Yeah, learning by reading at home definitely has a huge effect in many cases. In Terence Tao’s education, he was allowed to progress through multiple years of a subject per year (and to do so at different rates in different subjects), and since the classes he attended were normal ones, I think his academic progression must have been essentially determined by his ability to teach himself at home via textbooks. Unless perhaps they let him e.g. attend 7th grade science 2 days a week and 6th grade science the rest? I should learn more about his life.
The educational setup can also feed into the reading aspect. During my childhood, on a few occasions, I did explicitly think, “Well, I would like to read more of this math stuff (at home), but on the other hand, each thing I learn by reading at home is another thing I’ll have to sit through the teacher telling me, being bored because I already know it”, and actually decided to not read certain advanced math stuff because of that. (Years later, I changed my mind and chose to learn calculus from my sister’s textbook around 8th grade—which did, in fact, cause me to be bored sitting through BC Calculus eventually.) This could, of course, be solved by letting kids easily skip past stuff by taking a test to prove they’ve already learned it.
Yeah, learning by reading at home definitely has a huge effect in many cases. In Terence Tao’s education, he was allowed to progress through multiple years of a subject per year (and to do so at different rates in different subjects), and since the classes he attended were normal ones, I think his academic progression must have been essentially determined by his ability to teach himself at home via textbooks. Unless perhaps they let him e.g. attend 7th grade science 2 days a week and 6th grade science the rest? I should learn more about his life.
The educational setup can also feed into the reading aspect. During my childhood, on a few occasions, I did explicitly think, “Well, I would like to read more of this math stuff (at home), but on the other hand, each thing I learn by reading at home is another thing I’ll have to sit through the teacher telling me, being bored because I already know it”, and actually decided to not read certain advanced math stuff because of that. (Years later, I changed my mind and chose to learn calculus from my sister’s textbook around 8th grade—which did, in fact, cause me to be bored sitting through BC Calculus eventually.) This could, of course, be solved by letting kids easily skip past stuff by taking a test to prove they’ve already learned it.