This paper discusses appropriate measurement content and instructional strategies for courses in classroom assessment in the areas of grading and communicating assessment results. Classroom teachers need to understand a wider range of assessments than many textbooks cover, and an aspiring teacher's classroom assessment practices need to be developed in concert with the instructional repertoire and classroom management skills. Important skills about communicating assessment results support Standards 5 and 6 of the "Standards for Teacher Competence in Educational Assessment" (1990). First, classroom assessment must be taught to aspiring teachers in relation to both instruction and classroom management, not simply as a decontextualized application of measurement principles. In the second place, the measurement content for classroom assessment courses has different emphases from the measurement content for introductory psychometrics courses. Third, the content of classroom assessment courses can best be taught by a mixture of direct instruction in the concepts and application examples and scenarios for classroom practice, simulation and discussion. Classroom assessment contributes to every other teaching function and helps create the classroom environment. (Contains 3 tables and 16 references.) (SLD)