Standards-based grading (SBG) is an approach to assessment and reporting in which scores are attached to the specific learning objectives of a course, rather than to assignments or tests. Each score represents a student's mastery of that learning objective, and may change over time in response to evidence that her level of understanding has changed. SBG is increasingly popular in K-12 education, but has been poorly documented and studied in a university context. I explored the practicality and effects of using SBG in a moderately large university class by incorporating it into the two successive courses of an introductory physics sequence. Although design flaws and logistical difficulties plagued these attempts, most students responded positively to the basic intent and elements of the approach. Our experiences revealed likely implementation errors and suggested some wise design choices. More interestingly, I found that SBG foregrounds and forces us to confront some fundamental tensions present but latent within most or all teaching. (Contains 2 tables.)