When I was an elementary student, I'd suffered from understanding basic things like multiplication table and other simple things and I had to memorized them. Last hours I was searching for genesis of multiplication table for the first time (I was curious, If that wasn't folded by experience or observation, So how was multiplication table made?). After this question, I remembered my childhood whom I had been struggled with the most basic things and even I didn't know intuitively some of them currently.
I don't know much about the effect of IQ in rate of learning math or same stuffs, but my questions are:
Have you experienced or observed same thing as this situation that understanding and intuition of sophisticated subjects like abstract algebra or topology are simple for them, But They cannot perceive the simple things?
Is there any correlation between mathematical intelligence with presenting question from objects and awareness from what we don't know?
I'm a Computer Science undergraduate and I'm familiar with mathematical logic, Axioms and such things.
Just my 2c, from my anyway limited experience in/about teaching basic mathematics:
As for understanding, understanding division is especially difficult for kids, but persistent problems usually boil down to how capable to teacher was. (Except for extreme cases, most pupils are in fact capable of basic mathematical reasoning if properly guided/introduced to it.)
As for memorizing, that is also part of that learning, the practical part: the multiplication table and even the addition table before it, otherwise we get students that cannot even add small numbers without counting on fingers...