I "knew" enough calculus to get good grades in math courses through high school and college as an engineer.
But I didn't really "know" calculus until I read a book not too dissimilar from this one, "A Course of Pure Mathematics" from 1908 (!), which constructs calculus up from number theory (I think the fundamental theorem of calculus comes halfway through the book?). From that point it's impossible to forget.
As for why it's not taught this way today, I'd blame our testing regime and large classrooms, which incentivizes temporary memorization of key formulae and knowing where to mindlessly apply them, over deep/lasting/semantic understanding. I'd also blame the fact that we have a different maths teacher every year, so students come in with heterogenous understandings of the pre-requisites for the next year's material, so the first part of a section is spent reviewing + consolidating.
It takes maybe 10-20% more time to get a rich understanding of the subject that lasts a lifetime. But we value compression and instantly-measurable results more than actual learning. :/
Encountering material like this makes you really happy, but it's kind of bittersweet because it makes you realize that the modal state of modern pedagogy is pretty abysmal.
But I didn't really "know" calculus until I read a book not too dissimilar from this one, "A Course of Pure Mathematics" from 1908 (!), which constructs calculus up from number theory (I think the fundamental theorem of calculus comes halfway through the book?). From that point it's impossible to forget.
As for why it's not taught this way today, I'd blame our testing regime and large classrooms, which incentivizes temporary memorization of key formulae and knowing where to mindlessly apply them, over deep/lasting/semantic understanding. I'd also blame the fact that we have a different maths teacher every year, so students come in with heterogenous understandings of the pre-requisites for the next year's material, so the first part of a section is spent reviewing + consolidating.
It takes maybe 10-20% more time to get a rich understanding of the subject that lasts a lifetime. But we value compression and instantly-measurable results more than actual learning. :/
Encountering material like this makes you really happy, but it's kind of bittersweet because it makes you realize that the modal state of modern pedagogy is pretty abysmal.