Calculus helps define the underlying rules for the higher-level (simpler by appearance) math we use daily. "I know, I can solve this with calculus!" is unlikely to ever come up, but the vague idea that there's something there you can dig into when you need to can be helpful in rare edge cases, where other people might be lost.
An example using programming languages: If all you've ever been exposed to was python, and no CS, you may never have considered why using "insert" on a list may be slow. Python presents it as a single function call, so you probably think of it as a single operation and don't go any further. That's the equivalent of the higher-level (simpler by appearance) math. But if you've been exposed to something lower-level, like C where you may well have implemented "insert" yourself on an array, or general CS concepts where you had to use big-O notation, you'll probably have in the back of your mind "yeah, that's not a single operation, it's doing more stuff in the background". Usually not something you need to think about, until you hit that edge case where it's suddenly running really slowly.
Remember very early on in education when you had to memorize various equations like area of a circle? Those equations can be generated from basic calculus. One I could never remember was area of a sphere, until one day when I was bored at my part-time job, found a pencil and scrap of paper, and decided to see if I could use what I'd just learned in class to derive it. And it worked, and I've never forgotten that equation since, because instead of it just being a series of numbers and letters to memorize, each part now has meaning.
That makes sense, but suggests that calculus is perhaps the most difficult concept to wrap one's head around, which flies in the face of the idea that is easy to teach to children. It is not clear where the breakdown occurs here.
Calculus is not easy to teach to children. We fail to teach it adequately to most college students in their first two years of study. Even a few historically noteworthy mathematicians failed their first contact with the subject.
Elementary linear algebra is far easier to understand and motivate. We can deal with finite, concrete examples without having to delve into the subtle complexities of limits, continuity, and infinity.
That statement was clearly false. With an amazing teacher, an extremely bright student, focus, patience, time, etc., sure we can have the next Galois… but in the vast majority of cases, we should avoid setting kids up for failure by expecting them to easily grasp things which took humanities greatest minds centuries to grasp. Newton “invented” Calculus in the 17th Century, but these ideas had been percolating since Archimedes and even before going back two millennia.
Calculus helps define the underlying rules for the higher-level (simpler by appearance) math we use daily. "I know, I can solve this with calculus!" is unlikely to ever come up, but the vague idea that there's something there you can dig into when you need to can be helpful in rare edge cases, where other people might be lost.
An example using programming languages: If all you've ever been exposed to was python, and no CS, you may never have considered why using "insert" on a list may be slow. Python presents it as a single function call, so you probably think of it as a single operation and don't go any further. That's the equivalent of the higher-level (simpler by appearance) math. But if you've been exposed to something lower-level, like C where you may well have implemented "insert" yourself on an array, or general CS concepts where you had to use big-O notation, you'll probably have in the back of your mind "yeah, that's not a single operation, it's doing more stuff in the background". Usually not something you need to think about, until you hit that edge case where it's suddenly running really slowly.
Remember very early on in education when you had to memorize various equations like area of a circle? Those equations can be generated from basic calculus. One I could never remember was area of a sphere, until one day when I was bored at my part-time job, found a pencil and scrap of paper, and decided to see if I could use what I'd just learned in class to derive it. And it worked, and I've never forgotten that equation since, because instead of it just being a series of numbers and letters to memorize, each part now has meaning.