> Visualizing something, in three dimensions, can help you with a concrete “hook” that your brain can grasp onto and use as a model; understanding then has a physical context that it can “take place in”.
I'm still sore at the educational system in my country (Serbia) for ignoring and occasionally discouraging this kind of visual thinking. Remembering words and reproducing them at the time of examination was rewarded far more than constructing a mental model of how things work at the abstract level, and then deriving conclusions from that. Some teachers were exception, of course, and I remember them vividly and fondly to this day, but the rest are like some amorphous gray mass that barely existed somewhere in may past.
I still remember being told to memorize the Schrödinger's equation in high school, before we even covered, let alone understood the underlying maths. And I still don't. The funny thing is that this teacher was one of the "good ones" and she actually apologized to us for forcing us do this. But her hands were tied by the teaching "plan and program" that was obviously created by a committee whose members didn't talk to each other.
At the university (maths + CS), we would write-down (to our notebooks) the computer programs scribbled onto the blackboard by the professor, then memorize them for the exam, which was taken on paper. Nobody ever asked any questions. I still remember a colleague who didn't understand the concept of a pointer. That was in the third year and she had good grades.
I honestly hope things have improved in the meantime (the above was in the '90s).