This doesn't necessarily help for a traditional school situation, but when I homeschooled my son (high school), I told him that I would give full credit for a correct answer even if work wasn't shown. But if he got the answer incorrect and no work was shown, he would lose all points for the problem. If work was shown and the mistake was a simple arithmetic or copying error that was carried correctly through the problem, I would give partial credit. If the error was conceptual or there were multiple sloppy errors, he would receive no credit. This did seem to motivate him.
On homework, which I did not grade except to mark it complete, I told him that if he didn't write out his work a certain way (and I posted a detailed list of instructions in his work area), I would make him do the assignment over. That also motivated him. I did this in response to his making multiple sloppy errors when he got to Algebra II. He has dyslexia and his working memory is not stellar--even he saw the benefit of writing out the work properly, but the lazy side of him didn't want to do all that writing.
I'm still struggling with this issue with my younger son. He has a more severe antipathy for writing (bordering on dysgraphia) and his working memory is phenomenal. He is motivated by grades though.
With both of them, I keep stressing that math isn't just about getting answers but also about showing your thinking. The question becomes how much thinking do you need to show? Everything? Just the non-trivial stuff? I'm sure there is some standard, but I never went far enough in math (or paid enough attention) to learn the answer. Perhaps a math person here can enlighten me.
Last edited by Kai; 02/21/14 11:00 AM.
