| Let's talk about 4 things that you should have to make a good back tuck.
1. Strong jump
You need to have a really strong jump that will require the use of both arms and legs. It is very important to remember that the jump should go up and not back. You can work on strengthening the jump by doing lots of plyometrics and lots of bounding jumps on the floor. Make sure to use your whole leg to jump and push all the way through the toes.
Using the springboard is a good progression. Your next step would be to take the springboard to the floor and throw your tucks into an 8" crash mat. Another step after that is to stand on a box (12") and throw the tucks into the crash mat. Going to the box from the springboard allows you to do more of the jumping work but maintaining the height. As you strengthen the jump you can then transition to the floor.
Make sure you have spotting throughout this process.
2. Strong set
You need to have a strong set, or kip, with the arms. You want to lift the arms up as aggressively as possible and stop them right about 45º. Here it is important to have good timing. Your set should stop at the same time as you push off the toes for maximum lift. This strong lift coupled with the jump will help to get higher for the tuck. The higher, the better, of course.
3. Strong hollow body tuck
We jump first and then tuck but the tuck needs to be in a hollow position. (Refer to my other post to you about the hollow) Be careful NOT to simply bring the knees to the chest. Rather, think of it as pulling the knees up over your head as you would for a backward roll on the floor. You may also think of it as pulling the knees up through the arms like a football through the uprights in a field goal. You need to be aggressive about snapping into the hollow tuck position as that is the most effective way to generate the rotation.
4. Keep your head in
Don't throw your head back. Keep your chin to your chest and look for the knees coming up. It is common to throw the head back but you will actually make it harder and less safe if you do that. Good head position makes for faster rotation.
Make sure to take some time to visualize yourself making several back tucks on floor as well.
This is sort of the tip of the iceberg but it should give you plenty to start with.
Good Luck! | 
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