A Theoretical "Case Against Education" | Hacker News Reader

A Theoretical "Case Against Education"

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30 pointsisaacfrond71 comments

I think you basically remember what you think is important. And school can be a great place to teach you about important things you will probably not pick up at home. If only a fraction of that is permanently added to students lives, it's still a valuable exercise.

Of course education is not a constant thing, it keeps changing through time and it sounds like it could be improved.

Anyhow I'm personally very happy with the things I've learned in school and the friends I've made there. Sorry to hear about people apparently finding it completely useless.

I think the socializing part is the big part of schools value.

But even as I believe that, I have been rather appalled at how my sons school lets him (and presumably everyone) write by imitation only: starting letters from the bottom, making the shapes all wrong, etc. I have had to take control over that myself to make sure he's got the fundamentals right in shaping, line order, and kerning. Letting students repeat incorrect behavior from the start is the opposite of what school should do, it cements bad habits.

"Socialization" is a canard once you look at the "society" of schools, more like prisons than a place you would want your children to spend their days.

Children do need to socialize with family, friends, and the society they participate in, but they can do that without school. Children did that for millennia before we invented schools. There's no reason to lock children up for most of the day in an artificial and oppressive environment, day care so parents can work, and indoctrination masquerading as "education."

> Children did that for millennia before we invented schools.

What's the name for this particular rhetorical method? I see it often.

argument

you may feel that it is related to various fallacies - for example the fallacy of misplaced concreteness or the fallacy of false analogy?

Call to tradition/call to nature

Thanks, appeal to nature seems to be it

I'm sure you'll tell me, but I call it "pointing out a fact."

Prisons is an apt analogy. If you think otherwise you probably went to a uniquely good school or were high charisma and avoided bullying. But that's not everyone's experience.

Human children socialized just fine in the 100k years that we didn't have schools. The purpose of schools is to bring economies of scale to education. That's great, but if we can figure out a way to deliver education at scale without schools and all the negative side effects of schools, that'd be even better.

The primary purpose of schools is daycare.

Which sounded bad to me until I became a parent myself. I now appreciate the importance of daycare in the urbanized society of mostly nuclear families.

Homeschooling generally requires at least one parent not working out of the home, or both parents working from home, or juggling schedules. Unfortunately homeschooling is a realistic option only for more affluent families. When we did it with three kids, in Portland, OR, we got together with other homeschooling parents and they ranged from well off to struggling with the cost of sacrificing some income.

As a parent I can appreciate the importance of daycare, but for me the few years of foregone income in return for raising my own children was worth it. We decided to make it work because our kids were more important than our careers or making more money. I won't say it's easy, or that anyone who makes other choices is damaging their children -- every family has unique circumstances and goals.

> There's no reason to lock children up for most of the day in an artificial and oppressive environment, day care so parents can work, and indoctrination masquerading as "education."

But that's the reason right there! The government/society wants the populace to work, reproduce, and support the government. They're doing exactly as one might expect them to do!

I'm not against government or schooling, although much could be improved. I do think the things you complain of are natural consequences of the existing system, and you'd have to go to special effort to have anything else.

> reproduce

Well we can confidently say that doesn't work.

I meant sexually, rather than scientifically

So did I. The birth numbers are below replacement across the entire western world.

> Children do need to socialize with family, friends, and the society they participate in, but they can do that without school

Can they? How? The way we did it before was to have many children so they had siblings. And we also had child labor.

Yes, they can. And there's a big difference between kids learning from their family and community and helping out and Dickensian factories full of children. Nothing about homeschooling implies child labor.

I agree and am really frustrated at how little they’re actually allowed to socialize. Recess is 20 minutes in our elementary and a lot of days they just skip it if they’re behind in classes.

Then they have to put their heads down on the table for the last 5 minutes of the 20 minute lunch. No one can explain what that’s about. Getting calm to leave lunch I guess.

OMG these are just a bunch of random facts, and 'learning facts' seems to be the focus of the article. Who cares? Education is not about facts but about building capability.

Kids should be taught fundamental facts of course (atoms, place numbers, etc), but really, ways of thinking, systems, techniques, ways to approach problems and find answers, etc.

The article misses the point of learning, confusing it with "education." I wonder how many members of the rationalist community have children.

I haven't read the book reviewed in the article, I no longer have school-age children. For anyone interested in the difference between learning and school/education, and some alternatives such as homeschooling:

Deschooling Society by Ivan Illich

How Children Learn and How Children Fail by John Holt

The Six Lesson Schoolteacher by John Taylor Gatto: https://www.cantrip.org/gatto.html

> The article misses the point of learning, confusing it with "education."

They really don't. The book in question is specifically titled "A case against education", and it's not an anti-learning book. It's a case against the education system specifically, because he argues that the system isn't really about learning (and the things it is about cause large negative externalities).

I'll have to read the book, my questions about this weren't answered in the OP, but possibly are in the book.

But something I think both sides of this debate seem to miss, or not want to talk about, is that the childcare aspect of the education system is useful on its own terms.

My pro public education friends who work in that system don't love this point, because they are highly trained educators damnit, not babysitters! And I'm very sympathetic to that.

And the formal education skeptics also don't love this, because caring for their own children should be the responsibility of parents and families. I have some sympathy for this too.

But I think every "normie" parent I know who doesn't really have any particular dog in this fight would say that an important part of kids going to school is that they have a safe and stable place to go for a good sized chunk of most days while the parents get adult things done, either at work or for the household. The schooling / education side is very important too of course, but it's not the only important thing schools are doing.

Now, I do personally tend to think that a better setup would be like a big family or community commune with a relatively small number of adults watching a relatively large number of children throughout the day, and a few hours of dedicated schooling peppered in.

But the path dependency to get to a setup like that from the way our society is currently set up is mind boggling to me. Neither side of this debate has the goods here, in my view.

Homeschooling is a totally different thing than that. Yes, there is usually some community component, but it's limited and fundamentally still requires an extremely large time investment by a large number of parents per child. I think this probably is truly better for the right parents; if one parent really wants to be with the kids all day and is excited and able to teach them, and another parent is capable of making enough income to make it work, and there is enough of a family or community nearby to incorporate with socially, then yeah, I do think that can be excellent. But that's a lot of ifs!

Many (I'd say most, but I don't have data, so I'll keep it vague) parents have their own ambitions and want to work in the adult world, or even if not, they find it draining to be solely focused on their children all the time, and need time to be adults. And I think it is very lonely during the day, both for kids and parents, as everyone else in the neighborhood is working or at school.

A larger community sharing this work across more children per adult in a community speaks to all these issues, but such a setup just isn't readily available to most people, and it's unclear to me how to make it be.

(I always wonder if this is something that draws people to cults. They often seem to have a setup closer to this. If it weren't for all the brainwashing, maybe they'd be onto something.)

That's an interesting point. I don't think either the book or the blog post say there's literally zero value in the system.

But if the main value is taking care of the kids during the day, we can change the system A LOT. And probably get more value for a lot less money. Say, by hiring local grandparents to take care of 2-5 kids each for a while

I don't think I'd say it's the main value, but I think it is an underrated value.

But yes, my sense is that the current system under-utilizes a lot of professional educators' time by having them do childcare.

Education is more about learning to think & ask questions properly, using existing facts as tools …

But in practice, the thing that's actually rewarded is cramming for exams. Students respond to incentives.

> 58% know which gas causes most global warming (carbon dioxide)

Actually, it's water vapor.

  The absorption patterns of water vapor (blue peaks) and carbon dioxide (pink peaks) overlap in some wavelengths. Water vapor is the most important greenhouse gas overall, being responsible for 41–67% of the greenhouse effect, but its global concentrations are not directly affected by human activity.

https://en.m.wikipedia.org/wiki/Greenhouse_gas#:~:text=The%2....

Ironic to use a question to judge education quality and then judge by the wrong answer.

This claim relies on an pedantic definition of "causes". The biggest direct cause of global warming is water vapor. However, the main thing affecting water vapor concentration is other greenhouse gases. Therefore the root cause is other greenhouse gases, the most important of which is CO2. Water vapor simply acts as a multiplier to the effect of these other gases.

Global warming is the ongoing increase in temperature, which is primarily driven by increasing carbon dioxide levels. It's not the same thing as the greenhouse effect, which is the mechanism by which CO2 and other greenhouse gases affect global temperature. Water vapour is a stronger greenhouse gas but it is not the primary cause of global warming.

Water vapor is the primary greenhouse gas directly causing the warming of the globe. If the question is, what is the primary cause of the modern differential in the warming of the globe, there's a different answer. But if answering the literal question rather than an implied question is wrong, it's a lousy question.

"The modern differential in the ~warming~ temperature of the globe" is what "Global Warming" is.

If the answer to the literal question is different than the answer to a colloquial interpretation, it may be a good question for judging colloquial interpretation but bad for judging scientific education.

The question uses the literal words "global warming", which the parent commenter is saying is defined as "the modern differential in the warming of the globe". That is, they are not saying that is the colloquial definition, but rather is the definition of the term. And you seem to agree that the cause, by that definition, is not water vapor.

So I think the only disagreement here is a definitional one. It's famously impossible to say what the single right definition of a term is. In this case, I'm not even totally sure which of your or parent's definition seems to me to be predominant...

But I guess I do think it seems most reasonable to read an implicit "modern" or "contemporary" modifier of "global warming" into the question. If it weren't asking about the contemporary phenomenon, it would specify that.

> And you seem to agree that the cause, by that definition, is not water vapor.

I'm agnostic. I agree that solar variation is not the consensus explanation, but that's less settled than the predominance of water vapor as a greenhouse gas and would substantially work through water vapor if true.

But, sigh, claiming not to know is colloquially known as "climate denial".

> If the question is, what is the primary cause of the modern differential in the warming of the globe, there's a different answer.

This seemed to imply that you aren't disputing the answer, based on that definition of global warming which, again, is what the comment you replied to asserts is the definition.

But from this comment, it seems to me that you're smuggling a disagreement about the science into a more pedantic point about what "global warming" is defined to mean.

For what it's worth, as someone who believes that it's as close to a certainty as science ever gets that atmospheric CO2 concentrations are causal, I am also uncomfortable with the certainty implied by the wording of the question. I would be happier if it were something like, "What is the consensus among climate scientists on which gas is the primary contributor to the warming climate we see today?".

I think your point that sometimes the "educated" answer is not the correct one is still a good one, but to me "global warming" is about rates rather than levels - warming, not warmth - and the belief is that the change in atmospheric CO2 concentration is what is causing the warming (change in warmth), whereas water vapor concentration is not changing enough, or in a consistent enough direction, to be the culprit.

I feel like the midwit thing applies here... Sometimes the "mid" answer is wrong for subtle reasons that still make it essentially right...

TL;DR: people remember more factoids when they are recent and/or repeated regularly than when they are old and/or not repeated.

Somewhat it's an argument against education (don't ask me why)

tl;dr

The facts you learn at school are surprisingly ill remembered. But stuff learned by cultural osmosis is remembered very well. So why go to school?

Lacking a better alternative? Homeschooling works too but gets you only so far.

What do you mean by "only gets you so far?" Opinion, experience, or do you have some evidence?

Homeschooled kids can get high school diplomas in most states (all three of my kids did), and get into college (two of my kids decided to go to university, and had no problems get admitted). In the group of ~30 secular homeschooling families I belonged to when I had school-age kids, many of the kids went on to college, got jobs, and turned out just as functional (if not more successful) than kids who went to public schools.

My main concerns are where would they make friendships.

That's a weak reason. Instead of being locked up with a bunch of classmates which you have no choice about you get to associate with people you choose.

Yes, exactly. And children should have opportunities to socialize with adults, in ways that aren't based on authority and following arbitrary rules. All of us who went to school know the feeling of disorientation when school ended and we had to face "the real world," which has very different rules and expectations than the school environment. Imagine raising children who didn't have to make that adjustment, because they only know "the real world."

Not kidding but my real world is based on authority and arbitrary rules - see laws, police, bosses, army, traffic...

> a bunch of classmates which you have no choice about you get to associate with

This is actually extremely valuable as a life experience, and not gaining it as a child represents a major loss

I hear that said but I completely disagree. Being surrounded by mostly game-addicted goal-less classmates is a drag on even a motivated high achiever. It was such a difference to have the flexibility of homeschooling and be able to get him in with some like-minded kids and watch him bloom (my anecdote, n=1).

Both experiences seem useful to me. The first is useful as a lesson that lots of people are like this (which is just true) and maybe it's not what you want for yourself, and the second is useful for the obvious reasons. Finding time to get both of those lessons is hard though, I get it.

> This is actually extremely valuable as a life experience, and not gaining it as a child represents a major loss

Indeed: if you don't get this life experience, you don't learn to cultivate a fervent hate towards other humans. :-( Whether this is a desirable trait for you children to get is up to you to decide ...

The point is to figure out how to associate with arbitrary people without cultivating a "fervent hate" toward them.

Everyone will have to participate in arbitrarily composed groups of people throughout life. Is it more or less likely for that experience to be one of hatred if exposed to it earlier or only later?

> Is it more or less likely for that experience to be one of hatred if exposed to it earlier or only later?

Rather: is it better if you are exposed to this in a jail-like situation or not?

You can guess my answer.

School is significantly more like other totally normal settings where other people are present than it is like jail.

This happens with homeschooled kids too. My daughters didn't get to choose the other kids they took ice skating or salsa classes with. My son didn't get to pick the kids on his soccer team or Cub Scouts group. You're making a false dichotomy, as if homeschooled kids inhabit a parallel universe with no contact with kids who go to school. That just isn't the case.

Yes, but there's a sampling bias. Most people (where I live) send their kids to school. So the "people you choose" to associate with during has to be drawn from a smaller population that has self-selected into that group for reasons I may or may not be aligned with.

There's no reason homeschooled kids can't make friends with kids who go to school. All of my kids did. Most of our neighbors went to school. Most of the kids they met at sports, music classes, ice skating, friends of friends went to regular school. There's no hard partition keeping homeschooled kids away from other kids. Too many people imagine homeschooling as "kids locked up at home," cut off from the rest of the world and other kids.

Homeschoolers divide fairly neatly into families who keep their kids out of school for religious reasons, and families who choose to homeschool for other reasons, usually referred to as secular homeschoolers. Those groups can mix and do activities together, or they can stay partly or completely separate. I think that's what you allude to, but I'm not sure. We did not homeschool for religious reasons. Some of our friends did, and a larger number of homeschoolers we knew about chose not to associate with the secular families. But plenty of people homeschool for reasons other than religion or wanting to isolate their children from society, it's easy to find them.

For kids in school, all of those things are additive. They also do all those same kinds of activities in the hours between school and bedtime and on weekends and during the summer. For kids not in school, the options for social experiences during the school day are limited to the adult(s) with them, and other siblings or kids who are also not in school. During the school day, for most kids living in the US, that's a smaller pool of other kids to spend time with during the day. That's all I'm saying! Of course that doesn't mean they have no other ways to make friends! And I don't mean to imply it's a bad thing. "Having a larger pool of kids to see during school days" is certainly not the only metric worth optimizing for! But I think it just is true that, in most places in the US, kids who are in school spend more time with other kids than those who are not in school, just by dint of being in school being the default and more common thing.

They may be around more kids during the day, but they aren't necessarily socializing with a lot of those kids. During class time they are forced to sit still and pay attention. During recess and breaks and lunch they break out into cliques.

Homeschooled kids have different social experiences, of course, but I don't think those are worse or less rich or varied. Without the constraints of school, kids have more time to socialize with other kids and with adults. They can do "real world" things with their parents. I suppose you have to get to know some homeschooling families to see for yourself.

Plenty of kids in school experience severe loneliness and isolation, and spend too much time on social media getting depressed. It's practically an epidemic, leading to mental health problems and suicide. I won't say that school causes those problems, but I think it's fair to say that sending your kids to school will not necessarily give them a rich and healthy social life.

Yep, don't read too much into the point I made; I think it is entirely consistent with this comment that the experiences are different.

I do know homeschooling families, of the secular socialization-friendly kind you did / are doing, and I think it's just empirically the case that it is not as easy for them to find things to do with other kids, during school days, as it is for the much larger number of kids I know who are in schools.

That doesn't mean it's bad (or that it's good) to have fewer opportunities to do things with other kids during school days, just that "most kids are in school during school days" is a real constraint on the ability to do things with other kids at those times.

But getting out of pure observation and into my own ... uncertainties, this is a significant reason I'm personally hesitant to homeschool, at least if I were to be the parent actively doing it.

Frankly, even with the school day and all the many structured activities with other kids that she's doing, the older my daughter gets (and she's only 6), the more I feel like she spends a lot of time with us boring old fogies, when she would be happier running around and playing make believe and stuff with other kids. I'm sure a big part of that is a personal problem, that we have boring un-kid-like personalities, and not nearly enough imagination and spark of creativity. But like, I am who I am! I like books and chess and computers and charts and numbers and stuff. I love being with my kids, but it would be a massive self-deception to think spending all day with me is going to be awesome for them.

So then, I start thinking about: What would we do? Where could we go, what adventures could we go on, who could we go on them with? And I just come up pretty blank. There are only so many museums and parks and stuff. Best case scenario seems to me that I would find a community of people trying to figure out the same thing, and we could do things together. Maybe I just don't know about them! But I spend a pretty sizable amount of time in all the public spaces in my area, often during school days (because kids are sick and have to stay home a lot), and my distinct impression is that there's nobody around.

Maybe they're all getting together, just in peoples' private homes. But I know the families with kids in my neighborhood and the ones surrounding it, and they're all in school, so if this is a thing, I don't think it's nearby.

Note that I'm saying these are all personal concerns, and they are about me, not about the kids. I don't think the standard school model is at all close to my idyll of what my kids would do with their days, but I think it's a bit closer to that than me trying to figure out stuff to do all day and driving all around trying to find engaging activities during the day, maybe with some other kids sometimes. I'm sure this looks totally different to other people with different personalities in different places.

Same way everyone makes friends.

Homeschooling doesn't mean locking your kids in the house, unless that's the reason you homeschool (and some parents do, usually for religious reasons). Our kids went to sports activities, all kinds of classes, music lessons, activities, group trips to the park, etc. Depending on where you live you will find groups of other homeschooling parents. In some states homeschooled kids can participate in at least some school activities, such as sports. For older children community colleges and universities may have programs. There's plenty to do, and many ways for kids to make friends.

If you live in a rural or remote place that will be harder, of course, but that would affect your kids regardless. We moved to a place (suburban Portland) where we would have neighbors with kids, in a state that has liberal laws regarding homeschooling. People move for jobs and careers all the time, why not move to raise kids in a better environment?

Alternatively, how do publicly schooled children make friendships after their schooling teaches them that the default social interaction is hostility? A large proportion of socialization found in schools would be illegal if you tried it in the workplace.

I think this is pretty close to being equivalent to asking "how do people turn into adults when they were once children and adolescents?".

They grow up. Hormones change, brains develop, lessons are learned, wisdom is gained. The primary reason workplaces tend to be better than high schools is that they are not full of teenagers.

Sample size only 2, because not being interested in homeschooling I don't have those support groups. Getting admitted to university after homeschooling is easy, staying there is tough. One kid struggled, flew out then needed one extra year of preparation, the other kid went directly to two years of preparation to be able to successfully go through university. But it's true you don't need those higher studies to get jobs, and for that homeschooling works just as fine. If you ask why I wasn't interested in homeschooling: not interested in becoming a teacher either as full or part time job (because no, teaching latin grammar to your kids is not parent quality time), and same argument for the wife.

About one-third of students who start university drop out. Difficulty staying there isn't a homeschooling problem. And every university grapples with students unprepared for college, almost all of whom graduated from public schools.

No one needs to learn Latin grammar to get into university today, or to succeed in a professional career -- strange example to pick. The bar is actually quite low, have a look at the state exams for granting a high school diploma. We unschooled our kids (no curriculum) and just taught the basics -- reading, writing, arithmetic -- then let them choose what interested them and made those things available. They all passed the state diploma requirements exam on the first try, and scored in the higher percentiles.

Homeschooling doesn't mean re-creating the classroom environment and following the school curriculum at home. And it doesn't doom your kids to low-end careers.

I was a youth camp counselor, then a 'physics counselor' for a small non-profit that teaches a lot of stem via experiments and who got called at youth camps, schools and by other non-profit.

Let me guess how you were successful:

You had at least one adult not working but present (I saw that with parents, but also an uncle and a greatfather once).

- You probably lived near activities, in an urban or suburbian area, with OK to great public transportation (forgot you could drive as early as 16 in the US, maybe I'm wrong about the public transportation, but it help).

- you probably had a support network (non profit with other parents who homeschool their kids).

All this is practically mandatory for successful homeschooling.

Then stuff that help: access to the official curriculum, independant home, curious parents (all this non mandatory)

Also, when comparing success with homeschooling VS public school, you have to compare socioeconomic class and home stability. In country like France or the US with terrible public school system, I guess homeschooling 'the right way' should be a bit more successfull, I doubt this is the case in northern Europe or in countries with good to great public schools.

I mentioned our situation (back when we had young children) in other comments. I could work from home at least some of the time, my wife quit working while we had young children (because I make more money). We moved to suburban Portland to have other families and activities nearby, and because Oregon has relatively liberal laws regarding homeschooling. And we had family and friends there already. We found groups of homeschoolers -- easy to do, they're all online now.

We did not follow the official curriculum, just made ourselves aware of the requirements for obtaining a high school diploma should our kids want to do that (they did, all got it easily). We more or less "unschooled," which means no rigid curriculum, no trying to re-create the classroom at home, and letting kids choose how to spend their time, within limits (we didn't allow much TV and video games and social media weren't much of a thing back then). Our technique, if you can call it that, was based a lot on Montessori, which I recommend to parents who can afford that but can't manage homeschooling, or don't feel like they can competently do it.

I know not everyone can homeschool their kids, for practical or personal reasons. I don't suggest everyone do it, or that kids who go to school are necessarily getting damaged or harmed (though that does happen). Ask any teacher, the number one predictor of academic success is parental involvement. Whether that takes the form of homeschooling, or just paying attention and spending time with your kids, that time makes a huge difference in the long term. I don't mean going to school board meetings and screaming about snack machines or sex education classes, I mean spending actual time with your kids so they feel valued and part of the family rather than an inconvenience.

Yeah, I think homeschooling is a classic bimodal thing. It is probably better than a classroom of thirty kids with a harried teacher and not much play time, for the right families doing it for the right reasons. But many people choose to do it for ideological reasons and without the right resources, with worse outcomes.

Presumes the purpose of going to school is to be crammed full of facts.

But you also learn to write, express yourself, solve problems, use facts that you currently know to some purpose, encounter ideas and subjects you would not have otherwise, socialise, etc.

I do agree that the emphasis people place on facts is misguided. It just happens to be easier to test facts, so a lot of schooling is oriented around them.

My son just complained that he did a maths problem, got the correct answer using a simpler method than the one the teacher was looking for, and got zero points, because he didn't use the approved method. In my world, he exhibited great thinking. In school world he didn't do what makes it easy for them to give him a mark.

In my own time as a high school student, I would come up with alternative solutions all the time. I'd always get full marks, though sometimes I'd have to explain it to the teacher afterwards.

Recently, I did the same test as my daughter did, who is now in high school. It was a bet kind of thing. So anyway, after doing the exam, I figured I'd have 9 out of 10 marks. I though t I'd lose some marks for some clumsy arithmetic, but it went pretty well (I thought).

So my daughter then grades my test and carefully explains that maybe I might just have a passing grade (6 out of 10). Ok. whatever. That can't be right. So she takes my test to the teacher to have her grade it as well. The teacher's verdict: clearly, easily, a failing grade. Maybe 4 out of 10 marks.

Turns out getting the right answer in a clever way counts for nothing. What you are being tested on is: can you reproduce the algorithm we are teaching you in school. As I solved most of the problems in a different manner, I consequently got almost none of the marks. I suppose, that if you know and accept this, then you can accept the result as well.

It's disappointing I guess, but certainly it makes math more accessible. I suppose there are pros and cons.

Your son wasn't tested on cleverly getting the right answer. The test was: can you reproduce this algorithm. He couldn't.

Well, the test did not specify that a particular method should be used. It just asked for the student to calculate the answer and show the working (which he did). He knows the "correct" way of doing it too, and could have done it if instructed to.

He has other ridiculous examples, e.g. a question that asked what reason might explain why people were smoking less. He gave a perfectly good answer (better awareness of the risks), it just wasn't the "approved" fact they were looking for.

It was somewhat like this when I was at school, but it's much worse now. No thought, even correct answers with working not accepted. Sometimes you just have to guess what the approved fact you are supposed to regurgitate is.

I think both things have value, though. Finding the correct answers in creative ways is awesome, of course, and should be encouraged. But it's also good to learn the specific approaches to finding answers that they are specifically teaching. It's just two different things, which are both valuable.

For instance, my daughter (kindergarten) has been learning how to do addition and subtraction by "finding tens" and also with fives, and also / relatedly by thinking about hops on a number line, and combining them in different ways. And if she gets the right answer, but without using the technique being taught at that time, then she is redirected back to the intended technique. And I think that makes sense, when teaching a particular technique!

I often hear people complain about this style of answering arithmetic questions - "what's wrong with adding up columns and carrying tens?" - and I think they should learn that algorithm too, but I think it's valuable to learn multiple techniques, the techniques themselves that is, in addition to just being able to get the right answers in whatever way you choose.

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