[wslh]

> But wrapping their head around algebra and trigonometry and making them conceptually "think" about them was extremely hard.

You should abstract these concepts in some way. For example, when you are moving an object in 3D you don't need to spend time projecting 3D objects into a 2D display using linear algebra. You just set the x,y,z coordinates and the engine does the hard work.

[jcelerier]

> For example, when you are moving an object in 3D you don't need to spend time projecting 3D objects into a 2D display using linear algebra. You just set the x,y,z coordinates and the engine does the hard work.

but setting x,y,z coordinates so that they do the kind of motion that you want is exactly where you need linear algebra.

Say you want to make a ball move in a spiral motion, how do you do that, from code, without students understanding algebra and basic operations like "translation on a plane" ?

[mikepurvis]

As a young kid doing qbasic, everything moving around on the screen was x/y/xchng/ychng. The watershed moment for me was in highschool and suddenly recognizing that sin/cos were how to get from polar to cartesian, and atan2 was how to go the other direction. A week later my little platforming arena shooter had heat-seeking missiles in it.

I think a big part of the problem is a failure to emphasize the right stuff. I always see trigonometry presented in terms of all six functions and arcfunctions and the relationships between them— this is a bunch of abstract stuff that most people don't care about and will never need; it's nuts to present all of this at once when the small piece of it needed for polar coordinate operations is so immediately and obviously useful.