This study explored the predictive relationships of teacher efficacy, teacher knowledge, and teacher practices with student achievement. More specifically, secondary mathematics teachers' efficacy beliefs, geometry knowledge for teaching, and the cognitive complexity of the teachers' classroom practices were examined for 72 teachers in both urban and rural districts across Kentucky, along with the student achievement data of their students. Teacher and student data were obtained from the NSF-funded Geometry Assessment for Secondary Teachers (GAST) project, which administered geometry teacher knowledge assessments at the beginning and end of the school year, and collected cognitive complexity data from lessons through three classroom observations. Student achievement was measured using a modified geometry end-of-course assessment with a geometry readiness test as a covariate. Teacher efficacy data was obtained from the same teachers through an online survey at the end of the GAST project. Correlation, multiple regression, and hierarchical linear modeling techniques were used to analyze the data. Results revealed that the cognitive level of teacher practices significantly predicted student achievement. This finding provides support for increasing teacher awareness of the importance of high cognitive instruction by helping them recognize the essential features of classroom activities that provide this instruction and assisting them to plan and implement high cognitive tasks in their classrooms. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]