Well that's stupid. If anything they should introduce it sooner. There's tons of research that show the sooner it's introduced the better they are able to digest that (as in it becomes more second nature and are later able to reason with it and build off that knowledge better).
It's hard to introduce Algebra much earlier than 8th grade - the students just don't have the mathematical maturity for it. What you can do though is challenge and expose them to slightly more complex applications of ordinary math (often stated via increasingly elaborate "word problems") that make the introduction of algebra a lot more natural when the students are finally up for it. You tend to see this approach in the various "Singapore Math", "Russian Math", what have you.
Seems entirely arbitrary (if not false?). I was taught the basics of algebra and even trig (at least, how pi and radians work) in the 4th and 5th grade
You shouldn't optimize for the average student; you should stratify instruction so students of different levels are pushed to their limits and beyond.
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.
> You shouldn't optimize for the average student; you should stratify instruction so students of different levels are pushed to their limits and beyond.
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 agree, but stratifying too early can be harmful.
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).
Why/how exactly do you think people become a math whiz? For many of us it was because we were introduced to subjects at an early age and had supportive teachers/parents that encouraged our academic success even when (especially because!) it meant surpassing our peers.
So you propose we handicap the geniuses to make the rest feel better? Who do you propose will invent great things to keep our world thriving if you’ve made all the geniuses average?
If you're going to teach math to kids in a normal school and not an academy for geniuses, before stratification based on level makes sense (and there's evidence doing this too early is harmful), you need to figure out how to do it in a way that works for the majority of students.
And what is your policy for gifted students ? 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."
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).
I think a whole lot of kids can get algebraic ideas early.
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.
I introduced my kid to Algebra in gr.2 during that first stretch of covid last year. He's not particularly adept at Math(doesn't struggle with it - it was gr.2 though so simple + and -), but it really didn't take much.
> the students just don't have the mathematical maturity for it.
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.
> 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."
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.
> Some students have the mathematical maturity for it.
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.
Anecdote: I’ve tutored elementary school kids (in Massachusetts) who are doing basic algebra with shapes and emoji instead of letters.
> 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.
We were introduced to algebra in 6th grade. Talking about Indian subcontinent in the 90s. I (and a lot other kids) did fine with it. Well there were many that didn't and they switched to humanities or business studies later. But even if lives are not good at math, they should be taught math. Doing otherwise is how they grow up to become conspiracy theorists.
I, along with 30 other kids in my grade, took our first algebra class in 7th grade (early 90s). After a few weeks of struggling, I was entirely fine with it. I really think you're underestimating what kids can do if taught properly. If students don't have the "mathematical maturity" for algebra until 8th grade, or later, then that just means instruction in prior years was lacking.
Not everyone took algebra in 7th grade; those who did not, took it in 8th grade.
My elementary school was introducing algebra in 4th and 5th grade. Questions like "7 * ? = 21" aren't explicitly teaching algebra - student's aren't being taught the multiplicative property of equality, they're just remembering their times tables - but it's laying the foundation.
In Canada, ninth grade was around 14-15 years old, depending on the month you were born. I think the US has a similar timescale for primary/secondary schooling.
The difference between education across the world and USA is that you treat algebra as one subject and therefore don't do it every year. In India, you had to do algebra starting grade 6 all the way to grade 12. The more complex the theory, the later you learn it. Makes sense to have that kind of gradual learning imho.
In a US public school, I was doing very basic algebra— math with variables— in 6th grade, which is around age 11. The class called 'Algebra' in the US school system, which this article references, is a subset of what Algebra actually is on a whole. Very basic algebra before high school (which starts at grade 9, or age 14/15) is often called pre-algebra.
Germany solved this by past 4 years of primary school having three different advanced schools that prepare for different types of careers and that have different durations. That's in addition to having AP classes towards the end. It has the downside that it disadvantages late developing children, but there are also ways to continue at the higher schools if you do really well. Making the jump is harder though.
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.
This "single standard" to me is like outlawing adjustable seats in cars.
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.
But isn’t it unfair to saddle minorities with more generational debt by getting them to attend universities? I’m being snarky here but also legitimately asking. My student loan payments resume in a month because Biden doesn’t care about non-Boomers.
And you know this because you've seen it happen? In NL, pre-selection happens at 12 years but actual specialisation doesn't happen until 15 years old. That's three years for children to switch tracks, try things and see what works best for them. And even then, students can pursue an upgrade track after graduation that would still grant them access to university at the cost of an extra year of secondary schooling (which also gives them an extra year of maturity, which often also helps).
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.
Yes, this happens. My son could not take calculus in high school because he was mislabeled in 8th grade. The 8th-grade decision has had an impact on his college career.
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.
We used to have an accelerated/gifted track in US to take more advanced courses. One got evaluated around 7th grade to make that decision. The difference in skill level was huge because the final year I took it easy and did the regular courses and it was basically a cakewalk.
There is no single US. Each state has it own program to separate students into different tracks. In mine they identified "talented kids" in 3rd grade and they have advanced math and language programs going forward. They had additional evaluations in middle and high schools. So it wasn't like all doors are closed after the 3rd grade.
Regular public schools in a pretty big district that combines both urban and suburban schools.
> It’s the official shift from “we can lift everyone up” to “we need to hold everyone down”.
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.
what evidence and what data? I studied math in Syria and was doing Calculus at 8th grade, came to the states and was forced to redo basic algebra. Do you know how soul crushing it is to redo those classes?
edit: I dont understand how poor war-torn countries can have a better educational system than the most developed country in the world.
> No, its based on empirical evidence that the way things were done previously holds everyone down
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.
Looking out from this moment in history, if I wanted to prepare someone for the future, STEM wouldn't be the main focus. I know it's anathema to say. In a world where computers fold proteins and predict programmer's intentions, the value of technical knowledge is showing decay.
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 would say a strong counter to your argument is that Covid highlighted the need for much better STEM education, because of how painfully obvious it was that so many do not understand "the science". That's in quotes because that's the phrase that was bandied about so often.
> I would say a strong counter to your argument is that Covid highlighted the need for much better STEM education, because of how painfully obvious it was that so many do not understand "the science".
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.
Definitely agree that it's a data literacy problem. But I consider that part of STEM education. For example, people should be able to look at plots of daily infections early in the pandemic and consider that they likely are growing at an exponential rate and the implications for that, rather than dismissing the dangers because the daily case numbers are still small. And understand how false positive and false negative rates of tests implicate policy decisions.
But you are ultimately correct in that most people don't really care to understand it.
I don't think science education is going to help the particular problems we have. Understanding science doesn't change anything if you don't trust the institution running the experiments, and it's become very clear that a large percentage of the population doesn't trust the institutions we have.
> 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.
Sounds to me like you want some science, technology, engineering, and math curriculum.
We never needed people who can recite the Pythagorean theorem. We need people who can prove it. When you have a population who doesn't understand how the world works and is taught to simply believe facts given from on high, it is relatively easy to change who those facts come from, and in an age of easy publication via social media, this has been weaponized.
This undertone exists in to pretty much all liberal polices.
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.
This is not going to work well unless they massively improve math instruction in the lower grades. In fact they seem to be taking the opposite approach, where "equity" just means setting every student up for failure equally.
Many American K-12 education administrators dream of making schools into diploma mills: 100% graduation rates, 100% test scores, 100% meaningless and unaccountable. "Racial justice" is just their latest leverage to move closer to this goal.
I was doing algebra and Russian math word problems in 4th grade (maybe earlier, it's been a while). What exactly is the logic of pushing back mathematical training to later grades? [1]
" . . . as a means of promoting equity" and "The intent of the state mathematics framework, its designers say, is to maintain rigor while also helping remedy California’s achievement gaps for Black, Latino and low-income students, which remain some of the largest in the nation.
"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."
They're thinking that teaching people stuff is promoting a diversity of outcomes, which is anathema at the moment.
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.
I don't understand what this means. Where I went to school there were no gifted programs but we all were doing algebra and word problems much earlier than in the US. If people want consistent outcomes then teach everyone the same thing and hold everyone up to the same standards by investing more resources in students that are underachieving. That to me seems like a much better way of equalizing outcomes.
If you teach "hard" things to average US public school students, a minority of them will excel as a result. The rest will nod off, get bored, not pay attention, and not benefit.
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.
I still don't follow. What exactly in what I suggested is the problem with equalizing outcomes? If everyone is learning the same things then what exactly is the problem? There is no discrimination involved.
"Equalizing outcomes" is exactly what they want to do.
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.
What's the fallacy in teaching everyone the same things? That seems like a good way to equalize life outcomes and give everyone the required skills for succeeding in contemporary society.
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.
Yes, thanks. That clears it up. You're right. We must teach no one anything otherwise there would be some people that wouldn't be able to understand. That was exactly what I was thinking and your example helped me understand. What you were saying was clearly tautological and I just didn't have the logical training to understand it.
Your interpretation of what I was saying was clearly adversarial and uncharitable so I just got tired of it. It's entirely possible to have high standards for everyone (including the "stupid") without reducing the quality of the curriculum. But you're not interested in having that discussion because you're grinding some other axe about what you perceive to be the ideological takeover of the educational system.
>What's the fallacy in teaching everyone the same things? That seems like a good way to equalize life outcomes and give everyone the required skills for succeeding in contemporary society.
My position is that kids should be taught math at an earlier age and schools should be properly staffed and funded to ensure positive learning outcomes for all students regardless of their socio-economic background because that will lead to more equal life outcomes.
There is no way to fail in what I'm proposing because there are no grades. Everyone gets feedback on how to improve and students can receive all the help they need to keep up with the curriculum.
What's interesting is that beyond a certain threshold (perhaps around the left-hand normal distribution inflection point), further reducing failure rate ends up also reducing the rate of super-success among students in the same classroom.
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…
Yes, this is probably what is happening. Schools are understaffed and underfunded so programs keep getting cut. At this point it really just might be better to let kids learn from Khan Academy since the adults clearly have no idea what they're doing.
My third grader does simple equations like this in math. This is public school in Oregon. A lot of people in this thread are making big assumptions and just using it as an excuse to trash the American educational system for ideological reasons.
> My third grader does simple equations like this in math.
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.
Sure. The way I presented it was not an accident (abstract with little scaffolding).
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.
This sounds like the difference between basic understanding of the idea, and mastery. Mastery would always take a lot of repetition and diverse problem-solving -- true even for algebra.
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.
When I explained to my son that "X" was just another way of representing the blank space in equations, he got extremely mad about the world making algebra seem hard. He screamed about how "I've been doing that to calculate damage in video games for years" and stomped off.
He's never completely gotten over it. He's still mad about it to this day.
They dont do abstract manipulations. They dont do the "3 + ? = 10" and therefore "10 - ? = 3". Teaching algebra means teaching abstract manipulations too, like 2x+4=10 and therefore (2x+4)/2=10/2 and therefore x + 2 = 5 and therefore x=3.
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.
Spend some extra time figuring out why they're struggling. But I suspect what you have in mind is something else, something more along the lines of leaving them behind.
I don't know if that's what's going on. I suspect some haven't really sat down to think about what exactly they believe and why. Most seem to be parroting various mantras I've seen expressed on Twitter and Reddit without having thought about the implications of what they're parroting.
I struggled with basketball in PE. The teacher said that maybe it just wasn't for me, and had me sit on the bench for the rest of the basketball unit. For some reason they didn’t force EVERYONE to sit for six weeks cause I couldn’t basketball. Now explain to me how math differs.
There's still a lot of unfounded blank-slatism and autism (in the sense of inability to empathize) in our educated society, and proudly on display here on HN.
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.
> I met kids in 4th grade who struggled with their multiplication tables. What do you do for them?
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.
No one in any of my classes was a prodigy. We had good teachers that cared about the students (and parents that were involved in their children's education). But I do think we should have had more musical training than just choir singing.
Should Mozart have been kept away from musical instruments because his peers weren't at his level? In other words, should people existing define how we educate prodigies? Who gets to determine who is a prodigy and who isn't, and at what age?
This isn't that different from 2nd and 3rd grade math in the US. There's no algebra in your link, but either way, you're confusing algebraic concepts, which are typically introduced in grade school even in the US and Algebra 1, which is just a conveniently named part of the overall math curriculum, not one that introduces Algebraic concepts for the first time.
The page you linked to doesn't have a single problem that requires "setting up equations with unknown variables and solving them." And as I mentioned, even in the US, "Algebra 1" isn't when Algebra in the sense of equations and variables is first introduced. Algebraic concepts are explicitly introduced around 5th grade (https://www.khanacademy.org/math/cc-fifth-grade-math/imp-alg...), but problems that could easily be considered algebraic (whether through word problems or explicit placeholders) may be introduced as early as 2nd/3rd grade.
This isn't how that problem was meant to be solved - it's meant to be a straightforward subtraction problem. For instance, this is a US 2nd grade subtraction word problem from Khan Academy:
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.
The point is that the types of problems you're referring to aren't considered algebra problems in math education, because students are expected to be able to solve them when they are introduced to subtraction, not when they are introduced to actual algebraic concepts. It's like saying when you learn to add integers, you're doing group theory because integers form a group under the operation addition. From a purely mathematical standpoint, sure, what you're doing could be explained using group theory, but from a pedagogical standpoint, it's nonsense, because you don't have to know anything about groups to be able to add integers or even to understand and utilize these specific properties of the set of integers.
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.
"Yet for all the sound and fury, the proposed framework, about 800-pages long, is little more than a set of suggestions. Its designers are revising it now and will subject it to 60 more days of public review. Once it’s approved in July, districts may adopt as much or as little of the framework as they choose — and can disregard it completely without any penalty."
That's not a reason to ignore the stupidity of the premise in the first place. All your comment strives to do is highlight a lack of educational cohesion that will arise if they don't follow the guidelines.
Here's a revolutionary idea that pretty much all of the world adopts, if students are having trouble with a topic, get them to do more of it, instead of running away from it.
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.
> 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 for the rest of the high school, how about you do a little bit of everything every year from grade 8-12. Problem solved.
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?
Math in US high schools ends at what most countries would consider a middle school level. Algebra 2 is generally the only requirement. The vast majority of students graduate without ever even knowing what calculus is.
Not very useful, since most people don't work in technical professions. But if you want to pursue further technical studies, then that's a different ballgame.
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.
> Under Equitable Math, all children must be at the same level,
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.
You are mistaken. Under the Equitable Math proposal, all children are to be in the same technical class regardless of their ability. Children will not be allowed to take Algebra in middle school, and children will not be allowed to take Calculus until specifically the senior year. Differentiation may only occur at the senior year of high school.
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.
While this is true, I would like to point out a good portion of schools do allow students to continue to more advanced math if they elect to.
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.
That means nothing. I have met plenty of people that did calculus in high school and got pushed back into remedial classes in college. Exposure to a concept does not mean proficiency in it.
I'd have taken exposure over nothing. I had to teach myself - as an adult - calculus, linear algebra, probability (outside of the ever-so-brief introduction in school) and trigonometry. I personally don't think I did a very good job as my own teacher either. 3Blue1Brown was a lifesaver and every now and again I try to brush up on the topics - not for my benefit at all but for my child's benefit in the future.
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.
> Half of what I learned isn't even true anymore or were partial truths/mostly lies
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.
Yes, but often times the army of scientists had already done their work. Even in the late 90's a lot of what I was learning was already known to be false but the updates hadn't yet hit by textbooks published in 1982. The teachers even sometimes already knew it to be wrong but had to teach it anyway because it was still considered part of the state curriculum. But the more common and larger issue was the partial truths/mostly lies - even if some of the lies are arguably justified to make learning easier for some kids. The better teachers wouldn't lie but would simply say "You'll be taught about that later in a higher grade".
My wife grew up in China, went to a good high school, but is only proficient in math up to the algebra 2 level (maybe?) considering she took the liberal arts track. If you aren't working up to STEM, I'm sure you don't take calculus in many countries.
> Math in US high schools ends at what most countries would consider a middle school level.
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.
> 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?
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.
How many people that are good at math and love science / engineering decide to go into politics? I'm just talking without evidence but my guess is politics self selects for ambitious people that are completely inept when it comes to mathematics and critical thinking in general.
I think quite a bit. Congress regularly beats high end Wall Street investors when it comes to playing the equities market. This involves a great deal of understanding on mathematics topics involving everything from stats, probability and economics. They manage to do this part time while governing, so I'd have to say they are pretty adept.
Uh, what? The sharp drop in equities in February and March 2020 was a massive deleveraging caused by panic selling and leveraged traders being margin called.
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.
This policy has nothing to do with the topic of algebra. This is code for advanced math, because algebra is typically considered advanced for < 9th grade children. Since the organizations feel ashamed that they're failing certain demographics as evidenced by being under-represented in the advanced classes, they're just scrapping the advanced classes for everyone. Truly disgraceful
How old is a 9th grade student in the US? My cohort started Algebra in year 7 in Australia, which is 12/13 years old. And similar to GP's proposal, we learn age appropriate topics every single year, every single week.
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.
> The students with a delayed introduction caught up so quickly that the delay didn’t matter
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.
Gifted programs do very little or nothing as far as most studies can tell. Any gains in scores are very small, and they don’t appear to make any meaningful difference in student engagement or motivation.
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.
Gifted programs aren't the same thing as tracking kids into more advanced math 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.
> 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.
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.
I was in a program in the 90s which consisted solely of sending the smarter kids out of the classroom periodically to work on logic puzzles with each other.
The only educational purpose served was getting them out of the classroom so that more attention could be given to the dumber kids.
> Gifted programs aren't the same thing as tracking kids into more advanced math classes
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.
> 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.
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.
As someone who went through a gifted program, I seriously question the validity of any such study.
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.
Look at the first of the linked studies - it’s quite large (national across the USA and uses both between school and between student analyses), so I’m not sure what would make it completely invalid. As you asked, it does also look at student absence rates and engagement, and saw no significant differences - so “boredom prevention” doesn’t seem to typically be a working feature either.
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.
> Gifted programs do very little or nothing as far as most studies can tell. Any gains in scores are very small, and they don’t appear to make any meaningful difference in student engagement or motivation.
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.
My vague memories of my Australian High school math curriculum (year 7 to 12) was something like this, I went to high school from 1997 to 2002.
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.
America has absolutely shit-tier education for 80% of the population, and woke people want to make the other 20% also shit to lead to “equity”. Ironically, white parents being able to get around this and black parents not knowing how is the main cause of racial disparities today
Indeed. A disgrace for education but a win for educational communism. It’s a good thing the US can import talent because California’s students are being trained to be cognitively lazy. How will these children fare in a society that is getting more technologically advanced, dynamic and complex by the day without the problem solving tools to handle it? I can’t wait to find out.
> A disgrace for education but a win for educational communism.
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.
"Educational communism" in that it seeks to eliminate inequality (in education) by reducing everyone to zero, just as communism sought to eliminate inequality (in wealth) by reducing everyone to zero.
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".
Exactly. I have no idea how people can’t differentiate between educational communism and education systems that were implemented in communist states. Was my wording too confusing?
Read my comment again. I made no mention of education systems implemented in communist states. I said educational communism, education where everyone is pulled towards the mean no matter their individual effort or talent.
Spivak's Calculus is intended for use in a two semester course covering differential and integral calculus. It is a challenging but rewarding introduction to calculus; in my opinion, this text is appropriate for math majors while other STEM students might be better off with a textbook that didn't focus quite so much on learning proofs. It was used at MIT for the first year of Calculus, but only by the math majors.
Michael Spivak is an American mathematician born in Queens, New York.
Yes, I'm not disagreeing with your main point. I just had first hand experience with Spivak.
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.
> This policy has nothing to do with the topic of algebra. This is code for advanced math, because algebra is typically considered advanced for < 9th grade children.
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.
I took algebra in 7th grade as well, but it was considered advanced by 2 years. It was normal to take algebra in 9th grade. I went to an okay high school in a medium sized city in Michigan. That was about 20 years ago.
When I was in 5th grade, I was put into the advanced math class. We graphed equations, learned y=mx+b, slopes, etc. All the basic concepts that are introduced in Algebra 1.
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.
I don't know what to tell you. That's the state of the country. But hey, at least they're honest about why they're doing it:
> 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.
When commenting on the state of the country, I would look towards the states that have historically ranked poorly in education and see why they’re never improving. California is definitely not one of those states & seems to have no issue in keeping a higher than average educated populace.
The people doing this are destroying the future of these children and our nation as a whole. It should be criminal but I fear an idiocracy-like future where no one is smart enough to realize how stupid we have become.
For another data point, I took it in 7th grade too, that was only--oh god 2003 was nearly 20 years ago. Anyway, it was considered one year early for my public school district in Utah. Me and a few others in my 6th grade class who had good math grades were offered the chance to sign up for it early if we were able to pass a test administered by the junior high. I don't remember what the test had on it, I do remember asking people around me (at least parents and GED-holding brother) "What is algebra anyway?" and not receiving an answer, but somehow I passed. One friend also passed but didn't sign up, instead doing "pre-algebra" like most kids, which made me sad. (I'd guess the test had things like "if x + 3 = 10, multiple choice what is x?" as sort of a sink-or-swim filter, or maybe just some more advanced examples of whatever the 6th grade curriculum entailed.)
Ditto, 7th grade in Colorado. Yeah, they called it advanced, but they called everything advanced. You know the drill: grade school math is always "advanced," grad school math is always "introductory."
> then the situation in California must be deteriorating severely.
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.
How many of the employees in these companies that make the GDP so high were born, raised, and educated in 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.
Peter Thiel, Reid Hoffman (LinkedIn), Ben Horowitz (a16z), and many more. While you have some point, the Bay Area only raises so many kids while it's economic engine is unprecedented in attracting intelligent folks from around the world.
I attended underfunded rural public schools as well. The funding of a school district will often correlate with student performance, but in most subjects, it's not a causal link.
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.
You make some interesting points, but children are neither machines nor lab rats. Conditioning can have deep psychological effects; those successful people that complain about their parents might have done some introspection and arrived to a different conclusion from yours. Professional success unfortunately does not equal happiness.
Did you take standard high-school Algebra 1 in 7th grade? Algebraic concepts are often taught as early as 3rd grade, but much of it is considered pre-Algebra.
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.
It has everything to do with Algebra, because Algebra is only considered advanced because it's not taught until later. Primary school children are perfectly capable of doing algebra as shown by many other countries that teach much more "pure maths" in schools.
No I didn't mean 1 year of math. Rather I meant breaking down math into these individual topics (that may or may not be compulsory) that you don't teach every year, makes the experience very disconnected.
Good grief, how can that even work? If I had gone a full one or two years without any math class, I would have lost the habit and floundered when it came time to take a math class again. Are they deliberately setting kids up to fail in California?
Just because they're only required to take 2 years of math doesn't mean that is what most kids take.
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 literally the minimum possible requirements to get a diploma anywhere in the State of California; judging from the document, school districts may impose stricter requirements.
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'm British. For the lulz I decided to complete the US "GED":
"The General Educational Development (GED) tests are a group of four subject tests which, when passed, provide certification that the test taker has United States or Canadian high school-level academic skills." (Wikipedia)
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.
I guess you didn’t study the part where they teach you percentiles. 99th percentile is the highest you can score and means out of 100 people taking the class, you scored higher than 99 of them.
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.
> 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.
It didn't state 99th percentile on the form. It specifically says 99%. And at the bottom it explains that 99% is the highest mark and the results go from 0% to 99%.
The GED isn't our A-levels. It's mostly for people who dropped out of high school for some reason and don't want to have "high school dropout" be their identity. SAT's are more akin to our college-bound testing.
I don’t even think we have A-level equivalents in Canada. We have the American AP courses, which carry 1st year university / college credit. We also have the IB diploma program available (seems to be of European origin), which can also grant 1st year credit. However these programs aren’t available at all schools.
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.
This sounds identical to the system in the US: a mix of AP and more recently IB. It is interesting to me that the IB program has somewhat high status even in countries with (optional) academic tracks that are often more rigorous than the AP or A Level systems. It actually seems to be an effective equalizer for many students hoping to study in different countries.
The GED is for drop-outs and doesn’t really encompass the range of courses available at many high schools, it’s literally the bare minimum. I’ve known 14 year olds that have passed it.
To contrast I earned some college credits during my last two years of high school due to advanced placement tests.
I think there must be a language difference between us, since I usually interpret "for the lulz" as meaning "without a [good] reason." Kudos to you for doing well on it.
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.
That was actually a smart idea to fail the exam. As a SAT tutor your first instinct would be to show off and try to get a perfect score.
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.
"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."
In my experience, each year built off of the previous and implicitly provided a refresher.
Tell us a little bit about your Indian high school experience. Who were your peers? Who were their parents, where were they from, how wealthy were they? How wealthy was you? Did the school have competitive entry? Did kids get kicked out for failing or doing poorly?
There’s different schools: private, public, home schooling, religious etc. I went to a public school, mostly with kids from not so great socio economic backgrounds. I wasn’t “don’t have anything to eat” poor, but I was definitely “can only afford 2 pairs of new clothes every year” poor. Most other kids were in the same boat.
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.
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.
There are lots of stories like this. Lot of selection bias. That is, wealthier and/or smarter people who come to the US.
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.
You can't get people to 'do more of something' if they don't show up for class, and fundamentally don't care because none of their peers do.
'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'.
This isn't that different in the US. Algebra 1 to Algebra 2 to Precalculus to Calculus is a sequence that's taught over many years and there's no big dump. Geometry is the only exception from that sequence (unless you're counting Statistics or Computer Science, which are generally optional). Most students that are applying to competitive colleges are generally going to take a math course every year - there's no big dump that you seem to be envisioning.
Not being sarcastic, I think you misunderstood the political environment of the US right now. The media and the bureaucrats are not seeking truths but narratives. And doing more is immediately labeled racism because well, you don't appreciate the hardship and systemic racism that the oppressed have to endure.
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.
One more nail in the public education system. This will amplify the inequality through middle class folks hiring tutors and such or just opting for private schools where the curriculum is “modified”.
They teach that math is subjective. Objectivity is the corner stone of white supremacy.
> "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."
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?
You can only cram so many failures into one excerpt...
> 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!?
I'm curious to see how this will turn out as other countries are not buying into this nonsense. In an increasingly competitive world this is a recipe for disaster.
JKR was really spot on with the Dolores Umbridge character. For those who didn't read HP, the plot was that their ministry of education sent Umbridge to the (only) school with the only goal: prevent students from learning certain subjects. I feel like this Umbridge character is the inspiration for the radical left.
I always enjoy watching people experiment on themselves with this sort of social engineering when it doesn't affect me whatsoever. Even without this I would never consider sending my children to public schools anyway.
They are clearly excelling at math just to be racist.
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 very long multi-part document on white supremacy in mathematics does not mention Asians even once, despite that they are somewhere between 15.5% to 17% of the state population.
US admits only the top 1% of Asians with its immigration policies. Same for most other countries. If average rural Chinese folks could immigrate to US, we'd see a more "equitable" picture.
Then why would California school discriminate against Asians in admissions? Wasn't the point of affirmative action to counteract discrimination, but now it seems like it just makes the discrimination Asians already face even worse? If institutions openly discriminating against you is not "institutional racism" then I don't know what is.
The Asian advantage in education long pre-dates selectivity in immigration. You see the same pattern in the children of Asian peasants. See every generatio of Asian immigrants to the US since teh California Gold Rush.
Asians in the past who came over 100 years ago and have lived in the US did not have selective immigration rules based on education. Their prodigy are doing better than blacks who have also lived here for generations.
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.
My parents introduced it to me at home around 4th-5th grade? So I was ~9-10yo? Not sure why delaying it will help, if anything the earlier the better. Everything I hear about "equity in education" seems to be making it worse, but more equally I guess.
Like another poster already mentioned, reminds me of the Harrison Bergeron story by Vonnegut - seems like we are rapidly approaching that point.
And if we were any good at teaching math we would just naturally go with it from there, "algebra" wouldn't even be a subject, it would just be something you do by default as teachers first replaced _ with x (hopefully before you even got too used to _), and then started making the equations gradually more complex.
"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].
Yeah, I remember "learning" indices and logarithms at ~12 years old, using it for hacking video games (i.e. calculating the packet sizes, and bytes to bits, etc.) - then when we had to cover it in school it was super easy and relatable.
Ideally everything would be taught this way, like actually doing interesting things rather than just remembering things from textbooks.
My parents introduced algebra to me in third grade. It took me a long time in third grade to get it, so much so that I was a little bit afraid of algebra though certainly I didn't admit it to my parents.
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.
That's how I learned a lot of things. My dad would mention what atoms are and that kind of thing, and I'd read about them in magazines, so them when it came to school it wasn't so big a leap to add a bit of rigour.
My takeaway from your anecdote is completely different: when exactly a school introduces concepts doesn't matter as much as the stimulation a child can receive outside school.
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.
Not all students are like you. I went to a low-ranked university my first year before transferring out. I met freshmen who really struggled with basic concepts, like what a vector is. I'm not sure they would ever get it even with all the tutoring in the world.
They would in my opinion. I was a tutor in high school and college for algebra. I worked with people some people who struggled. They all eventually got it if they wanted to get it, which they generally did to not get held back :p. You just have to work with them and truly understand what they are not understanding. The big issue is concepts are not learnable in isolation. You said vectors are basic, but are they? They were initially just abstractions to model sets of physics problems. Without the context, its pretty difficult to understand them IMO, especially things like dot products. "oh, i multiply two vectors and I get a number? what? Oh and that number can be described as the multiplication of magnitudes of the vectors multiplied by the cosine of their angle? Oh how do I get the magnitude? What's cosine again? etc." It goes forever and generally you'll find that people will struggle with basic things because they never had an opportunity to sit down and genuinely internalize those ideas.
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.
I tutored a 20 year old CS major who could not understand the equation to convert from Fahrenheit to Celsius. Nice guy, talented guitar player. Was not meant to be a programmer.
From what I can see, most states don't teach algebra until 9th grade. Also most states are learning math better then California, so maybe it works? Of course, that might not be the cause, but just copying better performing states seems to be a safe way to try and fix California's problem.
"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. This has led to accusations from parents and educators that it holds back “gifted” students."
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.
These days when I need to vote for a representative or a school board administrator, I read their website and if I see words "equity" or "social justice" there, I cross that candidate out of my list.
The podcast "Nice White Parents" makes a good case that gifted programs in NYC were essentially used to create two separate-and-unequal systems of education for black and white students inside the public schools.
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.
> The podcast "Nice White Parents" makes a good case that gifted programs in NYC were essentially used to create two separate-and-unequal systems of education for black and white students inside the public schools.
And let's pretend Asians don't exist. Affirmative action is about keeping Asian numbers down. So is getting rid of gifted programmes.
> The podcast "Nice White Parents" makes a good case that gifted programs in NYC were essentially used to create two separate-and-unequal systems of education for black and white students inside the public schools.
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.
I have a better idea. Delay it indefinitely, as long as there's as much as a single kid who struggles with it! It's the only way for true equality of outcome.
There's more value in flexibility than catering to the lowest common denominator. There's plenty of money to do so, unfortunately it gets leeched out before ever reaching the classroom. People learn at a different pace. Algebra should be available as early as 7th grade, and can be deferred to 9th for those with different aptitudes.
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.
As someone who's never been in an American school, what does algebra entail in the US curriculum usually? Is this the first time "solve for x" is introduced? How broad is the amount of teaching that happens in algebra?
The article does a great job of covering what people think about these changes, but a terrible job of covering what on earth the changes actually are. I felt like I was trying to solve a mystery where every paragraph buried in the opinions were small clues about what they're actually talking about.
I guess one benefit of this approach is it costs nearly nothing. The better approach would be providing qualified tutors for free to struggling students, or to make current math classes smaller, or to add TAs to existing classes. But all of that costs money. You could also argue that a more holistic approach could help. Things like better meals at schools, better transportation options to and from schools or a wider range of class times. Again, all expensive options compared to simply limiting options and forcing students into fewer buckets.
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[ 3.1 ms ] story [ 369 ms ] threadSure, 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.
There are going to be some dumb kids coming out of California.
> 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.
Edit: fixed age range
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.
1: https://www.edhelper.com/geography/Russia_Math1.htm
It's Harrison Bergeron Math.
See https://infogram.com/mathdisparities-ag-1h984wd3y7lv2p3
"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."
https://youtu.be/TWzvXaxR6us
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].
[0]: https://news.ycombinator.com/item?id=27563357
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.
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.
Denying high-preforming, or average preforming students access to appropriate education in the service of "equity" reminds me of this:
https://unwokenarrative.com/content/images/2021/06/image-3.p...
The people doing this are destroying the future of these children and our nation as a whole. It should be criminal but I fear an idiocracy-like future where no one is smart enough to realize how stupid we have become.
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.
https://www.cde.ca.gov/ci/gs/hs/cefhsgradreq.asp
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.
... 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://equitablemath.org/
https://www.newsweek.com/math-suffers-white-supremacy-accord...
> 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!?
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.
Like another poster already mentioned, reminds me of the Harrison Bergeron story by Vonnegut - seems like we are rapidly approaching that point.
http://www.tnellen.com/cybereng/harrison.html
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.
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.
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.