partial credit

When you are a math teacher you are often faced with the dilemma of whether to assign partial credit to a problem that is incorrect, but that demonstrates some knowledge of the topic. Should I give half-credit? Three points out of five? My answer has typically been to give no credit…at first. However, taking a page from my colleagues in the English department (and grad school), I do allow for revisions, which ends up being a much better solution.