We can be too young to learn things - what implications does this have? (this "hedging of every opinion" requiring a caveat or question mark on every sentence is getting annoying)

I don't mean like

Little Timmy can't hear the words PENIS and VAGINA now!! He's only 10 - he'd be scarred for life! Though, this from Alice Dreger is very good on the subject, and I need to read her book.

I mean like you can't teach a baby how to differentiate or integrate y = x, but you can teach a (normal) 30 year old how to add, and you can (probably) teach them how to differentiate or integrate y = x. Like the ever-misused Laffer Curve, this means that at some point, that person became able to learn how to differentiate.

Importantly, before that, they wouldn't be able to, and trying to teach them would've been pointless. More than pointless - it would stop you from teaching them something actually useful!

Decisions/actions have opportunity costs - when you're at home reading a book, you could be watching a film in the cinema. Watching the film is the opportunity cost of reading the book (not exactly, but it's close enough and I can't be bothered writing the exact definition).

foregone opportunities ... what you’re giving up in order to get something else

And it can't be good for people trying to learn things when they're too young, either, self-esteem wise. Myself, I tried to do a hackathon in my first year of uni, and I was TERRIBLE and useless to my team, because I was too young, knowledge- and experience-wise, to help out. I felt awful throughout it. Wasn't amazing for how I thought of myself as a programmer. Much better, now, though, with years of programming under my belt (it's not exactly the same, I know).

Like, what is a child to think when a teacher tries to get them to understand how to multiply numbers together, and they keep banging their head off the wall, over and over again, because they physically can't understand how to do it yet?

Instead of them banging their head against the wall not-learning multiplication, they could be learning how to write/read/speak a foreign language ("but they're only 6! They couldn't!" - French children can speak perfectly good French at 6)/history/loads of things!

Benezet's experiment

benezet.txt

I don't know of any research about this, apart from this school experiment (more detail here) - a teacher called L. P. Benezet in New Hampshire, an American state, delayed teaching children arithmetic until they were 12 or 13:

For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning facilities." All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children's minds, from common sense, with the result that they could do the calculations as taught to them, but didn't understand what they were doing and couldn't apply the calculations to real life problems. He believed that if arithmetic were not taught until later on--preferably not until seventh grade--the kids would learn it with far less effort and greater understanding

In some of the schools in the poorest parts of his town, he got the teachers to stop teaching kids how to add, subtract, multiply or divide, until they were 11 or 12. Instead, they would speak English:

The children would be asked to talk about topics that interested them--experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he thought, would improve their abilities to reason and communicate logically. He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.

And the results?

The results were remarkable. At the beginning of their sixth grade year, the children in the experimental classes, who had not been taught any arithmetic, performed much better than those in the traditional classes on story problems that could be solved by common sense and a general understanding of numbers and measurement [...] by the end of sixth grade those in the experimental classes had completely caught up on [the standard school arithmetic tests] and were still way ahead of the others on story problems.

Actually, this reminds me of the effect of teaching kids Esperanto for a year, rather than a normal foreign language, then switching to the normal one afterwards.

In sum, Benezet showed that kids who received just one year of arithmetic, in sixth grade, performed at least as well on standard calculations and much better on story problems than kids who had received several years of arithmetic training

Of course, you should Beware the Man of One Study, but, I wonder how much time and money we waste teaching kids stuff they can't learn yet, when they could be more productive. Do we actually do research into when we should teach kids things?