There are so many really awesome, useful props in Pilates used to facilitate a more effective, challenging, focused, or comfortable experience. I, for one, am a huge fan of using them as often as necessary. The small ball is one that is often used to test stability, direct proper alignment and muscle engagement, and also create resistance against the body.
Here's a favorite variation of single arm swan presses using the ball 3 different ways. 1| to test shoulder stability 2| to guide the legs to parallel and initiate deep adductor and pelvic floor muscles 3| to challenge the hamstrings and glutes, testing hip extension.