Determining indicators and predictors of effective teachers is not only important to helping current practicing teachers improve, but is also important for the training of the new teaching force. There are now measures of effective teaching, but there are no sets of factors or attributes that define an effective teacher. Increased accountability falls on current educators and drives the questions of not only what makes an effective teacher, but how can teacher effectiveness be reliably measured? As the world looks to the United States to deliver advancements in the areas of science, technology, engineering, and mathematics, the questions remain - What qualities indicate effective Algebra I teachers and can student standardized assessments predict teacher effectiveness? A specific focus on Algebra I teachers is important as it is a required course for all students and it is a course that establishes future success in the areas of Science, Technology, Engineering, and Mathematics (STEM). This study established latent classes of effective and non-effective Algebra I teachers using measurements of teacher promoted engagement, teacher promoted understanding, and classroom management from the MET Project database and supports class identification accuracy with Principal effectiveness scores. Indicators of effective teachers are also determined through the Tripod 7Cs Student Perception Survey, the Classroom Assessment Scoring System, and the Framework for Teaching. Established categories of teacher effectiveness helped to identify teacher characteristics that defined effective and non-effective teachers. Teacher effectiveness classification was compared with student achievement data from the ACT QualityCore® Algebra I, and was not able to discriminate established latent classes of teacher effectiveness, suggesting student test scores did not predict effective teachers identified in this study. Knowledge of effective teacher characteristics will help to improve current teacher education programs, establish successful and meaningful professional development, and increase teacher retention rates in the United States, and shift the focus of teacher evaluation away from standardized test scores.