[orangeoxidation]

> I tried to, as much as time permitted, give the historical context for the math I was teaching.

This is great.

Funny how teachers generally aim for their students to 'understand' instead of merely 'replicating' (from memory). Yet math is often taught as a complex, fully formed system (especially in university).

Teaching math along the same path / outline it was historically developed teaches the 'why' alongside the 'how'.

[VyseofArcadia]

Exactly. The why is missing. The how is inadequate in a vacuum. Bright students make the connection on their own, but the others, even highly motivated ones, get left behind.

To make the problem worse, quite a lot of my former colleagues don't know the why themselves. They've always thrived on abstraction, and are unable to understand or help when motivated students come to them seeking the why.

Bit of a chicken and egg problem, really. The professors who made it did so without the why, and therefore don't understand the need for it.

I'm as guilty as anyone. I couldn't tell you much about where my PhD research came from and why. At least my calculus students got some context.