Data from 10,000 17-year-old respondents to the National Assessment of Educational Progress (NAEP) 1975-76 Special Mathematics Probe (Basic Mathematics Assessment) were analyzed. The primary purpose was to identify respondents' background characteristics associated with basic mathematics achievement. The achievement items and 241 background variables were reduced through clustering techniques to composites: academic orientation; comfort/confidence about mathematics; community characteristics; effort in mathematics; extracurricular activities; individual program characteristics; locus of control; mathematics courses taken; personal demographics; school program variables; self esteem; and television watched. Causal models relating achievement to background found some relationship between the availability of specialized equipment, specifically computers, and student interest as evidenced by the number and level of mathematics courses taken by students with similar academic orientation and background. After these variables were controlled, internal locus of control and greater levels of mathematics confidence were significant predictors of achievement. Although related to attitudinal measures, predictors were generally the same for both sexes. Predictor patterns were generally similar with respect to race but large differences in achievement levels were not explained by the variables. Descriptive analyses and summaries of achievement data from 13-year-old respondents are included. Primary type of information provided by the report: Results (Secondary Analysis). (Author/CM)