"Clearly, our calculus course does not prepare scientists in other fields to recognize, understand, and utilize the calculus that many of their fields are based upon. Thus, when it comes to calculus, we don't get it the first time around, our colleagues don't get it, and our students are still not getting it. It's no wonder that one of the most common occurrences in higher education is that of a non-mathematics faculty member discovering that something they were doing is calculus. And at the very least, we feel justified in asserting that there still is a crisis in calculus instruction." - Jeff Knisley
While I don't endorse all of Knisley's views, I think his statement says a lot about the state of calculus education, but more than that, it says something most academics don't like to hear: The calculus they have been using is flawed. In fact, the foundations of mathematics as currently taught are also flawed.
Note he admits they don't get it. They never did get it. It's one thing to learn how to use theorems and results, but entirely a different matter when it comes to understanding. How can there be real understanding if the foundations are flawed? How can anyone really understand calculus when it is based on ill-formed concepts and definitions?
Well, the answer is no one can. One of the powerful features of the New Calculus, is that it is easy to understand. It does not require years of study to master. Moreover, it is both simple and elegant at the same time. There is much one can do with the New Calculus that is not possible using the existing flawed formulation. How can you know for sure? Study it! :-)