Writing a problem-solution essay is much like writing any other essay in a few ways. First, it is essential to understand your subject matter, which means doing appropriate and scholarly research. Second, it is important to organize your thoughts effectively once you have done your research; third, you must identify your audience (ask yourself to whom you are writing). Finally, you must write your essay well, using proper language, grammar, and mechanics.
Those are all common considerations for any essay; a problem-solution essay requires special attention to several elements. First, your research must be an accurate reflection of the problem, not just what you assume to be true. With this subject, bullying in school, I think it would be easy to assume you know a lot about the subject because you are actually in school or because the subject has been reported on so often by the media of late. For example, if bullying is not a real problem in your school, it would be easy to assume bullying is not a major problem; the opposite would be true if bullying is pervasive in your school. Neither is probably completely true.
Instead of assuming you understand the topic, you might be best served by reserving judgment until you discover what the research says. In other words, you know it is a problem, but be sure to discover exactly where, to whom, and by whom bullying occurs. Once you see what the research reveals, you will have to express the scope of the problem using that data.
Second, the solutions are a little trickier because everyone seems to have an opinion about these kinds of subjects. Though you may certainly offer your own ideas to solve the problem, it may serve you best to look for programs and policies that are already working. We know that schools have been doing more to combat this problem, so there should be some good research on what kinds of things are effective in battling bullying.
I have attached an excellent eNotes site on writing a problem-solution essay, and it provides this wise reminder:
Don’t jump to conclusions—any. Let’s face it: we’re all know-it-alls; we all think we have the answer to life’s problems. Unfortunately, in our rush to judgment, we often miss key details that would help us make better decisions. The same goes for a problem-solution paper: those who establish their solution first and remain steadfast to it tend to demonstrate a limited understanding of both the problem and logical solution; in other words, they don’t do well on the assignment. It’s okay to brainstorm some initial ideas, but set them aside until later: the most informed decisions come when you’re well-informed. Wait until you’ve researched the topic and fully defined the problem before finalizing your call for action.
Again, personal experience and reasoning are acceptable in conversation; in a research work, it is essential that you discover what the problem actually is before you can determine how best to address the problem with proven or potential solutions. Your sources may show slightly different statistics, as in the two sources I linked below; determine the best sources and give a range of numbers, if necessary, to be as accurate as possible.
Finally, use persuasive language to convince your readers both to accept the problem as you have researched it and to support others' efforts to curtail bullying or do something about it themselves if they can.