The effects of classroom assessment environment (CAE) variables on yearly achievement in mathematics and science in grades 7 through 12 were studied through the Longitudinal Study of American Youth (LSAY), using cohorts of approximately 3,000 students each in the 7th and 10th grades who were followed for 4 years. While the LSAY did not include all CAE variables of theoretical interest, it did include reasonable approximations of many. The direction of CAE effects was consistent for some variables and inconsistent for others. Percent of homework corrected and returned to students had a negative effect whenever it appeared. Hours of homework assigned and percent of students completing homework on time had positive effects when they appeared. Percent of class time used for testing and evaluation had significant effects only on math achievement (two negative and one positive). Frequency of oral reports had a significant negative effect for science, while frequency of written reports had mixed effects. Results do show some CAE effects, and CAE theory does explain some, but not all, of these effects. Results support the beginnings of a theory explaining the relationship between classroom assessment and student achievement. Six tables and two figures present study data. (Contains 14 references.) (SLD)