What is the meaning of "methodology"?please give an example

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wordprof | College Teacher | (Level 1) Educator Emeritus

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Literally “the study of methods”, this term refers to the examination and selection of approaches to solving a problem.  In mathematics, this might mean arranging a word-problem into a solvable equation; in rhetoric it may mean attacking a thesis statement through the application of various argumentative “tools” (citation of authority, negating counterarguments, etc.); in science it is the selection of proofs, physical evidence, analytical methods, etc.; in auto repair it is the selection of tools, diagnostic methods, procedures. The exercise of selecting a means to solve a problem is what methodology is about, not the method chosen but the process of choosing a method.  Inventors, for example, identify a problem, and then invent a series of activities to solve it, by examining the methodologies available to the creative mind.