Purpose: Increasingly, school systems are forming improvement networks and using continuous improvement (CI) to realize more ambitious and equitable instruction. Yet networks reside in environments that place formidable demands on school leaders and house multiple, and sometimes contradictory, beliefs about educational goals and practices. Leveraging a framework derived from institutional logics, we investigate how three elementary school principals drew on competing theories, frames, and narratives to interpret and enact CI routines as part of a school turnaround network. Research Methods/Approach: Drawing on data from individual and focus-group interviews from a 3-year research project, we conducted a comparative case-study analysis to understand how three school leaders led CI efforts intended to improve mathematics instruction and student learning. Our qualitative findings emerge from multiple cycles of interview coding to describe how school leaders drew on different theories, frames, and narratives to enact CI. Findings: Despite access to common tools and routines, each principal identified markedly different types of educational problems and enacted substantively different solutions. The variable approaches corresponded to divergent "field-level logics" defined by fundamentally different beliefs about teaching and learning, as well as alternative ways of managing the demands of accountability, academic rigor, and community needs. Implications: A shared instructional infrastructure and networked improvement approach can help align CI efforts in large districts, but for district-based improvement networks to support coherent and sustainable advances to teaching and learning, leaders must cultivate a shared approach to managing the myriad demands of contemporary educational environments that often feature multiple and competing institutional logics.