I've seen arguments that calculus should be introduced earlier, like right after algebra. There's no reason why you need trig or geometry to understand the core ideas of rate of change, cumulative functions, and limits. I think a lot of people never get past the trig/pre-calc barrier and never really learn what higher level maths are like (no equation memorization, much more creativity) and have a completely wrong impression of math.
I think common core attempts to address that failing of math education. I know a lot of people don't like it and I'm not claiming that it's good, but I do think it's good at least that math educators recognize that people not really getting to see the beauty of math unless they make it to calculus is a good thing.
You could teach calculus principles without Trig. You just wont get very far. Ideally teachers early one would be hinting at what the fundamental concepts are of higher level math. Trig is only really required to solve specific problems since they have nice derivatives and identities.
No, it isn't. It's only required for taking derivatives of/integrating trig functions, which you don't care about before trig, and for using the identities to integrate some tricky functions.
It's required to make a good grade as it is taught today, yes. That's because it's traditionally taught after trig so they just go ahead and integrate it, but there's no reason why you couldn't teach it before and then, during trig, throw in how to differentiate/integrate trig functions as well as the useful trig identities that show up in integrating certain functions.
Trust me as someone half-way through an engineering PhD, as I said before, the core concepts of calculus do not require trigonometry to be taught. Rate of change, cumulation (integration), and limits can all be taught without trig. Hell, you can teach them all with just polynomials.
If you don't understand that, perhaps it's because you couldn't see the forest for the trees. If you came away from calculus thinking that it is closely related to trig in a special way moreso than other math topics (like algebra, logarithms, exponents, etc.) then the education system has failed you.
trig and geometry are super handy in the trades - building or making things or repairing them is made way easier with those math skillz built on arithmetic that is near instinctual.
calculus is a big shoulder shrug in terms of value in my life, but i viewed it as equivalent to reading the classics. our civilization is built on the stuff.
when i use real world stuff to show the power of math, people love the hell out of it. book learned math is like a cancer that ruins the whole field for most of us normies
I've seen arguments that calculus should be introduced earlier, like right after algebra. There's no reason why you need trig or geometry to understand the core ideas of rate of change, cumulative functions, and limits. I think a lot of people never get past the trig/pre-calc barrier and never really learn what higher level maths are like (no equation memorization, much more creativity) and have a completely wrong impression of math.
I think common core attempts to address that failing of math education. I know a lot of people don't like it and I'm not claiming that it's good, but I do think it's good at least that math educators recognize that people not really getting to see the beauty of math unless they make it to calculus is a good thing.
You could teach calculus principles without Trig. You just wont get very far. Ideally teachers early one would be hinting at what the fundamental concepts are of higher level math. Trig is only really required to solve specific problems since they have nice derivatives and identities.
No, it isn't. It's only required for taking derivatives of/integrating trig functions, which you don't care about before trig, and for using the identities to integrate some tricky functions.
It's required to make a good grade as it is taught today, yes. That's because it's traditionally taught after trig so they just go ahead and integrate it, but there's no reason why you couldn't teach it before and then, during trig, throw in how to differentiate/integrate trig functions as well as the useful trig identities that show up in integrating certain functions.
Trust me as someone half-way through an engineering PhD, as I said before, the core concepts of calculus do not require trigonometry to be taught. Rate of change, cumulation (integration), and limits can all be taught without trig. Hell, you can teach them all with just polynomials.
If you don't understand that, perhaps it's because you couldn't see the forest for the trees. If you came away from calculus thinking that it is closely related to trig in a special way moreso than other math topics (like algebra, logarithms, exponents, etc.) then the education system has failed you.
trig and geometry are super handy in the trades - building or making things or repairing them is made way easier with those math skillz built on arithmetic that is near instinctual.
calculus is a big shoulder shrug in terms of value in my life, but i viewed it as equivalent to reading the classics. our civilization is built on the stuff.
when i use real world stuff to show the power of math, people love the hell out of it. book learned math is like a cancer that ruins the whole field for most of us normies