Findings from previous studies suggest that the effectiveness of students' teachers can have a significant impact on student achievement outcomes. However, scholars have not updated research on the short- and long-term effects of this experience, nor have they tied the information to highly effective and highly ineffective teachers' beliefs on teaching and learning. Using mixed research methods, I sought answers to the following research questions: Question 1 - Does mathematics teacher effectiveness affect student achievement when compounded over multiple years? Question 2 - What are effective/ineffective mathematics teachers' beliefs about teaching and learning? I first employed quantitative methods to assess the effects of spending three years in a row with highly effective or highly ineffective teachers. When I looked for the short-term effects of these three years that the students experienced, there was a statistically significant difference between entering & exiting achievement across teacher assignment group, with a large effect size. Additionally, there were statistically significant differences of entering & exiting achievement across teacher assignment group for students of differing achievement levels, with large effect sizes. There was no statistically significant effect of teacher assignment group on the change in achievement by entering achievement level. When I looked for the long-term effects of these three years, there were statistically significant differences in students' Algebra I projections by teacher assignment group, as well as statistically significant differences in students' SAT Math projections by teacher assignment group. I then utilized blind, semi-structured interviews with five highly effective teachers and five highly ineffective teachers to compare their views on teaching and learning to (1) the prevailing views of effective teaching in the math wars, and (2) to each other. I found that the highly effective teachers expressed more constructivist views of teaching and learning and the highly ineffective teachers expressed more traditional views. I also found there were distinct characteristics between highly effective and highly ineffective teachers' beliefs, specifically around beliefs on student engagement and responsibility for learning. The quantitative and qualitative results of this study have many implications for policy makers, K-12 teacher professional development and support programs, and teacher preparation programs.