I like my wife's answer best so far: "I would have stopped marking them wrong when I noticed the pattern, and written 'see me' without a grade. Depending on what kind of kid you were, you might have gotten a do-over or partial credit."

I think what makes this example interesting is that I don't see it so black and white. Math is a combination of concepts and (to a much lesser extent) symbols. Of course the answers were wrong, but if the goal is to teach mathematical

Say you were teaching

I think what makes this example interesting is that I don't see it so black and white. Math is a combination of concepts and (to a much lesser extent) symbols. Of course the answers were wrong, but if the goal is to teach mathematical

*concepts*as opposed to mathematical*symbolism*, then the grade misses the mark.Say you were teaching

*elementary*music and asked a kid, "what are the first four measures of the allegro from Eine kleine Nachtmusik" and he wrote or played all the notes correctly, except in the key of C (as opposed to G). Still an "F"?
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