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."
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.
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'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.
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.
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.
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.
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.
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 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.
> 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.
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?
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.
Input:
move(1,X,Y,_) :-
write('Move top disk from '),
write(X),
write(' to '),
write(Y),
nl.
move(N,X,Y,Z) :-
N>1,
M is N-1,
move(M,X,Z,Y),
move(1,X,Y,_),
move(M,Z,Y,X).
Output:
- The code starts by writing "Move top disk from X to Y".
- Next, the code writes "N is N-1", which means that it's moving the next disk down.
- The code then moves the first disk up and writes "move(M,X,Z,Y)".
- This means that it's moving M disks down and Z disks up.
- Then it moves 1 disk left and writes "move(M,Z,Y,X).
–
- The code will move the top disk from 1 to 2.
We're probably headed for a recession. The pandemic showed me that most of my consumption was driven by anxiety and my guess is that other people are starting to realize the same thing. The current economy can not survive without anxiety driven consumption and once consumption growth starts to stall the rest of the economy will follow. But I could be wrong. [1]
We can start with social networks and then move on to search engines. Interoperability for social networks is already solved so it's a matter of getting the politicians on the same page to force Facebook/Meta and Twitter to support the protocols. [1][2]
They must not have heard about Composer. I'm currently migrating from Playwright to Composer. Will write a blog post about it soon but I can say that Composer is much nicer than either Puppeteer or Playwright.
Related: https://www.mintpressnews.com/ebay-founder-pierre-omidyar-is.... All billionaires do this. It's a common pattern because they know that media influences opinions and shapes the politics of large groups of people. There's nothing special about Bill in terms of donations to media outlets.
