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

Abstract

The modeling of a knowledge domain in a learning environment is a critical step with far-reaching implications, not only for the system design but also for the granularity with which student progress can be tracked. In the Math Garden learning environment, games are designed to measure one dimension of a broad knowledge domain (e.g., clock-reading). However, dimensionality is introduced in the games through the practice of specific knowledge components (KC; e.g., reading digital clocks with half hours). The assignment of specific items to these KCs is expert-based rather than data-driven. To investigate the vali dity of these mappings of items to KCs, this study employed a hierarchical clustering method on person-specific performance at the item level. The results revealed a clear pattern; items associated with the same learning goal tend to cluster together. This supports the notion that learning goals capture meaningful and distinct dimensions within the game. Finally, we illustrate the progress of some players in the game to emphasize the importance of detailed tracking of multiple abilities for effective instruction and timely intervention.