Maybe I just got lucky, but that's pretty much exactly how I remember being taught in high school calculus class. No ODEs or anything of course, but the teacher started from the geometry, then moved to the trig functions and identities, and finally to derivatives and Taylor / Maclaurin series.
It's a good post, and I agree--there is just no hope in getting students to develop any kind of intuition in math without starting from something really simple like the geometry of the problem. Plus, it's way more fun!
It's a good post, and I agree--there is just no hope in getting students to develop any kind of intuition in math without starting from something really simple like the geometry of the problem. Plus, it's way more fun!