For gifted students who are bored at their own grade level, skipping a grade might seem like the easy and best solution. That is not always the case, though. Not every gifted or smart child really needs or wants to skip a grade. More than just the child's academic level needs to be taken into account when making a decision like this.
One of the biggest things that needs to be taken into account is the child's maturity level. Yes, every parents wants to believe that their child is more mature than most children their age, but that is not always the case. A leap from one grade to another can be a huge difference, especially in lower elementary school where the children's maturity level changes a lot between grades. Maturity level is something you should really look at, especially if the child is already one of the youngest in his or her grade. Be honest with yourself about the child's maturity level. You are only hurting the kid if you send them to a place that they are not mature enough to face yet.
You may also want to consider if there are other programs that the child come become involved in that will keep the child from getting bored. Maybe the school offers a gifted program for the students, and the child can do this. Maybe the teacher is even willing to allow that student to do slightly different work in a subject or two. For example, maybe the child could have a math book that he or she works on while the other students do the regular math. This student can then come to the teacher for help if he or she needs it. If there are a few gifted students who are bored with the work on their grade-level, they could even work on the work together, supporting each other as they need help. An alternative to this is to see if the student could work as a peer tutor or help the teacher in some way to help the students who don't understand the work. Of course, these solutions take some cooperation on the part of the teacher, but they might help your child.
Before having a child skip a grade, especially in the younger elementary school grades up through about fourth grade, have the child associate with other children who would be their classmates. See how the child interacts with other children who are that age. You may find that they fit in with children their own age better than they do with these children, or maybe the child will connect better with these children than he or she did with children their own age. Also, have the child try schoolwork that is on that level. Although schoolwork on their own grade level might be easy for them, something a year ahead might be hard for them to grasp, especially if things like fractions, multiplication, parts of speech, and other subject have been learned in that year period. More than anything, it might be a matter of waiting for the schoolwork to catch-up to the child's level. This may not happen at the beginning of the school year. The child may have to wait a few weeks or even a month or two. In the end, you will probably find that it's better for the child to be ahead of their peers than to be behind them.
Another thing to consider is what this will mean for the child a few years down the road. What might seem like a good idea when the child is six or seven might not seem like such a good idea when the child is 16 or 17. The child may not want to grow-up that quickly. The child may want to be able to be a child for an extra year or two. They may resent the fact that when they are 16 instead of worrying about their high school grades and getting their driver's license they have to worry about living on their own miles away from home in a college dorm and the pressures of drinking without Mom and Dad there to support them.
I think there should be some serious consideration of all the consequences before a student decides to skip a grade. This should be something the student, the parents, school officials, and others involved in the issue should think about seriously before deciding that it is the right decision. All too often the child is unprepared for the change and just ends up worse than they would have been if they had stayed in their original grade.
When I was a senior in high school, I knew a girl who was a freshman. She had skipped a grade, but I think it was one not a wise decision. She was already one of the youngest in her grade, so she was about two years younger than some of the oldest people who were now her classmates. She was immature and always trying to impress people in ways that are cool when you're twelve and thirteen, but aren't so cool when you're in high school. She struggled with fitting in and with her new peers, and she found that the work was harder than she had expected. No, she didn't get horrible grade, but she also wasn't Honor Roll material either. Just because academically someone can skip a grade doesn't mean they should.
There are times, though, when skipping a grade is the best decision for the child. If the child is mature enough to move up a grade (or two), can really handle the work at that grade-level, connects well with those peers (maybe even better than they would with peers their own age), you feel that years down the road you won't regret the decision, and the family feels good about the decision, after careful consideration and discussion, allow the gifted child to skip a grade. It may be a great decision, and it may help to keep the child from getting too bored.