I am late to this post. Going back to TexasSummer comment about engineering math tgught him the "whys", engineering requires applied math. I started in premed and took calculus, but then switched to enginnering and had to take applied calcullus in the spring to make up.

I think teaching physics is a good way to teach applied math. My opinion. I think of physics as applied math, chemistry as applied physics etc. And there are many simple experiments to do in physics that help with math.

Ren