Digital disruption is not a new phenomenon in education; however, it has become more prominent during the COVID-19 pandemic due to school closures and the related emergency remote teaching (ERT) period. Our study aims to explore the different pedagogical strategies that primary school teachers adopted during this period and determine how successful these strategies were in involving and engaging students. Altogether, 4028 teachers from 343 primary schools answered our online survey from all the regions of Hungary. The sample adequately represents the Hungarian primary school teacher population in terms of gender and age. We used cluster analysis and identified four clusters of pedagogical strategies; then, we used analysis of variance to explore how teachers' digital competence and their ability to involve students in online learning varied across different clusters. Our analysis grasps the complexity of the issue, as it shows that two rather distinct strategies were both successful in involving students, and thus, there is no single solution best suited to digital learning. Overall, digitally competent teachers loosened the originally strict structure of education and provided more feedback, which proved to be an important element in successfully involving students in digital learning during ERT. The framework validated in our research can be used by policymakers and school administrators in different national and educational contexts, enabling them to understand the complexity of online teaching and learning. Furthermore, our results can offer some practical pointers for school teachers on how to combine different pedagogical strategies.