Mathematics requires an exact and expert hand. They are EMTs. This of your Calc 1 mid-term: "Quick, you have two minutes, resuscitate this equation!"
For example, why does C have a separate short and long data types, but javascript just has "var"? Because when C was made, memory was at a premium. When javascript was invented, everything could be a 4-byte value.
The point is, "Do we want to spoon feed sciences?" Looking at what we, western society, boil into pablum to get people to pretend to comprehend, in my opinion, causes more problems than helps. It gives a false sense of understanding, like the solar system model of the atom.
Having said that I concede that there is no reason to purposefully obfuscate sciences and higher level math.
Concepts like calculus, unfortunately, wait until high school or college, so it's being thrown in the river without ever having swum. Sure, some people survive, but most people end up having an aversion to math/science which leads to innumeracy and a host of other problems.
Kids could be taught the basic ideas (like the circle -> triangle) just as a way to get thinking. Later, they can cover them more rigorously, but they've had experience doing integrals on their own.
Even the solar-system model is "ok" to start with, and later you explain about probability distributions etc. You don't want to jump into quantum mechanics without covering Netwonian Physics (which, technically speaking, is "incorrect but useful").