The purpose of this study was to ascertain whether certain contextual factors pertaining to principals and teachers influenced U.S. eighth grade students' math achievement. More specifically, the study comparatively examined the direct and mediating predictive influence of teacher instructional approaches (i.e., teacher-directed; constructivism), academic optimism (i.e., academic emphasis; collective efficacy; faculty trust in parents/students), teacher self-efficacy, and principal instructional leadership (i.e., define school mission; manage instructional program; promote positive learning climate) between the first (lowest achieving) and fourth (highest achieving) quartiles by controlling for SES and students' attitudes toward math. The study employed a causal comparative design utilizing data from the data sets of Trends in Mathematics and Science Study-2011 for the United States. For the comparative purpose of the study, lowest and highest achieving student quartiles were identified. Participants in both quartiles included 3,187 students, 329 teachers, and 314 principals. Multivariate statistics (ANOVA and MANCOVA) were used for the group differences and path analysis was used for the analysis of relationship patterns. Results of the study revealed that low and high achieving students differed on a linear combination of all dependent variables. Teacher contextual factors that influenced the achievement of lowest achieving students included: utilizing a combination of direct and constructivist instruction and academic emphasis. Principal contextual factors that directly and indirectly influenced the achievement of this group included: managing instructional program and promoting positive learning climate. Both covariates, SES and students' attitudes toward math, significantly influenced the achievement of this group. In reference to the highest achieving students, results revealed that teacher contextual factors, such as constructivist instruction and utilizing a combination of constructivist and direct instruction; self-efficacy; academic emphasis, faculty trust (i.e., in parents/students), and collective efficacy (negative effect) significantly influenced the achievement of this group. Principal contextual factors that significantly influenced the achievement of this group were defining school mission and promoting a positive learning climate. Lastly, the study covariates, SES and students' attitudes toward math, were both found to significantly influence the achievement of the highest achieving group. The findings suggested that policymakers should take a closer look into principal and teacher variables to determine their differing roles in influencing low and high achieving student populations. To assist low achieving students, the results call for teachers to seek strategies to increase positive perceptions of math and employ a combination of constructivist and direct instruction. Principals may assist low achieving students by dedicating time to managing the instructional program and promoting a positive learning climate. In reference to high achieving students, teachers should look to increase positive perceptions of math, emphasis academics, cultivate trusting relationships with parents/students, and become more self-efficacious in teaching math. Lastly, the results suggested that principals may assist high achieving students by dedicating time to promoting a positive learning climate and defining the school mission. These direct and indirect relationships collectively suggested that the contextual variables pertaining to principals and teachers may create pathways for increasing math achievement in low and high achieving student populations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]