The other day, I happened to visit our local homeschool bookstore on an evening, when kids are not allowed. It was a fabulous time to relax and browse the used curriculum, but there were not a lot of people around that evening.
The one employee must have been quite bored, and we started a brief conversation and somehow got onto the topic of whether I have any gifted kids.
Of course, every parent thinks their kid is gifted in some way, and all kids do have a special gift, but I knew that he was talking about academically gifted. So my answer was, yes for both of my kids, but not really, since my kids are still little. Here's the thing, kids that are in early elementary school can very easily be gifted in some areas and incredibly far behind in others. So, while my almost 3 year old talks very well and knows most of his phonics, all his shapes and colors, counts to 14 and can do basic addition, that doesn't mean that I'm signing him up for Kindergarten next year. Kids don't need to be pushed to learn, they will learn on their own (the only thing I've "taught" him is when he wants to do his "reading lesson" like brother, I will pull out his phonics book, but he's only made it through lesson 10 because he's not ready for blending yet, so most of the phonics he's learned on his own).
So why not start Kindergarten early and let them keep learning at this blazing pace? Doesn't the world need more doctors and engineers? Well, certainly that's true, but the problem is, that if you let your child's pace stay blazing they will soon get too far ahead of themselves. They will start to hate math, science, reading or whatever their previous favorite subject was. Then, if you keep pushing them to continue in those subjects, you're going to face the sad realization that they are a burnt out 16-year old in college who has no idea what they want to be when they grow up.
I was a gifted homeschooler. When I was getting ready to enter private school, my parents allowed me to help make the decision of whether I wanted to go into 5th grade or 6th grade. Age-wise, I ought to have been in 5th grade (although I would have been one of the oldest, with a November birthday). Academically, I probably should have been in 7th grade.
What did I choose? I chose 5th grade. I wasn't ready for the boys and make-up and changing classes, I needed a gentle transition to a more traditional school.
There may have been a few times that I regretted it, like when I had to do math class by myself (after a few weeks of being bored by 5th grade math when I was already doing pre-algebra). But there were plenty of times when I didn't regret it. I was in the right place socially, and that made all the difference. Fortunately, when I got to public school there were more options. At my public middle school, the magnet program allowed me to take Future Problem Solvers of America as my English class, and "test out" of my math class to go play in the computer lab. I was frustrated by having to sit through "reading" class, but I only had to earn a certain number of points, so I read Crime and Punishment because it had the most points available for passing the test. In high school, I was accidentally put in a "regular" biology class the first year, which was a bit scary, but they fixed my schedule pretty quickly.
I took my share of AP classes, but when I started feeling burnt out my senior year of high school, the principal allowed me to get out of AP Calculus BC and switch to a more fun elective instead. I almost regretted it in college, because I turned 19 just after starting college, so wouldn't my "whole life" be over by the time I graduated? Actually, college only takes 3 years if you have enough credits. The only "intro" classes I had to take were a required Bible class, PE, one "art" elective, statistics, and World History (I had US History credits, but not world history). Even then, I didn't have to be bored in my Bible class, because they let me take Poetic and Wisdom Literature instead of New Testament or Old Testament.
I graduated at the reasonable age of almost 22 and had my whole life ahead of me. And, I still don't know what I want to be when I grow up!
So, don't worry about what to do with your gifted students. Of all the people to "unschool" gifted students are actually the best example of when it may be okay to unschool. I don't teach reading to my Kindergarten student, because he already knows how to read. I keep him "on track" in math, but he's already teaching himself most of next year's concepts. That doesn't mean that I have to go on to second grade math with a barely 6 year old. I can keep him at his own level, and he can learn whatever else he wants to on his own time.
Keep learning fun, for your child and you. You certainly don't have to "hold them back" but you also don't need to buy a more advanced curriculum until they are at least in later elementary (I cringe when I hear parents are buying "the next" curriculum because their child finished a math workbook).
Explore math concepts through play. Read for fun. Do science experiments regardless of your child's age or knowledge level. Take field trips. Play outside. Let them learn a sport. Find an art or music class. Have them help cook a meal, plant a garden, clean the house. There are all types of learning that take place, not just "regular school". Your gifted child might really grow up to be an engineer, or they may grow up to work at a coffee house and self-publish their own music. Both options are equally valid, if they are fulfilling their purpose in life. Try not to pigeonhole them too early, just because they are "gifted".