Seeing that you are looking for areas of improvement, I can suggest the concept of peer editing as being vital in this process. Writing is often seen as product based. This means that students see writing as something "to be done" and once it's finished, it's over. The more mature writer understands that in the realm of composition, nothing is ever "finished." There are always manners in which something can be made better. Even after several revisions, writing can always stand another draft. This is why most upper level papers and dissertations endure untold amounts of drafts before publication and then, even after it is "finished," the writer recognizes that different things could have been done at different points. Peer editing recognizes this process. Having your work read by several different colleagues that are composing their own work can bring more insight into the paper. You can even ask them or tell them for what you are looking. This will harness and focus their precision as they read your paper. Additionally, if your instructor is allowing drafts to be submitted, do so. If your instructor highlights areas of improvement before you submit it, there is a greater chance that taking heed of such advice can improve the score of your paper and yield valuable insights.
In the writing of an argumentative essay, structure is extremely important. Be sure to have a narrow enough topic that can be supported by three points, beginning with the most important one. It is advisable to include counterarguments in persuasive essays, counterarguments that are eliminated with logical reasons and solid data. Careful and thorough researching of the topic is essential, as well; in addition, a variety of evidence--statistics, testimonials from authorities, logical reasons--is essential.
It may be a good idea to let another person read your essay as that person will detect any subjectivity in your writing, or other flaws that are harder for you yourself to discern. This person will also detect any irrelevant sentences, as well, or notice that you may need transitional words or phrases between ideas.
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Since you are writing an argumentative paper, you should check the logic and development of the argument itself as it appears in the essay. Be sure to have a clear, concise thesis statement as the foundation of the essay and argument. Next, check to make sure that you have clear points of argument that are supported by evidence.
For more detail, consider the points of argument outlined by Stephen Toulmin. He argues that most people who try to make arguments end up leaving out crucial pieces of argumentation. In his model, there are three essential parts of an argument: claim, data, and warrant. After this, there are other parts of arguments that help to make them stronger (i.e. considering counterclaims). Follow the link below for details on Toulmin's model.
You should always check over a paper for any grammar mistakes. Also, make sure you do not use contractions with a formal paper. You should not use phrases such as "I believe" or "I think" when writing a paper. Obviously you believe what you are writing or you wouldn't be writing it.
Do make sure that all your sentences do not start the same way. Use a variety of sentence structures. Avoid using any slang.
The most important thing to include in your paper is other sources. Give examples to support your argument. Also, give examples that do no support your argument and counter them.