The purpose of this quantitative study was to explore the relationship between teacher self-efficacy beliefs and the level of student achievement their students obtain as evidenced by the Algebra I Virginia Standards of Learning (SOL) assessment. This study also explored teachers' mathematics content knowledge, mathematics pedagogical knowledge, and the relationship of each of these to their self-efficacy beliefs as teachers, and to student achievement. Finally, the study explored whether there were significant differences between teachers who teach Algebra I at the middle school level versus those who teach Algebra I at the high school level in each of the four variables under study. A strong correlation was found between teacher self-efficacy and mathematics pedagogical knowledge. The more mathematics pedagogical knowledge a teacher possesses, the higher his or her self-efficacy is likely to be. Teachers with high self-efficacy tend to exhibit behaviors in the classroom that lead to greater student outcomes. While this study did not find a significant statistical relationship between teacher self-efficacy, student achievement or mathematics content knowledge, these may be relationships worthy of future study. This study suggests that school leaders can impact student outcomes by providing high quality, on-going professional development for teachers in the area of mathematics pedagogy. Teaching teachers how to teach math will increase teacher's self-efficacy which may lead to higher goals and greater effort, persistence, and resilience. These, in turn may ultimately impact the overall achievement of the students. [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.]