Ahem. I took calculus as a freshman. In highschool. I only had to retake the second half because I was so horribly sleep deprived during the final, and so lazy about homework. I then got a 5 on the AP test (score maxes out at a 5).
Now I’m not typical, but I suspect that a school system that cannot teach calculus to the top ~10% or so of its math-inclined students when they’re in high school is failing somewhere along the way.
The question is not whether high schools can teach calculus, but rather whether they should. I believe the value of calculus education at that level is not very high relative to classes on, e.g., personal finances, logic, probability, economics, civics and etc.
That’s what was meant by “sane” in the grandparent: a non-efficient use of classroom time.
“not very high relative to classes on, e.g., personal finances, logic, probability, economics, civics and etc.”
But high relative to, say, teaching a class on postmodernism.
what I do know is this: the grade school that fed into my highschool had a nifty policy for math: you go to the math class at the level your ready for, independent of your grade level. This is on the assumption that (innate?) mathematical aptitude is relatively uncoupled from other “classroom skills”.
As a result, those who don’t have a super-duper knack for math don’t generally hold back those who do have a knack for math, so the upper end of the curve is already extending itself by the time those kids get into high school.
I’m sure at least 40% of high school freshmen could learn Mandarin, but you don’t see that happening. Therefore, merely because students are capable of learning a subject, does not imply that that subject is or ought to be taught.
Seriously. I’m talking about opportunity costs.
But high relative to, say, teaching a class on postmodernism.
Philosophy is not even a blip on the secondary education subject radar.
due to my experiences as a young kid (I could challenge Authority (my parents) on a math problem and sometimes WIN, and I learned how to factor quadratics in first grade) and the fact i see the application of math almost everywhere (computers in particular, but bridges and buildings as well) means that I see math as our best tool. time to start applying it recursively.
I believe that math is usefull for a human with ~99.99+% probability. (that number discards the probability of an AI for the sake of speed)
I believe, with about a 75% confidence (for now) that having calculus as an available, but not required, course, should be possible in at least 80% of high schools.
even an understanding of a simplified calculus is usefull in many other subjects.
if (#2), then a high school unable to offer calculus is either a particularly small highschool, or is being fed by an underperforming grade school system.
There is plenty of evidence that SOMETHING in the gradeschool system is underperforming regarding mathematics.
-Which belief elements do you want me to try to expand on the most when i get back?
Which belief elements do you want me to try to expand on the most when i get back?
None. You’re still in a “can = must” frame of mind, after three attempts to explain my position. Your one engagement with the idea of replacing high school calculus with something else was, as far as I can tell, facetious.
Conversely, I took calculus in high school, didn’t understand what the heck was going on with most of the concepts, got a 5 on the AP test and an A in the class, and forgot all the material immediately.
Then, years later, I took calculus in college and understood everything.
Ahem. I took calculus as a freshman. In highschool. I only had to retake the second half because I was so horribly sleep deprived during the final, and so lazy about homework. I then got a 5 on the AP test (score maxes out at a 5).
Now I’m not typical, but I suspect that a school system that cannot teach calculus to the top ~10% or so of its math-inclined students when they’re in high school is failing somewhere along the way.
The question is not whether high schools can teach calculus, but rather whether they should. I believe the value of calculus education at that level is not very high relative to classes on, e.g., personal finances, logic, probability, economics, civics and etc.
That’s what was meant by “sane” in the grandparent: a non-efficient use of classroom time.
“not very high relative to classes on, e.g., personal finances, logic, probability, economics, civics and etc.” But high relative to, say, teaching a class on postmodernism.
what I do know is this: the grade school that fed into my highschool had a nifty policy for math: you go to the math class at the level your ready for, independent of your grade level. This is on the assumption that (innate?) mathematical aptitude is relatively uncoupled from other “classroom skills”.
As a result, those who don’t have a super-duper knack for math don’t generally hold back those who do have a knack for math, so the upper end of the curve is already extending itself by the time those kids get into high school.
I’m sure at least 40% of high school freshmen could learn Mandarin, but you don’t see that happening. Therefore, merely because students are capable of learning a subject, does not imply that that subject is or ought to be taught.
Seriously. I’m talking about opportunity costs.
Philosophy is not even a blip on the secondary education subject radar.
due to my experiences as a young kid (I could challenge Authority (my parents) on a math problem and sometimes WIN, and I learned how to factor quadratics in first grade) and the fact i see the application of math almost everywhere (computers in particular, but bridges and buildings as well) means that I see math as our best tool.
time to start applying it recursively.
I believe that math is usefull for a human with ~99.99+% probability. (that number discards the probability of an AI for the sake of speed)
I believe, with about a 75% confidence (for now) that having calculus as an available, but not required, course, should be possible in at least 80% of high schools.
even an understanding of a simplified calculus is usefull in many other subjects.
if (#2), then a high school unable to offer calculus is either a particularly small highschool, or is being fed by an underperforming grade school system.
There is plenty of evidence that SOMETHING in the gradeschool system is underperforming regarding mathematics.
-Which belief elements do you want me to try to expand on the most when i get back?
None. You’re still in a “can = must” frame of mind, after three attempts to explain my position. Your one engagement with the idea of replacing high school calculus with something else was, as far as I can tell, facetious.
Conversely, I took calculus in high school, didn’t understand what the heck was going on with most of the concepts, got a 5 on the AP test and an A in the class, and forgot all the material immediately.
Then, years later, I took calculus in college and understood everything.
So, YMMV on how good an idea it is.
Agreed.