The purpose of this study was to explore the relationship between the use of a computer-managed integrated learning system entitled Accelerated Math (AM) as a supplement to traditional mathematics instruction on achievement as measured by TerraNova achievement tests of third and fourth grade high-ability students. Gender, socioeconomic status, and grade level were also considered. The population consisted of 624 students who were third and fourth grade high-ability students during the 2009-2010 school year. Data were gathered that covered a 1-year period for high-ability third and fourth graders. A series of independent samples t-tests were used to identify relationship among variables. The researcher's investigation of the relationship between AM and mathematics achievement might assist educators in planning for use of technology as a supplement to the normal mathematics curriculum. The findings indicated measurable differences in the performance of high-ability third and fourth grade students who qualified for free and reduced priced lunch and participated in AM compared to high-ability students who qualified for free and reduced priced lunch and did not participate in the program. High-ability students who participated in the AM program and who qualified for free and reduced lunch scored significantly higher on the TerraNova math achievement test than students who did not participate in AM and who qualified for free and reduced lunch. There were also measurable differences in the performance of high-ability fourth grade students who participated in the AM program compared to those who did not participate in the program. Fourth grade high-ability students who participated in the AM program scored significantly higher on the TerraNova math achievement test than fourth grade students who did not participate in the program. This study indicated no significant findings among gender, students in grade 3, and students who did not qualify for free and reduced price lunch who did and did not participate in the AM program. [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.]