My 15 month old girl has been playing up when her demands are not met,
- Rolling on the floor, screaming and crying
My current strategy is to leave her be, after a while she will stop.
Is there a more effective way to do it?
It is cruel and possibly damaging to ignore crying at this age - don't do that!
The advice that crying should be ignored to discourage manpulation is only valid, if at all, for much older Children. A 15 month old is not mentally capable of deliberate manipulation.
When your child cries because she didn't get something she wanted, she is in genuine emotional distress, and you need to help her learn to cope with it. Ignoring her may do that, but in the worst possible way - it will teach her that you are not someone she can turn to for help.
So what you should do in that situation is first of all to give her a hug and help her calm down. Then offer alternatives. Doing that as distraction can often speed up the calming down.
Another thing that works surprisingly well (for my daughter at least) is to talk to her and explain why she cannot have what she wants. Yes, talk to her. Even at 15 months they understand a lot more than is obvious, and even if she does not understand the words, she understands that you're taking her seriously.
Toddlers are demanding, period. However, they have short memory which balances the situation and there is always a way to handle it. How I do it for my 18 months old is by distracting. When he is extremely demanding and screaming, I would run and hide behind a curtains and start a peek-a-boo game. Once or twice he may not respond and then he would run to find me. The other approach is to distract with her favorite toys. Start playing with it and pretend to enjoy it a lot, as if her toy has become yours now. It will work to divert attention from the things she was demanding.
I think what you are doing is fine, if she soothes herself after a couple of minutes. I'd also add telling her that you sympathize with her feelings: "I know you are disappointed", because having a name to put to her feelings will help her to understand them. She has strong feelings, and that's okay, and it's okay for her within reason to show her feelings, they don't have to be instantly smothered or distracted away.