My "took 30 seconds to think about it" first impression is that the common thread is twofold: firstly that you can't die from being bad at the thing, and secondly that you are fundamentally capable of performing at the necessary level. That way the forced practice is both survivable and also leads to mastery.
In swimming or subsistence farming you might die before figuring it out. In math you might hit cognitive limits. Come to that, in child rearing it's also possible for it to go wrong if you hit some hard limits and resort to infanticide or neglect... tragic but not exactly unknown.
This, and...
Teaching math (and many other, but not all topics) requires finding where in the chain of necessary understandings between some fundamental skill and the current topic a student has not completed their learning, and working there. Parenting and immersive language are fields where the fundamentals are constantly being tested, and so provide unlimited opportunities for mastery. Likewise, the parenting and language skill trees are not as linear as the one for math: the former have a wide variety of skills that can be learned in relative isolation and in a variety of different orders. Not all the early lessons will even be applicable later (I haven't changed a diaper in years, now), and sometimes mastery in one area is sufficient to produce overall adequacy even if other areas suffer.
AllAmericanBreakfast has a post related to the topic that I found very insightful (and I think ryan_b is onto something similar). In this context it suggests that the commonality between >>parenting<< and >>language learning<< is that both categories point to aggregate skills that can be learned simultaneously and do not necessarily have strong interdependencies even at the higher levels, where >>math<< is more of a narrow tower of skills, each depending heavily on the last all the way down.
Why is immersion the best way to learn a language?
I submit that it is because you do not get to stop.
I'm not sure of this. I got quite good at English basically by immersion - reading English books, watching English TV and movies, hanging out on English forums, playing video games in English - so that by the time I was in my mid-to-late teens, people online were already mistaking me for a native speaker (or writer, rather). But it's not that I was forced to do those things. I could have read only books in Finnish, just read the Finnish subtitles in English TV shows / movies, hang out exclusively on Finnish sites / with Finnish people, and do things other than play video games. In fact most kids my age and in that area did not spend as much time learning English as I did, nor did they get equally good at it.
I'd rather say that learning English felt valuable in that it gave me new options for what to do. If I wanted to pursue some of the things that felt the most interesting to me (e.g. read Star Wars novels that hadn't yet been translated into Finnish, obviously a supremely important task), then I needed to learn English. That seems related to the "you do not get to stop" criteria in the sense that learning the language is high-value to you - if you are in an environment where you don't get to stop learning a language, it means that you need to learn the language in order to be able to do anything. But it seems like the key is simply in it being of high value, and "you can't do anything without it" is just a particular special case that makes it maximally high value.
On the other side, there are all the parents who aren't actually very good and neglect or abuse their children. Even though they are forced to be around their kids too, they don't put equally high value on their child's well-being as a good parent does, so the relentlessness doesn't translate into good parenting.
This sounds like the common thread to me. Humans tend to become proficient at things they spend a large amount of time doing, especially if it is something that requires active participation and generates utils. One does not have to be forcibly immersed to gain new proficiencies so long as becoming more proficient is sufficiently useful that the benefits gained exceed the effort required, especially when the benefit is realized in the short term.
To become proficient in math and truly internalize it, you must be able to use it like language, i.e., as a tool to interact with or understand the universe in a way that aligns with your utility function. Much like many people don't often find it useful to be fluent in Hungarian, many people don't find it useful to be fluent in mathematics. It just isn't high-value enough to devote the time to learning.
Being high value isn't sufficient on its own though. There has to be the opportunity to learn and improve over time, ideally at the boundary of one's comfort zone instead of entirely outside or wholly within. The ocean does not allow much opportunity to a non-swimmer. Life is the ultimate prerequisite to learning anything.
I hesitated before writing this post because I don’t know what is special about languages and childrearing—I can’t think of other obvious things in the category, though there are probably some.
Maybe the skills that are best learned by immersion and just doing them are those that were useful in the ancestral environment, and so come with a lot of preinstalled "machinery" in our bodies and minds that just need to be tapped into. It's easy to see why language acquisition and childrearing would be in this category; other examples are social skills, cooking, running, fighting. As opposed to skills like math or piano, where most people don't start out with the basic machinery, and need to laboriously install it by solving a hundred problems or playing scales over and over.
The difference may be a social one. What kind of immersion would cause someone to learn math? I’d guess a much more social immersion, where everyone in the subject’s peer group are math phds, they don’t outright reject the subject, and they often talk about math in the subject’s presence. It seems likely this person would learn math quickly, and without any traumatizing experiences.
I wonder if it would be possible to make an educational system with 1 month immersion (per year) in each subject. Like, one month you are only allowed to discuss math, read books about math, the walls are covered by pictures of mathematical theorems, etc. The next month you only paint and observe paintings. (Would be a bit cult-like, but given that schools already resemble prisons, this would not necessarily make them worse.)
I think this is more or less how you make programmers. "Oy! You can read documentation? Here's a ticket, here's the office slack, best of luck friend!"
I wonder if it is a question of dimensionality somehow. When a person is immersed in a language, they are being bombarded with all of the language's features repeatedly and more or less constantly. This means any language task they can succeed at, they will; then they can expand from these islands of competence outward.
Math class is a strictly sequential and linear endeavor. Normally we get exactly one sequence of problems, which has exactly one ordering, and once a type of problem is past it will never appear again. There is no flexibility at all in how to approach learning math in a class, unless initiative is undertaken by the student completely independent of the instruction.
I learned much more about math once I abandoned the math class approach; I did more immersive things like reading history about math concepts, and different applications, and explanations for why things are wrong.
Semi-separately, I also consider the issue of feedback loops. During talking and wrangling my kid, feedback is mostly instantaneous. Feedback in math class is usually delayed by at least a day, and usually only sparse feedback to boot, in the form of a binary correct-or-incorrect result. Reflecting on it, the sparse complaint is also an issue of dimensionality of a sort.
I think it can be argued that in the West that practical achievement and directed pursuit probably is like this at a core level - humans are capable extraordinary effort if the conditions (and pressures) are right. Parenthood is one of the things that is still like everything used to be - pushed to the edge of human capability because there isn't another option. I think for many other modern pursuits a common failure mode is indulging in the eases and luxuries of modern existence - no such option with parenthood or language immersion.
Related thought: slogans like 'Just Do It' are effective because people grok that the human mind will trick you into taking easy way out if the option is there. 'No excuses' is an attractive motivating strategy and does usually work in the short term, but long term environment design is more imporant.
Something that distinguishes child-rearing and immersive language learning from children in school is the seriousness that both tasks force. The parents want to create a new, well-functioning human being (when they don’t want this, it doesn’t go well), and you need the language in order to have any interaction with the people around you. At least, you do if you’re a newborn, and it still takes a good many years. (Is immersion actually the best way for adults? It’s the only way for children, but because of that there’s no other way to compare it with.)
That quality of seriousness, it seems to me, is what produces progress. The school child is rarely serious. Someone attending a course just for the socialising is not serious. There are teenagers who have won gold medals at the Olympics. Those ones are serious.
Reminds me a lot about how Zen training works. Much of the value of a sesshin (several days where you do nothing much other than meditate) is the persistent lack of distractions or other stimulation: you just have to keep coming back, sitting still, and being with yourself, eating the same bland food, doing the same chores, over and over for days. It sounds awful, and at first it is, until you break/surrender and give yourself over to the fact that this is how the world is, and in that space deep meditative states and realization often emerge.
The obvious alternative is: it's more practice than is optimal, but the diminishing returns/losses as a result of overdoing it are less than the alternative. But also - doing a thing constantly does sound like a recipe for getting really good:
If you are in a typical American math class
which is means this is a different thing - that's not immersion (usually).
I think relentlessness can also be a bad way to learn childrearing, if the child takes more spoons than you've got and you start doing really bad at it and end up abusing or neglecting your child or yourself.
Seems right, but, also, like, the point is that you don't really get the option. (I guess this is compatible with the other part of the post, about being a subsistence farmer or sailor)
1. You can think of a learning mind as a tool for mapping cause and effect relationships by being affected by them.
E.g.:
If you live among speakers of a language you experience a lot of interactions (e.g. people refer to an object with the same sound) ---> these change your mind (associations created via neurons) ---> better knowledge of language (better mapping between variables in this domain)
2. However, when you move a mind to a space with more data of a subject, other variables can also change, which might have a negative impact and can disable the mind.
E.g.:
If you want to find out how to float on water, jumping into a deep pool and experimenting with motions will help in finding the ones that achieve this (again, the mind is creating connection between movements done with the limbs and how they affect movement in the water). However, if you can't find the correct motions, you will sink to the bottom. ---> your brain will not receive oxygen ---> your mind is disabled (death)
3. So you want to be careful about which space you move a mind to. It is not enough to have more data, you should control other variables to make sure the mind is safe.
E.g.:
Learn the basics of swimming in shallow water.
4. As minds change through learning, variables may have different effect on them than before.
E.g.:
If you know how to swim, jumping into a deep pool won't kill you anymore in most circumstances.
If you are in a typical American math class, and you cannot stop being in a typical American math class, you might pick up more math than you would by playing in the woods, but you might also burn out and develop lifelong math anxiety.
Which is more common: hatred or anxiety?
On a physiological level, how would you characterize the difference?
My answer below (in case you want to take the time to work yours out first)...
Anxiety is an aversive reaction. In my body, it appears as a tightness across the lower abdomen, the whole-body zap that I associate with increased adrenaline, and (later) the whole-body fatigue that I associate with increased cortisol. In the case of our hypothetical math class, the main source of the anxiety is the immense social pressure placed on students by the entire culture and primarily embodied in the teacher and parents.
Hatred is a layer of meaning that I can place on top of some aversive reactions. I (probably not consciously) interpret the anxiety sensations as evidence of a threat associated with the current stimulus (in this example, the hypothetical math class, eventually generalized to the process of doing math since the reaction is less prominent in other classes), and my full attention turns toward the elimination of the threat. Since I can't eliminate math class, the process is frustrated and remains unresolved.
There’s not a great way to convey the merciless relentlessness of having a child who insists on continuing to exist and want and need regardless of how much sleep you got, how sick you are, how many times you have already read that book, how tired your arms or how aching your feet, how hungry or sweaty or needy-for-cognition you’ve gotten, how much or little support happens to be available that day. It’s a lot.
...
Parents aren’t better at parenting tasks because of magic or even because they responsibly read the entire parenting manual, they’re better at them because they are forced to practice way way way more than anyone would naturally choose to practice any such tasks (and accordingly your skills will be uneven depending on how you divide those tasks).
(from a tumblr post I wrote about having kids)
Why is immersion the best way to learn a language?
I submit that it is because you do not get to stop.
If you were in, say, Java, then you probably would pick up Javanese as long as you did things reasonably aimed at continuing to be immersed in Javanese (that is, not immediately finding the nearest English-speaker and latching onto them, or adopting a convenient orphan and teaching them English, or buying a ticket to Australia). In spite of the fact that this strategy does not necessarily draw on anything we know about deliberate practice, or language education, it would still probably work. It's how everybody learns their first language, and in that case it basically always works, because babies really can't do anything else about it since they don't already speak anything else. To communicate at all, a very basic human need, you have to match the standard of other talking entities around you, and you will not stop having to do this, so eventually you will.
Most things are not like this, or they are like this but not enough for it to be a good idea to try to learn them this way. If you are in the ocean, and you cannot stop being in the ocean, this is actually a terrible way to learn to swim and an even worse way to learn about sharks. If you are a subsistence farmer, and you cannot stop being a subsistence farmer, you might learn a ton about your plot of land, but also you might have bad weather one year and starve. If you are in a typical American math class, and you cannot stop being in a typical American math class, you might pick up more math than you would by playing in the woods, but you might also burn out and develop lifelong math anxiety.
I hesitated before writing this post because I don't know what is special about languages and childrearing - I can't think of other obvious things in the category, though there are probably some. And I worry that pointing out the efficacy of relentlessness will lead people to commit themselves to things that are more like typical American math classes in the pursuit of whatever it is they want-to-want to learn. Please don't do that. But if anyone else can come up with a common thread between my examples of successful-relentlessness, or more examples, that might be useful.