This study examines the impact of teachers on student mathematical achievement in Chicago public high schools. Using administrative data on students and teachers, the authors estimate the importance of teachers on student test score gains in mathematics. They find that teachers are educationally and statistically important, with a teacher rated two standard deviations higher in quality adding 0.3 to 0.5 grade equivalents to a student's math score performance. Teacher quality ratings are relatively stable over time and not significantly influenced by classroom sorting or selective reporting of test scores. Traditional human capital and demographic measures explain little of the total variation in teacher quality. The study also finds that teacher quality is not well explained by observable characteristics, including those used for compensation. The results suggest that teacher quality estimates are not significantly influenced by missing test scores, indicating that selection bias is not a major concern. The study also explores the impact of sampling error, finding that it can significantly affect estimates of teacher dispersion. The authors conclude that teacher quality is an important factor in student achievement, and that the results are robust to various controls and specifications. The study highlights the disconnect between teacher pay and productivity, and the difficulty in developing compensation schedules that reward teachers for good work based on standard administrative data. The findings are relevant to education policy, as Chicago public schools serve a large population of minority and lower income students, typical of many large urban districts in the United States.This study examines the impact of teachers on student mathematical achievement in Chicago public high schools. Using administrative data on students and teachers, the authors estimate the importance of teachers on student test score gains in mathematics. They find that teachers are educationally and statistically important, with a teacher rated two standard deviations higher in quality adding 0.3 to 0.5 grade equivalents to a student's math score performance. Teacher quality ratings are relatively stable over time and not significantly influenced by classroom sorting or selective reporting of test scores. Traditional human capital and demographic measures explain little of the total variation in teacher quality. The study also finds that teacher quality is not well explained by observable characteristics, including those used for compensation. The results suggest that teacher quality estimates are not significantly influenced by missing test scores, indicating that selection bias is not a major concern. The study also explores the impact of sampling error, finding that it can significantly affect estimates of teacher dispersion. The authors conclude that teacher quality is an important factor in student achievement, and that the results are robust to various controls and specifications. The study highlights the disconnect between teacher pay and productivity, and the difficulty in developing compensation schedules that reward teachers for good work based on standard administrative data. The findings are relevant to education policy, as Chicago public schools serve a large population of minority and lower income students, typical of many large urban districts in the United States.