Have a friend, fellow student or teacher watch you as you dance and correct any improper movements that you make. People with fallen arches tent to roll their feet inward as they move.
Practice exercises that will strengthen the arches of your feet and your ankle muscles as well as improving your balance. One exercise that will help with these muscles is the slow releve. To perform a releve, start with your weight evenly distributed between the balls of your feet and your heels. Slowly lift your heels and roll onto the balls of your feet. Then slowly lower your feet to the floor. Perform this exercise in various dance positions including first position with your heels together and your toes turned outward, second position with the heels slightly further apart and the toes turned outward, and fifth position with one foot in front of the other and the toe of each foot touching the heel of the other foot. For a slightly more difficult variation, stand on the edge of an aerobics step. Lower the heels of your feet as far as you can. Then lift them until you stand on the balls of your feet. Repeat this exercise as many times as you can with good form.
Stretch your arches by sitting flat on the floor with your toes pointing straight upward. Slowly point your toes without scrunching them. With practice you will eventually be able to put your toes or even the balls of your feet on the floor.