The public school system in the United States is facing severe criticism. There exists today, a constant stream of negative messages through media coverage, news articles and charter school marketing campaigns claiming the failing of the public school system specifically in the content area of mathematics. Current research exposes alarming statistics relating to Kindergarten through twelfth grade mathematics achievement of United States students. United States students rank towards the bottom on international mathematics assessments and are graduating from high school unprepared for college. Research suggests that providing accelerated mathematics instruction for United States public school students is one way to increase student achievement in mathematics. Accelerated mathematics instruction would set the bar higher for all students and increase the opportunity for students to work at advanced levels in mathematics. The purpose of this study was to compare the student achievement between non-gifted students who receive accelerated mathematics instruction one grade level above, and non-gifted students who receive on-grade-level mathematics instruction. In addition, this study explores the role and impact of parental involvement and open-enrollment on student achievement in mathematics. The researcher utilized a mixed-method research design for this study. The quantitative research methodology employed for this study was causal-comparative or ex post facto research design. An independent t-test was utilized with a significance alpha level of 0.05. A one-way analysis of variance (ANOVA) for multiple factors was also utilized with a significance alpha level of 0.025. A Tukey HSD post hoc was conducted to determine between which students groups the differences existed. The researcher applied qualitative grounded theory research methods as appropriate. A descriptive process, cross-sectional survey was developed by the researcher. The survey data were collected through unstructured item format facilitated through focus group interviews with participants. The interviews conducted were audio taped and transcribed. Grounded theory analysis was utilized and emerging themes were identified. The findings indicated a statistically significant difference in mathematics achievement between students who received accelerated mathematics instruction and those who did not. The findings provide evidence that students who are provided accelerated mathematics instruction demonstrate higher levels of achievement. The results also found a statistically significant difference in mathematics achievement between students who attend school on open-enrollment although contradictory results also occurred. The qualitative findings identified three significant types of parent involvement that may impact student achievement including helping with homework, providing tutoring, and researching school options. This study may help public school district leaders see the benefit of incorporating accelerated mathematics instruction in all public schools versus limiting accelerated instruction to specific campuses requiring open-enrollment. District leaders may better understand the benefit of providing all students the opportunity work at advanced levels. [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.]