Untangling complexity of competency evolution: Multi‐channel learning trajectories of score, engagement and problem‐solving efficiency

Students' competency–knowledge, skills and dispositions–evolve over time and interact with the learning environment, forming a complex dynamic system. However, little research has explored their joint evolution patterns. In this study, jointly mapping competencies by three channels: score, engagement and problem‐solving efficiency (code metrics), we analysed a large‐scale dataset from an introductory programming course using a blended learning approach, comprising 61,709 code submissions in 10 formative assessments for 209 students. Via Latent Class Analysis and Self‐Organizing Maps, we identified different states of each channel. Using multi‐channel clustering and Transition Network Analysis, three distinct learning patterns were discovered: disengagers, strivers and optimizers. Further subgroup analysis, with final exam performance as reference, revealed critical differences within these trajectories: persistently struggling disengagers and late‐emerging disengagers, successful strivers and declining strivers. Our findings also indicated that learning patterns remain highly stable throughout the semester, aligning with the universal dynamics of complex systems. Moreover, these trajectories were strongly associated with engagement across different phases of blended learning (pre‐class, in‐class, after‐class and self‐perception) and final exam performance. Through dynamic importance evaluation by Longitudinal Random Forest, we found that early learning patterns and performance played a crucial role in final success of the course, highlighting the importance of starting strong. Additionally, the in‐depth analysis of students' problem‐solving strategies through code metrics provided valuable insights into their authentic learning processes. Based on these findings, we discussed potential implications, which could be applied to broader educational contexts beyond computer science. Practitioner notes What is already known about this topic A student's competency is composed of contextually situated knowledge, skills and dispositions during the learning process. As one of the most digitally advanced disciplines, computer science typically employs blended learning environments, which allow for the collection of more comprehensive data during the learning process. Most existing studies analyse students' skills at the level of individual problems, with few tracking how these skills evolve over time. What this paper adds We introduce a robust method for mapping skills from their solutions, integrating a longitudinal analysis with other dimensions to explore joint competency evolution. Each student follows a distinct and relatively stable learning trajectory. These trajectories are significantly linked to engagement at different phases of blended learning and final achievement. The initial state of competency plays a critical role in determining both the learning trajectory and final achievement. Implications for practice and/or policy Longitudinal analyses of students' problem‐solving process offer valuable insights into authentic learning processes, which could be applied to broader educational contexts. Supporting substantive progress among struggling students requires targeted interventions that go beyond conventional practices. Establishing a strong foundation and fostering good learning patterns in early stages is crucial for long‐term success.