The pursuit of multiple educational outcomes makes teaching a complex craft subject to potential conflicts and competing commitments. Using a data set in which teachers were randomly assigned to classes paired with videotaped lessons, we both document and unpack such a tradeoff. Upper-elementary teachers who excel at raising students' math test scores often are less successful at improving student-reported engagement in class (and vice versa). Furthermore, teaching practices that improve test scores (e.g., cognitively demanding content) can simultaneously decrease engagement. At the same time, paired quantitative and qualitative analyses reveal two areas of practice that support both outcomes: active mathematics with opportunities for hands-on participation, physical movement, and peer interaction; and established routines and procedures to proactively organize the classroom. In addition to guiding practice-based teacher education, our sequential, explanatory mixed-methods analysis can serve as a model for rigorously studying and identifying dimensions of "good" teaching that promote multidimensional student development.