Pre-deployment Computational Audit for Adaptive Mathematics Games: Item-Bank Circumvention Affordances, Scheduling Diversity, and Session-Parameter Checks in a Fraction Addition and Subtraction Case

Source abstract

Existing research rarely reports audits of item banks, practice scheduling, and interaction rules before classroom pilots. Content legality alone may leave task-requirement circumvention affordances (TRCA) undeclared. Near-uniform within-level sampling may produce short-window practice homogenization. This paper proposes and instantiates, on a fraction addition and subtraction drag-and-drop game, a pre-deployment computational audit for adaptive practice systems with discrete response checking and explicit session rules, where bank and scheduling logic can be expressed as deterministic predicates and rechecked item by item. For RQ1, instructional constraints and four TRCA types (S1–S4) are formalized as predicates, while bank filtering (Production vs. Relaxed) is separated from scheduler design (Full vs. Naive). For RQ2, ASSISTments-anchored response profiles (P1–P3) and a random-try baseline (P4) are used to examine heart limits and upgrade–stay–downgrade thresholds under a three-check interaction shell, with session burden reported. Among Relaxed items, 59.5% of addition items and 39.4% of subtraction items hit at least one declared TRCA; Production cleared those hits while retaining usable pools. Compared with Naive, Full reduced adjacent denominator-set repetition (6.8% vs. 26.0% for addition; 0.0% vs. 26.5% for subtraction) and increased Stage 1–3 short-window coverage (mean K: 5.18 vs. 3.95; 6.03 vs. 3.76). Under provisional defaults of three hearts and product upgrade–stay–downgrade thresholds, P1–P3 all campaign-cleared within the 100-item cap with ordered burden, whereas P4 had 0% campaign-clear. These findings provide design-audit evidence, not evidence of learning effectiveness.