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"Students’ knowledge reminded us that our task is not to teach them how to argue, or even the importance of argument. Rather, our challenge is to convince them to argue in writing in an academic fashion."

What is argument?

Even though this seems like a simple question, it's quite debatable. Check out these definitions:
  • Argument: a reason given in proof or rebuttal; discourse intended to persuade

http://www.merriam-webster.com/dictionary/persuasion

  • And what about persuasion, according to Merriam-Webster? the act of causing people to do or believe something: the act or activity of persuading people; a particular type of belief or way of thinking (also from Merriam Webster)

Common Core has its definition: 

Argument:  Arguments are used for many purposes—to change the reader’s point of view, to bring about some action on the reader’s part, or to ask the reader to accept the writer’s explanation or evaluation of a concept, issue, or problem. An argument is a reasoned, logical way of demonstrating that the writer’s position, belief, or conclusion is valid. In English language arts, students make claims about the worth or meaning of a literary work or works. They defend their interpretations or judgments with evidence from the text(s) they are writing about. In history/social studies, students analyze evidence from multiple primary and secondary sources to advance a claim that is best supported by the evidence, and they argue for a historically or empirically situated interpretation. In science, students make claims in the form of statements or conclusions that answer questions or address problems. Using data in a scientifically acceptable form, students marshal evidence and draw on their understanding of scientific concepts to argue in support of their claims. Although young children are not able to produce fully developed logical arguments, they develop a variety of methods to extend and elaborate their work by providing examples, offering reasons for their assertions, and explaining cause and effect. These kinds of expository structures are steps on the road to argument. In grades K–5, the term “opinion” is used to refer to this developing form of argument. (Appendix A)

AND

“Although information is provided in both arguments and explanations, the two types of writing have different aims. Arguments seek to make people believe that something is true or to persuade people to change their beliefs or behavior. Explanations, on the other hand, start with the assumption of truthfulness and answer questions about why or how. Their aim is to make the reader understand rather than to persuade him or her to accept a certain point of view. In short, arguments are used for persuasion and explanations for clarification.”

Common Core also distinguishes between argument and persuasion:

“Argument” and “Persuasion” When writing to persuade, writers employ a variety of persuasive strategies. One common strategy is an appeal to the credibility, character, or authority of the writer (or speaker). When writers establish that they are knowledgeable and trustworthy, audiences are more likely to believe what they say. Another is an appeal to the audience’s self-interest, sense of identity, or emotions, any of which can sway an audience. A logical argument, on the other hand, convinces the audience because of the perceived merit and reasonableness of the claims and proofs offered rather than either the emotions the writing evokes in the audience or the character or credentials of the writer. The Standards place special emphasis on writing logical arguments as a particularly important form of college- and career-ready writing.

FOR AN INTERESTING COUNTERARGUMENT, 

BE SURE TO READ Tom Newkirk's "Speaking Back to Common Core."