> My second son is taking AP calculus BC as high school junior (eleventh grader).
Your example has a 15 year old going to community college or university in order to go to a calculus course. You named it the "calculus trap", which includes as a negative the social problem of having a 15 year old in a class full of 19 year olds. This implies that it's unlikely that the high school offers calculus.
My observation is that more and more high schools offer calculus in the high school, so the 15 year old you described, who was taking college courses to learn calculus, is now more likely to be a 15 year old at high school taking courses with 16 year olds (like your second son).
In that case, the severity of the trap is lessened, no? If only because the age gap is so much less.
I'm not saying that you are wrong about how math knowledge should be developed. I point out only that the arguments from your hypothetical case feel a bit out of date.
Than again, suppose the 15 year old does take calculus at high school, then takes a tertiary education class at age 16. What class might that be? That's about the time the standard college curriculum branches away from calculus, to include algebra, differential equations, or discrete math.
In that case, it's not really a "calculus" trap, no? :)
Also, I read the reviews of KTEM. Cross-cultural observational comparisons are often enticing, but it's hard to draw firm conclusions from them. Had you read, say, a comparison with the Finnish model then perhaps you might have drawn different conclusions?
My hypothesis, btw, is that the US is entirely too car dependent. Extracurricular activities like a city math club would be much easier if teens had ready access to transportation independent of their parents.
Your example has a 15 year old going to community college or university in order to go to a calculus course. You named it the "calculus trap", which includes as a negative the social problem of having a 15 year old in a class full of 19 year olds. This implies that it's unlikely that the high school offers calculus.
My observation is that more and more high schools offer calculus in the high school, so the 15 year old you described, who was taking college courses to learn calculus, is now more likely to be a 15 year old at high school taking courses with 16 year olds (like your second son).
In that case, the severity of the trap is lessened, no? If only because the age gap is so much less.
I'm not saying that you are wrong about how math knowledge should be developed. I point out only that the arguments from your hypothetical case feel a bit out of date.
Than again, suppose the 15 year old does take calculus at high school, then takes a tertiary education class at age 16. What class might that be? That's about the time the standard college curriculum branches away from calculus, to include algebra, differential equations, or discrete math.
In that case, it's not really a "calculus" trap, no? :)
Also, I read the reviews of KTEM. Cross-cultural observational comparisons are often enticing, but it's hard to draw firm conclusions from them. Had you read, say, a comparison with the Finnish model then perhaps you might have drawn different conclusions?
My hypothesis, btw, is that the US is entirely too car dependent. Extracurricular activities like a city math club would be much easier if teens had ready access to transportation independent of their parents.