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Knowledge spillovers in the classroom provide important policy implications for school and classroom design. This study quantifies the ability spillovers among six-graders in public schools and investigates the structure of peer effects. The study combines a unique data set and an innovative research strategy to identify peer effects in the classroom. The findings imply that peer effects are heterogeneous in nature and that peer group composition matters for individual achievement. Thus, low achievers benefit from high-achieving peers while the progress of high-achievers is not affected by their low-achieving classmates. This suggests gains from evening out the ability distribution across classes within a school.