Where are you from that the school system is sane enough to assume calculus for undergrads?
There are places that don’t? Australian here too and calculus is assumed (for undergrads doing appropriate degrees). It is assumed because the applicable subjects are either an outright requirement of the course or there are remedial level subjects required as prereqs (that most students in the course will skip) for those that somehow managed to avoid learning calculus in school.
In canada, almost nobody learned calc in high school, it was an advanced placement course. We started learning calculus in first year engineering but didn’t really start using it in other courses until third year.
Partially this was because the 4 year degree program piggy backed on a 2 year technologist program. So we learned the basics and applied practicalness of everything without calculus in the first two years, then went back and learned all the deep theory in last two years.
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.
Brown University (where my brother went) assumes that incoming freshman have already had math equivalent to the first two semesters of college calculus. My high school’s calculus course only covered Calc I.
My first-year courses in engineering (in Canada) made basic use of calculus without assuming any real understanding of it. By second-year, the calculus was assumed and for linear ODE’s and similar. Third-year, we moved to Laplace and Fourier transforms and the final year finally started to get into applications and standards and “real” things.
I’ve always wondered how different other engineering school curricula are.
Also canadian engineering school. First year we learned calculus but did not use it. Second year we learned even more calculus (up to PDEs, inear alg, and vector calc), but still didn’t use it. Calculus started being assumed in third year. We suggested to the school that they make more of an effort to use the skills that they teach between classes, so this might change soon.
dynamics? assuming algebra but no calculus.
you say one was polar/cartesian
one was
x = x0 +v0*t + 1/2*a*t^2one was
f = m*aone was either quadratic formula to reverse #2, or reversed #2.
Doing dynamics at a tertiary level without calculus? o_O
Where are you from that the school system is sane enough to assume calculus for undergrads?
There are places that don’t? Australian here too and calculus is assumed (for undergrads doing appropriate degrees). It is assumed because the applicable subjects are either an outright requirement of the course or there are remedial level subjects required as prereqs (that most students in the course will skip) for those that somehow managed to avoid learning calculus in school.
In canada, almost nobody learned calc in high school, it was an advanced placement course. We started learning calculus in first year engineering but didn’t really start using it in other courses until third year.
Partially this was because the 4 year degree program piggy backed on a 2 year technologist program. So we learned the basics and applied practicalness of everything without calculus in the first two years, then went back and learned all the deep theory in last two years.
Australia. (I have a little bit of culture shock now.)
I’m not very confident that a school system that teaches calculus to high schoolers is sane.
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.
Brown University (where my brother went) assumes that incoming freshman have already had math equivalent to the first two semesters of college calculus. My high school’s calculus course only covered Calc I.
My first-year courses in engineering (in Canada) made basic use of calculus without assuming any real understanding of it. By second-year, the calculus was assumed and for linear ODE’s and similar. Third-year, we moved to Laplace and Fourier transforms and the final year finally started to get into applications and standards and “real” things.
I’ve always wondered how different other engineering school curricula are.
Also canadian engineering school. First year we learned calculus but did not use it. Second year we learned even more calculus (up to PDEs, inear alg, and vector calc), but still didn’t use it. Calculus started being assumed in third year. We suggested to the school that they make more of an effort to use the skills that they teach between classes, so this might change soon.
All engineers at my public US alma mater learned calculus up through differential equations and calculus-based physics was required.
This does not, unfortunately, mean that anybody graduates with a functional understanding of calculus...
We also learned calculus, just not in time for first year dynamics.
I should probably do something like dig up the curriculum. (University of Western Australia, 1988, bog-standard first year engineering.)