MULTI-OUTPUT GRADIENT BOOSTING FOR TPACK COMPONENT ESTIMATION FROM CONTAINER-LEVEL PROGRAMMING TRACES

Assessing the simultaneous development of programming competence and pedagogical content knowledge in preservice informatics teachers is an open measurement problem. Survey-based instruments capture beliefs rather than behavior, and standard programming analytics pipelines track a single skill objective without modeling the pedagogical knowledge dimension that differentiates teacher candidates from ordinary computing students. This paper presents a multi-output gradient boosting architecture that estimates all four TPACK component mastery levels Technological Knowledge, Pedagogical Knowledge, Content Knowledge, and Pedagogical Content Knowledge- from behavioral traces collected at the container runtime level during programming laboratory sessions. A six-category feature taxonomy is derived from Docker daemon event streams, application-layer compilation logs, keystroke sequences, version control snapshots, help-seeking interactions, and a fine-tuned DistilBERT pedagogical reflection classifier. Experiments on a synthetic benchmark of 850 annotated sessions evaluate eight model configurations against four baselines, including standard Bayesian Knowledge Tracing and single-output gradient boosting. The proposed architecture reaches a macroaveraged F1 of 0.791 across all four TPACK components, exceeding the strongest single-output baseline by 6.8 percentage points and reducing mean absolute error on continuous mastery estimates by 18.3% relative to BKT. Ablation results confirm that the pedagogical reflection features contribute 9.2 points of F1 to PCK prediction specifically, with negligible benefit to TK and CK, validating the trace taxonomy's component-specific design. Feature importance analysis reveals that inter-key pause placement and compilation error transition patterns are the most informative signals for CK assessment, while lexical PCK features dominate pedagogical component prediction.

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