streamline teaching like we are spoon-feeding..."
A thorough, conceptual understanding is superior to a surface-level ability to step through a process without understanding? Sign me up!
I poked around for anything more aggressive, but from what I can tell that's generally the vibe of the PDF. Yes, the framing is unnecessarily antagonistic, but if we took the white supremacy dressings off of it I doubt the ideas inside would be divisive at all.
Of course, I've only skimmed that one document! But if "Dismantling Racism in Mathematics Instruction" is this inoffensive I'm not sure where they're hiding the real good stuff.
[0]: https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
If you click on that item, it takes you to a page where they suggest non-standard classroom activities like "Have students create TikTok videos, silent films, or cartoons about mathematical concepts or procedures."
I'm pretty open minded about education pedagogy, but you completely lose me (and 99% of teachers) when you suggest creating TikTok videos so students can adequately express their mathematical understanding.
“White supremacy” is an accurate but excessively polarizing term; “cultural favoritism in favor of status quo elites, whose preferences and cultural practices are encoded in the prescribed methods of demonstration” would perhaps both be less inflammatory and easier to see the connections between the specific practice and the broader problem.
> I'm pretty open minded about education pedagogy, but you completely lose me (and 99% of teachers) when you suggest creating TikTok videos
I think the particular examples are not because any of them are individually to be preferred but because providing a range including them illustrates the general principle, which is “provide students a broad set of mechanisms to demonstrate understanding rather than a narrow set of forms, as the latter introduces cultural biases based on comfort/familiarity with the form, both for the child immediately and among parents and the rest of the support network on which they rely.”
Say there's a real problem, the police are killing people. Instead of solving that... well few of us have any power over that, so instead we resort to changing things we do have power over.
Like… watering down math classes and pretending that is even the thousandth thing on the list of solutions that should be tackled first as a response. It's so far down the list (and has better remedies) that it actually hurts the cause.
Its not an anti-solution, and you provide neither evidence or reasoning to support your claim that it is part of a class of things that backfires.
> Say there's a real problem, the police are killing people
That is a real problem. Education is done in a culturally biased manner which perpetuates the disadvantage or marginalized groups is also a real problem. As is the fact that education is done by outdated methods which underserve even the best served, on top of the inequities. The former one doesn't negate the latter two.
> Like… watering down math classes
This is not about “watering down” math classes, but the opposite; it is about applying evidence to improve the quality and equity of mathematical instructions.
I don't except that my tax dollars should be wasted on broken on biased math just because we haven't fixed racist violence by police.
This ignores a majority of students that are are well severed through the current curriculum and would advance more slowly under the proposal.
The framework cites the research that that isn't the case, where is yours that says it is?
People recognize that pretty easily and are instantly turned off. So yes, it backfires, poisoning any hope they had to convince. Re-read this comment section from top to bottom for your evidence.
It is most akin those who advocate for harsher penalties for white criminals to because penalties are disproportionately harsh for minorities.
I find it akin to forcing all K-12 students learning computer science to stay on Scratch and block-based programming (which is easily accessible to everyone), simply because the students taking more advanced programming courses who have a software developer for a parent will be unfairly advantaged over the ones who don't. I know people who have had all the resources available and wasted most of them, and others who had few resources available but took every one of them.
At the end of the day, I'd rather have the opportunity to hire a great software developer who has been developing their skills since a young age, rather than someone who was intentionally kept from real-world computer science until college in the name of equity. Similarly, I'd rather see prodigious mathematicians cultivated from a young age - I cannot imagine a situation where the next Ramanujan [1] is created by the California public education system.
By the way, I really appreciate the illuminating alternate description you provided of white supremacy - I hope you don't mind if I start repeating that one :)
For instance, my kid drew a rather detailed human face in the desmos (http://desmos.com) graphing program using line segments, quadratics, cosines, and sines.
Doing this teaches you about what the graphs of these functions look like, and how to translate/scale/rotate the axes to get the curve you want.
It's basically like parametric typography, or SVG.
The controversial stuff is not stated explicity: Removing advanced classes, forcing all students to adhere to the same curriculum, and grading based on subjective criteria are what people are upset about.
It's a typical motte and bailey switcheroo: put some generic language in a document claiming something like 'rigor expressed only in difficulty' to conceal the reality of what is actually happening.
Without the requirement that all children must be at the same level, some children would still race ahead, and in terms of appearances, that would severely risk the reputation of Equitable Math as the way to fall behind. The battleground is not on whether the Common Core should be deeper, or even whether the Common Core ought be reformed at all, but rather that all children should be at the same level.
The claims about white supremacy are not merely dressing. The ideological claims are the only interesting part of the document. All the pedagogical stuff you cite approvingly is just the same empty fluff that has dominated US education since the 1960s.
The recommendations are quite sane--seek student understanding over the correct answer, use examples students can relate to, etc. It's basically a few dozen pages of very sensible (perhaps even cliche) guidelines.
But throughout it's couched language claiming the opposite is white supremacy. Eg. grades stress getting the correct answer over comprehension, and are part of a White supremacist model.
I can allready see how the debate is going to end up, with each side talking past each other. The reformers will claim that the only reason you're opposed to it is because you support White supremacy. The traditionalists will say it's using race as a cudgel to silence opposition.
I took AP Calculus in high school and studied physics in undergrad so I've done a lot of calculus, but it honestly seems like a pretty niche subject when I think about it. It's hard to think of any times that it's applicable in my life any more. Some of the concepts are very beautiful, but a lot of things like the rote solving of integrals to get to a closed form solution can get pretty tedious and can be done by computers these days anyway.
At the same time, I didn't take any statistics or computer science in high school and really only had my first introduction to programming in college. Both of these seem like topics that should be prioritized above calculus for most high school students.
It is understandable that some students do not wish to pursue further mathematical studies, but should that translate into the requirement that all students must be at the same level? Or that Algebra shall not be offered in middle school? Note that schools are already free to offer Statistics or Computer Science, neither of which are respected by universities.
It is very difficult to create a program with sufficient reliability that universities are willing to accept some form of credits earned or requirements met.
All these delaying important subjects is going to let immigrants from other countries like India, China, Pakistan, Bangladesh etc excel while Canadians and Americans to fall behind. This is a stupid idea.
You are extrapolating from N=1 to a state of 36,000,000 people. Your experience is not the guiding star for state-wide policy.
Also consider this... the people who work on this stuff, have spend years and years on this stuff. Perhaps... they... know what they are talking about?
As someone with a kid, introducing subjects before kids are ready for it is counterproductive. It can cause confidence issues later, and doesn't help them learn earlier. By way of a small example, try to teach a 3 month old how to walk. Good luck, you aren't doing anything useful.
Now back to the immigrant thing, by now you surely must have realize you are in the upper X percentile of your peers from India. There are many many many, in fact most, Indians, who cannot do what you can do. Not even close. Basing educational policy on what you found easy with your Xth percentile intelligence is not going to be a great idea.
CBSE and ICSE boards, 2 of the major boards of education in India had calculus in grade 11 and 12. This wasn't me being exceptional, it was standard practice and millions of us learnt it. The millions of kids in India in CBSE and ICSE board education is much higher than CA's population.
You can check out the syllabus for grade 11 for ICSE board:
https://www.cisce.org/pdf/ISC-Class-XII-Syllabus-2016/17.%20...
Very basic differential calculus was introduced in grade 9/10 and then by grade 11, we were performing decently advanced differential calculus. In grade 11, integration calculus was also introduced and it went on to pretty advanced level by grade 12.
Calculus was also used in our Physics classes, so it was pretty much needed.
> try to teach a 3 month old how to walk
That's a ridiculous comparison.
[0] Search for "algebra" in https://www.kolmogorov.com/Books.html
I always find it hilarious that the pre college education in US is so messed up. Instead of doing Algebra 1, Algebra 2, calculus, geometry as one subject that you do in a year and then completely forgetting about it till the next time you have to do it, how about you do a little bit of everything every year from grade 8-12. Problem solved.
For e.g. in India you learn geometry, algebra, etc. every year from grade 6 to grade 12. i.e. You have a single subject called "Math" that teaches grade appropriate concepts in all the topics in math. Trains the mind gradually over 7 years instead of one big dump. In undergrad in USA, I cruised through most of my freshmen math classes because I had learnt most of it in high school.
A: If there's a geometric interpretation :-)
I don't understand. US high school kids only do math one year out of the 4? And nothing else math related during the other 3 years?
I mean, instead of doing a little bit of math spread across all the years so you know, they don't forget everything?
Does this go for other subjects as well?
To me, the question isn't whether Calculus will be useful to somebody who intends to study nursing, but rather whether the doorways to other venues will be made that much narrower, or closed altogether. Under Equitable Math, all children must be at the same level, whether they wish to pursue nursing or engineering.
Children and their families ought to have a choice, including the choice to march forward toward their individual academic ambition and ability.
That's not true; the proposed Framework model shifts from a focus on breadth differentiation to a focus on depth differentiation.
You could just as well argue that the existing approach tries to force all students to be “at the same level”, since it neglects the differentiation opportunity that the proposed framework focuses on. That would, also, be wrong, but no more wrong than your characterization.
The Common Core does not neglect differentiation opportunity, and neither does it dictate or detail that children must be in one class over another; that is left up to each state. Under the Common Core as implemented in California, children may take Algebra with an Algebra teacher based on their individual ability. The entire Common Core specification for math can be read in one day.
The Common Core does dictate learning targets to be met for any particular official class, whether that is Algebra I/II or Geometry. The Common Core also emphasizes deep learning over rote memorization, but it critically does not require that all students must be at the same level. This is the central point of contention, and not whether the Common Core ought go even deeper.
As a detail, note that Californian classrooms may have around 40 children in a math class, and that penalties for classroom sizes end in middle school. These are the conditions under which math teachers must address individual variability.
Equitable Math would be a SOLID win for private schools and after-school math programs such as RSM.
Should we be striving for equitable or equality?
"Children and their families ought to have a choice, including the choice to march forward toward their individual academic ambition and ability"
This doesn't sound equitable.
Do nurses actually use calculus?
I went to high school in California, I was able to take all the way up to what was called Calculus BC, which covered up to learning integration techniques. This was in a bay area high school that was underfunded, and the majority of our senior class didn't graduate.
But the vast majority of students stop at Algebra 2, and struggle through it.
I think schooling absolutely failed me in almost every regard once I made it past the 4th grade. Half of what I learned isn't even true anymore or were partial truths/mostly lies to make it easier for a 5th/6th grader to grok and they'll be told "the truth" at some point later in high school or college only to never be told the truth or not have the opportunity to attend college where you finally would have been told the truth.
Exposure to something is the first step in learning about something.
This is true of most levels of education. What you learn in elementary turns out to be bullshit because of what you learn in high school which turns out to be bullshit because of what you learn in undergrad which turns out to be bullshit because of graduate school which turns out to be bullshit because of the work of an army of scientists.
I agree that the nationwide baseline is abysmally, or even tragically, low. This is clearly problematic in and of itself. However, there isn’t a standard curriculum for US high schools as this varies widely by state and town/district/school.
No, he/she meant that US high schools divide Math into algebra, geometry, trig etc. which are taught in different years as opposed to simply having these as sections in a single Math textbook which increases in difficulty every year.
High school is too early to divide up Math into these subjects especially if you are going to be studying only one of these in a whole year.
I could be missing something though.
Politicians are not using math to decide which stocks to pick, they are using insider information.
edit: ok, it's clear that the parent comment was sarcasm now but you never know
99pi did a story on this some time ago. Having an election means that kids who are shy or not popular miss out. But who would otherwise have valuable skills and want to contribute. So randomly selecting kids but giving them an out if they don’t like the job ended up working really well.
Can this be applied to government???
I agree with you WRT age appropriate-ness. Just because something can or has been introduced at a certain age does not mean that is optimal. I recall a study I saw recently that showed delaying introducing one subject - it may have been math - to very young students had negligible impacts on their scores (compared to students who were introduced earlier) a few years later. The students with a delayed introduction caught up so quickly that the delay didn’t matter. I’ll see if I can dig up a link - EDIT, I’m struggling to find it under all of the COVID-related student-delay-catch-up articles.
9: 14-15
10: 15-16
11: 16-17
12: 17-18
Yes and there are some kids that act up or learn to hate education and the system for being forced into what amounts to remedial classes. Sometimes the brightest children are the most difficult precisely because they're not being challenged.
The ideal would be to have every student learn at their own pace. Some children could comprehend algebra in 8th grade, others may never fully comprehend it.
Obviously that's impossible at scale. So the best we can do is to separate kids based on ability and interest. Some children can grasp more advanced concepts at an earlier age, while others struggle. That's why generally in schools we have standard classes, special education and gifted classes. The best schools separate it even further offering additional lessons or tutoring to children that are especially curious or require more work.
Everyone benefits. This is common sense.
There's no such thing as "appropriate topics" for an age. It's all child specific.
https://journals.sagepub.com/doi/10.3102/01623737211008919
https://www.nber.org/papers/w17089
These programs are relatively expensive, and there’s a strong argument the gifted programs should be overhauled, or that the money could be better spent elsewhere.
Those are modern cut rate gifted programs.
The 90s had gifted programs where students who tested well got placed into a separate cohort for core classes (English, History, Math) in Middle and High School, or were in a dedicated classroom for elementary school.
The only educational purpose served was getting them out of the classroom so that more attention could be given to the dumber kids.
In elementary school gifted programs are often tracking people into advanced math, reading, and other subjects all at once. Plus teaching them extra stuff.
At higher grades, if it exists at all, its often tracking them into a different school that has both more advanced and more diverse classes.
> A gifted program is where you take some kids aside and teach them some random extra stuff, at the end of the day they're still in the regular classes with the other kids also and don't really have a chance to go any faster.
I’ve heard of lots of different gifted programs, and most don't fit that description.
My kid's school did exactly this for "gifted" elementary school kids. What saved him was being in split grade classes in 2nd and 3rd grades where he could move to the older student's side of the room for math and reading instruction. Eventually, he skipped 4th grade altogether and ended up with the peer group he was already spending much of his day with.
In middle school, the gifted kids got to go on one special field trip each year. By HS, there was a gifted program in name only. We paid someone to run the "gifted" program but I have no idea what she actually did. She wasn't even available to assist in college apps and there weren't any special programs that I ever saw. My kid, and his most motivated peers, all ended up at very good universities in spite of the lack of support from the school.
So much more was expected of us, that of course we came out learning more. 8th grade was a 20 page research project. 6th grade math was algebra, in 7th grade we learned logarithms and binary math.
When I went back to mainstream academics in high school, the difference was stark. In one of my city's top schools, students were still reading books out loud during class. Expected reading assignments were around a couple dozen pages a week. Math was all repeating what I had learned in middle school. Essays were a fraction the length and difficulty.
And in high school I knew plenty of smart kids who were bored to tears and misbehaved. Hell I watched one kid in Latin class piece his own nipple. (The teacher did nothing, possibly because said student was also pretty darn good at Latin...)
I wonder how a study is going to account for "smart kids who dropped out of school from sheer boredom".
Another aspect to examine is that behavior problems in gifted programs were, IMHO, much less than in mainstream classrooms. When all the students in the classroom are there to learn, no big surprise, learning gets done. Students turn in HW on time, listen when the teacher talks, and have expectations of not only themselves, but of each other.
Yes, gifted programs need to be accessible across socio-economic levels. The fact that I had to be bused to the rich part of town to go to a gifted program is a great example of classist and racist policies in action.
> while being fairly expensive.
I fail to see how gifted programs cost any more than regular programs. You are literally taking the highest achievers and placing them in a separate classroom for a few core subjects. For middle school and high school, there are no additional teachers, no additional programs in place, it is purely a cohort.
> and they don’t appear to make any meaningful difference in student engagement or motivation.
As someone from a poor working class family, gifted programs gave me the opportunity to rise up out of generations of being poor.
Gifted programs need to be made available to everyone who qualifies.
The fact is, one college graduate can help elevate an entire family. Every student needs to be given the chance to reach their full potential, and for some, that means placing them in an environment which has an expectation of academic excellence and lifelong achievement.
Edit: I just reviewed the study my local school district did to justify shutting down their spectrum program. None of the reasons (!!!) had to do with student outcomes.
I would suggest that your experiences may not have been the norm. Anecdotally - I was also in a gifted program, and it was essentially a waste of the school’s money. We had an designated educator for the gifted program, and we mostly did things that were interesting… but didn’t really advance our education a lot. Even when we did cover advanced material, it didn’t really make a difference because we would have learned it in a year or two anyways. That assigned educator would have made a bigger difference helping struggling students rather than us.
It sounds like your program was maybe better targeted than ours, or you were a better fit for the model than me and my cohort. But on average, the data seems to suggest that most students are not significantly changed by gifted programs.
I really don't need a study telling me my child won't benefit from a gifted program. It's a parent's right to decide for themselves. I personally know many people that have benefitted and it made their childhood bearable.
Barring a time machine or the discovery of a way to skip across a multiverse, this is an assertion without much of a control group.
That’s why we need studies.
Year 7 was geometry focused, Pythagoras theorem a lot of graphing things with protractors compasses etc. Calculating angles from parallel lines stuff like that.
Year 8 was much more algebra centric quadradic formula, simultaneous equations, expansion of brackets.
Year 9 was Trigonometry I remember there was a lot of 3d shapes and volumes. Volume of spheres, cones, pyramids etc.
Year 10 was Conic sections circles Ellipsis Parabolas hyperbola etc a lot of graphing again and more advanced trig.
In Year 11 and 12 I took the most advanced of the math streams I had two math classes. My other courses were Physics, Chemistry, Biology and English So math was a third of my course load, more if you counted physics which was highly math based as well.
Year 11 One class was Calculus focused, limits, fundamental theorem, basic derivatives and simple integration (Simpson's rule and stuff like that). The other class was linear algebra, vecrors, dot and cross products basic matrix manipulation and matrix transformation - reflectons skew etc.
Year 12 We covered parametric calculus, complex numbers more advanced integration and derivatives (Chain rule, substitutions etc). I vaguely remember we covered a bit of hyperbolic functions (cosh, sinh etc). The other course was statistics and probability as well things like sequences and series, stuff like binomial theorem.
I studied Engineering at uni and my first year university math was pretty much a repeat of year 11 and 12 math but a bit more in depth.
I was under the impression that (actual) communist educational systems were geared predominantly toward the most advanced students, rather than the other way around. Cranking out prizewinning physicists, mathematicians, and chess grand-masters at a somewhat greater than expected rate.
Not "educational communism" in the sense of educational systems modeled on those of communist countries.
The analogy is from "if I can't afford a car, then nobody should be allowed to have a car" to "if I can't understand algebra, then nobody should be allowed to learn algebra".
Read about Spivak's Calculus.
Michael Spivak is an American mathematician born in Queens, New York.
Your point reminds me of an experience I had in grad school. A good friend in the program was from (communist) Romania. We were both looking at the weekly math challenge that one of our professors posted in the hallway. It was something like construct with compass and straightedge the eight circles that are tangent to all three given (arbitrary sized and positioned) circles.
I was good at geometry in school, very good, head and shoulders above my fellow students. I really had no idea how to solve the problem and was fumbling around with it when I Romanian friend took a look and knew the correct approach immediately. It involved an isomorphic mapping of the circles into some alternate collection of straight line segments, solving the problem in that space, and then inverting the isomorphism (I think. It was many years ago--before the fall of the Berlin Wall). His high school training in geometry was clearly much deeper than mine was.
Seriously? Basic algebra was like 7th or 8th grade for me.
I sincerely hope you're not serious about this. I took algebra in 7th grade and I was considered a remedial student with habitually poor grades. If you're telling me I was actually 2 years advanced by present standards, then the situation in California must be deteriorating severely.
For reference, this was in an underfunded rural American public school. I was 12.
When I was in 7th grade, we were taught "what a negative number is." That entire year was a complete and utter waste. But fortunately, 8th grade offered Algebra where I could get back on track.
This was 30 years ago, in California. Public school math standards are a joke here, and apparently getting even worse.
> San Francisco pioneered key aspects of the new approach, opting in 2014 to delay algebra instruction until 9th grade and to push advanced mathematics courses until at least after 10th grade as a means of promoting equity.
The school failed the most vulnerable children by objective measures, so they're just trying to get rid of those measures entirely.
Really, truly worrying that instead of focusing resources to help kids improve and overcome a challenge the answer is to remove the challenge instead.
On national standardized tests, California ranks in the bottom quartile among all states and U.S. territories for 8th grade math scores.
Hmm…
Worlds 5th largest GDP, internationally desirable cities, some of the highest housing prices that’s always being bought over asking price, often in cash - internationally acclaimed state wide university system, one of the cultural & academic centers of the nation…
I know it’s like, my opinion, but I think the situation in California is fine. I’d look towards the states that have ranked last & near last in education for decades without any movement in a better direction before commenting on California.
Even more, for those who do well enough in k-12 in those dead last states… well, they brain drain to greener pastures. Like California.
You know damned well that it's not many. California is a success because of immigrants from other countries and states. Think about the founders of the current top valuation tech companies in California. How many were raised in California? Zuck? Nope. Maryland. Sergey Brin? Nope, educated in Maryland as well. Larry Page? Nope, raised and educated in Michigan. Steve Jobs was educated in California, 60 years ago, so you've got that. Not relevant to this conversation. What about his successor Tim Cook? Oops, he was raised and educated in Alabama. Reed Hastings? Nope, raised and educated in Boston.
So while the above proves your final point, it basically highlights the fact that California does well for structural and historical reasons, like the fact that many VCs required any company they invested in to relocate to the Valley, and other things like network effects.
Kids with families who value education do better. Kids with parents who punish them if they don't do their homework do better.
When you isolate for income, there are large discrepancies in success between various cultural groups. Appalachian whites (my family) don't do well compared to many groups of the same income. The culture doesn't prize education, and even views it as being effeminate or "selling out". But that's only a small piece. A big piece of it is that parents don't give a shit about their kid's success in school, and that is very big in certain cultures.
My wife is the daughter of Filipino immigrants, and from the day my son started 1st grade, if he doesn't get all As, the attitude is that he has failed. At one point, I was going to argue with her, but I looked at my siblings, and my cousins (primarily white trash losers), and then looked at her family's success, and decided that she knew something I didn't.
My son has a TV and an Xbox in his room. The controllers and remotes are all kept locked away in my closet. If he doesn't get straight A's on his report card, all of it stays locked in my closet, even on weekends. We did this in the Fall of 2020 when he got all A's and a B+ in one class. He went all of the spring semester with no access to his TV or video games. He got them back in the summer after getting straight A's on his report card. (He's a 10th grader now). Contrast this with my poor, white working class siblings and how they raise their sons. My sister frequently complains about how bad her son's grades are (he's the same age as my son) and throws her hands in the air as if she's unable to do anything about it. He has multiple game systems in his room, and the last time I visited, when I woke up to take a piss, his light was on and he was playing games at 3 AM. This was a day after she had complained about his low C average. She coddles him, has low expectations for him, and ignores her own obvious parenting failures. She's a great representation for why so many American public schools are filled with thoroughly mediocre students.
If you have kids, get the fucking electronics out of their hands. If they aren't bored and regularly bugging you about being bored, it's probably because they are being entertained by their smartphones or video games, and you are fucking up as a parent.
Look at Nigerian American parents, or Asian American parents. Instead of doing what my redneck sister and many others do, and rationalizing the obvious differences by assuming that "they are too strict and are raising maladjusted nerds", imitate them. They will happily share their parenting strategies with you, and rule number one is that they aren't their kid's friends. They don't give a shit if their kids like them NOW. They care if their kids will like them when they are winning as adults.
Far too many successful people I meet complain about their parents being too hard on them, never stopping to look around at their current success and realizing that their parents made it possible.
I didn't take Algebra in highschool, so.. maybe? 5th and 6th grade were called Pre-Algebra. 7th and 8th were Algebra. 9th was Geometry, 10th was Trig, and 11th and 12th were Calc.
If I recall this is how my high school was ~20 years ago and almost everyone still took at least 3 years of math with what felt like the majority still taking 4.
Those are unusually lenient from what I've seen; my home school district [not in California] currently requires 4 years of English, 3 years each of math, science, and social studies, 2 each of PE and foreign language or fine arts, 1 year of economics/personal finance, and 4 electives. And apparently 1 course must be AP, IB or honors. As a matter of practice, you'd be expected to take 4 years of English, math, science, and social studies, and at least 3 of foreign language anyways (and indeed, there's an 'advanced degree' that has those requirements; it looks like 2/3 of students graduated with the 'advanced degree').
I had not looked at what it encompassed before I signed up. I was given a huge book to study from. I glanced at it briefly each day for two weeks and then sat for the exams.
I got 99% in all subjects. Apparently that was the maximum possible as the score went from 0-99% for reasons I didn't bother to explore.
It was disturbingly easy. And bear in mind that I was thrown out of my British secondary school at 16 because my exam scores were the worst on record at my school, allegedly.
That is good, but also consider that most people taking the GED have some sort of problem preventing them from completing a regular high school diploma.
Don't assume it's an academic problem though. My grandfather beat my father for years, until my father ran away from home when he was 15, consequently never finishing highschool. He got a GED years later, then eventually a masters degree. There are unfortunately many people in circumstances like his or similar, unable to finish highschool for non-academic reasons. It's important to keep this in mind because otherwise GEDs will be associated with poor academic performance, which is unfair.
A regular Canadian high school graduate is not eligible for admissions to many of the UK universities based on the little time I’ve spent looking at the admissions standards.
To contrast I earned some college credits during my last two years of high school due to advanced placement tests.
There must have been some use in taking it for you, right?
Otherwise, I guess I am missing the joke.
The oddest reason I've ever heard for taking a standardized test was from a fellow who was an SAT tutor. He would take the test in order to covertly write down good math questions onto his calculator while the instructors weren't looking. He made a point of telling me that when you do this, you have to make sure you answer most questions incorrectly. He knew other tutors who took the tests, got perfect scores, and then were told they couldn't take it again. There was almost pride in his voice when he said to me (paraphrased), "If CollegeBoard sees a 30-year-old man acing the SAT, they're going to look at him funny if he tries to take it again. If they see a 30-year-old man bombing the SAT repeatedly, they're just going to think he's stupid."
Doing this is of course morally dubious, to put it nicely. But I still am amused by the whole thing. There's a degree of "sticking it to the man" both in pilfering question examples from CollegeBoard and lowering the curve by an infinitesimally small amount when he takes the exams.
To add another anecdote, I know many people who have been through the prison system. Certain prisons will give you a test on entry to see where your skill level is on the 3 Rs. The firm rule is FAIL THE TEST. Do not try to be smart. The dumbest ones get the priority for school places in the prison. Schooling = extra credits = early release from custody.
In my experience, each year built off of the previous and implicitly provided a refresher.
The thing with schools in India though is, regardless of your status as a school, your curriculum is decided by one of the central authorities, either at a national level or at state level, and since the standardized tests for college admissions are the same for everyone, the variations in curriculum among these different schools are small.
Kids would repeat grades or have remedial classes for doing poorly. And the answer was to not lower the bar for everyone, but make students work harder for doing bad.
Things are just spread out from 6th grade to 12th grade and specialization only happens during the last 2 years of high school.
Literacy Rate of India 2021 - To know development in a society, Literacy is another proper indicator of economic development. For purpose of census, a person in age limit of seven and above, who can both write and read with understanding in any of the language is considered as a literate in India. ... Although India has raised its current literacy rate of 74.04% (2021) from 12% at the time of Independence in 1947, its still lag behind the world average literacy rate of 84%. Compared with other nations, Republic of India has the largest illiterate population.
I’ve taken though linear, diffeq, and discrete. Rarely use them. It’s a massive waste for most people.
They should be concentrating on what I would call “home economics”. That is, economics of the home. Edu on budget balancing, taxes, cost of things so you don’t eat out so much, cost of repair so you learn to fix things, etc.
'Regular Teaching' works 100% well everywhere around the world where students show up ready to learn.
This is 100% a community/parent/student issue.
More conscientiousness, community participation, stable / 2 parent / married homes, 'Some Kind of Health Insurance', steady jobs, low crime, no druggie/prison parents, not living in fear, no gangs, no gang culture, other students who have normal levels of academic (and other) interests.
And they'll do fine.
Big reforms in Healthcare, Justice and for Economic Stability / Jobs would go a long way, but it will also take community participation.
It's not the curriculum or teachers. They work fine everywhere else, they work fine in Cali.
Kids that have something resembling what we might think of as a 'normal childhood' will do 'mostly fine'.
As for why shooting basketball 10,000 times day is considered heroic hardworking while doing 10 math exercises a day is considered being privileged and cramming and prepping and Asian? Well, that beats me too.
SFUSD claims their reforms pushing algebra to 9th grade decreased the algebra re-take rate from 40% to 7%. However, the drop in re-take rate was actually caused primarily by the removal of the requirement to pass a curriculum exam. Quite simply, if “knowing algebra” is removed as a requirement to pass algebra, more people will pass algebra.
More at https://www.familiesforsanfrancisco.com/updates/inequity-in-...
I grew up in a diverse city where all the advanced schools and classes were filled with white kids, and it was incredibly obvious that it was due to socioeconomic factors.
Kids in my classes were going to expensive tutors and had parents in high paying jobs that could be around to help them.
My neighbor on the other hand was an immigrant taking care of younger siblings after school and eventually working to help his mom when he was old enough. No time or money for tutoring, or even homework for that matter. I was in the same boat for a long time but was fortunate enough to not need to study as much as my peers, some who had enormous amounts of help. As an adult I still can’t afford the amount of tutoring they were getting, some even paid someone to write college admission essays.
It’s 20 years later and it’s all the same, if not worse, and I still get mad about it.
Look, kids who love math and nerd out in their spare time will still be tearing into calc in uni.
Those who don't will still pick up enough to hit the trades or JOB.
The kids who don't need advanced maths might actually get more out of what they do learn as it's delivered at a higher age.
Ok who knows maybe it has marginally lower outcomes over all. No one knows and the people in this thread decrying the end of exceptionalism are deluding themselves into thinking life outcomes are extremely sensitive to high school educational content. I don't think that's verifiable.
Getting people to school and keeping them from dropping out is likely a better first order optimization to overall outcomes. Kids are still going to get their calcs in uni and the universities will still be pumping out overly-educated overly-indebted young adults...
Once we take this to it's logical conclusion and reset the achievment bar to absolute zero, it will be impossible for there to be any inequality.
All classess straight through undergrad could be limited to a combination of nap time and snack time.
Calculus? I wonder how that's taught today. I had way too much stuff about summing infinite series, which you don't really do very often. I think calculus should be taught in conjunction with Newtonian physics, so you see how it predicts what happens in simple physical situations. This provides motivation.
Let's take away the opportunities to get ahead early, because it may disrupt some egalitarian principles that are totally absent in the real world. As someone who majored in mathematics and was involved in educating K-12 students for many years, I find this to be completely ignorant of the reality behind school districts like those in the Bay Area, where affluent kids take Russian math after school to compensate for the inadequacies in their school's mathematics curriculum.
This is basically what we're dealing with here in California: https://equitablemath.org/wp-content/uploads/sites/2/2020/11...
"The framework for deconstructing racism in mathematics offers essential characteristics of antiracist math educators and critical approaches to dismantling white supremacy in math classrooms by making visible the toxic characteristics of white supremacy culture with respect to math."
On page 8, the authors claim that one way white supremacy manifests itself is when "students are required to show their work in standardized, prescribed ways". This is literally the definition of mathematical notation, and the use of standardized notation is fundamental to being able to communicate with other mathematicians.
By the end of high school, I'd taken the equivalent of two semesters of university-level calculus, which allowed me to skip those classes when I went to college, and take more challenging courses. It's hard to imagine students who first take algebra in 9th grade progressing to anything beyond the most basic of calculus (at best) before graduating from high school.
Judging by other responses here, I'm not even a particularly special or advanced case, with some kids being introduced to basic algebra many years before I was. Which makes sense. If you can teach a kid "1 + 1 = ?", then at some point shortly after, you can start to teach "1 + ? = 2". Bam: basic algebra.
It just sounds like instead of getting students to stretch, we're pushing the gifted kids down to the lowest common denominator. It makes me assume that school administrators just want to avoid conflict with parents and hurt feelings among kids when they bucket students between remedial/standard/honors classes. We're sacrificing education for temporary good feelings.
Without even mentioning the word variable, algebra, or any other terms, they began teaching us about these concepts.
They started with a problem where the answer is so easy everyone can get it. No formalization to start with, just, here's a simple example that you can immediately relate to. Only after doing this do you need to learn and understand the formalization and theory of the concepts.
I find the same is true in programming. Often to learn something new, it's better to copy and run a code snippet that does the new thing. Only after running it, seeing the result, seeing it work is the formalization and theory needed. Then you just rinse and repeat to get better and better at it.
As an aside: I think had the teacher asked us for a name as well instead of using the ?, we could have even started learning about using variables earlier. By our own laziness as kids, someone would likely have gotten tired of writing out "my number that I'm trying to find" + 3 = 7 and thought about shortening it by some degree. It would have felt empowering to have that insight come from a class mate, and if not, the teacher could always introduce it on their own.
ETA
I also had a college professor who started each new unit by explicitly motivating why we were going to learn, what we were going to learn, and how it related to what we just learned.
That context was a huge help in learning the material.
It's the principle of experiential learning. Pushing back such a basic concept of math would only disadvantage society.
What are the psychological effects of daily reminders of inequality, equity, and systems of white supremacy. Could this grow resentment, hostility, and/or entitlement?
How is delaying mathematics equitable? How does this represent equity in a global economy?
How does equity and social justice in education respond to individual talent, aptitude, mental health, physical health, and/or socioeconomic status?
Maybe one section that's relevant here is the one on "pseudo-mathematics":
> The cultural problem is a self-perpetuating monster: students learn about math from their teachers, and teachers learn about it from their teachers, so this lack of understanding and appreciation for mathematics in our culture replicates itself indefinitely. Worse, the perpetuation of this “pseudo-mathematics,” this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values. Those who have become adept at it derive a great deal of self-esteem from their success. The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it’s about making new directions.
Many people on this website did well at the pseudo-mathematics taught in schools and think of themselves as being improved by learning it. If this (pseudo-)math is what distinguishes the "smart kids" from the rest, our "smart kids" will be harmed by delaying it. But what if the pseudo-math and the concept of "smart kid" it creates is actually harmful, both to the practice of real math and to the kids' own sense of self-worth?
An old short story about enforced equality. Intelligent people had noise makers on ears to keep them from concentrating. Beautiful people were made to look like clowns.
No one could stand out, no one could excel.
My parents immigrated from Romania and were part of the Florida Romanian community. Many were poor, didn't really have a great support system, and didnt really get America. Many of the kids in that community just dropped out or didn't do well in school and that's largely because of a poor home life and just not having access to anything. All the countries that have great education systems also have great support systems for families.
Algebra isn't hard (though it is time consuming imo), you can pass all the tests with memorization since it's applying a few patterns over and over again. Delaying it isn't going to make people better at it.
https://www.apa.org/pi/ses/resources/indicator/2014/06/child... It seems like alleviating poverty will help? It also just feels... obvious?
Language issues are actually a likely challenge for some Latino students.
Which could actually be a reasonable design for school.
If public schools can't teach advanced topics, they could still handle the basics, provide childcare, and help to socialize kids.
And then tutors (backed by a voucher system), parents, and the internet can do the teaching of advanced topics.
> San Francisco Unified School District touted the effort as a success, asserting that algebra failure rates fell and the number of students taking advanced math rose as a result of the change
> "There’s a huge problem with math instruction right now. The way things are set up, it’s not giving everybody a chance to learn math at the highest levels"
This really feels like they lowered the bar and are now excited that more people are able to jump over it.
Also, that last quote is infuriating. Nobody will have a chance to learn math at the highest level now, at least not in high school.
Rather than lift those who struggle, let's drag down those doing well, or so it seems.
The “equitable math” is clearly a crime against children.
But another thing is, basic maths is a life skill. Schools aim for an ambitious curriculum, but many people leave school and can’t add, or don’t understand fractions (i don’t know about the US but certainly true in the UK and Poland). These are all people who passed through many years of maths teaching, algebra and all, and can’t add 1/2 to 1/3.
At some level, we have to do something about this. People make life decisions based on their [lack of] understanding of maths, and it’s rarely algebra and calculus we’re talking about.
We were solving more complex polynomials in 5th grade. By 8th grade, we were already through trigonometry and some were taking entry level calculus.
To me, the concept that you won't be introduced to algebra as a class until 9th grade is frightening.
Even in regular classes by the 5th grade they were introducing the concepts of algebra to the rest of the class.
In an Ivy League PhD physics class more than half of the students thought that equality was something between a mechanical operation, e.g. 1 + 3 = 4 means you add 1 + 3 and the result is 4, or assignment, e.g. x = 3 means that for everything that follows you can replace x by 3.
The idea that it's a binary predicate was something that only people who had done logic or something adjacent at undergrad even understood. Viz. the type of = is (* x *) -> Bool, or in words an equality just returns true if there exists a way to transform one input of the equality to the other and false otherwise.
The confusing part is that for an equation like x + 2 = 3 you're given the predicate for the of set/tuple defined by abstraction using that predicate, e.g. the set {x | x + 2 = 3 and x in R} or the tuple (x | x^2 = 0) if we care about repeated answers. Something that is not at all obvious from just being given x + 2 = 3, which without a lot of implicit context is a well formed sentence of algebra with no intrinsic meaning.
If all algebra problems were reduced to something like "List all members of the set {x | x^2 - 3 = 9 and x is real}" then we have solved a huge part of the problem.
Along with NYC mayor deBlasio seeking to terminate that city's gifted and talented education programs as well as Virginia's recent approach to "equity" by decontenting gifted education. The examples demonstrate the illiberal trends we are seeing in the U.S. wherein novel concepts like "equity" replace "equality" and merit is seen as racist.
See https://www.nytimes.com/2021/10/08/world/nyc-schools-will-re...
See also https://scottaaronson.blog/?p=4979
See also https://bariweiss.substack.com/p/mit-abandons-its-mission-an...
If you don't want to call that a "racist" system we can call it an unequal system or a caste system; but the trend you're seeing is an effort to fix that system.
The people who were (unknowingly?) on the PLUS side of the equation, they're going to complain loudly as it gets leveled out.
And let's pretend Asians don't exist. Affirmative action is about keeping Asian numbers down. So is getting rid of gifted programmes.
I'd say the podcast is a lot more racist than the school system, since it worries about people of the wrong race learning too much. But in terms of educational caste systems, it's true that education does create a caste system because we have no good trade school or vocational infrastructure.
To address that, provide more opportunities for students who don't require advanced math skills to succeed by establishing and funding quality vocational training, rather than preventing those who are faster at math from getting the best education they can.
Don't worry about students learning too much. Don't assume that every area has to have equal racial outcomes, because no area will have equal racial outcomes.
It doesn't. It worries about the students being warehoused in sub-par schools while claiming to give everyone the same education.
> Even for the highest-achieving students, pressures to use mathematics courses as social capital for advancement can often undercut efforts to promote learning with understanding. This often results in what some deem a “rush to calculus,” which has not helped students. Bressoud (2017) studied the mathematics pathways of students moving from calculus to college. He found that out of the 800,000 students who take calculus in high school, roughly 250,000 or 31.25 percent of students move ‘backwards’ and take precalculus, college algebra, or remedial mathematics. Roughly 150,000 students take other courses such as Business Calculus, Statistics, or no mathematics course at all. Another 250,000, retake Calculus 1 and of these students about 60 percent of them earn an A or B and 40 percent earn a C or lower. Only 150,000 or 19 percent of students go on to Calculus II. This signals that the approach that is so prevalent in schools––of rushing students to calculus, without depth of understanding––is not helping their long term mathematics preparation.
This basically lines up with my experience. I was in accelerated math and took AP Calc AB in High School. I got an A, but only by memorizing the symbol manipulation rules: I could't have explained why they worked. I don't think I could have even explained what calculus was for—and I was too busy trying to maximize my grades in 5 other AP classes to bother finding out. I got into my first choice of college and was sufficiently dissatisfied with math that I didn't take any classes in it until I was required to do so after I declared a major in Computer Science. I took Calc II and Linear algebra and got Cs in both.
... huh? Does anyone know what this looks like?
> "The concept of mathematics being purely objective is unequivocally false, and teaching it is even much less so. Upholding the idea that there are always right and wrong answers perpetuate objectivity as well as fear of open conflict."
https://www.newsweek.com/math-suffers-white-supremacy-accord...
Incorporate the history of mathematics into lessons.
• Verbal Example: Why do you think we call it Pythagorean’s theorem, when it was used before he was even born? What should we call it instead?
> She noted that an earlier draft of the framework included sample lessons on calculating a school cafeteria’s food waste — but that many of her students would have found the entire exercise alienating because they lack food security at home.
.... .... how about we fix the lack of food security instead of all of this!?
It’s an exceedingly dumb setup. In my highschool it was optional in grade 9 and like another commenter said only 2 years of ANY math was required. Despite passing a placement test in 6th grade they made we wait till 8th grade to join the 9th grade “advanced” math class which taught algebra. My school did not even offer calculus for any grade which made it more or less impossible to even apply for any of the top us universities
Quote source: https://www.usatoday.com/story/news/education/2020/02/28/mat...
More people should know stats, and this doesn't need to be strictly sequenced with those other concepts. Yes, integrals show up with continuous distributions, but we don't need to really care that much. But if we had a population that understood confidence intervals, (in)dependence, correlation etc at a conceptual level, would we fall for fewer dubious claims?
Discrete math, like enough combinatorics to understand why some families of things that sound simple are huge? Or enough to communicate the idea of a homomorphism?
What if our concept of "woke" math introduced posets, and the idea that things can be literally incomparable?
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First off, I believe in and trust the policy experts. If they are saying that algebra for everyone as a compulsory subject in grade 9 isn't helpful, it's quite possible they know what they are talking about.
A lot of the comments in here are varities of "if you don't try harder then you wont win" basically. The problem... is that really how teaching kids work? How do you know that is how it works? Your N=1 personal experience is not really the right evidence for running a state-wide policy. Additionally, some of you are probably 99th percentile intelligence, and really what worked for you won't work for, say, the other 99% of people.
Secondly, education is a complex issue. Schools are being expected to pick up the slack from every single societal problem, all the while Oh So Smart People endlessly shit on them. I'm not even joking about every single societal problem... here are some things schools are expected to pick up for: - Food poverty: Feeding kids at school because they didn't eat at home - Food quality: Feeding kids RIGHT with GOOD food - Parental availability: Hard to read to your kids when you are working tons of hours or extra jobs. Schools are expected to paper over this deficit. - Redlining/poverty: Schools are expected to raise kids up out of poverty, with practically no other help, and a lot of un-help (police at schools arent helping) - Gun violence: Kids are expected to do active shooter drills, nuff said. That's messed up.
One thing to remember about people who are from other places like India and such, if you are here and commenting here, perhaps your school isn't a representative sample of everyone where you were from. Here in the US, it's common for private school to kick out kids who don't academically perform, which means you have a self selection effect. So pointing out that "private schools do X why can't everyone do X" is useless, because the schools have, by definition, selected those students that can do X and everyone else was dropped on the floor.
Edit: fixed age range
I was curious and followed some of the links in the article, some of the PDFs seem to imply that the first concepts of algebra are in fact introduced in grade 6 (which wouldn't be too bad). But I couldn't find a definitive answer (I got bored by too many policy documents and couldn't find an actual curriculum document).
Many of them carefully plotted their way through college, doing as much as they can to avoid math.
Of course the kids are bored when it's taught with this attitude.
1. Enrollment in AP Calculus decreased and enrollment in AP stats increased:
AP Calc BC -27%
AP Calc AB -12%
AP Stats +30%
2. The percentage of students who met CAASPP standards dropped from 53% to 49%
https://twitter.com/SteveMillerOC/status/1400948830397341698
As such, there is no incentive to make the best of home-grown talent. There is no skin in the game.
This is the left-wing version of discouraging the teaching of evolution. Unfortunately in California these irrational folks have a big influence.
From my own experience, I would have been more enthusiastic with less homework, less rote problem solving (of dozens per night) and more visualization. Unfortunately animation/video wasn't really a thing until recently, but might help in the future.
This is obviously not a reasonable metric due to many factors such as age, brain development, maturity and additional adjacent curriculum.
I don't get it though.. algebra is just variables right? Aren't we teaching programming to elementary schoolers? I know I'd written my first MMO bot by 9th grade...
Perhaps programming is a more 'tangible' way for children to experience algebra, rather than paper abstractions?
not only do they provide additional space for engagement in a healthy environment, they also provide something that was always important for me when i was younger, longer goals or projects that learning lands in the critical path for.
problem sets are pretty boring, especially grade school calculations, i always needed a carrot to do boring things.
Delaying is not going to do thing for kids who are not into math, but will screw others who are into it.
Just imagine if Ramanujam has to wait till 9th grade to learn math.
Seriously speaking, this is going to increase the social divide between the families who rely on the public schools, and the families who are educated enough to teach their own children or can hire the tutors.
Also my brother's Chinese wife is on faculty at an Ivy League school and she was explicitly informed that when discussing diversity issues, she is white.
The mind boggles
Because immigration policy and conditions highly selects Asians for educational achievement.
Hispanic immigrants are basically selected inversely, whereas blacks are overwhelmingly not immigrants or early-generation Americans.
https://items.ssrc.org/from-our-programs/it-takes-more-than-...
Some Asians were even put in concentration camps 80 years ago and were heavily discriminated against.
I understand the argument about Hispanics since many are new immigrants though.
I wish the article gave some examples and explanations for this.
That was annoying. If I was able to take Algebra in 7th or 8th grade, I could have gone further in high school.
I ask since I have taken a course on QFT lite. We had to spend three weeks just doing tensors, and this was after everyone was comfortable with linear algebra and calculus and so forth.
/s, or is it??
That presumably means any kind of complex education will have problems. And adjusting to the bottom half of the distribution means that smarter or even average people suffer from this focus on the "least common denominator"! People are NOT all the same and interchangeable so the best education strategy is to tune the process to fit individuals instead.
Glad I'm gone from California. It's sad but I've written off all emotional attachments to the state and accepted that California's best times are a good 50 years ago.
Back when I was a kid, I was in the California state "Gifted Child" program and it was instrumental in getting me into technology as a career. That can't happen now to anyone like who I was back then. And that demographic that is defining this change in education focus will never achieve anything like I have in my career because this is aligned to the state IQ of 95.5!
https://www.nbcsandiego.com/news/local/san-diego-unified-sch...
Are they talking about moving those 6-8th grade parts to 9th grade?
It’s going to have the complete opposite effect that they’re going for
The liberals were 100% for the change, and said it will achieve more equity, inclusion, etc.
The conservatives were equally supportive of the change, but for an entirely different (and probably selfish, though equally valid) reason. They argued that this would actually give their kids a leg up over the general population, because they were going to continue to take advanced math and advanced placement tests, it'll just be in a more private, exclusive, concentrated setting than before, with other highly motivated, self-selected kids, which they took as having a positive effect on their own kids. By making something that was widely available more exclusive, it's actually a net-benefit to them.
I thought it was an interesting take.
The implication should be I NEED TO WORK MORE. Not lets lower the level.
readiness of the kid is as important as the quality of teachers, rest is just bunch of opinions
Teach children what variables are as soon as you can.
In the 80s it was not uncommon (at least in the Jesuit schools I attended) that Algebraic concepts would be introduced to students at early as 5th grade, but definitely by junior high (7th/8th) and while I hated math (especially at the time) it wasn't something I thought I needed to be older to grok...I needed less psychotic, rigid teaching from nuns with all the compassion of Stalin, and more guidance, which other students in similar schools got in spades and had no issue with.
A few examples...(highlights mine)
>Does the draft Mathematics Framework eliminate middle school mathematics acceleration programs?
>No. The draft Mathematics Framework does not eliminate middle school mathematics acceleration programs (including programs that offer Integrated Math 1 or Algebra 1 courses to grade eight students). The draft Mathematics Framework emphasizes the importance of following the sequenced progression of topics laid out in the Common Core State Standards for Mathematics (CCSSM) and considers the latest research on the impact of skipping grades or undermining the sequences progression. Additionally, the CA CCSSM are significantly more rigorous than those from previous grade eight content standards. They address the foundations of algebra and geometry by including content that was previously part of the Algebra I course, including but not limited to a more in-depth study of linear relationships and equations, a more formal treatment of functions, and the exploration of irrational numbers.
>Does the draft Mathematics Framework remove high school calculus?
>No. The draft Mathematics Framework includes calculus in the possible high school pathways, while also presenting research that the “rush to calculus” without the depth of understanding is not helpful to students’ long-term mathematics preparation. Data shows that about one-half of all high school students who take calculus repeat the course in college or take pre-calculus in college.
In summary: everyone is looking counting how many math courses students manage to get through and presuming that taking a course = mastery which it does not. The basis of this, frankly, is similar to the common core argument - different assumptions about evidence. Parents want to see their kids taking algebra and calculus because that is (to be frank) the best evidence they have of their learning while educational researchers (not teachers, researchers) are looking at meaningful assessment data.
I teach college course to engineering students at a highly ranked research university in the US. Frankly, the majority of my students have taken more math classes by the time they get to me in their junior year than I did by the end of my masters degree. The problem is they understand very little of it. Sure, sometimes, they can execute procedures. But they do not have mastery, they do not have teh ability to apply math to meaningful situations, and they absolutely do not have the ability to use math to evaluate technical problems. They are calculators not users of math - that is the problem this seeks to address
Back when I was in junior high and high-school in the late 80's and early 90's... math classes had hard-bound printed math books that actually had lessons and clear examples so that it was possible to learn math concepts, on your own, even if the teacher didn't know what they were doing. Whatever happened to good books?... it is not like the subject matter has changed in the past 20-30 years. I thought it is proven that students learn better from quality printed material, with appropriate use of color, over e-screens (correct me if I'm wrong) and yet all education is going to screens.
I had great teachers in HS; both my physics teacher and math teacher had masters degrees in their respective fields. Today, there is no good financial reason to be a teacher with a Physics, Math, or Engineering degree in most CA school districts and that is, I think, a big part of the problem. If you don't have good teachers who can present a topic well and engage a class-room then students aren't going to learn the topic and progression through mathematical curricula is going to fall.
Another factor is probably demographic. This is anecdotal but I switched high schools after my freshman year from a HS in a lower middle class area in Sacramento to a pretty wealthy, upper middle-class area in Southern California and the level of the average student was quite a bit higher. The teachers were probably better overall in the SoCal HS but I don't think the teachers were that much better. But there was huge cultural difference in the student body of the two schools. At the Sacramento HS, I took geometry as a freshman and there were a lot of juniors and seniors in the class. None of them were dumb people... it is just that doing well in math and the going to a good college was not something on the average student's mind in a poor community. At the SoCal HS, most students were very interested in doing well in school, took math and science semi-seriously, and looked towards going to best college they could get into. Almost every student at the SoCal HS at least took Trig/Pre-Calculus.
Bring this all to the topic at hand... this does feel like some Kurt Vonnegut stuff and I am really disappointed. Holding back math education in mainstream public schools is going to push more parents, who can afford the time/money [read: the more affluent], to put their kids in charter schools, private schools, or supplemental education for math [e.g. Kumon]. This going to limit opportunity for the less affluent and probably increase the gap in math education across economic dividing lines. This may also pull money away from public schools over time.
It’s a trip that it’s couched in language that apparently is pissing a lot of people off (and bringing up some resentment about race in a direction that I find somewhat surprising.)
A lot of folks seem to be posting that if kids have to wait a little longer, it’ll somehow negatively impact all of the super smart 13 year olds’ ability to learn at maximum speed and adversely affect the talented and bright students that just want to learn math due to the fact that the school is somehow withholding knowledge from these poor kids!
I was a VERY gifted young student that was on to trig in 8th grade, pretty much entirely self taught with what I could find online (in the mid 2000s). It turns out that the fact that something wasn’t taught at school didn’t “hold me down” or “delay my education.”
The anger around this seems… weird. The insistence that this is actually harming 8th graders sounds like somebody who hasn’t actually asked an 8th grader if they give a shit, while pearl clutching about the status quo not being exactly maintained.
In an age where advanced applied math skills are the shortest path to six and potentially seven-figure salaries, by all means dumb down California further than it's already been dumbed down, but I have to ask questions about where all that 10 to 14% state income tax money is going besides those ridiculous six-figure pensions for retired state employees.
You obviously have to build up mathematical skill and intuition the right way, but there is an age-appropriate way to do this. NOT doing it seems rather backward.
It wasn’t that long ago the California was touting the success of Algebra for everyone in 8th grade.
I think this is a decent trade-off between going slower for some kids and holding others back who could go faster and more advanced.
In the UK, they start separating students into separate tracks around 8th grade. Some will excel in math and science, so give them the opportunity to really go for it and take hard classes. Others will excel in other areas.
But if everyone is lumped together in the same bucket and forced into the same mold, the average student's highest level of achievement across all subjects goes significantly down.
I don't know how it is in the UK, but your comment strikes me as a typical boogieman from someone who hasn't actually seen the system in action.
The school system has as a track of classes leading up to calculus. A student can jump forward on the track by passing a test on the next class in the track.
Because there were other demands on my son's time, it was not practical for him to learn a year's worth of material outside of school time.
Regular public schools in a pretty big district that combines both urban and suburban schools.
No, its based on empirical evidence that the way things were done previously holds everyone down, and they should be done differently if you want to lift everyone up.
Educational approaches are technologies, and old familiar technologies are, often, just not as good at their purpose as newer ones.
edit: I dont understand how poor war-torn countries can have a better educational system than the most developed country in the world.
Ahla fik khayye :)
Could you expand on this?
On the surface, I agree. The curriculum that is pervasive in contemporary high schools was developed at a time when few people (~5%, iirc) went to high school and most of those who did went to tertiary education or white collar support jobs.
That said, this may not be the direction you mean.
In the world we're hurtling toward, we don't need people who can recite the Pythagorean theorem. We need people who can cooperate with other humans, who can leverage technology to achieve their goals and who can evaluate information critically. Throw money at THOSE problems.
Personally, I think the most devastating impact of COVID will prove to be the shift of younger people's focus from the social realm to the technical/virtual. Imagine an entire generation specialized in playing Minecraft, making YouTube videos and scripting Python Discord bots... All the while, AI embeds deeper in government, gains control of resource production and perfects the mechanisms of social control.
I could not have designed a simulation with the goal of a cyberpunk outcome, better. High tech, low life. Hey, at least I know how to do long division in my apartment, alone.
I'd argue that information literacy is more important. I know plenty of STEM-credentialed people who might have insight into their narrow STEM field, but are effectively data illiterate when it comes to evaluating data that's from outside of their field of expertise.
Even then, I don't think the majority of the people that COVID exposed as "not understanding the science" really don't understand it. It's just that they don't care. We're mistaking their lack of giving a shit about the truth for a genuine misunderstanding of the science.
But you are ultimately correct in that most people don't really care to understand it.
Sounds to me like you want some science, technology, engineering, and math curriculum.
For example, instead of making more energy, we have power cuts like a third world nation. We could instead build solar farms and nuclear energy, but California (and largely progressives) want shittier world for themselves. Wanna inspire people with values of perseverance and hard work? Nope, that’s not allowed. Want to eliminate homelessness? Nope, too ambitious. There isn’t a single public park in Oakland where homelessness isn’t rampant.
Basically, the entire thinking is about regression, not progression.
I only vote for Democrats because the alternative is worse. But it’s becoming harder.