A great replacement for the Roll Up on the Mat is the Half Roll Back. It's considered a beginner or Pre-Pilates exercise. Whether you're new to Pilates, not able to Roll Up without your legs coming off the mat, you have a back issue, or just want to supplement a more difficult flexion exercise this Half Roll Back is a great option. It's easy to cheat on though so be sure to maintain your feet on the floor, your legs tight together and try not to use your arms to help you roll back up.
Press your feet down into your mat to engage your seat and hamstrings.
Begin sitting up with your knees bent in front of you. You don 't want your knees too bent though. If your knees are at 90 degrees walk your feet a little further away from you. Press your feet down into your mat to engage your seat and hamstrings. Hug your inner thighs together and even feel as if you're wrapping your outer thighs to gain more connection to your seat. Place your hands behind your thighs and then connect your shoulders on to your back. If you do use your arms you want to keep your shoulders out of your ears. To begin, find the tallest round shape and then begin to round back. Your arms will get straighter. Try to go back until your arms are straight or your lower back touches the mat without your feet lifting off the floor. Then, moving from your center, pull your stomach in, connect your front ribs and round forward. You'll be tempted to sit up and lose what you just connected but try to stay in the longest round shape you can make 3-5x. Over time your goal is to straighten your legs and roll all the way down and all the way up.