The school essay is designed to be writable within the time constraints of an in-class exam, and to let teachers grade a whole five class's worth of essays fast enough to get them back long enough before the next exam.
As a kid I was always confused about why schools had libraries. In elementary school you got sent to them once a week and were allowed to take out one book, and the librarian taught how to use a library. Otherwise, there was never a time you could actually go to them and do research on anything. (Ok, except for once in second grade, when I corrected the teacher on something and she sent me to the library to find a book that proved it). The buses didn't arrive early or leave late enough to go outside class time, and the library wasn't open to visit that way anyway. In high school if you had a study hall it was held in the cafeteria or auditorium, and they did not grant people passes to go to the library, either. As a teen I decided school libraries existed so that adults could fight about what books would be in it, not realizing no one ever saw any of them. As an adult I decided it was pure cargo cult mimicry of what an institution trying to educate people would be. I also found it strange that they had a full-time librarian on staff but in 2004 we still used history books where the maps were from before the reunification of Germany.
If we were, no one ever told us, and no one I knew ever did. If nothing else, to do so, we would have had to skip lunch entirely, because we weren't allowed to be in the halls without a pass signed by a teacher, and there would not have been anyone in the cafeteria to write one.
Admittedly, after 9th grade I stopped taking lunch so I could fit in an extra elective. Also in 9th grade, we had 4 instances of students calling in fake bomb threats in order to get out of class, and ended up with much stricter rules about who could be where, when, than had been the case prior. For example, outside of lunch periods, all but one bathroom in the whole high school was locked, so if you asked for a pass to go use it, then depending on where you were it might mean missing close to 10 minutes of class just to get there and back, or to find out which one was open that day. And they banned teachers from giving out more than one pass at a time, for any reason.
1The ‘learning too much too soon is bad’ paradigm seems categorically insane.
I think most people (including most teachers) don't have flexible models when they think about "learning". When they try to imagine "learning faster", they imagine taking textbooks written for older people and forcing small children to read them. And they conclude that this would be bad, because children need easier texts with more examples and illustrations, etc.
The underlying problem is not seeing the difference between essential complexity and accidental complexity. Some topics are inherently difficult. Some topics are just explained in a complicated way -- maybe because the author of the textbook sucks at writing, or maybe the bad writing feels high-status. What typically happens is that for children, we write textbooks with both low essential and accidental complexity: we teach them simple topics, and try to explain them in a simple way, ignoring status (because small children are low-status). For adults, we write about more complex topics, but also often write in a way that is not optimized for clarity too much, because optimizing too much might be perceived as offensive. Imagine a textbook for adults full of big colorful pictures, with lots of simple examples for everything -- it might be better for understanding the topic, but many adult readers would be offended that they are "treated like kids". I think this is stupid, but you can't fix most adults. However, if we made textbooks for bright kids, I would like to see them made exactly like this.
Yet another problem is that people see learning as a linear process instead of a "tech tree". For example, if you asked "how difficult is it to explain complex numbers to kids?", most people would think about square roots, quadratic equations, then add some complexity about the square root of a negative number... and would conclude that it is impossible. But if you limit yourself to Gaussian integers (complex numbers with both integer coordinates), explaining their addition and multiplication rules along with their geometric interpretation is simple even for a 10 years old. But you have to do it differently than it is typically done at school.
A ‘fast learner’ is really just someone who’s been exposed to this problem/material before, maybe multiple times.
Maybe not exactly the same problem, but a prerequisite for that problem.
In general we have the problem of teaching math in ways that make many students hate math. [...] However, in terms of the math-based disciplines, as long as we are gating on actual ability I think weeding people out here is in principle fine?
I see this as a conflict of interest. The school is supposed to do two things:
- teach children knowledge
- separate children by their ability
Unfortunately, the easiest way to separate children by their ability is to teach them inefficiently... and then the kids will clearly separate to those who get it regardless of your teaching, and those who don't get it.
(In other words, what from inside feels like "the camel has two humps", from outside feels like "you suck at teaching". There is a concept you failed to explain clearly, some kids get it anyway, some don't. If you explain everything well, you will get a bell curve, not two separated groups.)
Weeding out people by their ability may be necessary in many situations, but you need to make sure your are not making your situation easier by failing to teach them properly.
The top 0.1% are no longer more competent than they were 10 years ago. Take math. About 1% of high schoolers participate in the American Mathematics Contest, and about 10% of those score >100. Ten years ago, they had a strict "top 5% or those scoring above 100 advance to the next round" rule. Five years ago, the contest got much harder very quickly (the class of 2022 was exceptionally good, and the contest writers probably anticipated that by seeing MATHCOUNTS results), and where the cutoff had been ~105, it dropped down to ~84. Note that I'm talking about the AMC 12 here, and participation had declined at this point, so they took the top 10% instead of the top 5% to keep the same number of contestants in the next round (the AIME). The most recent contests are easier than they were five years ago, but the cutoff has remained in the 80s.
I bite the bullet. I do think it’s fine and actively good to have 7-year-olds and 17-year-olds in the same math classroom. Of course, if you think that learning is bad, you won’t like this plan to have kids learn
I'd be keen to hear an explanation of this bullet biting. My instincts tell me it's a very bad idea and I imagine most people would agree but I'm interested in more details.
For the sake of argument, I'll at least poke a bit at this bullet.
I have been in an advanced math class (in the US) with high school seniors and an 8th grader, who was probably the top student in the class. It was totally fine? Everyone learned math, because they liked math.
From what I can tell, the two key factors for mixing ages in math classes is something like:
- Similar math skills.
- Similar levels of interest in math.
So let's imagine that you have a handful of 17-year-olds learning multivariate calculus, and one 7-year-old prodigy. My prediction is that it's normally going to be fine.
And historically, the US had "one-room schoolhouses", which mixed pretty wide age ranges. Even today, I know of rural schools that combine regular classrooms across two grades. And at least one of them is a very good school.
Where I do think this would be a terrible idea is if the 7 year old is a prodigy, and if the 17 year olds hate math and don't want to be there.
Where I do think this would be a terrible idea is if the 7 year old is a prodigy, and if the 17 year olds hate math and don't want to be there.
Exactly.
In a 12th-grade/early college class with generally friendly students: I imagine if there was some very young prodigy attending they would quickly become the beloved "class mascot" kind of micro-celebrity.
Table of Contents
Lack Of Tracking Hurts Actual Everyone
Gifted programs and educational tracking are also super duper popular, it is remarkably absurd that our political process cannot prevent these programs from being destroyed.Not Tracking Especially Hurts Those Who Are Struggling
An important aspect of denying the reality of different learning abilities is that it is absurdly cruel to those you are gaslighting – they are told that they are just as smart and good at learning as everyone else, so what are they to think about their failure to get those same results?No Child Left Behind Left Behind
What happened with No Child Left Behind? One of its architects explains that they knew you can’t actually leave no child behind. That’s impossible. You obviously have to leave some children behind. They were declaring a goal of none with the plan to modifying it to some. Then they met Congress, which has become unable to do reasonable things, so instead of the usual ‘quietly change the rules and declare victory’ the insane requirements stayed on the books and everything went to hell trying to work around them. Whoops. The good news is that now everyone knows that Congress is unable to fix broken things, so we can correctly plan that laws will stay on the books indefinitely exactly as written no matter how broken they get, and write them accordingly. I endorse both the fully serious and sarcastic versions of that sentence.Read Early, Read Often
Reading is a godsend. The earlier your kids can read, the better, on so many levels. One that is vastly underestimated is this makes parenting vastly easier, you’ve unlocked unlimited cheap, healthy and non-disruptive education and entertainment. It unlocks all the things. Erik Hoel here says that with a year of dedicated effort, he got his 3-year-old to read at 9-year-old levels, and offers a guide: Part 1, Part 2, and Part 3. The core is simple, phonics plus spaced repetition plus books as the center of entertainment. In my experience, you need to push to the critical point where they can largely teach themselves via more reading plus a little adult help (and AI voice help?) and then you are home free. Eric seems to have focused entirely on reading first and ignored other subjects, including math, while he was doing that. This actually seems exactly right to me, if you can (as he did) get your child to buy in, because reading unlocks all the things and builds on itself. Get to that critical point first, worry about everything else (that isn’t a short term practical need) later.Mirror, Mirror
A woman virtuously notices she is confused about why mirrors work the way they do and asks, essentially, ‘mirrors how do they even work,’ as opposed to most other people who have no idea how mirrors work the way they do. That’s great, thumbs up. Then this gets quoted with ‘this is why we need the department of education,’ but no, actually we had a department of education and not only does no one know no one asks the question. This is why you don’t need the department of education. You need an LLM, and you need to teach people to be curious and give them actual education.Spaced Repetition
We all know it works. So why don’t schools use it? Spaced repetition works so well that it ends up causing me to memorize a lot of spoilers that I actively don’t want to remember. As in, I’ll keep trying not to think of the pink elephant, to remind myself to forget, at increasingly long intervals, which cause me to remember, and whoops. Damn it. One could use this power for good. Paper suggests new way to teach economics nonlinearly, supposedly so it will line up with how people learn. I think this is essentially ‘include spaced repetition in your lecture plan.’ Which is one of those obviously good ideas that no one implements.Learning Methods
Interruptions
It seems like something you could study and measure, but it seems no one has? I’m not even sure ‘learning time lost’ is the right measure, as time is not created equal, and there are different types of learning, some of which are far more disruptable than others, so this can shift learning composition, likely in ways we do not want.Memorization
The problem, identified. Drills and rote memorization are not ideal, but they work. If you can do better, great, but way too many parents and schools think they can do better and are wrong.Math is Hard
In general we have the problem of teaching math in ways that make many students hate math. I don’t think this is especially a problem in calculus, at least the way I learned it (in a high school class)? Autumn suggests the college method is somehow worse. Obviously ‘won’t comply with hazing’ is a terrible reason to drive someone away, calculus is vital to understanding the world (for intuition and general understanding, not for actually Doing Calculus, I actively do a happy dance every time I get do Do Calculus which is very rare) and at minimum we want everyone who takes such a class to learn calculus. However, in terms of the math-based disciplines, as long as we are gating on actual ability I think weeding people out here is in principle fine? In the sense that if you design a good filter, you’re doing a favor for those you filter out, except that now they don’t get to understand calculus.Get to Work
I strongly agree with this. It is very obvious interacting with kids that they yearn for meaningful work in the ordinary sense of work Putting children to pointless industrial work is not a good idea. But if they can understand why what they are doing is useful, yeah, they really dig it, and it seems obviously great for them and also great for you. For trips, you have to calibrate to your particular kids, but yes, absolutely, especially once the kids cross the ‘can be entertained by a book’ threshold.The Whiz Kids
High School Does Not Seem To Teach Kids Much
Is are children learning? In high school math, the answer seems to be no. The 50th percentile student gets a 230 in 8th grade on this test, and then a 234 in 12th (a second source said 232→237, but that’s the same thing), and we know from the higher percentiles that the test is not being saturated here. Note that reading scores only increased 5 points, from 224→229.Two Kinds of Essays