Evaluating the impact of STACK-based formative assessment on final examination performance in first year linear algebra

Online assessment tools offer new opportunities to enhance formative assessment in large courses. This study examined how the System for Teaching and Assessment using a Computer Algebra Kernel (STACK), an open-source online assessment system for mathematics, was used in two first-year Linear Algebra courses at a large public university in Italy over consecutive academic years. Using an ex-post facto design and hierarchical clustering analysis, we compared patterns of student engagement and examination performance before and after the introduction of STACK. The two courses differed in implementation intensity: one integrated ten graded quizzes supported by in-class feedback, while the other offered six optional self-practice quizzes. Results showed that stronger integration of STACK was associated with higher student participation and improved examination performance. Clustering analysis identified three engagement profiles, strategic, disengaged and frequent users, reflecting diverse learning behaviours. These findings suggest that the effectiveness of automated assessment depends not only on the technology but also on how it is embedded in course design and pedagogy.