Forward Stride Circle/Mill Circle
At first glance, the forward stride circle (also commonly known as the mill circle) resembles something that kids do on the metal bars in elementary school. You sit on top of the bar in a stride position: one leg in front of the bar, and one leg behind. Then you circle forward until you come back up to a sitting position.
There are quite a few differences between that and a true stride circle, however. Most kids, for example, circle the bar with their front knee hooked around the bar. In a stride circle, however, both legs are straight. A stride circle also requires you to be pushed up away from the bar before you start the circle, and to maintain that distance throughout the entire circle.
A stride circle relies on the mechanics of bar circling that is used in sole circles, seat circles, and giant swings. That is, the further away from the bar your body is, the more angular velocity (that is, speed in circling the bar) you can attain. That means, your body (especially your torso) has to be as extended and straight as possible.
To begin learning a true stride circle, practice just holding yourself up in a stride hold. Use your arms to push your body up and off the bar, split your legs as wide as you can, and make both legs straight. Your back should also be straight, not rounded. You should be able to hold this for at least 30 seconds, maintaining the correct form.
Now, you need to learn how to begin the fall into the circle. This is very important because this is where you begin to generate the speed that will get you around the bar. Contrary to what most gymnasts believe when they first start learning this, you don't just fall straight down. You have to push yourself up and out forwards. So to practice that, get a block or stack of mats that is about 6 inches below your front foot when you're in a stride hold. Place it just under your front foot, and practice stepping out onto the block. You should feel the bar resting on your thigh of your back leg, your back should remain straight, and your legs still split as far as possible.
When you have that down, you're ready to try the circle. Don't forget what you have practiced before. You need to stay pushed up away from the bar, pushing forward so that the bar is on your back leg thigh, and back flat. When you come around to the top of the bar, you have to rotate your hands so that you can support yourself and not have your wrists prevent you from finishing the circle. The timing of this flip of the wrists is crucial -- too early and you will stop the momentum of your circle; too late and you will not have the support to finish on top of the bar.
When you've made a complete circle on the bar, you should practice finishing in a pushed-up stride position, just like how you began the stride circle. For Level 4, the judges are looking for that pushed-up position.
Some common problems you'll want to be aware of:
Hopefully these tips will help you perfect that stride circle. I would also recommend not doing those "fake" stride circles on the bars at school. They will only confuse you. =)