One popular variant on homeschooling is called “unschooling.” The practice varies, as practices always do. The essence, however, is that the student does what he wants. He studies what he wants. He studies for as long as he wants. If he asks you to teach him something, you teach him. Yet if he decides to play videogames all day, the principled unschooling response is: “Let him.”

Almost every parent is horrified by the idea of unschooling. Even most homeschoolers shake their heads. Advocates insist, however, that unschooling works. Psychologist Peter Gray defends the merits of unschooling with great vigor and eloquence. According to unschoolers, the human child is naturally curious. Given freedom, he won’t just learn basic skills; he’ll ultimately find a calling.

On the surface, unschooling sounds like Social Desirability Bias run amok: “Oh yes, every child *loves* to learn, it’s just society that fails them!” And as a mortal enemy of Social Desirability Bias, my instinct is to dismiss unschooling out of hand.

One thing I loathe more than Social Desirability Bias, however, is refusing to calm down and look at the facts. Fact: I’ve personally met and conversed with dozens of adults who were unschooled. Overall, they appear at least as well-educated as typical graduates from the public school system. Indeed, as Gray would predict, unschoolers are especially likely to turn their passions into careers. Admittedly, some come across as flaky, but then again so do a lot young people. When you look closely, unschoolers have only one obvious problem.

*They’re weak in math!* In my experience, even unschoolers with stellar IQs tend to be weak in algebra. Algebra, I say! And their knowledge of more advanced mathematics is sparser still.

Staunch unschoolers will reply: So what? Who needs algebra? The honest answer, though, is: Anyone who wants to pursue a vast range of high-status occupations. STEM requires math. CS requires math. Social science requires math. Even sophisticated lawyers – the kind that discuss investments’ Net Present Values – require math.

Won’t kids who would greatly benefit from math choose to learn math given the freedom to do so? The answer, I fear, is: Rarely. For two reasons:

First, math is extremely unfun for almost everyone. Only a handful of nerds sincerely finds the subject engaging. I’m a big nerd, and I’ve done piles of math, yet I’ve never really liked it.

Second, math is highly cumulative. Each major stage of math builds on the foundation of the previous stages. If you reach adulthood and *then* decide to learn math to pursue a newly-discovered ambition, I wish you good luck, because you’ll need it.

What’s the best response? Mainstream critics of unschooling will obviously use this criticism to dismiss the entire approach. And staunch unschoolers will no doubt stick to their guns. I, however, propose a keyhole solution. I call it: Unschooling + Math.

What does Unschooling + Math mean? Simple: Impose a single parental mandate on unschooled children. Every day, like it or not, you have to do 1-2 hours of math. No matter how boring you find the subject, you’re too young to decide that you don’t want to pursue a career that requires math. And if you postpone the study of math for long, it will be too late to start later on.

While most people *don’t* wind up using much math on the job, ignorance of basic math is still a severe handicap in life. And when smart kids don’t know advanced math, they forfeit about half of all high-status career opportunities.

We should have a strong presumption against paternalism – even the literal paternalism of a parent for his own child. “Maybe the kid is right and the parent is wrong” is a deeply underrated thought. The value of math, however, is great enough to overcome this presumption. To be clear, I *don’t* mean that the government should force homeschoolers to teach math. What I mean, rather, is that homeschoolers should require their kids to learn math. Guilt-free.

## READER COMMENTS

## Saint Fiasco

## Oct 27 2020 at 11:05am

When I was studying for my college’s entrance exam, there was a class that taught basic math very fast. The class was intended for students who had gone to terrible schools all their life and wanted to catch up before the entrance exams. It was amazing how much those students learned in only a couple of months.

I think teenagers learn math so much faster than children that it might be worth it to delay math education even after taking into account the fact that math is cumulative.

## AMT

## Oct 27 2020 at 11:33am

This is a good counterpoint. I recall something from possibly slate star codex where students who had no formal math education up to grade five could catch up within a year of starting to learn it. If you take that logic further maybe if you skip it all the way to grade 12 you could just focus on it for a year and be caught up? But perhaps if you take it that far no one could do that, because as Bryan points out, most people find it really boring and you cannot focus too extremely on just math to catch up?

Also, I’m wondering how much of this is due to selection? If you see your child is not doing anything productive because they are not very ambitious and naturally curious, you’re not going to continue unschooling them if you want them to be successful. Maybe you aren’t so certain your child’s calling is being a professional Call of Duty player…

## Douglas Knight

## Oct 29 2020 at 4:33pm

The experiment with not teaching math was by Louis Benezet. Here is Peter Gray on the topic. Here is Benezet’s original writing. He even claims that waiting produces better results, that traditional teaching is brain damage.

## Thomas Knapp

## Oct 27 2020 at 11:28am

Kids vary.

One of my unschooled kids was weak in math.

The other taught himself quite a bit, including significant amounts of trigonometry, because he was interested in computer programming and game design and the projects he undertook led him there.

## Michael Carey

## Oct 27 2020 at 12:04pm

I like the keyhole solution, but it should probably be limited to those students who show some proclivity toward math. I displayed some early math ability by age 5-6. I loved it and eventually became a math major in college. My daughter is completely different from me, and it is very unlikely that she will want to go into a STEM career, so I honestly don’t care if she is good at Algebra. She has other powers.

## Radu Floricica

## Oct 27 2020 at 12:30pm

I fear this would poison the well and make the whole concept of curiosity-driven education not work.

Also 1-2 hours of math is per day is enormous – if, as an adult, I could find the time and patience to study something 1-2 hours per day… Moon, here I come. And I don’t think children are inherently stupider. The key is that whatever learning they do out of curiosity is usually very close to perfect “deliberate practice”. Forcing them to do math daily would quickly teach them that education is also yawning and finding excuses to waste time. Not a great lesson, I’m afraid.

I’d propose the concept of boot camps, where kids focus on doing something for a week (together with parents, ad hoc teachers or, where practical, other kids). I think it’s long enough to maintain interest but not as long as to become a nightmare memory. Best if they can chose first few bootcamps themselves, or if they’re stuff they’re going to like, so they don’t get cold to the concept of itself. This is also useful because they’re bound to need this skill later in life.

## Amy

## Oct 27 2020 at 12:32pm

As a homeschool/unschool parent I agree and disagree. I went to public school and there are massive holes in my math education. I went to school at a time when various methods of teaching math were being tried and tested on us. We were guinea pigs and the experiment failed at our expense.

I find the idea that math is the most crucial subject quite limiting and stagnant. Did you ask these adult unschoolers about their arts education? What about their knowledge of plants and wildlife? If you look for holes you will always find them! Maybe we should ask ourselves what’s so great about math? And if you live a life in which you do things how is it even possible to not learn math? I had a horrible maths education, but I use math all the time! Would my life be easier if my education had been better? Maybe, but there is also a good chance I wouldn’t have been taught the right kind of math for my life and would have had to learn it myself anyway. What if I had grown up in an environment where I learned how to ask the right questions and the best methods to find the answers. So that I was better prepared to be a lifelong learner.

My son is quite gifted at math. At a very young age he figured out basic multiplication on his own. It was the first indicator to me that, left to their own devices kids will learn things that interest them. They will create problems in their mind and seek to solve those problems. Will there be holes? Sure! But what education doesn’t have holes? I can tell you right now I’m having to unlearn most of the history I was taught in public school.

The idea behind unschooling that maybe you have missed is that if a child is called to a certain trade or profession they will be driven to learn and master the skills needed to work in the field. If they are called to a STEM career they will want to learn the math skills they need to be qualified in the field. This may require more adult assistance, resources and accountability. But even if certain subjects are boring or hard for them, the sheer fact that they have created the goal for them self will give them the motivation to learn what they need to or in some cases find a loop hole around it!

If math is important to your family then it is perfectly okay for your family to agree on learning math skills. The important thing is that the kids are apart of the process. They get a say in their own education. If they absolutely don’t see a point in algebra for their future and no one is able to make a case to convince them otherwise, should their opinion, not be respected?

That brings us to the core of unschooling, respect. Everyone in the family is valued, everyone has a voice and is listened to. It’s a leap away from the authoritarian model we see in public school. While the adult has a broad perspective to share, the child is an expert on themself and is capable of setting age appropriate goals and working towards them.

## MarkW

## Oct 27 2020 at 12:40pm

STEM requires math. CS requires math.But mostly only in the ‘what if I had failed all of the courses I’ve forgotten’ sense. CS programs usually require advanced math (which is quickly and thoroughly forgotten and not used again). This is not the case for a few specialized mathematical niches (encryption, image-processing), but most people working in CS use packages developed by those specialists — they don’t write them themselves (and wouldn’t begin to know how). This is true of game developers, too. Only a small number work on the engines — and the rest use those engines. And it’s not just CS–the researchers I know don’t do the stats themselves, they farm it out to statisticians (who, in turn, use sophisticated applications that do the actual math for them — you do have to understand which kinds of approaches to use with which kinds of data, but you don’t have to be able to do the math). It seems that the only ones stuck doing their own stats (even at the level of using the apps) are grad students who don’t have the grant money to pay a statistician.

In general, the level of specialization is such that even in ‘STEM’ fields, only a specialized few really know the complex math.

## JayT

## Oct 27 2020 at 2:05pm

I think this is less true than you realize. I can always tell which of my software engineer coworkers had to do a bunch of extra math and which didn’t. Almost none of them could actually do any of the math they learned, but the extra few years of math makes coming up with algorithms second nature. I’ve had coworkers that were very good developers come ask me for help on things that were really just simple algebra questions disguised as a coding issue, and it’s always the self taught programmers that never went beyond high school algebra.

## MarkW

## Oct 27 2020 at 5:49pm

Almost none of them could actually do any of the math they learned, but the extra few years of math makes coming up with algorithms second nature.Eh, maybe. There are certainly huge differences in developer quality, and I’m sure many of the best tend to come from top programs where math requirements were more stringent. But I doubt that their strength comes from having taken the math class vs being smart enough to get into and graduate from a top CS program.

## Henri Hein

## Oct 27 2020 at 4:21pm

I agree with JayT. I also pity the programmers who needs to download a math package, or faithfully copy/paste from SO, to do a simple conversion between, say, km/l and mpg.

Another area that is often overlooked is you need at least a decent understanding of probability and stats to interpret many test results.

## MarkW

## Oct 27 2020 at 6:03pm

I agree with JayT. I also pity the programmers who needs to download a math package, or faithfully copy/paste from SO, to do a simple conversion between, say, km/l and mpg.By the same token, if it were in my power, I would instantly fire any developer I caught rolling their own encryption algorithm — or anything else where there was already a good, highly refined solution readily available. I’ve run into characters like that who either wanted to get paid to play with interesting stuff or who were deluded into thinking that they were lone geniuses who could invent a better mousetrap. Well, I really doubt it, but if you can, go get a job with the mousetrap company. Or do it at home as a hobby as long as you don’t bring it back to the office. Even though some these guys are really smart, they can cause a lot of headaches.

## Henri Hein

## Oct 27 2020 at 6:54pm

True. I deliberately chose an example where knowing just a little algebra moved the problem from impossible to trivial.

I do wonder if people that try to roll their own encryption algorithms do so precisely because they do not really understand the complexities involved in the underlying math. As just one indicator, I have several times had to explain the Birthday Paradox to someone. OTOH, there could just as easily be a ‘know just enough to be dangerous’ factor going on.

## JW

## Oct 27 2020 at 1:16pm

I am a homeschooling parent who takes an eclectic approach, letting my kids direct their learning but requiring them to study certain things, especially if they are neglecting certain areas. I disagree with the author that math is not fun. After lots of searching, we are using a curriculum that uses games and hands-on manipulative (“toys”) everyday and in all levels up through geometry and algebra. My kids ages 3, 6, 9, and 12 all ask to do math everyday since we started playing math games everyday.

I myself ended hating math by the end of highschool- I went through advanced calculus- because 1. it wasn’t fun, and 2. I didn’t understand the purpose of any of it. Luckily the 1st math class I took in college had a professor who taught us through games and hands-on activities. She also taught a math enrichment club at local elementary schools and she used the same techniques with us college students as she did with the kids but with advanced math… And it was hugely successfully.

One last example, a friend of mine who could be considered an unschooler teaches her kids math entirely through card and board games. Look on Amazon and you can find games for pretty much every math level and subject. Some are just glorified flashcards but there are plenty of complex strategy math games. I also have lots of math games on my children’s tablets that they move playing in their free time. This method of teaching is called gamification or gameschooling.

## Justin

## Oct 27 2020 at 3:48pm

When I was in middle school, I remember telling my parents that I will never use the stuff that was taught in my math classes (it was probably basic solve for x algebra). Now I’m a data scientist, have several statistics publications, and learn advanced math for fun. If I was unschooled, I doubt I would have received the background needed for what I ultimately accomplished. Even after graduating high school, I thought I would pursue a major with low math requirements. So for people who develop the interest late in life, not having the background would be a huge barrier.

MarkW points out correctly that many software engineers just call packages that implement advanced math rather than carrying it out themselves. This is true in data science as well. But I see the type of data scientists who do this making a lot of elementary errors that could be avoided with a real education on the topic. I see similar problems with a lot of academic researchers who apply statistics mechanically in their publications without actually understanding what they are doing.

## John Scott

## Oct 27 2020 at 5:05pm

David Friedman once commented in an interview that his kids were unschooled. But his son wanted to be an engineer, so he was doing a lot of catch-up on math, to succeed at the university and in the profession.

## Daniel R. Grayson

## Oct 27 2020 at 6:01pm

Based on my own experience, unschooling would have worked for me, but only if I was exposed to the subject that I became interested in. How does a child ever discover that they want to be a professional in field X without ever seeing anything about X? That rebuts the idea that a child is an “expert on themself” — the child also needs to know about the world.

Here’s what’s “so great about math” : you can figure it out by thinking about it. You can’t figure anything else out this way. Everything else is basically memorization.

In response to “teenagers learn math so much faster than children that it might be worth it to delay math education”, I would say that the intellect and understanding of a child (and the adult he or she will become) is best developed by teaching the child each topic as early as the child can take it in. Addition of 4-digit numbers at age 4? Yes, if the child can “get” it. If not, try it at age 5. And so on.

## JK Brown

## Oct 27 2020 at 9:21pm

The real value of Algebra + math instruction is that it is the first rigorous exposure to abstract thinking for the student. The concepts learned are of value, but the training of the mind is more important. Unfortunately, schooling, as Paul Graham wrote in December 2019, incentivizes getting good grades rather than real learning. This skewed incentive structure causes the focus to be placed on what is regurgitated overlooking the mental training.

Students should be told this so they would understand why their brain hurts, or for the math-talented, suddenly they feel set free. Also, a diligent student who struggles in the abstract maths, should not be made to feel a failure, but rather just resistant unconscious adoption of the rigor. Similarly, we should abandon the sink or swim method of instruction where if you struggle with a concept you are left behind to drown since concepts are cumulative. Similarly, if the student who gets the concepts is held back to the pace of instruction. Flipped classroom and online instruction work very well with math instruction.

For the unschooled, perhaps if the student is shown the map rather than just the next milepost, they would become incentivized to do the work themselves.

For this overview, I recommend

A trip from number lines to Calculus in 100 pages. Then the student could build up what the struggle with and then find similar for Trig and Geometry.

PS, My Geometry class back in the ’70s was my first exposure to inductive and deductive thinking. Doing proof sucked, but it trained my brain with a skill I’ve used outside of math.

## John P Palmer

## Oct 28 2020 at 8:58am

In the 1960s, the idea of unschooling (though it wasn’t called that) was evident in the book SUMMERHILL by A.S. Neale.

Later in life I had a friend who actually attended Summerhill School. She wasn’t enthusiastic about it.

## A Country Farmer

## Oct 28 2020 at 10:09am

You need a catchier term. Maybe Munschooling?

However, I don’t find this argument compelling:

> Won’t kids who would greatly benefit from math choose to learn math given the freedom to do so? The answer, I fear, is: Rarely. For two reasons: First, math is extremely unfun for almost everyone. Only a handful of nerds sincerely finds the subject engaging. I’m a big nerd, and I’ve done piles of math, yet I’ve never really liked it. Second, math is highly cumulative. […]

I have a B.S. in Computer Science from a good school, which means I basically have a minor in math. Like all topics that I was schooled, I didn’t enjoy math at all. When did I start enjoying it? When I actually needed to learn queuing theory in my job (a topic that I did “learn” in school and forgot after the test).

And when I picked up queuing theory and the complex math behind it 10 years after graduating, I really enjoyed the math that I needed to learn. A classic prediction by unschooling theory applied to your supposed “tough” problem for unschooling.

## Ezekiel

## Oct 28 2020 at 11:08am

## andy

## Oct 28 2020 at 2:07pm

I loved math as a child… a teacher who would pose more challenges, more inidividual approach would make wonders… so much lost time :/

You may learn math quickly when you are adult; you won’t learn that much quicker to learn a classical musical instrument. It takes years of daily practice. You will be slightly faster when you are adult, maybe twice as fast, but then, you will have much less time. I have experience with people who were already musicians and wanted to learn a new instrument. They can focus only on the technical part, so they are super-fast learners and it still takes years. And it’s not like 1 or 2.

Most children do not like to practice; you may have a great teacher who makes the child want to, but this is rather an exception. A reasonable approach seems to be “if you want to play the instrument, you have to practice; there is not point in playing that without practicing”. How does that go with ‘if he wants to play video games, let him’… I don’t know.

## David Merkel

## Oct 28 2020 at 3:07pm

Unschooling is not that common. It is not worth writing about.

## Alexander Khost

## Oct 28 2020 at 6:00pm

Please, consider actually learning about unschooling before writing about it. For starters: https://www.self-directed.org/tp/math-beyond-school-mindset/

## David Friedman

## Oct 28 2020 at 7:12pm

My kids were unschooled, first in a small and very unconventional school, where classes happened only when kids wanted them, then at home. In the school, they organized a math class. It lasted a year, started with kids who knew no math, made it into algebra by the end of the year. That suggests that your hour or more a day is way too much.

Neither of my kids much liked math, although my son did learn probability theory early on because he did gaming and wanted to be able to calculate odds. Both of them got respectable SAT math scores, although not nearly as good as their verbal — after themselves studying math for the SAT on their own initiative, because they wanted to get into good colleges (and did).

## Fred_in_PA

## Oct 28 2020 at 9:14pm

Some observations from my own somewhat crippled learning of mathematics:

I think my learning suffered from teachers who did not see the point of having a point. I don’t know how many classes I had where we spent our time proving theorems. Or walking through the derivation of a formula. (My guess now is, that my math teachers were all math majors / mathematicians. And since they enjoyed the subject for itself, they thought all the rest of us should, too.)

The only maths where I really feel comfortable — and please note, “comfortable” is not the same as “masterful” — are grocery store arithmetic and some statistics. That’s because I worked in a grocery store (in high school) and quickly had to master such things as “if an item’s on sale at three for $2.50, how much should I charge the customer who only wants two?” (And I’m so old, the cash register wouldn’t calculate it for you back then.)

But it was statistics where I really learned this lesson. I struggled through three or four college level statistics courses, never really learning very much that I could recall beyond the final exam. Finally, at UICC, I got a professor who taught the entire course as

statistics! It finally made sense (and became attractive) when I saw what it could be applied to (and how to apply it).appliedIt seems to me that this theme is just below the surface of many of the above comments. That unschooling even works with math. That the student will be naturally drawn into mathematics if it can be demonstrated as a useful tool for something else that they want to do (and, yes, that “something else” could even be mastering a game).

## Amy Fischer

## Oct 29 2020 at 6:46am

An hour or two of math? While I think it’s appropriate to have our children learn math (even if they don’t love it), that seems out of proportion. 15-30 minutes depending on age seems more like it.

## mark

## Oct 29 2020 at 7:15am

First, a caveat: A fine impression on unschooled-kids one meets at GMU says

very littleabout the merits of unschooling. You may just be seeing a tiny sub-group of a sub-group., not a representative sample. It is like saying theCaplan-twinsare proof that the Caplan-homeschooling works. (They are kids with rather bright parents. And thus might have done exceedingly well even in pub. school. Judith Harris – Btw.: Are they using much math in their present fields – mainly history?) – Homeschoolers/Unschooler are a very mixed bunch, indeed, and not mixed in the same way as the “public-schoolers” are. We know how bad/good public-schools are, because we have all the numbers. We do not have enough useful numbers about unschooling. I guess there are even some very fine students in Prof. Caplan’s courses that came from public schools. And I agree, that this is does not prove that ps, well, what-is-the-right-word, oh, yes: suck (in most of the US and at least in all countries with even worse TIMMS/PISA results. And also here in Germany.)IfI had the energy (I know the math) to follow the Caplan-schedule with my kids, I would. If I “tried unschooling” it would just be due to lack of energy (aka”lazyness”). Anyways, all but “school-schooling” is illegal here.## Debur

## Oct 29 2020 at 10:34am

One key aspect that’s not discussed here is the availability of job opportunities. In western / developed countries, employers are quite forgiving (in many industries) since the demand is higher than the supply. In most countries though, without grades and certifications you’re in eligible for the job market.

This is a big obstacle for unschooling.

## Catherine Holloway

## Oct 29 2020 at 12:34pm

I could not agree more. When I was 10 I declared that I was no longer going to study math because “girls just aren’t good at it”. My mom, an economist, refused to let me use that excuse, and enforced math lessons. I now work in software engineering at a hedge fund and have a very exciting and well compensated job. My sisters in law, also unschooled, were allowed to skip math and now complain about being innumerate.

## Douglas Knight

## Oct 29 2020 at 4:49pm

In my experience, unschooled children believe that they are bad at math, but they are wrong. They have perfectly ordinary abilities, but have extraordinary standards for what it means to learn a subject. Much of what people learn in math class is how to bluff, to extract points from the teacher for partial credit. Math is cumulative, but most students do not actually learn the material, and thus do not have the foundation for the next step. The curriculum is not designed for accumulation, but for the actual experience of social promotion.

Bluffing is a valuable skill, though an antisocial one. It is probably the most important deficit of unschooled children. But it probably interferes with ordinary students learning math. Louis Benezet observes this in his experiment. If you insist that a child work on math for an hour each day, will it be productive? Probably the child should be forced to learn math, but only around high school age, after having learned what it is know and to learn.

## Thomas Sewell

## Oct 29 2020 at 11:15pm

Math can be fun, even for unschoolers, if used purposefully.

So if you do some programming, work at a bit of surveying, go do a complex land navigation course, figure out what’s going to happen for some physics experiments, take and analyze some polls, decide what to do or plan based on a data set somewhere, divide pies/cakes/pizzas/Halloween candy/whatever between different numbers of people, figure out how long a trip is going to take, example gas mileage differences, calculate a supply/demand curve, etc… you’re going to learn lots of math.

But yeah, a much smaller percentage of people will voluntarily sit still and listen to a math lecture for a couple of hours a day for fun. Competency-based math programs like ALEKS.com are an improvement for self-directed learners, but there’s no substitution for having a real life situation to use it in for actually developing a skill which will be kept.

## Rob Fox

## Oct 29 2020 at 11:35pm

I try to convince my granddaughter that those who have studied advanced mathematics belong to an exclusive group of humans with special insight into truth and logic. It also helps to give one’s mind the structure and discipline to process many other areas of knowledge.

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