There has been little discussion of two conventions common within classroom assessment: the convention of representing student's performance on an assessment using a single score; and the convention of using the average score to summarize a student's performance over a set of assessments. This paper attempts to demonstrate that the assumptions underlying these conventions are questionable at best. The paper also attempts to demonstrate that the use of these conventions renders classroom assessment a poor feedback device. Alternative conventions that make classroom assessments more accurate and useful feedback mechanisms are presented and discussed. Suggestions made in this paper can be summarized in brief statements: (1) classroom assessments should be given throughout the cycle of learning; (2) separate scores should be assigned to each trait addressed in a given classroom assessment; (3) a common scale should be used for all traits on all assessments; (4) summary scores for the various traits should be combined in a way that acknowledges their dependence; and (5) the summary scores for a given trait should be estimated by predicting the final score in the set of scores based on some mathematical model of learning. (Contains 5 tables, 4 exhibits, and 37 references.) (SLD)