My 5 yr olds do recreational gymnastics. They love it.
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If they DO want to be on the team later, fine. But not until they are 8+ or so and UNDERSTAND better the time and financial commitment. If they still like gymnastics at 8- then they are absolutely invested in it and worth a try.Â
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Before 8-- eh. I would probably wait. I want them to have time to rest, play, hang out with friends (not just ones in gymnastics), and explore other interests. Not to mention it is pricey.Â
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Our local gym requires a year commitment to team. That is a lot. My 9 yr old niece is on the team and has wanted to not go several times (after doing gymnastics for the two years previous). She enjoys it, but really 6+ hours and the weekendful of team events, school, girl scouts....etc leaves her tired all the time and overscheduled. On gym nights she has practice is 4:30 -8 (with a dinner break) so is in bed after 9:30--- then has to get up at 6 for school. Not enough sleep for a 9 year old, nor  anytime for homework (she is done w/ school at 3:45 and goes straight there).It is also pricey for uniforms, team sweats, etc.
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I just think 6 is too young to make that large of a commitment (no matter how much they enjoy it) to one specific thing. It really should be an age to explore many options and learn how to navigate  new friendships, school, etc.
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Try recreational gymnastics for another year or so and see if she is still interested- then try a year on the team. I am not saying no to teams - some kids really enjoy it and it provides scholarships, part time jobs, etc for older teens that are successful at it. Gymnastics teach some great skills and older kids can really benefit from learning how to balance school/gym/play and have a high sense of responsibility and teamwork. But really, 6 is young.
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Another thought is to consult your Pediatrician. Our niece has had splinter breaks in her wrists from gymnastics. It is hard on her body and she is still growing. Not that young athletes dont get injuries (they do) but you need a good Dr and dedication to the sport to make sure that everything possible is done to reduce/avoid injuries. Some Coaches are just better at this than others- esp with their youngest athletes.