The research supports the contentions that teachers' beliefs influence classroom practice and student achievement. Although research has been done to examine teachers' beliefs and classroom practice, limited research has investigated how one's culture and community affect teacher identity and mathematics classroom practice. The development over time of teachers' perceptions about mathematics and teacher identities has been overlooked in research that compares education in the United States and Japan. This study investigates how teachers' views on what effective teaching looks like and how their views, beliefs, and preferences (dispositions) influence the ways in which they teach mathematics, as well as their pedagogical content knowledge in the four primary classrooms in United States and Japan. Because the process of understanding an individual's identity is complex, the language and actions the participants use within a certain context are examined to explore the socioculturally-situated identity being expressed in each case. The findings of this study may contribute to efforts that seek to understand how mathematics identity relates to how mathematics is taught. [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.]