All of a sudden my DD3.5 is acting very motivated for learning math and reading. Instead of me reading to her at night, she wants to play learning games on the Ipad. She recently completed the math portions of TeachMeKindergarten, and has made it a goal to finish the reading portions as well. She is also working her way through TeachMeFirstGrade. Last night she was clearly over-tired (a new girl at daycare wakes her up during nap time), and couldn't concentrate enough to reliably get correct answers. I told her it was time to stop.... and she threw a fit! It was terrible. She kept begging me to let her play. My rule is that if she cries for something, then she does NOT get it.
Normally I try to do everything I can to help her learn, as long as there is still enough time for everything else: trips to the park, riding her bicycle, pretend play, drawing, sleep, etc. My concern is to create a healthy, well-rounded girl. I don't concern myself with leaving anything academic for her to learn in kindergarten. Most of the advice I've seen on this site has directed me to worry about things 1 year at a time. At her Montessori preschool, they give her appropriate challenges, and assure me there is no limit to what she can learn in her time there. At the same time, her teacher makes a concerted effort to help DD with her shyness, and helps her deal with routine changes, to which she often reacts very negatively.
For each child there will be different priorities, but I think it's important to make sure that they feel challenged often. I don't want my daughter to become accustomed to a pace of learning that is effortless. Nor do I want her accustomed to being the smartest student in her class. At her school there is another 3 year old girl who is also doing addition worksheets, and they have become good friends. Plus, there are 6 year old students in her class doing multiplication, so even if she were the smartest child for her age, she is not the most capable child in the class. I hope that her new-found drive has positive roots. I hope she isn't becoming competitive... especially not with her friend.
I think the usual traps for gifted learners are laziness, poor study habits, disorganization, and insecurity. The first three all stem from expectations that are too low. The last one comes when children value their position as the smartest child in class as a necessary part of their identity. They fear losing that position, or being outsmarted, especially publicly. These insecure students refuse to ask questions in class, because asking a question implies that they don't understand something. If anyone else in the class does understand it, then their position is threatened. This, of course, is not the optimal way to learn.
So, to summarize, I suggest enriching your child (academically and otherwise) at every opportunity. Keep him challenged, allow him to work well ahead of the pack, but don't let him define himself as the kid who is more advanced than all the other kids.