Clusters to Validate Knowledge Components: Analysis of an Adaptive Clock Reading Game

The modeling of a knowledge domain in a learning environ-ment is a critical step with far-reaching implications, notonly for the system design but also for the granularity withwhich student progress can be tracked. In the [System X]learning environment, games are designed to measure one di-mension of a broad knowledge domain (e.g. clock-reading).However, dimensionality is introduced in the games throughthe practice of specific knowledge components (KC; e.g.,reading digital clocks with half hours). The assignmentof specific items to these KCs is expert-based rather thandata-driven. To investigate the validity of these mappingsof items to KCs, this study employed a hierarchical clus-tering method on person-specific performance at the itemlevel. The results revealed a clear pattern; items associatedwith the same learning goal tend to cluster together. Thissupports the notion that learning goals capture meaningfuland distinct dimensions within the game. Finally, we illus-trate the progress of some players in the game to emphasizethe importance of detailed tracking of multiple abilities foreffective instruction and timely intervention.