The first pretest-posttest hypothesis was tested using the dependent t test. Null hypotheses for test score improvement over time were rejected for the end of fifth-grade pretest compared to ending sixth-grade posttest math Essential Learner Outcome scores converted to standard scores for randomly selected sixth-grade girls meeting measured test score criteria for challenge math placement (n = 15): pretest M = 120.07, SD = 4.32; posttest M = 121.87, SD = 2.17; t (14) = 1.73, p = 0.05 (one-tailed), d = 0.500 and rejected for randomly selected sixth-grade girls not meeting measured test score criteria for challenge math placement (n = 15): pretest M = 117.80, SD = 3.28; posttest M = 119.73, SD = 3.13; t (14) = 1.95, p < 0.05 (one-tailed), d = 0.503. However, null hypotheses for test score improvement over time were not rejected for the end of fifth-grade pretest compared to ending sixth-grade posttest math Essential Learner Outcome scores converted to standard scores for randomly selected sixth-grade boys meeting measured test score criteria for challenge math placement (n = 15): pretest M = 120.00, SD = 2.54; posttest M = 121.47, SD = 2.85; t (14) = 1.59, p = 0.07 (one-tailed), d = 0.415 and not rejected for test score reduction over time for randomly selected sixth-grade boys not meeting measured test score criteria for challenge math placement (n = 15): pretest M = 119.00, SD = 4.52; posttest M = 118.80, SD = 4.35; t (14) = -0.15, p = 0.44 (one-tailed), d = -0.038. Comparisons for sixth-grade boys meeting measured test score criteria for challenge math placement, sixth-grade girls meeting measured test score criteria for challenge math placement, sixth-grade boys not meeting measured test score criteria for challenge math placement, and sixth-grade girls not meeting measured test score criteria for challenge math placement was statistically significant, (F (3, 56) = 3.03, p = 0.04). Because a significant main effect was found "post hoc", contrast analyses were conducted using independent t tests. Significant differences were found in the A (Boys Tested In) vs. C (Boys Placed In) comparison where t (28) = 1.99, p < 0.05 (one-tailed), d = 1.517; B (Girls Tested In) vs. C (Boys Placed In) comparison where t (28) = 2.45, p = 0.01 (one-tailed), d = 2.036; and B (Girls Tested In) vs. D (Girls Placed In) where t (28) = 2.17, p < 0.05 (one-tailed), d = 1.917. No significant differences were observed for the other post hoc comparisons A (Boys Tested In) vs. B (Girls Tested In); A (Boys Tested In) vs. D (Girls Placed In); and C (Boys Placed In) vs. D (Girls Placed In). Importantly, for all groups, a pattern of statistical improvement over time was found for end of fifth-grade pretest compared to ending sixth-grade posttest Orleans-Hanna Algebra Prognosis Test scores, with no significant posttest-posttest ANOVA results observed (F (3, 56) = 0.47, p = 0.70) observed. Posttest math test scores for girls, both tested in and placed in, did not decrease significantly while the boys posttest math scores, both tested in and placed In significantly decreased over time. However, final grade test scores for all groups were within the B average range based on school district criteria. Null hypotheses for student math course grades over time were rejected in the direction of lower grade scores for the first trimester sixth-grade pretest challenge math course grade score compared to last trimester sixth-grade posttest challenge math course grade score for sixth-grade boys meeting measured test score criteria for challenge math placement t (14) = -3.22, p = 0.003 (one-tailed), d = -0.840 and rejected for sixth-grade boys not meeting measured test score criteria for challenge math placement t (14) = -1.80, p = 0.05 (one-tailed), d = -0.466. Furthermore, null hypotheses for test score improvement over time were not rejected for the first trimester sixth-grade pretest challenge math course grade score compared to last trimester sixth-grade posttest challenge math course grade score for sixth-grade girls meeting measured test score criteria for challenge math placement t (14) = 0.13, p = 0.45 (one-tailed), d = 0.035 and not rejected for test score reduction over time for sixth-grade girls not meeting measured test score criteria for challenge math placement t (14) = 0.32, p = 0.38 (one-tailed), d = 0.033. Posttest-posttest results were not statistically significant, (F (3, 56) = 1.18, p = 0.32). Overall study results indicate an equivalent positive response to challenge math placement regardless of student gender or placement conditions. [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.]