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Prior work in the achievement gap has focused on the subject-level gaps. While this line of research has provided useful policy recommendations, it does not necessary help teachers and school leaders design classroom instructions. This study digs deeper in this topic and examines socioeconomic and race/ethnicity gaps in the cognitive domain (i.e., knowing, applying, and reasoning) to provide them with practical recommendations. Using assessment data from the Trends in International Mathematics and Science Study, I find that large achievement gaps exist in all of the cognitive processes with some variation among them and that they are widening over time. I also find that school fixed effects reduce the gaps substantially, underscoring the importance of public education in narrowing the gaps.