This dissertation examines how eight urban high schools responded to mandates to raise graduation requirements in mathematics. The change process was complicated by challenges such as the conditions of poverty, lack of adequate financial support for schools, and large numbers of students who come to high school with inadequate preparation in mathematics. Using a qualitative multiple-case study approach, the dissertation examined and compared patterns of change in four public charter schools and four district-accountable high schools. The schools used a range of school reform models such as early college, schools within schools, and schools with curricula linked to career themes. Data was collected from interviews with teachers, administrators in eight schools and with students, adult mentors, and program directors in four schools. Additional information sources included document analysis and observations. The study used a three-level approach to analysis: differences in organizational adaptation in public charter schools compared to district-accountable schools; schools' adaptation of the mathematics curriculum to meet new requirements; and social support processes that helped motivate students. The comparison reveals that: 1) the charter schools were free from centralized district governance, but school-level adaptivity could be constrained by other management structures exerting top-down control; 2) mandates for college-preparatory standards posed capacity-building challenges for all eight high schools because most of their students were prospective first-generation college students without basic math skills; and 3) the charter schools had greater flexibility to adapt the curriculum locally than the district-accountable schools, but only two of these schools took advantage of this freedom. Although the district-accountable schools were constrained in their ability to adapt the mathematics curriculum locally, they were able to build capacity to provide social support interventions for students through partnerships with a non-profit organization. Student interview data indicated that these interventions motivated them toward higher achievement and college aspirations. Three of the charter schools had also formed partnerships to provide interventions. However, as there were no interviews with students or parents, the evidence supporting positive outcomes was indirect. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]