When dealing with an erratic tester or a kid who misses a lot of points for silly mistakes: transferring the wrong answer to the answer line, not showing work, making calculation errors, etc., I wish that my 2e kid's homework actually did count for some of her grade b/c she knows more than her test scores show at times.
I see your point.
Some of those problems can be cured with better test design (e.g. long-answer tests that don't require transferring an answer to a line). And teachers should be crystal clear about the definition of "show your work." For example, I can solve a multiplication problem by writing out partial answers in chunks instead of the stepwise individual multiplication steps. I don't necessarily write every digit; that would slow me down too much. If I showed this on a test, it would be "my" work. But a teacher might argue that I've "skipped steps." So the teacher needs to be precise about what's expected in terms of "show your work." Mrs. Jones, do you want to see MY work or the work YOU would do?
But as for calculation errors...well, they're errors. If you make a mistake on a test, you should lose points. That's life.
I think there's a larger problem with giving homework (and additionally, class participation) too much influence over grades: these two things make a system more prone to being gamed. Say Little Johnny doesn't usually understand how to do the hard math homework problems. His mom or dad or the internet can help him get the answers, but he might not really understand in spite. Yet he'll get full credit for the assignment. Come test time, it's unlikely that all of the problems he doesn't get will show up on the exam, and their effects on his exam grade will be reduced because of homework and participation. When you throw in high homework scores and high marks for raising his hand all the time, and his overall grade has been gamed up higher than it should be (IMO): he can get a higher grade while knowing less.
If homework and participation weren't scored outside of a small number of points for done/not done, this wouldn't be possible. In this situation, the kids would have more incentive to try to understand problems, more incentive to say, "I really couldn't figure this out," and less incentive to GET 100%!!
