I think that there are a couple of elements to address here. The first would be to figure out what it is you are going to say about discipline on playgrounds. I would presume that you won't be arguing that there should not be discipline on the playground. Thus, the question becomes how you feel discipline should be pursued. Given the requirements of your assignment, it might lie in what you can prove. This will require you to do some research and identify what needs to be present in a successful approach to discipline on the playground. A part of this might lie in being able to assert your own opinion on the topic and what is out there on it.
I would think that talking about how there needs to be more adult supervision on playgrounds would have to be part of this approach. It seems to me that part of your essay would have to address how adults need to be present on the playground, to a certain extent, in order to deliver swift punishment, or even to be proactive enough to assert a role so that misbehavior stops before it even has a chance to start. At the same time, you might want to investigate which discipline approaches work with children who misbehave on the playground. This might be something that should be featured in your essay, driven by both what is out there in the literature and what your own opinions of the topic might be.