Floor-based knee raises that fire up the lower abs.
Roll your hips up at the top. Don't just rock your thighs back and forth.
Pulling your knees to your chest and curling your hips off the floor targets the lower portion of your abs, the bit that only fires properly when the pelvis actually tilts. The bent knees shorten the lever, making it the most accessible of the floor-based raise family while still training real hip and spine flexion. It is the sensible starting point before straight-leg raises and hanging work.
Lever length. Bent knees bring the weight of your legs closer to your hips, so it is easier to control and easier to feel your abs doing the work. Straight-leg raises are the progression once these are strict and smooth.
Because that is the actual ab work. Your abs tilt your pelvis, they do not swing your thighs. If your hips never leave the floor you are mostly training your hip flexors and rocking through the easy part of the rep.
If your lower back arches off the floor, yes, hands under the glutes tilt your pelvis and protect the position. As your abs get stronger, move the hands to your sides so your core does all the stabilising.
