Behavioural engagement as a dynamical system of effort and time: Investigating web-based engineering mathematics practice

Mathematics plays a foundational role in undergraduate engineering education, yet many students find it challenging. To address this, programs such as PRIME at TU Delft have adopted blended learning approaches that combine traditional face-to-face instruction with web-based practice environments. The Grasple platform (www.grasple.com), used within PRIME, supports self-paced mathematics practice. While such environments offer flexibility and opportunities for individualized learning, their effectiveness depends critically on students' ability to engage consistently and productively over time. However, many students struggle to sustain this engagement, particularly in low-stakes contexts. At the same time, substantial heterogeneity in prior knowledge and motivation is likely to give rise to diverse engagement patterns. Despite this, empirical research explicitly examining differential and evolving engagement in web-based mathematics practice remains limited.

The overarching objective of this dissertation is to advance the understanding of behavioural engagement (BE) in web-based engineering mathematics practice and to inform the design of evidence-based support strategies. To achieve this, three interrelated research questions are addressed: (1) How is student engagement (SE) conceptualized, measured, and associated with learning outcomes in undergraduate mathematics? (2) How do BE patterns vary within and between students over time? (3) How can BE be enhanced? Across four chapters, the dissertation combines systematic review methods, learning analytics, and person-oriented approaches to examine BE as a complex, multidimensional, and dynamic process.

By investigating BE in web-based mathematics practice within undergraduate engineering education, this dissertation offers three main contributions. First, it advances the understanding of BE as a heterogeneous and dynamic process, showing that engagement is not adequately captured by aggregated indicators alone, but instead unfolds through distinct patterns that vary across and within students over time. Second, it highlights the role of individual differences in shaping these patterns. Students' motivational beliefs and prior knowledge are closely linked to how engagement develops and how students respond to support, underscoring that BE is shaped not only by effort and time but also by students' beliefs about themselves and the value they place on learning activities. Third, the dissertation illustrates how theory-informed learning analytics can support more meaningful interpretations of behavioural data and inform the design of targeted interventions. Rather than assuming uniform effectiveness, the findings suggest that support for engagement should be sensitive to both students’ behavioural patterns and their underlying motivational characteristics. Taken together, these contributions emphasize the importance of moving beyond simplified and static views of engagement toward approaches that better reflect its complexity, variability, and context-dependence.