Hm.
My dad taught me some light algebra before I took the sat when I was in 7th or 8th grade, I think I picked it up ok. I am very strong verbally and visually although pretty sketchy with actual computation. (At least one of our apples did not fall far from this tree.)
When I got to 9th grade to take it (again) it was soooo boring, it was one of the few classes I really hated. Geometry I have very much enjoyed and did well in calc.
OT, but on the 'manipulating shapes in space' thing, one real 'aha!' moment for me in school was in college chemistry class; the spectography just really clicked for me. I found myself raising my hand with 'wild' guesses about 'what molecule this is' and getting a lot right. Very bizarre.
