The objectives of this study were to determine (1) the reasons why successful mathematics students have been able to thrive in schools labeled academically unacceptable and (2) why they have chosen to stay in these academically unacceptable schools despite having the option to leave for a better performing school. Qualitative methods including group interviews, individual interviews, and open ended questionnaires were used to address the above issues. The study involved eleven successful mathematics students, two teachers, and two principals from two Louisiana high schools deemed academically unacceptable according to the Louisiana's accountability system. For the sake of this study, successful students were defined as those students who scored at the Advanced or Mastery level in mathematics on Louisiana's Graduate Exit Exam (GEE) required for high school graduation. In spring 2003 only 6% of Louisiana's African-American students scored in the Advanced or Mastery range. Results indicate that students attribute their success in mathematics to good teachers, personal character traits (ability to focus, desire to succeed, determination, curious/inquisitive nature, and overall belief in self), and parental influence. Adult participants attributed students' success to aptitude, fortitude, and purposeful commitment. The participants chose not to attend better performing schools because they feel comfortable at their current school, and have developed a degree of trust at their current school. Moreover, the participants believe that graduating from a school with problems such as those associated with academically unacceptable schools will better prepare them for the "real world." It is unlikely that the designers of accountability systems can fathom the conditions present in academically unacceptable schools. Educators and those who aspire to improve low-performing schools must take heed of the advice of those who have experienced success under the duress of attending an unacceptable school. Very few solutions include the suggestions of students who actually succeed while enduring troubling circumstances. If input from successful mathematics students is consistently ignored, it is likely that the current achievement gap will persist. Consequently, a generation of underserved African Americans from inner-city schools may become disenfranchised--with no high school diploma and limited means to fulfill the American Dream. Appended are: (1) Consent Forms; and (2) Survey/Interview Questions. (Contains 12 tables.) [Ph.D. Dissertation, Southern University and A&M College. Abstract modified to meet ERIC guidelines.]