All arguments do not have to be persuasive. In general, there are four purposes of argument (to assert, to inquire, to dominate, and to negotiate), and not all of them involve persuading someone to do, think, or act in a certain way. That being said, the main elements of an argument depend upon the type of argument structure being used. Below are some of the elements involved in argumentation. The terminology varies based on which type of argument structure someone uses.
1. Claim or Thesis--a specific statement which discusses the argument's main point. Ex: School districts should consider 4-day school weeks in order to . . .
2. Data or Evidence--normally found in the body paragraphs, data often includes the rhetorical appeals (logos, pathos, and ethos) and consists of anecdotal support, statistics, historical evidence, etc., to prove that the claim/thesis is valid. Example to support the above claim: Researchers have found that by lengthening the school day and shortening the school week. . .
3. Warrant or Major Premise--A warrant is a general truth that is generally accepted and that is broadly linked to the thesis statement. Many writers/speakers include warrants in their introductions to pull in their opponents and to demonstrate that they are reasonable. Ex: The United States' current economic state has forced many government agencies, including local school districts to consider drastic budget cuts. (Notice how the warrant is something that most people would agree with, is tied to the claim without being controversial, and makes someone opposed to the claim more likely to consider the writer's argument.)
4. Concession--Most reasonable arguments include a concession which is a writer's admitting that there is some truth to his opponent's argument. Concessions normally begin with phrases such as "Admittedly, problems exist" or "Granted, exceptions occur." Similar to a warrant, a concession establishes more credibility for the writer/speaker because it prevents dogmatism.
You can find information such as the above in most argument textbooks. These terms come from The Informed Argument by Robert P. Yagelski and Robert K. Miller (6th edition).
Argumentative writing is persuasive writing. It always begins or surrounds itself around a claim that is then shown to be true or valid through the support the writer uses.
To tell if an essay is argumentative, first ask yourself if the author is making a claim - is the writer attempting to persuade me to do something, think or feel in a particular way? Does the writer seek my agreement in any way? If yes, then you are looking at an argument.
The writer should then support the claim with enough facts, statistics, examples, and expert opinions to guarantee that a reasonable reader would be likely to agree with the claim.
The writer might also include te opposing viewpoint as counterarguments that are given consideration and then negated.
Also, argumentative writing often ends with a class to action for the reader.