When writing to take a position, the writer is arguing for one side of an issue. The focus is on presenting your position--your opinion--as being supported by evidence and valid. Taking a position is a persuasive or argumentative. In presenting your reasons why your position is the best, the strongest, or the correct one, you may also "refute" the opposing position--explain the strengths and weaknesses of the alternative view in order to show why your position is better.
Writing an Academic Argument and ENG 102 Part Four: Writing Persuasively may have additional tips that apply to this type of writing.
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Writing a Position Paper (Simon Fraser U)
Writing a Position Paper (U of Hawaii)
Writing Effective Position Papers (Agnes Scott College)
Writing an Argumentative of Position Paper (The College of St. Rose)