Every mathematics teacher who uses online practice platforms has likely experienced the same pattern: a course begins with enthusiasm, students actively solve exercises, deadlines are respected, and participation appears strong. Gradually, however, some students begin to disengage. They submit fewer exercises, postpone practice, or stop participating altogether.
The challenge is not only identifying whether students engage, but understanding how engagement changes over time. Learning analytics can provide valuable insight into this process.
In our recent study (Papageorgiou et al., 2026) involving 236 first-year engineering students enrolled in Linear Algebra courses, we explored how students interacted with an online mathematics homework platform during seven weeks of blended learning. Rather than focusing only on final grades or total clicks, we examined engagement as a dynamic process that evolves throughout the course.
This perspective is inspired by research viewing student engagement as a Complex Dynamical System (Hilpert & Marchand, 2018; Symonds et al., 2024). From this viewpoint, engagement is not fixed; students move between different states of participation depending on workload, motivation, confidence, and the learning environment.
Using learning analytics, we analyzed students’ online behaviour through indicators connected to behavioural engagement, including effort, regularity, persistence, and time investment (Flunger et al., 2015). The analysis revealed four weekly engagement states.
Some students were Diligent: they practiced regularly, worked across many topics, and invested substantial time in learning. Others were Compliant, consistently following deadlines and course expectations. A third group showed a more limited pattern of engagement, which we called Minimalist. Finally, some students became completely Inactive, showing no participation during certain weeks.
What mattered most was not only the existence of these states, but how students moved between them over time.
Using sequence analysis, we identified three broader engagement trajectories across the seven weeks. One group followed a stable Highly Compliant trajectory, maintaining regular engagement throughout the course. Another displayed a Fluctuating trajectory, moving unpredictably between more and less engaged states. A third trajectory was Mainly Inactive, characterized by persistent disengagement.
One important finding was that inactivity tended to become an “absorbing” state. Once students entered an inactive pattern, they rarely returned to sustained engagement without support. In contrast, students who regularly followed weekly deadlines were more likely to maintain stable engagement over time.
These findings have important implications for mathematics teaching practice.
First, they suggest that the early weeks of a course are critical. Learning analytics can help teachers identify students at risk before disengagement becomes entrenched.
Second, the study highlights the importance of structure in mathematics learning. Students who consistently followed the weekly schedule tended to display more resilient engagement trajectories. This does not necessarily mean students need strict control, but rather that carefully designed routines and pacing can support sustained participation.
Third, learning analytics becomes most valuable when combined with timely instructional action. Analytics alone does not improve learning; what matters is how teachers respond to the information. Personalized reminders, low-stakes catch-up opportunities, adaptive exercises, or short teacher interventions may help students reconnect before disengagement stabilizes.
Another important result concerned motivation. Students with stronger expectancy beliefs, that is, stronger confidence in their ability to succeed, were more likely to belong to the engaged trajectories. This finding aligns with expectancy-value theory (Eccles & Wigfield, 2020) and suggests that fostering students’ sense of competence early in mathematics courses may play a central role in sustaining engagement.
This finding resonates strongly with mathematics education, where feelings of competence often shape participation. Supporting students’ confidence early in the course may therefore be just as important as designing good mathematical tasks.
Interestingly, the trajectories did not significantly differ in final course grades, although students in the Mainly Inactive trajectory showed lower average performance (not sufficient) overall. This reminds us that engagement is complex: students may compensate for lower online participation through other study strategies, prior knowledge, or external resources. Learning analytics should therefore support, not replace, teachers’ pedagogical interpretation.
For mathematics educators, the challenge is therefore not only collecting data, but transforming it into meaningful teaching practices that support students’ long-term engagement.