I'm not an expert on gifted kids, by any means. I'll leave that to the professional educators and psychologists. But two of my three sons are Gifted, as identified by state standards in Pennsylvania. My husband and I have been through the process of having them tested and qualified for services. And we deal daily with the challenges and rewards of raising sons who are more than just "smart" or "bright."
There are many definitions of what makes a kid Gifted. Generally, if kids score over 130 on intelligence tests, are working more than a couple of grades above their age levels, or they generally function on an adult level, they may be gifted. And parents need to know that gifted kids qualify for special education services, just as kids who may have learning difficulties do.
Here are my thoughts on some things parents might want to think about and discuss with each other, teachers, and school psychologists if you suspect your child might be gifted.
Find out what some of the early indicators are. We learned that gifted kids often talk very early. This was true in my sons' cases. They literally talked before they walked. Others read very early, or are able to do math, without actually being taught addition, subtraction, etc. One of my favorite sites for information about gifted kids is http://www.hoagiesgifted.org/. They have lots of tips to help you make an initial determination as a parent. Other good sites are listed here: http://www.ri.net/gifted_talented/parents.html#General.
You would think gifted kids would love school. We learned this isn't always the case. Often, because they learn so quickly, gifted kids get bored. They may become disruptive. In the case of one our sons, his first grade teacher wouldn't give us the required recommendation for testing because she felt our son didn't "act like a gifted student" when he had verbal outbursts or doodled all over his papers. When he was tested, his score was exceptionally high. When he was given more challenging work, he behaved and focused much better.
Not everyone may agree with this, but I think you should talk with your child about whether they want to be evaluated to see if they're gifted. They may have concerns about being labeled, or pulled out of their "regular" class. Some may even think they've done something wrong, if they're suddenly pulled out of class, given tests, and have to speak with a school psychologist. I would never force a child into a gifted program. Encourage? Yes. Push? No.
Providing services for gifted students costs school districts money. So, parents often have to be very persistent to get the school to evaluate their child. Then there are lots of forms to be filled out and annual meetings with the gifted program educators who map out your child's GIEP (Gifted Individualized Education Plan). If you're not willing to put time into all this paperwork, your child won't be able to benefit from the services to which he/she is entitled.
In our house, we don't make a big deal about the boys being gifted. They go to their Challenge classes, where they get to do some cool stuff in a small group setting and where, with other gifted kids, they can feel comfortable expressing thoughts that many of their peers might not quite understand. They are expected to complete all their "regular" schoolwork - and do it well. And when they do or say surprising things - like linking seeming disparate concepts or events, or coming up with unusual solutions to problems or challenges, we love to ask them about their thought processes. They keep us on our toes. But really, just like having curly hair or enjoying sports, being gifted is just one small part of who they are.