This is false, there are a few genius mathematician who early in childhood proved it is easy for some humans.
I think the whole thing revolves around mental models
Exactly! There is even more specific concept in programming psychology, it is called “notional machines”. Small little machines in your head which can interpret using rules.
I think those also can transfer to math learning, as after rule-based machines concept is grasped, all the algorithmic, iterative, replacable and transitive concepts from math start making sense.
This is false, there are a few genius mathematician who early in childhood proved it is easy for some humans.
Some outliers are hypernumerate. I’m hyperlexic, so attuned to words that I was able to teach myself to read before my childhood amnesia kicked in, so I never had to learn phonics. This doesn’t mean the vast majority of humans aren’t congenitally literate or numerate. OP’s statement may be nominally false, but the exception proves the rule.
As for teaching the aesthetic beauty of math, I would give each student their own blank copy of the 10x10 multiplication table (with a zeros row and column, making it 11x11) at the start of grade 2, and teach them how to fill it in themselves. After that, they can use it in any math class that semester, but they have to make a new one at the start of each semester after that.
The inherent laziness of humanity will drive them to “cheat” by copying from lines above: filling in half the 4′s from the 2′s, half the 8′s from the 4′s, half the 6′s from the 3′s, and so on. And while they’re doing that, they’re learning in an indelible way.
This is false, there are a few genius mathematician who early in childhood proved it is easy for some humans.
Exactly! There is even more specific concept in programming psychology, it is called “notional machines”. Small little machines in your head which can interpret using rules.
I think those also can transfer to math learning, as after rule-based machines concept is grasped, all the algorithmic, iterative, replacable and transitive concepts from math start making sense.
Some outliers are hypernumerate. I’m hyperlexic, so attuned to words that I was able to teach myself to read before my childhood amnesia kicked in, so I never had to learn phonics. This doesn’t mean the vast majority of humans aren’t congenitally literate or numerate. OP’s statement may be nominally false, but the exception proves the rule.
As for teaching the aesthetic beauty of math, I would give each student their own blank copy of the 10x10 multiplication table (with a zeros row and column, making it 11x11) at the start of grade 2, and teach them how to fill it in themselves. After that, they can use it in any math class that semester, but they have to make a new one at the start of each semester after that.
The inherent laziness of humanity will drive them to “cheat” by copying from lines above: filling in half the 4′s from the 2′s, half the 8′s from the 4′s, half the 6′s from the 3′s, and so on. And while they’re doing that, they’re learning in an indelible way.