I was listening to an interview of Jordan Ellenberg on NPR, and he makes a comment that when grading students' work he will only take half points off if the student tells him that "my answer is wrong, but I can't find my mistake" when the answer is nonsensical, i.e. "Suzy has -4 oz of water in her cup".
I like his idea of encouraging students to be aware of what they are doing, rather than just being breathing calculators. However, I'm not quite sure about the low level of expectations of students that giving half credit for knowing that they are wrong communicates. However, if we look at it theologically, perhaps "apophatic mathematics" is closer to the way to go, "not made", "not possible to not sin".
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