The way most people with the ability visualize a warp is...

[He makes a vague hand gesture, trying to find the words.]

You don't entirely visualize the item ever leaving your hand. It's not simply that I throw a spoon and appear at the end - I move with the spoon in the first place.

And it is less teaching than sharing - the bond of magic involved is permanent and draws off my strength as much as the recipient's.