Student achievement is inconsistent when comparing subgroups of students in public schools (Finn, 1999; Spellings, 2008; Teale, Paciga, & Hoffman, 2007). According to research, effective school principals believe that the problem is internal and subject to their control to effect change by addressing inequities. The changes required in closing achievement gaps between groups of students are of a second order of magnitude (Davila, 2009; Trybus, 2011). If school principals do not understand the magnitude of change required, they may not implement the appropriate strategies to realize that change. This quantitative-causal comparative study researches the question: Is there a significant difference in the mean scores of principals' beliefs relative to order of change for closing achievement gaps in high-performing schools as compared to low-performing schools? The population was comprised of a stratified random sample of principals in the United States who currently lead schools identified as Blue Ribbon, Title I Distinguished, or low-performing. A survey developed by Siegfried (2005) and modified by this researcher measured the construct of beliefs of order of change to close achievement gaps. A one-way analysis of variance (ANOVA) was conducted to find the difference between the means of these groups. The results of the one-way ANOVA support the hypothesis that there is a difference in the means between high-performing (Blue Ribbon and Distinguished) and low-performing schools. It was expected that the principals of high-performing schools may hold second-order change beliefs and principals of low-performing schools may hold first-order change beliefs regarding the closing of academic achievement gaps. However, all three groups scored closer to the belief that changes required to close achievement gaps are of a second order; additionally, the low-performing schools scored stronger in second-order belief. Hypotheses of this result are included in this research, which includes recent steps taken nationally to address low-performing schools that may have already effected change in those schools. Being aware that the achievement gaps can be addressed internally and knowing the factors that may affect leaders' beliefs regarding the magnitude of change may benefit future professional preparation and leadership development programs that aim to produce effective transformational leaders. [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.]