While doing research at the University of British Columbia, Lee Swanson gave a "metacognition" survey to students. One of the questions was: "Who is smarter, someone who knows the answer to a math problem without having to figure it out or someone taking some time to figure out the problem? Why?"
This is an interesting question, and I wonder how most mathematics teachers would respond....
Before responding, I would want to know the intended meanings of "smarter," "knows the answer," "math problem," "without having to figure it out," "taking some time," and "figure out the problem." All of these terms or phrases are value-laden...and underly the students' constant claim: "I know the answer, why do I have to show my work!"
Just writing this "lint" generates memories of discussions (i.e. arguments) with students about my grading policies and use of a scoring rubric.
And what is your response to the question...and assessment implications?
Source: Journal of Educational Psychology, June 1990