This study's major purpose was to identify school-related variables that affect the achievement of eighth-grade pupils in mathematics. The data are based on results of a basic skills test administered statewide in Tennessee. The main problem of the first phase of the research was to identify factors that may account for relatively large differences in mathematics achievement scores among schools that do not differ in their reading or language achievement scores. Thirty-two schools and sixteen feeder schools were selected for the study, with six of the buildings chosen for a pilot study. Variables studied in this investigation were classified into the following seven clusters: leadership, curriculum, instruction, school policies and practices, teacher, pupil, and parental/community. Many statistically significant differences between high and low-achieving schools are detailed in this report. The study cautions against drawing conclusions about the quality of the programs offered at any of the schools, but states that the data should point out areas of future research in which selected dependent variables can be isolated and cause and effect relationships determined. (MP)