I find the topic of education fairly fascinating because having information which cannot be transferred to another is almost useless. However, something that goes hand in hand with education is the ability of the learner...both the psychology and physiology.
The Eide Neurolearning Blog had an interesting post on the differences between mathematical and non-mathematical minds. One paragraph, in particular, resonated with me.
While most people would agree that "math people" are not like "non-math people", it's not always easy for non-mathematical minds to recognize (and appropriately nurture) mathematical ones. The reasons for this are several - mathematical kids are often independent and internally-driven problem solvers who may or may not excel in the standard math tasks of the elementary school classroom (if he's such a math kid, how come he's getting C's on his timed drills?...) Many students with extreme talents in math may also be relatively verbal-poor, so are less obviously the "smart" children in class. Also they may be reluctant to show what they know or what they are interested in to relative strangers, and may have difficulty explaining how they arrived at answers. Many mathematical minds are dyslexic or twice exceptional in another areas, too, complicating their identification with standardized tests or screening tools. (Bold emphasis added by myself.)
This is a notion which I've always felt to be true but for which I've had no conclusive evidence. Through observation, however, it seems that many teachers, especially pre-high school, have a strong aversion to maths. Through my background and well as my children's, I have run into this time and time again. It seems that a commonly held notion among elementary school teachers is that a good mathematician is one who can execute arithmetic operations flawlessly. My experience, however, is that arithmetic is usually taught as a memorization exercise in schools. Thus, children who are more interested in the higher level view or abstract concepts describing how these operations work (and possibly have no interest in solving specific problems) are often viewed as being "bad at math" when they may be, in fact, extremely talented in the area. This probably follows along the lines that a student cannot be verbally gifted unless they are an adept speller, which is also generally not true. A person who can put together words in a meaningful way but cannot spell well is generally going to have an advantage over someone with impeccable spelling but who cannot communicate their meaning effectively.
By temperament, strong math minds will tend to be introverted and have high focus and task persistence for activities of intrinsic interest. This may mean they are difficult to direct in the traditional or even non-traditional classroom (prefer studying lines of own interest), and they may be benefited particularly by mentors (often relatives or math teachers at higher levels of education) willing to discuss topics, ideas, and problems far in advance of their years. (As before, bold emphasis added.)
This disinterest in following a teacher's plan for study will probably confound identification further. The student who is bored with concepts as presented and seems to struggle with "basic concepts" such as tables is generally not one to be identified as gifted and in need of additional stimulation or acceleration.
How does one identify students as such? There are, of course, traditional instruments. One possible way is to examine most standardized test scores. Several of them, especially Iowa Basics, break down math into further areas such as "math concepts" and "math operations". A student who places high on math concepts probably has a knack for math, regardless of their score in math operations. In fact, if there is a large disparity between the scores, this may be an indicator of a twice exceptional student: the student could be gifted in math but be fighting a learning disability.