Every math teacher can tell you about a few.  Every student knows a couple.  Many parents claim they have one.  The really, really smart-in-math kid.

We know them when we see them.  These kids learn concepts quickly.  No lengthy practice sessions necessary.  “Got it.  Let’s move on.”

They’re curious.  They see math everywhere.  They notice patterns in everything – nature, architecture, music, human behavior.  Their favorite question is “Why?”

They’re persistent.  When they set their minds to figuring out a concept or a puzzling challenge, they focus on it, try many hypotheses, and keep striving, analyzing, and testing until they figure it out.  They love to ask, “How?”

They’re deep thinkers.  They’re not satisfied with just memorizing.  They want to understand why a formula works, why a problem can be solved in many ways, and which way is the simplest and most elegant.

Sometimes they’re “gifted,” where their special acumen comes naturally, without work. Like, well, a gift.  It’s “given” to them.   

Sometimes they’re “talented,” ready to work hard and put in time and sweat.  Not necessarily the same as gifted, but just as valuable.  (Some say even more so.  Perhaps we value what we work for more than what’s given to us.)

If you know a really, really smart-in-math kid, and you’re wondering what you can do to help her along, here are a few ideas I’ve learned from experience and from some really, really smart math teachers.

1. Enrich.  Encourage the deep thinking that often comes naturally to these kids.  A constant barrage of “Why?” questions might become exasperating, but think of them as signs of curiosity and cognitive growth.  You don’t have to provide all the answers.  Sometimes answering a question with another question is a good strategy.  “Why do you think the seven-times-tables are harder than the two’s?”
2. Accelerate.  Every teacher knows the value of picking up the pace for those students who “get it” right away and need to move on before they succumb to boredom or mischief.  Have puzzle books, stimulating games, and other brain-exercising activities around the house for those “I’m bored” moments.
3. Stretch.  Challenging his imagination and curiosity with a question that requires him to stretch his abilities can lead to all kinds of new skills and knowledge.  Just as kids need to stretch their bodies daily, they need to stretch their brains.
4. Group.  Put a bunch of like-minded kids together in a room, give them a problem to solve, and then get out of their way.  Watch the brain power in action, the ideas fly, and the possible solutions emerge.  Notice how the math group may be different from the writing group, which may be different from the music group and the art group.
5. Talk.  Support him by talking about what interests him.  Encourage him to talk about the math questions he’s curious about.  Ask him to “teach” you what he’s learning. 
6. Play games.  There are lots of games especially appropriate for super-smart kids.  Here’s a website I like.
7. Play with toys.  Same with toys.  Try this website for ideas. 
8. Branch out.  Encourage her to learn about other subjects into which she can sink her teeth.  Math-smart kids are very often perfect fits for technology, music (there are those patterns again, right, Herr Bach?), science, and engineering.  Don’t forget writing, painting, and other arts.  They’re all connected through precision, problem-solving, and expression.
9. Get a tutor.  Sometimes a talented tutor can make a huge difference.  Someone who’s an expert in a particular subject, someone who can inspire excellence, someone who’s maneuvered the obstacles.  A little individual attention, a little motivation, a little guidance.  Try a National Honor Society high schooler.  Try Sylvan.
10. Research.  There’s no shortage of information, research, and resources.  One of the best is the Johns Hopkins University’s Center for Talented Youth .

A word of caution.  Balance.  Don’t push too hard.  Even the quickest elementary school kid probably still needs the cognitive development and maturity to tackle the highest level math and understand it.  Just because he can memorize and go through the motions doesn’t mean he’s ready for advanced algebra and geometry.  Follow your common sense and his behavior.  He’s a kid, remember.