We homeschool for this very reason, because the public school system has failed us. I have studied early childhood and primary school teaching at university and knew the signs of giftedness and talent when they popped up.
Instead of being seen as gifted at school, my son (although on par with a gifted girl in his class) was seen as a trouble maker with behavioural problems. He is now 10 (year 5 level) with the ability to work at a year 7-8 level in a lot of areas (confirmed by the board of studies representative who assesses us). He was reading and writing before he started pre school. He is very mathematically and scientifically minded, and has shown a keen interest and understanding in computer programming.
My daughter is 7 and academically is also advanced in most areas, but falls behind in maths. She is much more creative than my son, writing lengthy stories, making elaborate artwork and has a keen interest in performing arts (she started ballet at 2, and tap dancing at 3.5)
My 2nd son has just turned 5 and has been computer literate since about 2.5 yo. He is mathematically bright and already has a solid understanding of basic fractions. He also understands different sums that have the same outcome. He is able to write all of our names without being told how they are spelled and has been able to count to 100 for about 2 years, by ones, twos and tens. He solves math problems in head, even ones his sister can't do.
My 3rd son is almost 3 and also started TTing at 16 months. He has amazing hand eye co-ordination, and can play many video games that I can't even complete!! He has a very extensive vocabulary and tells great stories. He has wonderful recollection skills and can tell you something that he told you 6 months ago, exactly the same way. He is an amazing swimmer - he was put up to a 4 year old level at just under 2 years old.
My 2nd daughter is not yet 9 moths old, but already shows signs of early swimming and is trying to stand and walk (but I attribute that to her wanting to keep up with her older siblings!) At this age, I'm not really looking for signs from her.
Socially, we meet with other home schooling families, where they kids don't feel the need to be anything other than themselves (nobody hassles anybody else for being smart etc) and we do extra curricular activities such as swimming and dance, and we are looking to start music classes too.
I think the most important thing is to encourage your child/ren in the areas that they show interest in, not just try to "make them" reach their full potential. As Kaz said, they can easily become distracted, or find things difficult, if the interest isn't there. I avoid specialists and experts and follow my instinct and my kid's lead, cause I don't want them to end up like me - at age 4, I was tested and deemed to have the IQ and capabilities commensurate with a 14 year old. I was pushed (not encouraged - there is a difference!) and had finished primary school (per se) by 5th grade, but skipping grades was relatively unheard of back then, so I spent alot of time doing teacher's assistant things (leading reading/math groups etc) until I was tested and accepted into a selective high school, by which time I'd simply given up and taken the attitude that it was easier to do nothing and come last than compete with 149 other kids to come first!
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