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deletedJul 7, 2022·edited Jul 7, 2022
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I just have an anecdote from doing this as a TA, not data, but in my experience flipped classrooms work great for motivated students; they can jump right in to problem sets or labwork, having completed some preliminary reading, and take advantage of 1-on-1 conversations as needed with the instructor. But unmotivated students will skip the preliminary reading and then get even further behind because the whole class period is supposed to be occupied by experiential learning; there's no time for lecture. And this was in a college class; I suspect it would be even worse in, say, junior high.

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Agreed. It's something that works really well...for small, selected groups. Like every other educational fad, it doesn't scale. And it requires a very strongly-motivated, very good-at-creating-content teacher as well. And those don't scale either.

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I had a colleague who tried it. Nice guy. But the students hated it, and him. So I never tried it.

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I had to teach maths lectures this way (at the undergrad level) and hated it. However I think it can work in some circumstances, depending on 1) the personality of the teacher, 2) the subject taught (maths does not work very well with this format but maybe history would work great) and 3) the autonomy of the children/student

Overall I think it's the poster case for the main problem with evaluating education methods : something may be hugely positive for some combination of teacher and student and a complete bummer for some other combination.

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I tried it once and I got the worst results + teacher evaluations of my entire career.

My main error was to underestimate the time and effort it takes to organize classroom activities Instead I put all the effort in the videos/home reading part. Half of the students, on the other hand, came to "class" unprepared hoping to wangle it...

Horrible, just horrible.

(The class was introductory mechanics for first year students at a European university)

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One of the math teachers at my daughter’s middle school does this. My daughter says kids “hate her.” That is interesting that hate is the reaction in some of the other comments.

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Jul 7, 2022·edited Jul 7, 2022

I've had one flipped class, and it was pretty decent. I think it has the potential to waste far less class time than typical education. Actually interacting with a teacher when you're struggling beats the heck out of watching them present a set of information. But it suffers HEAVILY from being unconventional. It relies on people to actually do their reading/watching ahead of time, and requires people be prepared for class. Since that's mostly never necessary in normal classes, compliance tends to be low.

My class had a graded pre-class quiz every day to help force the required transition. Super-easy multiple-choice quiz, just testing that you actually read the assigned text. That helped, and I think the class would have fallen apart without it.

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I supoose that it isn’t actual research, but my department had an extra 10% of their classes pass precalc after swapping to the flipped model.

That said, I think part of this success is because a flipped model helps to make what would be an otherwise incompetent teacher be able to do a bit better

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I've found that *any* change will be positive, even strongly negative changes, for a small amount of time.

But yes, if an actually competent teacher is the one preparing the materials, it takes some of the downsides of having an incompetent teacher away. But I'd rather just fire the incompetent.

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That is interesting, hadn't heard of that before. My mom (former homeschool teacher now in public elementary) does something similar in that her time is spent on one on one interactions working problems and most students at any one time are on computers doing problems and receiving instructions.

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I'm a teacher (a Latin teacher, as a matter of fact, so I quite enjoy the fact that we've had a post on vocab acquisition and a post on homework in consecutive days). I wouldn't say I do a "flipped" classroom; I do mostly upper-level classes and I'm not teaching lots of brand-new grammar material like someone teaching lower-level classes would. But I don't tend to assign much homework (apart from AP, where it's basically a necessity to plow through the syllabus). In class I want my students to read & translate Latin. What I want students doing away from the classroom is focusing on vocabulary (and some of the other basics as well, but mostly vocab). Most of them use Quizlet; I don't know if it's the best spaced-repetition software, but it seems to have the teen market cornered.

I think the ideal way of scaling the flipped classroom method is to have people watch something along the lines of Khan Academy videos. The teachers I know who have done a lot of flipped-classroom stuff have usually ended up putting in a crazy amount of time recording videos. If you have a huge variety of well-made videos with a good teacher, you don't need to do everything yourself.

And as has already been mentioned, the flipped classroom still requires students to do stuff outside of class. If they don't watch the video about how to figure out the equation of a circle by completing the square, they're not going to be able to do it in class the next day.

As for homework itself, I think it works--sometimes. Its effectiveness will vary across different subjects and ages. I wouldn't want to be prevented from assigning it, and I wouldn't want to be forced to assign it every night either.

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> The teachers I know who have done a lot of flipped-classroom stuff have usually ended up putting in a crazy amount of time recording videos. If you have a huge variety of well-made videos with a good teacher, you don't need to do everything yourself.

Some teachers in my country produced a lot of YouTube videos as a reaction to covid, during the months when kids stayed at home and learned online. Those teachers realized that making a video and then having a Zoom discussion about it is more efficient than trying to explain stuff on Zoom. The kids can watch the YouTube videos at a time convenient for them; they can pause them whenever needed; they can watch the videos twice. And if you teach multiple classes, you only need to make the video once. You could even reuse it the next year.

What I was thinking someone should do (but I was too lazy to do it myself) is to collect all those videos, group them by topic, and arrange them according to the school curriculum. So you would have a web page where you could click e.g. "Math, 3rd grade elementary school", see a list of topics, and then a list of YouTube videos for each topic. After two or three teachers made a good video on a topic, you do not need to make your own; so people would only have to make new videos if they believe that there is something wrong about the existing ones and they can do a better job.

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I do a flipped class where I've made videos for all my lectures, with a time investment of about 1 hour for every 5 minutes of content. Class time is for kinetic demonstrations, projects, lab time, etc. Seems to work well. I went this route after I realized I'm a much more effective teacher 1 on 1 than 1 on 30, despite the efficiencies. Then covid happened, and I was pre-prepared for remote content delivery.

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Sucked when I tried it in high school (just meant that class time was spent doing boring busywork instead of that busywork being homework). Worked a lot better in junior-level fluid mechanics in college, where the professor spent class time lecturing but expected us to watch videos about each derivation before class rather than doing it in lecture.

From what I've experieaced, hard part about a flipped class seems to be making class time valuable for every student if most of the content delivery is happening somewhere else. Also, if you get through a homework assignment in half/double the time it takes your peers, you're free to either go do something else or put in an extra couple of hours. That doesn't work as well if you're in a classroom and trying to work in parallel with everyone else.

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deletedJul 7, 2022·edited Jul 7, 2022
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NAEP data (National Assessment of Educational Progress) suggests that over the past 50 years we've seen no or very little progress for white males and females, more for Latinos and much more for blacks, especially females (40% improvement).

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Just FYI there are concerns about how NAEP is not dealing with declining high school dropout rates: https://www.chalkbeat.org/2022/3/31/23005371/high-school-test-scores-underestimate-naep-dropout-nces

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Interesting, thanks. In any case, the numbers broken down by race and gender show some (if very little for whites) improvement. The flatness of the aggregate is a classic Simpson Paradox. Every group is doing better but Latinos made up only 5% of the dataset in 1970 compared to close to 20% today, and since they are below average, although improving too, they've kept the average flat.

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Of course the claim that there was no improvement could still be true if one only considered whites. Students most likely to drop out are non-whites, and results of whites have remained flat-ish over 50 years.

In other words, we spend a lot more money on K-12 education today (spending adjusted for inflation per student has tripled over 50 years); that spending has had near zero effect on whites; but it has possibly helped non-whites, especially African-American females. (It's also possible that it's not the spending that helped.)

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Hmm, sounds like selection/confirmation bias to me. Lincoln is an outlier. I’m not Einstein or Shakespeare either, but somehow I still consider myself well educated. Do you have anything more substantial to back up this sentiment?

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Where are you living where teachers have gobs of money to throw at problems? I have never met a teacher who hasn't had to buy their own pencils, let alone having actual support and resources

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https://www.cato.org/sites/cato.org/files/styles/optimized/public/wp-content/uploads/Cato-tot-cost-scores-Coulson-Sept-2012-sm.gif?itok=NdJTUsYh

This trend has continued all the way up to 2022; it now costs something like 3 or 4 times as much to send a kid to public school as it does to send them to the Manhattan Preparatory Academy, or Willowbrook, or any other private-school-for-future-presidents. Tuition at Ravenscroft (an expensive elite private school with famous powerful alumni) is about $200,000 for a full thirteen year K-12 education for one person. Public school in the same area ends up costing about twice that.

From my privileged position as an evaluator/auditor of federal grants, I can say with some confidence that almost all of the added money above 1970 values has been spent on corruption, usually in the form of the principal hiring his brother-in-law to run an afterschool program using GEARUP money, or similar. Very very occasionally, we evaluate a program that was actually well-meaning (but which still had purely negative effects). Often these programs are accidentally hugely racist or classist. Ask any student what it's like to get referred to a dropout prevention program, you'll find that it has horribly negative consequences for their academic career, like a black mark on their permanent record that makes every future teacher automatically perceive them as a failure who needs compassionate remediation... yet many of the programs are designed in such a way to 'help' as many minorities as possible by placing them in such programs, even if they are currently a straight-A student who hasn't missed a day of school in their entire life and just finished their applications to Harvard and MIT.

I strongly suspect that if we actually gave all the added money to the teachers, it would be enormously good... but the way party politics intersects with education policy currently makes this impossible. Instead, every 2 years some bright young congressperson has the great idea for a new bill to finally fix the problems with education by increasing the annual budget by a few billion dollars, the money gets allocated, then the money mysteriously disappears into the black hole of bureaucratic corruption and do-nothing NGO nonprofits. Then 2 years later we get another pack of naive junior congresspeople and someone has the same bright idea all over again.

And all the while, teacher pay stagnates.

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John, your comment certianly reifies my innate pessimsim, but beyond that I appreciate your insight as someone close to these problems. What published work would you recommend that documents the corrupt allocation process of educational monies?

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Jul 8, 2022·edited Jul 8, 2022

Honestly there's nothing. The only proof I can show you is that if you try to figure out where the money is going, you won't be able to find out, because it's not documented. That should immediately raise a bunch of red flags, but it doesn't actually prove that 90% of the money is vanishing into NGO pockets as I suggest.

I've got a couple of evaluation reports I can show you, but they only document problems at individual schools

Edit: that said, I have tried to point this problem out to the lesswrong / effective altruism / rationalism crowd on many occasions over the last decade. Starting with the first Lesswrong post: https://www.lesswrong.com/posts/EuMkZ67vDincGSkYp/problems-in-education

People almost universally thought I was making bullshit up, so I got my boss to let me treat this as a full project, and we got our writer involved, and pulled up the mendeley library with all of our citations, and wrote a real full-on paper describing what we'd seen: https://www.lesswrong.com/posts/DxFFeJoczRp2rPS2K/?commentId=oHHRcwxX5HAfcdG9t

The first post got 300+ comments, the second got seven. Once I could actually prove what I was saying, it was a bit like, nobody even knew what the fuck to do, the situation was so much worse than anybody had ever believed before that they just kind of ignored it. It was not a ringing endorsement of less wrong rationalism, I'll tell you that.

Then about 5 years later I tried with a different tack, then maybe if I could get some of this grant money in the hands of rationalists it would be better. I wrote https://johnwhale.tumblr.com/post/137912141447/grants-aka-using-government-money-to-do-good and it got widely spread, retweeted by Scott et all. I followed up with: https://johnwhale.tumblr.com/post/138534613532/funny-sad-grant-funded-projects-pt-1

After that, nothing.

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Thanks for the reply! I'll certainly read everything you linked.

If your work is correct, it's horrifying that it's not getting more attention, but I can't say I'm surprised. In my own field (medical oncology) there are enormous methodological problems which lead to untold mountains of money being wasted on meaingless clinical trials, but when I point this issues out to colleagues, they just shug and say, "yes, that's probably true" and they follow it up with some empty saying like "some data is better than none" or "we have to work with the system we're in."

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I've seen numerous data points on private school tuition at $40k plus per year. In comparison, I believe California (my state) spends $14.9k per year on public school. So it seems like the actual figures are largely the opposite of what you're claiming.

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Jul 7, 2022·edited Jul 7, 2022

It depends on how you measure things. I taught at a ~$20k (tuition)/year private school in Florida, which officially spends ~$9k per pupil per year. But that's a combination of secondary school (much more expensive) and elementary (much less expensive) while we were only high school. Also, that usually only considers the direct state spending, and a lot of things get pushed into other budgets and so don't count (such as capital expenditures, which are a huge chunk of change and had to be accounted for in our budget but not in theirs, as they're funded separately largely via bonds). And the variance between locations in each state is huge--florida in 2021 varied between ~7.5k (rural Gadsden county) and 37.2k (the specialist Florida School of Deaf and Blind). Even without that outlier, it was 7.5k - 16k. And that's just operating budget, not capital budget.

I think you can make the numbers come out just about any way you want. But what you can't do is obscure the *trend* in spending--that's up. Way way up. But mostly for a couple things:

1. students with special needs/disabilities. When you need a 1:2 (at most) staff:student ratio with a bunch of specialists, that gets expensive, fast.

2. Admin overhead, especially compliance at the district level. This includes useless "technology" that never actually makes it down to the classroom level, as well as junkets, trainings, staff, etc.

Teachers and classrooms saw very little of this ballooning spending. And there's effectively 0 correlation between spending and outcomes beyond the extremes of the distribution. It's as if there's a certain minimum, below which you get bad results. But above that other factors dominate and more spending doesn't change much.

What private schools get is selectivity--being able to curate the student population. But that's a different issue.

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I would like to point out that students with special needs or disabilities, as soon as school started getting more money for them they started applying the label to almost everybody. Here in North Carolina the state put a cap, no school can have more than 15% if their students labeled as disabled (I think the actual percent changed recently). I do know that every school in the state is right at the cap. They followed their incentives all the way down the gradient.

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Yeah. And it's not just the school--the parents also play a major role and are reinforced in doing so by the school. And it's not just that (at private schools)--if your school starts getting a reputation as being "good for kids with <X>", the population starts shifting until you have more and more kids with <X>. Even if that wasn't your intent. Happened at the school I taught at, and not in a good way. <X> there was "substantial, but not crippling autism" (as in "verbal and can deal on their own, but extremely maladjusted and needing substantial support". Which we were *not* equipped to give them without compromising the education of everyone else.

It's a hard issue.

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Oh, I wasn't even counting state spending. I was just counting Federal spending. That state spending is on top of the spending I'm talking about.

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Which federal spending?

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Department of education. Just look at the chart man, it explains itself pretty well.

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I'm a elementary school board trustee in California. Which penny do you want to trace from when it enters my public school district to when it exits?

I don't know about other states, but in California, it's the publicly funded private schools, i.e. charter schools, that are the most cause for concern. No new for-profit charters are permitted, but existing ones are allowed to continue. Think about the incentives at a for-profit school. Are they aligned with the educational needs of students or of investors? Perhaps they are designed to produce high quality teachers?

As Greg G points out below, private school tuition is multiples higher than the per-pupil cost of public schools, at least in California. I should know the cost of educating children in my district because at every board meeting we approve every purchase order, i.e. before the money leaves the district in the form of a check. And we review and vote on a budget, then we approve three more budget documents: two interim budget variances, and one final independently audited financial statement. The basic requirement is that they all add up.

I don't know if anyone has made a California Public Records Act (CPRA) request to a district for the raw SACS data that is sent to the county and then on to the state. It's a summary of all the activity in every fund that districts manage. (All financial activity in public schools goes into or out of some fund, e.g. the Cafeteria Fund. The General Fund, not unexpectedly, is the most active.) The format of the SACS file is well-known and the tools used to view the data are widely available (MS Access). I also don't know if anyone has requested the raw financial records of a district as opposed to the detailed-but-not-raw SACS data.

So, if you want to track a particular penny from when it enters the district to when it leaves, the data and the tools are there.

Your first link is to the Cato Institute. I don't think the Cato Institute is interested in education. To a conservative, any successful public program is an anathema and must be destroyed because a successful public program invalidates a core belief: profit is all that matters. The Cato Institute's agenda is firmly to promote right wing conservatism. They are going to do everything in they can to show that public education is not worth the money spent on it. One of the things they do is to completely ignore the value of the outcome of public education, i.e. the nearly $28 trillion economy that is the United States where almost everyone was educated in public schools. They focus exclusively on the cost of education, and to make the numbers even scarier, the total cost of a K-12 education. The benefit side is ignored.

The Cato link you provide shows a graph of total cost of a K-12 education vs NAEP scores. What do you think NAEP measures? Certainly not educational outcomes because the U.S. has built the world's largest economy since WWII with NAEP scores that have essentially remained static over that period. So what is NAEP measuring? Nothing that I as a parent, teacher, or board member is interested in. Perhaps NAEP measures test-taking ability which I would expect to stay more or less constant over time.

All that being said, it is [unfortunately] not the case that public schools are examples of what can be done to provide a high quality education that matches the needs and aspirations of every child. Our district does particularly well, but I am not convinced that we do as well as first appears if income, health, employment, educational attainment and food/housing/personal security are taken into account. Could we all do better? Of course and so we try.

My district tries to meet every child's needs. For example, we spend five times as much on average on a child with special needs as we do on a child without special needs. We offer a summer program to children who need the extra help to get to grade level. We track the progress of every child in becoming proficient in every subcategory that we have determined to be an essential part of the Common Core. We practice differentiated instruction and we use project-based learning wherever we can. We have a robust program of professional development and we encourage teachers to share the tools and techniques that they have found improves educational outcomes.

After that extended pat on the back (we are totally wonderful), I need to mention that we are failing to provide about 15% of our student body with the education they need to achieve their college or career goals. Suggestions?

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I do not understand what you're saying. I've read civil war letters [and we must remember the selection bias in which get read- it is mostly a handful of civil war letters that are read over and over]. They read like they were written in a particular style. That style has its charms, certainly, but it in no sense seems to me to be clearly superior to contemporary style.

Consider Sullivan Ballou's letter, which seems to be quoted everywhere, and take up 30%> of the mental space people assign to civil war letters:

"As for my little boys, they will grow as I have done, and never know a father's love and care. Little Willie is too young to remember me long, and my blue-eyed Edgar will keep my frolics with him among the dimmest memories of his childhood. Sarah, I have unlimited confidence in your maternal care, and your development of their characters. Tell my two mothers, I call God's blessing upon them. O Sarah, I wait for you there! Come to me, and lead thither my children."

Now I'm not denying it's good, but when we factor in the selection bias that goes into bringing it to us, it doesn't seem especially remarkable. It's profuse, affectionate, but wordy and melodramatic. I see better writing than this on Twitter everyday. Not reliably, or in every tweet, but I do see it, perhaps every 50th Tweet.

To prove I'm not bluffing about the selection bias, here's another civil war letter:

My Dear Wife,

I now take my pen in hand to let you know that I am well and hope these few lines will find you the same. I am well at present. I have got over the neuralgia in the head.

We had a great parade on last Thursday, the 19th. The governor of Rhode Island was here and presented the regiment with a nice silk flag called the regimental flag. There was also present the governors of Massachusetts & Connecticut with a large number of the members of the Assembly, as was also one of the old 76 soldiers who said that we were good soldiers, very good. And we also fired 8 of our largest cannon from our newly mounted fort, the work of our own hands. We had a very fine band of brass music from Massachusetts.There are now 8 full companies on the ground, commencing at “A” and going down to “H”. There is now in Providence another Co. by the name of “I”. It is full and about 80 in Co. “K”. The Company I belong to is “E”. We are about building barracks for 1200 men.

There is a young man coming home with me when I come--I don’t know when that will be--by the name of Mr. Johnson. Tell Mary(1) to have her cap set for him when I come home as he is the handsomest man on the ground.

I have got an office but I don’t like it though it is something similar to that like I had in church assistant secretary(2). We have meetings every night in the week.

I want you to have your daguerreotype and Mary’s and Sis all in once case if you can send it by the next letter; and if you don’t put them in one case, have them taken separate as I should like to have them to look at, being that I cannot see your face. Write to me twicea week and let me know how you are getting along and how produce is selling, as we do not get but a loaf of bread and a cup of coffee during the day.

We live in cloth houses and lay close to the ground but we are in hopes if we trust in God to be in the barracks. And then I am in hopes that I may gain my strength and through the divine providence of God and his mercy, I yet live and one day or another I expect to arrive at home through storms and hurricanes. I expect if I never meet you on this shore or never see your face anymore, I expect to meet you in heaven, God being my helper.

My dear little daughter, I want you to write your papa a letter as it would please her papa very much to have a letter from his dear little daughter. Papa sends her 5000 kisses. Papa thinks a good deal of her.

Tell Sarah to tellPresilla(sic) to forward this letter to William(3), in the name of the Lord, as he is all the time “grumbling.” I had forgot it almost to the last, I want you please to send me those flannel pads that I wear on my bosom to keep me from catching cold. Give my love to all enquiring friends, especially to Julia Mary(4) and mother and the baby. Tell Mary not to forget to write me a letter.

Dear Wife, I send you 10,000 kisses. No more at present but remain your true and affectionate and loving husband Simeon A. Tierce. The reason why we cannot get any furloughs is because there has [been] too many run away.

Poetry

The rose is red, the violets blue

sugar is sweet and so are you.

Since woman to man is so unjust

it is only you that I can trust.

And if in war by battle slain

my love for you shall never frain.

If you loved me as I love you

no knife would cut our love in two.

As blood and water will not blend

my heart is true unto the end.

So good bye dear, I now must close

in these few lines with love below.

Please to direct your letters to Camp Bailey, Dutchs Island, 14th Regmt, Rhode Island Heavy Artillery Colored Battalion, Co. E in the care of Lieutenant Harard for Simeon A. Tierce.

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Lots of confounders there...if you used the same teaching method but you had 10% non-english speaking at home kids and/or immigrant etc. and then that numbers goes up 40% in your school..then the success rates will go down. When you look at more homogenous or non-immigrant heavy populations in some European countries vs others or the USA with higher rates of immigrants etc. you'll find most of your answer there.

Education is doing well enough and the rich kids in private schools are doing just as well as ever. We are seeing demographics and cultural shifts much more than any sweeping changes in education with the main difference being the removal of physical punishment.

Certainly not a knock on anyone's intelligence or capability, but an influx of poorer people who are also struggling to learn to speak the language and the culture...they're just not going to do as well on average and it can take 2-3 generations to linguistically and culturally acclimatise.

This is well known in immigrant families and educational studies. It just takes work, time, and generations even to overcome all the challenges faced by people in those circumstances. I know I'd struggle if I moved to France and didn't speak French and couldn't' use my education and the people there spat on me and refused to offer me jobs, anyone would struggle and that's what is largely happening in the USA.

While if you look at easier transitions such as the kids of an English or Irish medical doctor who moves to Canada or something where there isn't a huge transition cost or cultural challenge, then you wouldn't see that effect. While an impoverished person from Hondouras with no education moving to the USA and working menial jobs...their kids will struggle more and have less support at home to even learn English, much less do well in school.

The broader decline in speech patterns, formal speech, etiquette etc. are a separate matter and not part of schooling. People used to all wear hats and even poor men would wear a suit of some sort when leaving the house. Is that cultural shift also due to schooling? It would be silly to attribute everything to education, especially when people back in the 1960s received so much less of it with high school completion rates being lower than today.

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Parents (probably moms) with more than a couple kids or other responsibilities may not have time to help their kids with homework. A parent needs to be involved to get the kid started doing his homework and maybe with any tough spots, so finishing is more likely.

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I've been guilty of spending excessive time on one subject's homework in order to procrastinate on doing a different subject...

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I don't quite get the alleged joke. Thinking back to my secondary school days, I think the subjects I spent the most time on homework were those I enjoyed *most and least*. Least, because it was excruciating to force myself to slog through the tasks; and most, because I genuinely enjoyed those subjects and put extra time and effort into trying to do the work particularly well.

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Alfie Kohn is a longtime anti-test, anti-grades fanatic. Similar to the FairTest idiots.

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author
Jul 7, 2022·edited Jul 7, 2022Author

I'm giving you a minor warning (25% of a ban) for this - it sounds too close like an Argument From My Opponent Believes Something (https://slatestarcodex.com/2013/06/13/arguments-from-my-opponent-believes-something/), a personal attack, and the "idiots" comment is over a line.

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Questions:

1) Do you keep a record of ban percentages so that you know when a user reaches 100% and gets banished to the outer darkness?

2) Do the percentages degrade over time, allowing a user to one day, far in the future, cleanse his shame and once again know peace?

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Behold, the prophets have told that Scott shall one day ban his only begotten son, so that whosoever believes in him shall not be banned, but have everlasting accounts.

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author

1. Yes

2. No, but I'll probably do something informally like that.

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Scott refer to him as an example of the anti-homework camp, not some neutral arbiter.

For those unfamiliar with him, here he discusses something other than school:

https://www.econlib.org/archives/2010/11/in_defense_of_s.html

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Good link. Thanks.

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Jul 7, 2022·edited Jul 7, 2022

There's homework, and there's homework. When I was in school most of it was busy work. In college though, most of my problem sets were actually a good way to practice things.

I wonder if parents could just say to their kid that they didn't have to do any elementary school homework. Would a kid who otherwise performs well get away with not doing any homework? It would probably depend on the school.

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Right, the idea of comparing two hours of word matching compared to 20 minutes of something compelling in the same research under "time spent" seems futile.

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It also depends on the kid, whether they'd be willing to go along with that.

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Are projects homework? I remember spending quite a lot of time on things like the science fair and various presentations, dioramas and posters. These were probably not particularly edifying but I rather enjoyed them. I could spend infinity hours painting tiny houses for a 3D visual representation of the feudal system.

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A friend recently was telling me a very interesting anecdote from the great depression, turns out he learned it when he was assigned to interview his neighbor for a class. I had a similar assignment, and never stopped to think about how valuable that sort of thing is. I would never have done that on my own.

School projects are often just a really great way for kids to spend their free time. Not always, but it happens. I'm generally pretty anti-school, and I tend to think of school as preparation for something (effective or not). Worth remembering that sometimes it's just a straightforward good use of your time.

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School and homework have another effect. They use up your time in a positive way. Think of the trouble kids could get into without direction. Germany kept kids in college because they didn't have enough jobs for everyone. Better than loose on the streets.

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IIRC, they did something similar in Kosovo in the 1980s.

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I definitely agree that there are multiple types of homework and I would not expect them to have comparable effects. The trickiest subset is homework that's drilling known material to be automatic material - comparable to doing scales in music. It's boring as hell, and doesn't teach you anything new, but it is effective at making a particular task both faster and effortless, so it can have utility *if the task itself is worth the investment*

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It wasn't customary for kids in my family to do HW (primary through to secondary), but I did learn a few French verbs at school. As a teacher>35 yrs (Eng.Lang/Lit, including 'special'(dyslexic/complex needs students) I was expected to set HW, and students mostly complied. There is lots of evidence, in my experience in the UK, of parents having a big hand in HW tasks, especially at Primary level, less so in the case of older 16 -18yr students. It seems deeply unhelpful to set lengthy, time-consuming HW tasks when there is no support (space,time,or interest) in the home. Schools and colleges demand that teachers set HW, whether individuals benefit in terms of acquiring knowledge, thinking skills, or learning how to learn, must depend on a multiplicity of conditions. Years ago, somewhere (?), I read that doing HW was a waste of time i.e. had not been shown to be effective. In the UK the education system is inadequate in many ways as it's a political football. If HW was proven to be useless the state school and many private schools here would do it anyway.

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My elementary school didn't assign homework and I found it very difficult to develop the habit when I went to high school (England has a single seven-year secondary school rather than splitting secondary into middle or junior high and high school).

I wonder if there are elements of school education that are most useful because they develop habits of time allocation and learning skills rather than for the substance of what is learned?

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Some would argue this is the main point.

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My parents told my primary school they wouldn't get me to do the busywork homework, and I didn't have to do it. I did perform well otherwise. In high school, I was one of the worse people in my class for not getting work done on time, and I'm still not great at time management.

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I'm tempted to just sit and do all my elementary school aged daughter's homework for her - or rather, sit with her giving her all the answers. I wonder though if that's the worst of all possible worlds. Time still wasted on lots of writing (for both of us) - challenging problems always results in immediate capitulation.

I think will adjust my prior away from painful homework interactions. Assume she's going to be able to learn something easily next year and move on rather than labouring something until its nailed.

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That balance between avoiding the crap and encouraging/allowing autonomy.....That mad assumption that we all develop our interest and focus at the same time, in the same degree...

I currently teach primary maths to a delightful boy who seems to share my memory deficits and is not helped by his lovely parent who wants to answer every question, about anything, for him.

You know your child best - lots of forced writing? Noooo! Whatever a child does is enough; schools differ. 'Elementary school curriculum' - I think of play outdoors, groups of kids, fun, stories, experiments, dance, song, music, swimming, mostly child-led seems optimal; a bit of English 'n' Maths as can be made useful. My son went to the local Primary school, learnt guitar and other stuff. I don't remember him doing homework. Could have been neglect on my part.

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I never did homework in elementary or high school. My parents were fine with that so long as I got good grades, and would back me up to the teachers.

If you already know the material, homework is useless and boring and a waste of time.

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Did you ever start needing to do the homework (e.g., college)? Was that fine, or did you feel like you could have used better habits around getting it done?

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I'm not Angus, but I had a similar "problem". I never did any homework, until the last minute, which essentially meant I was rushing homework during the breaks right before the session I was meant to turn it in started. I taught me to work well under pressure. And I was able to sail through my entire school career like this.

However, when I went to university I had to learn some very painful lessons about time management, which resulted in me finishing my degree several years (!) late. I could have completed my degree in 6-7 years, but took 10. For two of those I blame the institution I wrote my thesis at, the rest is on me.

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Interesting. In most schools in the US that I am aware of, it's literally not possible to get good grades AND not do homework as the homework component may represent anywhere between 25 and 50% of your total grade for the course. Someone that got a perfect 100% score on every exam, test, and project that did not do any homework would likely end up with a C for the class and your transcripts would look like absolute garbage.

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I remember when I was in middle/high school, I did most of my homework in study halls. Why not just make school longer, and add mandatory study halls, so kids aren't still doing algebra problems at 8:30 pm, 14 hours after the school day started?

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founding

Or just 'get rid of schools'! Kids are pretty good at learning when they're motivated to do so.

_Some_ algebra is pretty useful, but I'm _very_ sure basically 'zero' adults ever need or want to solve quadratic formulas, let alone anything more 'complex'.

I've (happily) done some mathematical research/literature-review as part of my jobs/career (mostly software) and I have a Mathematics BA, but almost everyone else seems pretty happy/content to just use a calculator/formula/software for anything beyond basic arithmetic.

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thing is, "doing homework" is in itself a skill. i got pretty far without, as long as doing homework wasnt really necessary. then when the subjects got sufficiently complex i decided to maybe do some homework but struggled hard.

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I think a lot of this has to do with "how much you already know", which is why elementary school homework seems so pointless for higher performing students.

By 3rd grade, I was reading high school level texts. The benefits I got from anything other than math assignments and French assignments in school was probably pretty close to 0.

Conversely, going out during summer learning activities on field trips to the local swamp and learning about the local wildlife and plants and animals, I learned a lot, because it was stuff that was literally in none of my books - they were more focused on macro scale things (evolution) and cool things (tigers, whales, etc.) than local flora and fauna.

If we did more tracking, I suspect people would have more appreciation for homework.

That being said, I also suspect that elementary school is not very useful in general compared to middle and high school, and that most elementary school teachers are not very good at their jobs or are following rules that existed since ancient times.

You know what was useful?

My 2nd grade classroom (in 1992!) had a bunch of computers in it, one per student. This was in a public school. We got to mess around on them, play games on them, use them for various minor tasks (I believe we used early word processors sometimes), etc. I am sure that a lot of kids had never used computers before then, and they learned the basics of using a desktop computer from that class.

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Tracking works best in large schools, and primary schools tend to be much smaller because primary-aged kids are less independent and can't travel as far as secondary-aged kids. If you only have two classes in a given grade, then you can only split students into a top 50% and a bottom 50% which isn't all that great for assigning radically different school work: both classes will be predominantely students close to the median.

You need five tracks just to get a top (and bottom) class that averages a full standard deviation from the mean.

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Jul 23, 2022·edited Jul 23, 2022

You are making two assumptions:

1) The student body follows a single bell-shaped curve (which is often untrue).

2) All classes must be the same size (you can have smaller classes for the gifted and severely disadvantaged students - in fact, most classes for severely disadvantaged students are already smaller by necessity).

Also, your math is a bit off.

With four classes, even with a standard distribution and identical class sizes of 25 students per class, if you were looking at, say, IQ, you would have two classes in the middle (90-100 and 100-110) and then two classes for the extremes (110+ and 90-); the median in the above and below average courses would be above115 and below 85 (16% of the population is above 115, 16% below 85, so as each class has 25% of your student body in it, the median would end up around 118 and 82 for the extreme classes, if I am doing my math correctly).

You would only need a student body of 500 students at a grade 1-5 school to track out the top 25% and bottom 25%. If you assume class sizes of 30, then you still only need 600 students.

If you wanted to make it so no one in the "gifted" class was below 1 SD above average, you'd have to have at least 6 classes, which would be a student body of 750 with class size of 25 and 900 for a class size of 30.

If you allow the classes to be of different sizes, and maximum class size of 30 and a minimum of 16, you can track out all the students 1 SD above average and 1 SD below average with only 100 students per grade level.

If you want to track out the 2 SD students, then you will either have to settle for very small class sizes or a large population - you'd be getting only 2.5 per 100 students, meaning you'd need 1,000 students per grade level to get 25.

On the other hand, when I went to elementary school, myself and the other most advanced student were given alternative work to do by the teacher while she was teaching the rest of the class lower level math at one school I went to (one of the things I recall is that we got to learn exponents and square roots while the rest of the class was still working on lower level multiplication and division; I recall we also got to do some applied math, which was saving the book club parents time and effort but hey), while at another school, there was a small "TAG" group which had its own meetings outside of the usual class during normal class times where we would be taken out during certain subjects and basically learn about other things with less supervision.

This sort of alternative arrangement is possible even without a huge class size.

You can also potentially pool the gifted students and the disadvantaged students across the school district into particular tracked schools.

Disadvantaged students need extra support anyway and this is probably more efficient and effective than spreading out these resources thinly across a lot of schools; if you put them all in one place, you can have more specialists there.

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Let's just continue with something of unknown utility. Why not?

Schools went overboard on homework for common core. It sucks. Most of it is poorly designed. It seems more designed to indoctrinate students to be complaint than to learn.

As a parent dealing with schools for almost 20 years, learning doesn't seem to matter anymore.

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Compliance is the lesson perhaps. And not a bad one for most kids who will be working on jobs where they will be told what to do most of the time. Some see this as onerous or take a conspiratorial attitude, but most schools formally or in recent history were quite up front that obedience is part of schooling.

That's what school uniforms do in most of the world and/or where they are used. That's what being 'on time' means and it is why missing too much class/school will fail a kid even if they can pass the exams. Compliance, reliability, consistency...these are the lessons kids learn for the life most will lead.

Is it shitty...sure...the world is shitty...but is it the wrong approach to take? A high school diploma if that's all one has shows a person is reliable and comes from a steady enough home or mindset to be a good worker. For those bound for intellectual greatness or whatever in University, then the high school diploma is left behind and doesn't matter after they get into university/finish it for an UG degree.

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There are better ways to do this then making everyone wage zombies while pretending to educate kids.

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Isn't that a far broader argument about social/economic structures though? Most people will be wage zombies once they turn 16/18/21, so gearing education towards it seems logical. Pretending what you're really doing is turning them all into Voltaire may seem a bit ridiculous, but I don't see that a democracy could do anything else short of not educating people at all.

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We can do like Germany and push people into trades and services. Let's stop pretending college is for everyone. Let's get kids to train to be carpenters, plumbers, nurses, dental hygienists, electricians, bookkeepers, fireman, programmers, etc. earlier.

We are not educating people, training them to think for themselves, anyway. Schools are against education, and more about socialization and programing.

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"Schools are against education, and more about socialization and programing."

More than one teacher has said that to me. If John Taylor Gatto is to be believed, the last thing they want in a school is for the students to be educated, for the educated are intractable.

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Exactly. The truly educated student has a mind that questions and inquires and refuses to accept the narrative. These students become "difficult" and "challenging" and the schools push the parents to medicate them. These are the students that score high on SATs with poor grades, the lost smart kids ignored by the meritocracy.

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If this is true, why not let kids test out of "can be punctual and reliable"? Many high school kids have jobs. If they can provide a letter from their boss saying they're a good employee, maybe we should let them complete less homework as long as they can still pass the course. For that matter, is reliability and showing up on time really such a difficult thing to teach that it takes 12 years of a person's life? I suspect that, if anything, school is measuring reliability rather than teaching it. Just collect attendance and assign homework for a month or two and you'll have enough data to make a pretty good estimate of a person's potential as an employee.

This reminds me of the thought experiment where there's a tradition of people hitting themselves on the head with hammers all the time, and coming up with justifications after the fact for why that's a good idea, except that in this case we're hitting our children with hammers and saying things like, "in life most of these kids will lead, they'll bang their heads on things from time to time and it's important that they develop a thick skull early", or "of course being struck repeatedly on the noggin with a wooden mallet isn't an exact simulation of the modern workplace, but the ability to remain stoic and focused in the face of adversity is a trait that is highly valued by employers".

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In the current system, lots of people accept that students who have jobs are more reliable than students who aren't. Partly, this is because someone "independent of" the students is vouching for them/prefers to keep employing the student instead of replacing them, partly it's because the students will probably become responsible if they can attach a time and effort cost to money, but also, partly it is because the student can demonstrably juggle the commitments of work and study. Therefore, the students get advantages in interviews and such.

I suspect that if homework exemptions for working became more common, all of those benefits would be lessened - some employers would pay less and accept a lower quality of worker, if the workers got a separate benefit from the job, and it would take less effort and show less responsibility to hold down such a job. These wouldn't be everywhere, but they'd reduce the status attached to having a job in high school. (Also, high school is when there is a benefit from homework.)

(See how cognitive dissonance/"sour grapes" sounds from someone who didn't have a job in high school?)

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A lot of things in the modern industrialized human world are unnatural, so unnatural that it takes decades to socialize a human kitten into accepting them.

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Jul 7, 2022·edited Jul 7, 2022

Obedience is anticorrelated with any job actually worth doing. In fact, junior employees usually have to _unlearn_ obedience-based habits to get anywhere, and these habits drive their mentors up the wall. Importantly, obedience-based education teaches you to _conceal your uncertainty and errors_ , which is the single most disastrous thing an employee can do.

A different thing is Heinleinian "be able to give orders, be able to follow orders" mindset - also known as teamwork, taught in schools not at all.

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On the other hand, self-discipline is important in all aspects of life -- the ability to (sometimes) do the unexciting thing that's required of you rather than the fun thing you'd rather be doing right now.

I'm not sure whether homework teaches that effectively (I never learned it until I hit university) but I don't think you can write it off as "evil Prussians want to turn us into wage slaves"

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Personal projects teach you that as well, beyond a certain point of complexity/skill everything contains drudge work. If anything we should put a heavy focus on building things and finishing them, which will inevitably teach self-discipline instead of bouncing off the hard parts.

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How would you get everyone to do that, even the people who don't want to?

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I’d venture that the obedience-value anticorrelation shows up significantly more in jobs that (in our society) require undergraduate education or higher than in jobs that don’t.

Those obedience-centered habits are more likely to be useful in e.g. waiting tables than in computer programming, though both jobs are (or at least can be) valuable.

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How are obedience habits useful in waiting tables? You have a room full of guests and have to handle their requests, juggling a whole bunch of ongoing issues at the same time. A person strictly doing what they are told will be a pretty terrible waiter that lacks initiative and ability to handle unexpected situations.

Obedience habits are maybe useful at a 19th century assembly line, that's about it. Perhaps first line staff at a call center benefit from them, but that kind of job is miserable, based on humans pretending to be script-driven machines, and already being automated out of existence.

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I suppose that a curriculum designed by Heinlein would run along the lines of:

“A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.”

Which would actually be a pretty fun education.

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Apart from the "die gallantly" test, that would suck.

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You can skip this test if you score A at "fight efficiently".

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"Graduate with honors."

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As a cat, it is odd for me to hear a dog downplaying the importance of obedience.

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Our reputation for obedience is wildly exaggerated.

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I've never heard that most of the world uses school uniforms for compliance. That's interesting. Where do you get that from?

Everyone I've talked to that has taught in schools with uniforms or has students in one in the US the professed reason behind uniforms is to remove clothing/class bullying and reduce sexuality.

Not saying the US is "most of the world" but it seems like those two problems are present elsewhere as well and wondering where the alternative explanation (compliance) is coming from.

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I attended school in the UK in the late 90s through to the early 2010s. Uniform standards were enforced at all ages – teachers would tell you to tuck your shirt in, students were only allowed to remove their ties on hot days if the headmaster's office announced it, etc.

I understood it to be partly about teaching standards compliance, partly about being good advertising for the school, and partly a broken windows argument that being "dressed to learn" would promote the right mindset.

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Anecdote. Many years ago, I met an university lecturer from Singapore who had been sent to Britain to look at how the education system encouraged rebellion, or at least free-thinking. The Singaporean government were concerned that their education system produced clever, obedient drones who failed to innovate at a rate necessary for their future economic success.

I have no idea what the outcome of this study tour was.

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Interesting idea for a story: a 1984 / Brave New World / Public Schooling System designed to be repressive and banal not because it creates drones, but because it foments rebellion, and rebellious minds advance and benefit society much more than a bunch of well-adjusted happy people. Therefore justifying the suffering / broken students / poorly educated students the system creates.

When the rebels go off and advance society, the designers know their work is worth it. If any of them decide to start trying to bring down the system that caused them to suffer, they are shown behind the curtain and realize they love Big Teacher.

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This is pretty much the plot of Stalky & Co, Rudyard Kipling's semi-fictionalised account of his school days.

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founding

My complaint/criticism is that 'school' probably isn't even that great even for teaching this stuff – and I'm happy to admit that this stuff IS useful.

Just let kids work a job!

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Homework sucked all the joy out of my childhood and caused me to hate learning, so much that I totally failed at college, fast and hard.

Whatever the positive effects of homework may be, there has got to be a better alternative.

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I don’t know you so I have no basis to contradict you, but how do you know you wouldn’t have hated learning, or failed at college, even without the homework?

I mean, I hated homework too, and didn’t have either of the adverse effects you reported. Without a larger sample, how can we tell if homework actually caused those effects?

* * *

A completely irrelevant anecdote, just so my comment is not too antagonistic: Somewhere around what we called 10th grade, i.e. the second year of high-school, my math teacher noticed a couple students hadn’t done their homework, and started going desk-by-desk to check everyone.

I hadn’t done my homework. When he reached my desk and found out, he looked a bit surprised. (I was a relatively good student.) I don’t remember if he asked anyone else, but if so the answer was probably in the usual dog-ate-my-homework category.

So he goes “Why didn’t you do the homework?” and I just say “Out of habit, Mr. Professor”. After a bit of speechlessness he say “what do you mean?” and I explain that I hadn‘t done my homework all year.

Good thing he was a decent person, nothing bad came out of it. I think the stopped checking the other desks at that point.

Next year he moved to Australia, but I’m pretty sure that was unrelated.

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> Let's just continue with something of unknown utility. Why not?

When faced with a lack of compelling studies, the right thing to do seems to be to fall back on intuition. And intuition says that if you spend more time on something then you'll probably get better at it.

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If you spend more time doing something that is counterproductive, then you should stop. Intuition is often wrong, unfortunately.

As a parent who has dealt lots of stupid homework assignments, that did not contribute to learning, I have seen the disservice this has done to children. One school went so far as to count all assignments, tests, and quizzes the same, so a busy work assignment counted the same as the final. Teachers didn't care if students learned, but only if the work was done, even for children with disabilities.

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Thanks for this post! Short, crisp, interesting summary about something I've meant to research but never got around to.

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the graph does look like returns diminish quickly though - you've already gotten nearly all of the benefit at 50% the amount.

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Advance of 50->100 and 100->150 actually seems pretty linear. 0->50 probably has very quick growth from having any homework at all, and after that it's linear for some time...

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author

I don't know how their metric works, but it looks kind of like standard deviations which I worry is already close to grading on a curve and makes it hard to say things like this. In general this is a hard problem: if controls gets 75% on the test, and the intervention group gets 100%, it it fair to say the intervention "improved performance by 33%"?

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Jul 7, 2022·edited Jul 7, 2022

The purpose of homework isn’t learning. The purpose of homework is to sort those who will conscientiously put the new cover sheets on the TPS reports from those who won’t. It’s to filter for conscientious and agreeable personality traits as well as work ethic.

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Yeah, as a musician, I’ve always been confused by the claim that homework is completely useless. If you only do math during the hour or less per day that constitutes math class, I would have thought it would go sort of like just showing up to orchestra rehearsals and never practicing the music beforehand. Which, unless the orchestra plays at a level far below your own, such that the music is too easy for you, is usually a very bad idea.

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Orchestra and sports have something in common, which is that people only play one or the other if they have the talent to perform at their chosen level, so it's a really pointless comparison.

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I'm not sure it's that pointless. Skill playing the violin is useful/necessary for performing as a violinist. Skill with middle-school maths is useful for all sorts of things, from shopping, budgeting, route planning, anything you might want to engineer, cooking, anything you might want to measure statistically. There's a *lot* of roles to play in adult life where it matters.

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There's no evidence that homework guarantees mastery of middle school maths, nor that homework is necessary to achieve mastery of middle school maths.

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I don't think the musician example works. The musician knows how to play all of the individual notes, knows how to read the music. The repetition is creating the muscle memory to do it effectively.

Homework isn't reinforcing muscle memory - if you know how to solve the problem, you are just demonstrating

1) You know how to solve the problem.

If you don't know how to do the problem then maybe:

2A) it forces you to figure it out?

2B) Guess?

2C) Skip it?

I doubt homework has much, if any effect. Any result that occurs happens all at step 2A or perhaps 2B if you have a parent that reviews your homework.

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Writing is absolutely a skill that benefits from practice and feedback. With the exception of a writing class homework isn't about 'writing' per se.

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I think mathematics homework in particular is an exercise in pattern matching. The way I recall the most useful homework was: each type of problem has 1-2 clearly worked out solutions, followed by 4-5 very similar practice problems and maybe 1 harder variant. Then, a section where all the "problem types" are mixed together and the student needs to figure out which technique to apply to each problem.

Learning the technique, then practicing recognizing the pattern is essentially creating muscle memory so that when similar problems pop up on the standardized test or whatever, the student immediately matches it to the correct technique and is able to execute it.

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I think the key in maths homework is that recognising the pattern is hard. You do a handful of variants of the exercise because they all look slightly different so that it's not immediately obvious how the pattern applies, but because you're doing all the exercises at once you know which pattern to look for, and then you can learn to see the pattern even with less of a hint about which pattern to use. Maybe homework is less relevant in lower years because there are fewer patterns to recognise, you just need someone to explain things so you can understand them.

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I’d say that math homework can do two different things (but usually the first thing).

First, it can build that muscle memory. I can factor a quadratic very quickly in my head, simply because I’ve done it so many times. Times tables, basic integration/derivatives, etc can all benefit from this sort of “muscle memory” approach. And it helps long term when you get to complex problems, since if it has 20 basic steps, you need to be able to do your basics quickly.

Secondly, it can help reinforce the sort of analytical thinking that’s useful in advanced math. But homeworks aimed at that are rare.

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Jul 7, 2022·edited Jul 7, 2022

Problem solving has it's own form of muscle memory, even abstract mathematical problem solving. Look at something like Sudoku. You can learn the general solution to every single Sudoku in five minutes but that doesn't mean you're as good as you'll ever be at the puzzle You learn short cuts, patterns and more advanced or niche processes while practicing which make the puzzle easier and faster to solve.

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I don't think that works either - homework would be like doing a different puzzle (perhaps related to prior) every day.

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In high school, I took calculus, and it was clear to my teacher that I knew the material on a conceptual level. I often wouldn't remember the formulas while taking the test, but I would rederive them during the test as needed, and he knew that. But I wasn't finishing the test at all in the time I was given. This was partially because I was working slowly and carefully; I rarely made mistakes. But it was also because I knew the general idea of the subject matter, and I knew it well enough to rederive it, but I didn't know it so cold that I didn't even need to think about it. His goal wasn't just to get me to take the test faster so I could get a higher score, his goal was to get me to know the material really really well, so I didn't need to waste energy thinking about it, and then it would be easier to learn the next unit in the curriculum and handle more complex material.

The solution was lots of homework with lots of practice problems. After only one homework problem, yes, I had already demonstrated that I knew the material. But doing it over and over again helped cement it in my mind so that I could do it faster and with clearer thought than before. It really was the mental equivalent of reinforcing muscle memory.

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I have no doubt that is true - but I also don't think your experience is generalizable to the overall population or related to whether or not homework 'works'.

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No, I think it is generalizable based on my discussions with multiple math teachers. They are concerned with the "automaticity" of doing lower-level calculations, and if the kids don't get enough practice doing those so they can do them quickly and accurately, it's going to be very frustrating when they go to upper-level math and have to spend all their time remembering how to do the lower-level calculations.

It is actually very similar to practicing lower-level music muscle memory so that you don't have to think about it while playing, so that you can concentrate on the musicality and more "upper-level" considerations.

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This is something actually in my area of expertise (I taught physical sciences at a relatively pricey private high school for 7 years). Math homework and drilling lots and lots of practice problems was actually crucial for everyone. Because by the time they got to chemistry or physics (even the baby intro versions that were all that were required), those who didn't have that automatic "muscle memory" were lost as soon as a number went up on the board/paper. Yes, they could eventually figure it out, but spending 2-3 minutes (no exaggeration) doing a simple "convert 1 m to mm" problem and not having any mathematical intuition when they'd plug it into a calculator and get something bizarre (because they put in garbage) meant that they'd mostly just get lost.

Drill-to-perfection is critical especially for arithmetic and basic skills. No, common core, it doesn't really matter if you know why 2 + 2 = 4 (which isn't actually something they teach anyway) or have 27 different ways of doing that operation. What matters is that you don't have to think about it--you see basic operations such as shifting a decimal place and it just happens transparently in your head with no mental overhead. So you can get on and do the real interesting part. And that only happens by repeated, frequent practice until it's not even a conscious process anymore.

And I saw it with my own physics homework--there was a literal "ah ha" moment when someone had practiced enough variations of the same problem. The light came on and then that kind of problem was easy from then on. And it generally took quite a few repetitions and almost-identical-but-not-quite variations. It was a phase transition between "this is impossible" (in teen-speak meaning "this requires effort") and "why was this so hard? This is trivial." Different people hit it at different points. But everyone who had the necessary foundation hit it some time.

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From the point of view of someone who has spent more than 20 years teaching students unfamiliar concepts, I have to say that this comment strikes me as very, very, strange. The point here is that the claim is really a circular argument. “If you know how to solve the problem”, has no meaning before having practiced it, does it? How would someone “know” how to solve it then? Is the implication that the teacher shows students how to solve the problem in class, then the students practice it in class, say, a few times, and, at that point, they “know” how to solve the problem, and therefore all future practice is irrelevant? What school, class, curriculum, activity or skill does that resemble that exists in the real world? I can think of no non-trivial skill for which that is true. Nothing, from woodworking to math, vocabulary, learning a foreign language, etc. for which additional practice outside of the initial exposure to the concept would be needed before a learner would be able to describe themselves as “knowing” how to solve the problem without substantial practice. My son is quite gifted in math, and I teach honors students, and even for those types of students I have not found that I simply demonstrate a concept once and that zero additional practice is then needed. Certainly when kids learn fractions, decimals, complex grammar rules, how to craft an essay, etc. I have never observed that a single exposure is sufficient.

Thus, I agree with you: continuing to drill past the point of mastery is not good. But the only route to mastery is practice. Theory is that HW is an opportunity for practice. The counter argument is that many students do not do their HW, the parents do it, they don’t use it for practice because they do only a perfunctory job on it, etc. None of that changes the point, which is that the sine qua non of developing skill and expertise in a given subject still requires additional practice, and the musician analogy is pretty good.

By the way, there are numerous good papers in the literature on the development of expertise on how differently experts and novices look at problems, and just how much can be gained by additional reinforcement / development of expertise through practice. One seminal citation by Nobel Laureate Herbert Simon & colleagues: “Expert and Novice Performance in Solving Physics Problems”, Jill Larkin, John McDermott, Dorothea P. Simon and Herbert A. Simon, Science (1980) - sorry, paywalled, or I would paste a link.

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> “If you know how to solve the problem”, has no meaning before having practiced it, does it? How would someone “know” how to solve it then?

Of course it has meaning. Having a skill is independent of having demonstrated that skill.

> Is the implication that the teacher shows students how to solve the problem in class, then the students practice it in class, say, a few times, and, at that point, they “know” how to solve the problem, and therefore all future practice is irrelevant?

Yes, that's the underlying question of 'Does Homework Work?' If it transparently obviously worked it would be easier to detect positive correlation between homework and results.

> Nothing, from woodworking to math, vocabulary, learning a foreign language, etc. for which additional practice outside of the initial exposure to the concept would be needed before a learner would be able to describe themselves as “knowing” how to solve the problem without substantial practice.

Practice without a feedback loop is worthless. Homework, largely, is a one-time demonstration - the answer is right or wrong and you move on. Underlying skills can get exercised more often - but simply going through the motions of homework isn't practicing any specific thing often enough to make 'muscle memory' a convincing argument.

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On the other hand, in a homeschool environment and a "homeschool teacher teaches in a public school" environment, I have seen 5-15 minutes of one on one instruction, combined with 45 minutes of human-computer interaction and an infrequent group activity to work wonders.

It may not produce people who can do math at the London Symphony, but most people don't need that level of skill.

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Took a sec to pick up the reference. You may be on to something there.

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Jul 7, 2022·edited Jul 7, 2022

Whose purpose is this? The teacher's assigning the homework? I can't imagine any teacher I know saying that - it seems like they assign homework because they genuine believe it's an important part of learning, and do so despite that it makes more work for themselves.

I know the ACX answer to "whose purpose" for these kind of questions is usually "Moloch", but I don't know that that's true - are there actually meaningful Molochian forces pushing teachers to assign homework? It's not part of college admissions, it's not really part of the huge standardized test pushes, and, surprisingly enough, when I interviewed for a job, they didn't ask if I had done my homework. (Which is good, because I didn't)

(On the other hand, I do increasingly think a 4-year college degree is more about establishing work ethic than actually imparting specific knowledge: but you can see that in how it's an important filter in the job application process, in a way that homework - especially elementary/high school level - is not)

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Jul 7, 2022·edited Jul 7, 2022

“ It's not part of college admissions”

What? GPA is usually about 1/3 homework these days, it’s a huge part of college admissions.

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That's fairly unique to the USA, fwiw. Most of the world bases university admissions purely on end-of-high-school exams

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Lots of countries have some continuous assessment element to those exams - usually project-type work rather than routine weekly homework, though.

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America stands out as making IQ tests functionally illegal for employers.

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Has it decreased to 1/3? When I was in high school it felt like every other class had 70% of the grade be homework...

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Jul 7, 2022·edited Jul 7, 2022

The _assignment_ of homework is not necessary for college admissions. Yes, if you are assigned homework and don't do it and your GPA drops that's going to matter.

But we're talking about the reasoning why homework is assigned in the first place. If my teachers had all collectively decided to not assign homework because they stopped believing it was useful, it's not like I'd get to college admissions and be told "well, we see that your teacher never assigned you homework..."

So again, I don't think "college admissions" is the reason teachers are all assigning homework.

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Are the teachers freely choosing to assign homework as a conclusion from their reasoning and observation that it works best, or are they required to, or do they just replicate the tradition of teaching that includes homework? And if they are required to, who is requiring them?

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I think this is an underrated response. The reason most teachers assign homework is because it was assigned to them in school, their peers do it, the curriculum given by the admin provides it, and they may have heard in some lecture somewhere that it was useful.

And the reason it is in the curriculum is because most teachers expect it.

And the reason it is talked about in lectures is because the lecturers did it, and assigned it, and their peers assigned it, and they had their own (possibly confounded) opinion about it.

It's inertia with no rigor. Like many things.

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Do teachers get a choice whether to set homework? I always assumed it would be a school policy, based on some education authority policy, that they had to do it. Even if it's not explicit, would a teacher get a load of flak for not setting homework?

I'm asking this, because not setting homework seems massively advantageous from a lazy teacher perspective. Unless they get paid overtime to mark it, but aren't they generally salaried?

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Every district is different, but in many cases yes.

Now, get a reputation for being a bad teacher, or have enough students "fail to progress" and you get called into annoying meetings, which means sticking with what you know / what the community does is a safer bet. And also a lot of teachers want to have done a good job.

I have known some teachers give out a large stack of homework and then only grade a random portion of it. I have also known other teachers that share students complaining that teacher X puts out so much homework the students don't have time for THEIR homework.

My mother doesn't follow the curriculum very much for some of her subjects. If/when curriculum providers (private company) catch her, they mark her down to have the admin address the matter with her and other teachers. The admin dutifully admonishes the other teachers for not following the curriculum and when my mom brings it up the admin tells her it doesn't apply to her. Because she usually gets several years of progression with her students each year.

Heck, the school even mixes grade levels so they can get some students to work with her for a few months during the year in mixed-age groups. It's really stressful for her to keep changing students every few months, but it maximizes her impact to a wide variety of students (and the other teachers can't complain if a student that is on the record "theirs" suddenly shows improvement on a subject they didn't even teach them...)

You have to wonder about how many studies about X curriculum actually check to see if the successful (or failing) teachers actually use the curriculum as provided.

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This seems silly. Is there actually a level of employment where people are chosen based on GPA and yet some of the people who are chosen are too incompetent to properly format and present a relevant report? This is certainly not the case in my (tech) industry.

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“ This is certainly not the case in my (tech) industry.”

It certainly is in my (tech) industry. You’ve never had a new employee with a good educational background flame out?

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Of course we see college hires that can't cut the mustard in the role they were hired into. We put them in marketing. ( \S sort-of)

But we never see grades when hiring (even college hires). They never asked for my grades either and only for proof that I had in fact graduated after offering me the job. Even if we did see grades, I do not think it would strongly impact who we hire.

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Jul 7, 2022·edited Jul 7, 2022

Interesting most tech companies I’m familiar with ask for SAT and GPA some also require a college transcript.

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We are not tech (kind of...) and recently we have been seeing GPAs on a lot of the applications we received for unknown reasons. And a lot of those GPAs are sub-3.5 so we ask ourselves why this person is volunteering this...

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Does your hiring process involve 8 hour long technical interviews?

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Absolutely for regular white collar office jobs for random college grads you absolutely get people who can’t work a computer or printer or think/spell there way out of a wet paper bag. Absolutely tons of people who get college degrees without basic skills. Especially in math or anything analytical.

Fuck practically 1/3 of my career is having a basic working knowledge of computers, being able to learn quickly, and middle school math. I provide pretty high level financial consulting and have used say calculus or above less than 5 times. It is almost all being great at arithmetic and analysis.

You might say “only accountants need to be able to handle a ledger”, except tons and tons of white collar workers have random little ledgers and tables and tracking spreadsheets they need to be competent with. Way too many are not.

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> or think/spell there way out of a wet paper bag

🤭

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Believe it or not typing on my phone does always lead to typo free text.

But I am not posting here on a job application!

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Muphry's law never fails!

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In college, maybe, but what's the point of filtering in 1st grade? Everyone is going to get passed on to 2nd grade whether they do the homework or not, and potential employers are never going to look at their grades from elementary school.

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We would see better results from our educational system with more filtering. We spend a lot of resources pretending everyone can be an astronaut.

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Kohn is not "[taking] the studies seriously anyway." He argues that the studies are, as you wrote, inconclusive at best and that one should recognize the demonstrable harms of homework and limit its use (seeing as it's not particularly compelling that it does much). It is easy to find compelling articles on the harms, including physical health, and it extends to even competitive environments where it actually negatively impacts learning (but helps with the educational rat race). e.g. https://www.tandfonline.com/doi/abs/10.1080/00220973.2012.745469

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Kohn acts many times like there's strong evidence homework isn't useful. For example, in Rethinking Homework:

"The positive effects of homework are largely mythical. In preparation for a book on the topic, I’ve spent a lot of time sifting through the research. The results are nothing short of stunning. For starters, there is absolutely no evidence of any academic benefit from assigning homework in elementary or middle school. For younger students, in fact, there isn’t even a correlation between whether children do homework (or how much they do) and any meaningful measure of achievement. At the high school level, the correlation is weak and tends to disappear when more sophisticated statistical measures are applied. "

If it were me, instead of "the results are stunning", I would have said "the results are meaningless and can't tell us anything". If he in fact doesn't believe the studies, then he's doing a particularly annoying version of the "no evidence" thing - see https://astralcodexten.substack.com/p/the-phrase-no-evidence-is-a-red-flag

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Unless you have other reason to think that Kohn is generally intellectually honest, that "particularly annoying version of the 'no evidence' thing" seems like a very plausible explanation for the quote provided.

Maybe I'm too cynical for my own good, though - sure, I save a lot of time by being dismissive but it's a lot harder for me to be corrected on assumptions I'm mistaken about.

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> Kohn: "The positive effects of homework are largely mythical. In preparation for a book on the topic, I’ve spent a lot of time sifting through the research"

Is there any compelling RCT-based evidence that spending more time sifting through the research makes you more knowledgable about it?

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I think he does believe the studies.

" any meaningful measure of achievement. "

That's not the same as "any meaningful measure of improvement". He's saying that doing homework is not correlated with any objective measure of success--that is, it's not necessary for success and there's no guarantee it will help you achieve it.

If people can achieve at a higher level without doing homework than those who do homework, then there's no meaningful measure of achievement.

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Surely *some people* can achieve at a higher level without doing homework than *certain other people*. For instance, if you took me at twelve years old and had me do my algebra homework and put Euler at twelve years old in the same algebra class and told him not to do the homework, I guarantee you he would out-achieve me. But the relevant question is whether homework helps ceteris paribus. (Which it seems like it probably should. How could practice not help?).

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Ah, thanks for this.The only point I wanted to make was based on 'ceteris paribus' - I know no Latin! The fact that eg today in the UK children in poverty, with working parents, is around 72% matters when one considers the state of education. HW, set in the context of a particular education system, has inherent barriers. Many, many children do not even habituate a home environment where homework might comfortably happen.

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What do you mean by child poverty in the UK being 72%? The first Google result is a group called Action for Children, and they say it was 31% in 2019-2020. Yes, that's two years ago, and it's missing the "with working parents" disclaimer, but surely they don't make that much of a difference?

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Jul 7, 2022·edited Jul 7, 2022

Yes, this does allude to families with at least one working parent; we have increased use of foodbanks and benefits needed to top up their poor pay.I went to this link from the Joseph Rowntree Foundation, admittedly 2019, my understanding is that it is now worse link: https://www.jrf.org.uk/blog/its-wrong-so-many-working-families-are-trapped-poverty?gclid=CjwKCAjwiJqWBhBdEiwAtESPaBR7SoCW5eFmGIUN-y1-54gNsi9WyGe7f87s4_IIEGfA1iU0k-6D4hoCimwQAvD_BwE

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Jul 7, 2022·edited Jul 7, 2022

The Child Poverty Action Group ( excellent history of involvement with CAB in UK and supporting people through government 'benefits' legislation

https://cpag.org.uk/child-poverty/child-poverty-facts-and-figures

says this too "Work does not provide a guaranteed route out of poverty in the UK. 75 per cent of children growing up in poverty live in a household where at least one person works."

and "

There were 3.9 million children living in poverty in the UK in 2020-21.1 That's 27 per cent of children, or eight in a classroom of 30."

I think it seems too great a percentage to be true ie it is shocking - we are regularly informed by the Tory govt. that the best way out of poverty is 'work.' 'Working our way out of poverty' is not working.

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"But the relevant question is whether homework helps ceteris paribus. "

My point is that this is not a relevant question. Homework is not essential to learning, nor does it guarantee learning. It might improve understanding slightly, but even that's not known.

Forcing kids to do homework when it doesn't improve and doesn't guarantee mastery is just nonsense. Just extend the time needed to learn *in class* for those who need it.

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I would hazard a guess that homework vs proficiency would produce the exact same results in elementary school. If you throw more time at a skill the better you get, that seems pretty straight forward.

Practicing piano is another good example they should study. If you don’t practice every day, your progress would be limited. And the age works as well because the most amount of kids in piano lessons is likely elementary school. If they don’t have the drive to practice (such as myself) eventually they will quit.

The same goes for sports. Starting early and spending more time practicing will produce oversized results.

However if you graph enjoyment vs homework, I’m sure the graph would be inverted but that’s the whole point of parenting, isn’t it? To force your kids to learn skills they otherwise wouldn’t on their own?

One of my friends was essentially neglected as a child and spent most of the 80s and 90s watching TV. He’s in his 50s now and has no skills except for being a substitute teacher. I love him to death but I would never let him teach my child anything. He’s basically the poster child for forcing your kids to do homework.

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One huge question is how much of elementary school is actually helpful for children later in life and how much is just busy work so that the schools can function as daycare. Teaching reading and writing is definitely important while memorizing state capitals is probably less so. Plus, many of the skills taught in elementary school can likely be learned more quickly later in life. So if the homework is helping you to practice a useless skill, it's useless.

Beyond that though, not all skills are like piano or sports. There's some maximum possible amount of arithmetic that an average eight year old can learn, and it's very possible that the amount that elementary schools assign is more than that. So that homework would be a complete waste of time.

There's a good middle ground above your friend and below "all elementary schoolers do school work 24/7". Evidently no one knows where it is, but I suspect it's somewhere below the current level that most elementary schoolers are assigned.

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A significant amount of what kids learn in early school is socialisation, cooperation, attention, learning-to-learn, etc. You wouldn't to wait to later life to get onto this, though it's probably less important if you're getting a good version at home and elsewhere.

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Jul 7, 2022·edited Jul 7, 2022

I agree that using homework to take the place of good teaching is the wrong approach. It should be used to reinforce taught material. I don’t think kids should be inundated with homework but I do think that homework is important. Putting in the time to solidify what they learned in important otherwise they will forget.

My kid is in that camp, he goes to a private school with a no homework policy and while it’s great for us parents I worry that he’s not getting anything he’s learning reinforced. He’s advanced in math so he has a minimal amount of homework for that every day but not in a way that I think is productive but i guess we will see how things turn out.

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Kids are normally in school for about 6 hours a day, right? that would seem to suggest that approx 1-2 hour per weekday of homework, total, is "ok" and anything more would be overtime, going by standard full time hours. I think a lot if the issue is that homework can be very "spiky" - if all your teachers assign a lot the same week, it doesn't really help that the previous week was easy.

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> I'm quite confident that the most successful students in my school were those who most consistently worked the hardest at their homework.

Me too, although I'm also quite confident that the students who worked especially hard weren't the ones who achieved the greatest success in later life. My observation is that high-school super-swots tend to start struggling when life becomes a little less structured. Doing exactly what you're told very conscientiously is a great strategy in high school, but an okay-at-best one in real life.

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Successful meaning best grades or most knowledgeable? Kids with best grades usually get them by doing homework. Most knowledgeable? Not really.

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And in the homeschool world (selection effects apply) many people do far less schoolwork and homework than schooling, sometimes even only one or two hours a day or less.

Sure, you can say "but those are students who would excel in any environment", but the traditional school crowd has the same problem. You can't tell if a kid succeeded or failed because of homework or teacher or curriculum design or because of who they are.

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I think a lot of what you learn in early school years is about giving you a framework to fit other facts into.

Memorising capital cities has gone out of fashion as a way of learning geography has gone out of fashion, but it's not totally useless. A kid who has memorised every national capital in the world has at least _heard_ of every country in the world now. Knowing that a country's capital is called Georgetown or Santo Domingo lets you guess a bit about those countries' histories. You learn a bit about the languages of the world when you learn cities like Mbabana and Ljubljana. And you have a little box labelled "Sierra Leone" in your head so that when you hear another fact about Sierra Leone you can file it away alongside Freetown.

Maybe all that still doesn't justify memorising national capitals. But still, primary school education is largely just about applying layers of intellectual undercoat; at some point you have to learn things like "There was a Roman empire" and "water is a liquid" and "other countries exist" and so forth.

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An MD of my acquaintance tells me that undergrad biology is mostly memorization.

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This is absolutely true, but it's a feedback loop rather than a waterfall process - a conceptual framework gives you something to hang the facts off, which makes it easier to think about the concepts, which gives you more places to hang facts off... I've spent a lot of time learning facts using spaced repetition, and I've learned the hard way that cards for which I have no use or context quickly become leeches. Wozniak's first rule of effective spaced repetition is Do Not Learn What You Do Not Understand (https://www.supermemo.com/en/archives1990-2015/articles/20rules).

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I think you have this backwards. I was made to memorise national capitals at school (and my bête noir, English county capitals), and sure, I could remember the famous ones like Berlin and Beijing but not the more obscure ones like Majuro or Maputo. What made a difference, years later, was watching Geography Now on YouTube, which does a 10-30 minute video on every country in the world (they're currently up to Trinidad and Tobago). Once I know a bit more about the country, I have something to hang the bare facts of its location, capital and flag on, not the other way round.

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Agree. And not only that, elementary-aged students are frequently (judging from my own interaction with them at least) *hungry* for facts about things. It's the kid who can tell you everything about dinosaurs or trucks or whatever. They're at an age where most of them are sponges for facts.

You can't critically think about things where you don't know the foundation. And having context knowledge (which comes from repeated exposure, mostly) is critical to even *understanding what's being talked about*. I had students who would deadlock on problems because they didn't understand basic words even when those words were entirely filler. They could do the problem if it was phrased differently (throwing a football vs firing a gun, same ballistics problem, just different context) so it wasn't incapacity with the subject matter. But it was basic "I don't know anything about the real world" lack of context. And if you don't learn it when it's easiest, it's way harder to cram in later.

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Learning to "see through" the irrelevant words to the common maths underneath is a *huge* part of learning maths, especially at school level. Was the problem that they didn't understand that bullets behave like very fast footballs (lack of object-level knowledge), or that they didn't have that habit of generalisation? The latter is a definite (and learnable) skill.

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IIRC, the actual problem was something about dropping something from a plane (vs throwing it from the top of a building) and the word that caused utter blockage was some (irrelevant) part of a plane. I often said that the hardest part of physics (and chemistry) *wasn't* the actual math or science. It was the reading. Because most of the time, that was the core blocker. If you boiled down the problem for them, they could (mostly) do it. Or at least start. But they were either such slow readers or had so tiny a vocabulary that they'd lock up just trying to parse the english words of the questions themselves.

But both of those problems (object-level knowledge) and the inability to generalize were quite common. Especially the latter. It was as if some kids just had boxes for things. THIS happens in math class, THAT happens in science, etc. Or even worse--when I was a grad student teaching at college (pre-med Physics I, aka basic algebra-based mechanics), I did a problem as an example (hitting a baseball over a fence) and told them "this will be on the test." It was, except I changed the words to "football" and "goal". But the underlying problem was identical. Many people who could do the first problem absolutely failed to even start the second. Because they'd memorized the problem statement verbatim and so their pattern matching just failed if you changed even one small, irrelevant detail.

So you really need both parts. And the ability to abstract (generalization, but more) seems to be really really hard for some people. Those who had it found physics really easy. Those who didn't, floundered. In high school, it seemed to just "turn on" at some point for many kids. They'd be incapable as sophomores in Chemistry, but by the time they took Physics the next year, their brains had turned on and it was, if not easy, at least tolerable.

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> THIS happens in math class, THAT happens in science, etc.

I have very very little autobiographical memory, I can barely remember what I did last week, but here’s one thing stuck with me:

The main subjects we had when we began school were “writing” — where we started with stuff like straight lines, slanted lines, loops and such, and the advanced to letters and short words – and “math” — which mostly meant learning the digits, then one-digit addition and so on. I imagine that’s how it goes everywhere, but I don’t really know, so take it as context.

Anyway, one of the very few memories I still have from a very young age is when, somewhere in second or third grade, the *math* teacher started writing *words* on the blackboard for the first time. (It was probably some problem statement like “I have X apples, etc”.) I can still remember the shock, and turning to my desk-mate and asking in bewilderment “There’s writing in math class?!”

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If you are going to learn a foreign language, I know of no substitute for memorizing vocabulary, memorizing grammar rules, memorizing the exceptions.

If you are learning Latin, and you strike up a conversation with an Ancient Roman, you can't be constantly thumbing through lists of words because you can't remember the word for "fish sauce".

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Vocabulary, yes. Grammar...sort of. I learned Spanish in school for 5 years (and didn't take it seriously) and then Russian "on the streets" (limited formal study, especially around the alphabet, but mostly just talking to people). And my Russian was (comparing peaks) WAY better than my Spanish ever was. In fact, I'd say I spoke better Russian after 2 months in-area than I ever did Spanish, despite living (as a child) in Spanish-speaking areas. Why? Constant immersion and needing to use it to communicate.

But yes, there's a lot of memory work involved in doing just about anything worth doing. Some doesn't have to be list-based memorization (which I hate doing)--learning a new programming language (syntax, standard library, common library routines, etc) is mostly about doing and context, but it's all memory work. You can't get away from it.

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1) Memorization of simple facts about the world is underrated. Where is Brazil? What continent is it on? Where is the Amazon? Why is the Amazon important or interesting? These types of general knowledge facts require a basic knowledge base about the world, and arguing that people can simply Google every fact or question will not work.

2) There is only “sort of” a maximum amount of arithmetic that an average 8 year old can learn. American children are quite behind the rest of the world in math, on average. It is simply not possible that American kids are genetically inferior to the rest of the world in mathematical ability. Thus, (a) our kids could be much more facile with arithmetic, and earlier (in my son’s relatively wealthy, suburban classroom, there were still children in the 5th grade who were not 100% on their times tables!), and (b) we could move much faster in math for many children, if not the average. (c) homework is quite likely to help with almost all the tasks that develop quick facility — problems like times tables. In some sense, we know that this is true, because cultures that drill a lot of problems get very good at these types of activities (Asian countries, for example), and they develop these skills quite broadly, as well.

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The Amazon is in Seattle and it delivers crap I don't need directly from the internet to my front door :)

(I was in an "advanced placement" program in elementary school and they didn't even try to teach us multiplication/division until we were in ~4th grade. Then again, the insistence that arithmetic is the first and most important kind of math is weird? We could be throwing calculus and logic at kids much younger and leaving the times tables until they're old enough to understand how they're useful.)

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My kid is advanced in math. I introduced him to basic concepts of calculus like limits and derivatives and relationships beteeen distance, speed and acceleration. he finds them interesting but without a strong fundamentals in algebra you can’t put them together.

Do I disagree that you can push those fundamentals off and introduce higher concepts usefully without them. You can only scratch the surface and then you’re stuck without deeper fundamentals.

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I guess I feel like arithmetic is also just scratching the surface, except it does it in a boring and unnecessarily painful way (especially the rote memorization of tables part). Understanding concepts like rate of change even without the algebra loops in well with kid-level science projects and, like you said, they're *interesting*. Basically the entire reason I like math now and liked it as a kid is that it leads to interesting places. Plus, I feel like even a 10-minute introduction to calculus would help kids understand why they're being asked to memorize a billion facts about parabolas.

Then again, I'm not a teacher and I don't have a huge amount of experience with kids. I could totally be wrong! Most of this comes from my own experience learning math. (Which reminds me, another thing we could be doing a lot more is math competition style logic problems. I was never particularly good at them, but I have fond memories of math club and they're a good challenge for advanced students.)

Oh, and if you haven't shown your kid Vi Hart's "doodling in math class" series you totally should - she's awesome, and any kid who can get the basics of calculus can follow her math videos. I think I was introduced to them at 11ish?

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Sure, Algebra comes before the advanced stuff, but algebra has very little dependence on arithmetic. One is in trouble if they can't do times tables accurately at all, but drilling for speed seems largely pointless.

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Jul 7, 2022·edited Jul 7, 2022

I disagree pretty strongly about the basics being delayable. Last year I taught precalculus and watched many students struggle with being hamstrung by being unable to do basic manipulations of fractions and distribution

EDIT: Part of the problem is that there are actually only so many different kinds of word problems that you can ask (and hope that the students will be able to answer). If your students couldn’t even do basic things like multiply, there would be even less

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This. Or even basic things like recognizing that 2*10 = 20. I had students pull out their calculator to divide small numbers ending in 0 (like 100) by 10. And not being able to do it. Or who insisted that (1/2 + 1/2) == (1/4). As premeds in college. And if the calculator gave them something weird (because they forgot a parentheses, for instance), they'd not recognize it as weird at all. Had some tell me that the drift speed of electrons in a wire under current (usually ~1 cm/s or so) was either ~10^-45 m/s or ~10^20 m/s. And had no clue why either of those was nonsense. Because they had no number sense and were blindly writing down what their calculator said.

Basic arithmetic serves to give you a number sense. It also lets you see patterns because you can group and ungroup things without mental effort.

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People who are good at math frequently favor math that delves into “deeper explanations” and “why”? This is, in my view, totally misguided. Every functioning adult in a developed nation needs to be able to perform certain mathematical tasks, which include taking percentages, working with fractions, reading graphs, etc. in order to fully participate in a democratic society, but also to even understand basic consumer finances, business, insurance, etc. They do not need to understand “why” any of these techniques work — they need to be able to reliably produce the right answer to “what is 6*7?”, “an item is $60 and is 33% off, how much will it cost?”, “a recipe calls for 2/3 of a cup of flour. You are doubling the recipe. How much flour should be used in doubled version?” My students (in college) routinely misunderstand percentages, compounding, etc. Many students in many High Schools in America have trouble with questions like the ones above, and they are necessary for everyone.

Would it be useful to some students (likely the most interested/advanced) to have some exposure to interesting concepts from advanced mathematics at younger ages to see where things were going? I’m open to that idea. But I think this overstates how much intrinsic interest there is in these concepts. Well-chosen word problems in general make the problems relevant. All word problems are more difficult than “bare” problems, however, and thus there is a tradeoff while students are learning. One of the skills that we would most like students to develop in math is the ability to translate words into equations.

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Yes. This weekend, Nikki Haley put up a tweet saying that inflation was 67.2% this year:

"The graphic said the price of hot dogs had increased by 15.6%, soda by 13.2%, condiments by 11.9%, ice cream by 9.6%, bread by 8.7% and watermelon by 8.2%.

After these six items, the graphic summed everything up by saying that the total increase was 67.2%."

Yes: she added the percentage increase of each item to get the overall inflation rate. And, yes, the tweet was soon deleted because it was so incredibly wrong. But I'm torn between thinking that her staff actually made this mistake and thinking that the staff thought that enough voters would be swayed by it that they didn't care.

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I think the pandemic has given us a very good example of why every citizen needs to understand what a derivative is in order to participate in society. I've watched many people have unbelievably hard times grasping ideas like "the number of covid cases is going up, but it's going up more slowly than it was in the past and that means something about the world".

As for the "why", I don't think we need to, like, *test* kids on why things work. But kids love knowing how things work! They're little scientists who love to pick apart systems and solve puzzles. All I want is for kids to grow up with an understanding that there *is* a reason why math works and for some of that reasoning to be available if they're interested in exploring it.

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> People who are good at math frequently favor math that delves into “deeper explanations” and “why”?

After you have mastered the basics, it becomes interesting to talk about more abstract stuff. That doesn't mean that teaching the abstract stuff before the basics is a good idea! It's the other way round; having mastered the basics allows you to discuss the abstract stuff meaningfully.

Trying to teach the abstract stuff first would encourage kids to "memorize the teacher's password", because that's pretty much the only thing they can do with the abstract stuff at the moment.

Now, before someone generalizes this too far, it makes sense to explain some "why" right after the basics were explained. For example, if I teach kids addition, and they notice that e.g. 7+5 gives the same result as 5+7, we can discuss this interesting fact. (Discuss it using the kids' vocabulary; avoid words like "commutative".) But we should discuss this after they noticed the fact, not before; and definitely not before they learn addition.

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My point was that we do far too much of this right now in America. Kids learn 3 ways to multiply 3 x 3 digit numbers, they learn about commutivity as you said (even without the word), etc. This is all actually irrelevant to becoming a functioning, productive adult, and is actually completely uninteresting to 99.9% of students (and parents) who simply want to know how to quickly and accurately get the correct answer to problems that they will encounter in everyday life. We should make math, in particular, more interesting by first drilling basic concepts to mastery, then embedding them into more interesting word problems. Advanced students only can learn theory and abstraction. All students can learn theory that is necessary for the next necessary concepts (e.g., cannot ignore distributive property if we want to teach algebra). There is way, way too much focus right now on “why” and not enough on getting the right answers.

Same thing, by the way, in writing. Teachers no longer reliably teach the “5 paragraph expository essay”, on the grounds that it is “too formulaic” or “too limiting”, etc. Know what? 95%+ of my students would have their writing improved if they wrote using a formula. Their problem is that they haven’t been taught basics of grammar, style, organization, etc. It is the same problem. Too much complexity. Introduction culminating in a thesis sentence. Supported by exactly 3 points, covered in 3 paragraphs. Conclusion paragraph. Teach kids to write that way. The 5% top writers will learn to deviate from that, and they will exceed the constraints of the system. For the rest, practice, feedback, constraints, and more practice is good.

Not *optimal* — to be clear. For optimal, send your kids to a $30-40,000 / year private school (or even better, an even more expensive boarding school like Exeter or Andover), provide private tutoring, or be fortunate enough to have the educational attainment to be able to pass on a legacy to them through by having one or both parents tutor the kids themselves without the need additional money.

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I'm still not 100% on my times tables, and I have a PhD in maths.

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I find this inspiring! I don't feel so bad as I stumble with maths:)

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