Stanford comes this study looking at the difference in brain fMRI patterns of 2nd vs. 3rd graders working on arithmetic.
It turns out a lot of differences can be seen in just one year - and accompanying greater accuracy and quicker reaction times, are changes in several brain areas that suggest that math is done by large scale brain networks interacting with each other rather than a single location for 'math'.
As the developmental steps for problem solving become clearer, expect more developmental guidelines guiding curriculum. Working memory (visual as well as verbal) also takes quite a while to develop (see here). Being able to know where a student is starting from the cognitive standpoint makes the educational process all that much easier.
Working Memory, Math Performance, and Math Anxiety
For math tips, check out some of Marilyn Burn's articles here.