Nature v. nurture. Age-old debate on relative importance. Not gonna settle it here. Not even in the limited context of factors influencing mathematics success.
There is lots of interesting research going on, of course. I want to tell you a quick story about a very small subset of that research.
A few years back, a group of educational psychology researchers published a study that phys.org headlined, “Math ability is inborn“.
The study investigated the ability of 4-year olds to choose the larger of two sets of dots when these sets were viewed briefly (too briefly to allow for counting).
They found that children who were better at this task also knew more about numeration and counting.
A quote from one of the researchers, Melissa Libertus:
“Previous studies testing older children left open the possibility that differences in instructional experience is what caused the difference in their number sense; in other words, that some children tested in middle or high school looked like they had better number sense simply because they had had better math instruction. Unlike those studies, this one shows that the link between ‘number sense’ and math ability is already present before the beginning of formal math instruction.”
Read more at: http://phys.org/news/2011-08-math-ability-inborn.html#jCp
Let’s pause for a moment to think, shall we?
If a child has not had formal instruction in mathematics, is the only remaining possibility that her mathematical performance is due to innate skill?
Of course it isn’t.
There is also the possibility that the child has absorbed some mathematical knowledge from her environment, and that different environments might provide differential input.
Maybe the child who is better at discerning the larger set has more practice doing just that. Maybe that child’s parents have been asking her how many? how much? and which is more? for the last two or three years.
Maybe that child’s parents have been Talking Math with Their Kids.
Overthinking my teaching 
Chris,
Annie Murphy Paul just posted something on the importance of talking math with kids that you might find interesting:
http://anniemurphypaul.com/2014/01/the-importance-of-talking-math-with-kids/
-mike