When I took calculus getting the area of an irregular object blew my mind. Its important for engineering/structural shapes though.
EVERYONE should take an advanced math, not that they would actually use the formulas; rather it trains the brain to create new neural connections for analytical/critical thinking.
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.
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
When I took calculus getting the area of an irregular object blew my mind. Its important for engineering/structural shapes though.
EVERYONE should take an advanced math, not that they would actually use the formulas; rather it trains the brain to create new neural connections for analytical/critical thinking.
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.
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