The COVID-19 pandemic required educators and learners to shift to emergency remote instruction with little time for preparation. To understand how teachers managed the transition, we surveyed nearly 1,500 teachers from 118 countries from April to September 2020. Using cluster analysis, we detect two readily distinguishable groups of instructors: a group who was more engaged with remote instruction and had better coping in terms of online teaching challenges, and a group who had lower levels of both engagement and coping. We compare the two groups in terms of their sociodemographic characteristics, and also assess the relationship between each sociodemographic marker and teachers’ engagement and coping. Overall, our results suggest that teachers were most engaged and coped best with the transition when they had prior experience with remote instruction, taught in the higher education sector, and taught using real-time synchronous modalities. We also find non-trivial results regarding teachers’ gender, years of teaching experience, and their country’s level of economic development, and observe no relationship between teachers’ age and engagement or coping. The detection of the contextual effects underscores the importance of large multisite research.