To combat high failure and student drop-out rates, universities have developed strategies to monitor online student engagement through measurable activities. In this study, we explore if and how these monitoring activities accurately measure online engagement. We interviewed nine highly engaged online third-year students throughout a semester to find out more about what engagement meant for them and how they enacted it in the online space, both visibly and invisibly. According to students in this study, traditional measures of online engagement were not perceived as valuable to their learning. The students complained about the 'busy work' -- tasks that kept them busy or that monitored their engagement through a metrics-based tool. The students reported a number of other activities that prompted their engagement in learning; many of these would not be picked up by the usual ways of measuring engagement. These findings invite educators to move away from having fixed ideas about where and how and when online students should be engaging. They invite critique of the superficial, descriptive, tick-the-box exercises that are usually designed to monitor engagement by computer rather than through human interaction. They offer educators an opportunity to explore other ways of understanding student engagement in the online space.