The PISA assessment indicated that the United States performs at the bottom tier among OECD membership nations in secondary school math education. The dearth of math proficiency presented a significant problem for the United States to maintain its future leadership in global technology. The purpose of this exploratory multiple case study was to investigate secondary school math teachers' beliefs and perceptions about how their students are learning math and what could lead to better learning results in grades 7 to 10 in the United States and Taiwan. The study was conducted under the framework of social cognitive theory. Online surveys and interviews were used to collect input from math teachers. A total of 30 survey respondents and 12 interviewees were included in the study. The study found consensus among American and Taiwanese teachers regarding the wide range of incoming students' math levels, the necessity of differentiated instructions, and the importance of teachers' roles and students' willingness. The findings also revealed differences between American and Taiwanese teachers regarding their perceptions of the magnitude of student math deficiency, the impact of student innate ability, the limitation of teachers' roles, and the driving sources of student learning outcomes. The findings implied that American teachers focus on teachers' roles to elevate students' math learning outcomes, while Taiwanese teachers also emphasize students' responsibilities. In addition, American teachers focus on low-performers to close the performance gap; Taiwanese teachers appear to pay more attention to high performers. Regarding ways to improve American students' math learning outcomes, the study suggested using an elective math curriculum system that requires students to achieve mastery in real-world-connected math topics and cultivating a strong sense of responsibility among students. Future research could involve studies on student math performance ceilings, effective usage of intrinsic and extrinsic motivations, methods for cultivating students' sense of responsibility for their own learning, curriculum design based on real-world math applications, and students' perspective on effective math learning. [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.]