A few of the top problems I find myself having to fix with poor back handsprings are:
1. Head position: are you keeping your head in a neutral position or thinking of keeping your chin tucked in throughout the skill? I know most kids learn to, but you should never be watching your hands in a tumbling skill like a back handspring. If not that usually results in the second issue...
2. Entry into the skill. Many of the kids I have to fix tend to jump back and through the handstand instead of up and over into the handstand position. Which can be caused by a number of things. Throwing your head back and not getting your arms up to your ears fast enough and not actually leaving the ground before landing on your hands.
3. In my experience anyone having problems with their back handspring *kind of* be doing a back handspring but the fact is that they are not landing in the handstand position. If you don't land is a handstand you can't block. Or at least you'll block but it will be too late because you're body will have completed most of the flip already by that time. And you end up landing super long and unable to rebound.
Sometimes you can get away with little things, but more often than not if you're learning or trying to improve its because you're trying to get away with too much.
Have a coach watch you do both skills they should be able to see what you're doing wrong and help you correct the problem; which if you've been doing them like that for a while may be a challenge, but that's typically the case when you have to FIX tumbling skills.
If you're doing it on your own try recording yourself so that you can see what you're doing. iPhones have that slow-mo feature or use an app like coaches eye. That way you can see what you're doing and watch it in slow motion to see if and where and technical errors occur. And it will allow you to see improvement.
More than blindly doing drills you need to know that you are doing them correctly and improving the small things I your technical execution or you won't see improvement.
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