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We explore the dynamics of competitive search in the K-12 public education sector. Using data from Boston Public Schools, we document how teacher labor supply varies substantially by position types, schools, and the timing of job postings. We find that early-posted positions are more likely to be filled and end up securing new hires that are better-qualified, more-effective, and more likely to remain at a school. In contrast, the number of applicants to a position is largely unassociated with hire quality, suggesting that schools may struggle to identify and select the best candidates even when there is a large pool of qualified applicants. Our findings point to substantial unrealized potential for improving teacher hiring.