"Most mathematicians did not just take up math as a "job"...(most) get more pleasure out of mathematics than almost any other activity. And they often discovered this pleasure when they were young..."
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.
Numbers Kids The numbers kids are perhaps the easiest to recognize - and they often come from families where one or both parents have a special affinity to mathematics (engineers, computer science, academics). It may start out with children interested in patterns and facts within mathematics (divisibility rules, cube roots, etc.), card and other games, recreational math topics (Fibonacci sequence, fractals, probability, solving problems for 'fun') or mathematics in the world of adults (e.g. Philip Davis' cousin who let him be bookkeeper at the age of 7, keeping track of a race horse's handicap and winnings).
Tinkering Kids Tinkering kids tend to enjoy conceptual science books, building and unbuilding (gears, taking apart ball point pens and toys, clocks, cameras, origami etc.), computer-related activities, projects (completed and incomplete), and beautiful and unbeautiful design.
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.
Silverman and Feldman have distinguished engineering / math-gifted individuals into sensor (likes facts, data, experimentation) and intuitor (prefers principles and theories) groups. Both were capable of becoming "fine engineers", but sensors with less direct success in traditional academics.
Recently, some investigators have begun to look at brain-related differences in mathematically-gifted students (to our knowledge this has not been done in professional mathematicians, engineers, physicists); in his study of mathematically-gifted adolescents, Michael O'Boyle has found that superior mathematics performance was correlated with increased bihemispheric activation (vs. unilateral activation) for mathematics tasks, enhanced involvement of the right hemisphere for information (including linguistic) processing, and strong prefrontal cortex activation. As seen in the figure above, math-gifted adolescents performing mental rotation tasks activate much more brain bilaterally than average math-performing peers.
The optimal educational pathways for young math thinkers may also vary widely. Some thrive with subject acceleration, while others plenty of free time to explore topics of personal interest - whether conceptual or technical.
Perhaps the most common feature seen in young mathematical minds is their interest is solving problems. If you have a young mathematical mind in your house and he or she hasn't seen the PBS special on Fermat's Last Theorem, check it out.It's great - sort of what Race for the Double Helix is to budding scientists. The PBS video on Fermat's Last Theorem (Youtube.com)
From Andrew Wiles:
" I loved doing problems in school. I'd take them home and make up new ones of my own. But the best problem I ever found, I found in my local public library. I was just browsing through the section of math books and I found this one book, which was all about one particular problem—Fermat's Last Theorem. This problem had been unsolved by mathematicians for 300 years. It looked so simple, and yet all the great mathematicians in history couldn't solve it. Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it."
Learning Styles in Engineering Students
Discovering Mathematical Talent
Cognitive Profiles of Mathematical Precocity
Interhemispheric Interaction in Mathematically Gifted Adolescents pdf
Developing Mathematical talent
Parental roles of mathematically gifted students pdf
Aha Moments in Math
Fermat's Last Theorem
Autism occurs more often in the families of physicists, engineers, and mathematicians pdf
Education of a Mathematician