Despite its importance, research on the dynamic nature of student engagement and its relationship with academic success is limited. In this study, we investigate the consistency of student engagement and its relationship to academic achievement. We conduct an analysis of digital trace data on students' interaction with webinars. Specifically, we examine the attendance records of 426 high school students participating in the online literature course designed to prepare them for university enrolment. We demonstrate engagement's path dependency as well as categorise different types of engagement strategies. We found that stable strategies do not lead to more engagement, however adaptive strategies do lead to greater engagement. Importantly, higher levels of engagement lead to better student achievement. These results demonstrating the strategic path-dependent nature of engagement, as well as give insight to the importance of engagement in online learning when considering students' learning paths.