The Penn State study findings, published in 1994, confirmed the expert consensus described in this paper.Do the people you regard as good critical thinkers have the three cognitive skills described so far?Again, can you come up with some examples of analysis?
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You can monitor and correct an interpretation you offered.
You can examine and correct an inference you have drawn.
How about this: after judging that it would be useful to you to resolve a given uncertainty, developing a workable plan to gather that information?
Or, when faced with a problem, developing a set of options for addressing it.
How about what you did above when you clarified what "offensive violence" meant?
Again from the experts: analysis is "to identify the intended and actual inferential relationships among statements, questions, concepts, descriptions, or other forms of representation intended to express belief, judgment, experiences, reasons, information, or opinions." The experts include examining ideas, detecting arguments, and analyzing arguments as sub-skills of analysis.
What about picking out the main claim made in a newspaper editorial and tracing back the various reasons the editor offers in support of that claim?
Or, what about identifying unstated assumptions; constructing a way to represent a main conclusion and the various reasons given to support or criticize it; sketching the relationship of sentences or paragraphs to each other and to the main purpose of the passage?