Tracing Systematic Errors to Personalize Recommendations in Single Digit Multiplication and Beyond

In learning, errors are both ubiquitous and inevitable. It is widely understood that these errors may provide a clue about a person's misconceptions. In this article we propose and investigate a model that aims to identify misconceptions from observed errors. We apply the method to single digit multiplication; a domain that is very suitable for the method, is well-studied, and allowed us to analyze over 25,000 error responses from 335 actual learners. The model, derived from the Ising model popular in physics, makes use of a bigraph that links possible errors to possible misconceptions. The error responses were taken from Math Garden, a computerized adaptive practice environment for arithmetic that is widely used in The Netherlands. The results show that the model outperforms a random selection from the observed errors' possible causes, and correctly predicts the possible cause of a person's subsequent error up to over 75% of the time. Finally, we discuss the model, the findings, and the implications.

Set-theoretical and Combinatorial Instruments for Problem Space Analysis in Adaptive Serious Games

The Computerized Adaptive Practice (CAP) system describes a set of algorithms for assessing player’s expertise and difficulties of in-game problems and for adapting the latter to the former. However, an effective use of CAP requires that in-game problems are designed carefully and refined over time to avoid possible barriers to learning. This study proposes a methodology and three different instruments for analyzing the problem set in CAP-enabled games. The instruments include the Guttman scale, a ranked order, and a Hasse diagram that offer analysis at different levels of granularity and complexity. The methodology proposes to use quantified difficulty measures to infer topology of the problem set. It is well-suited for serious games that emphasize practice and repetitive play. The emphasis is put on the simplicity of use and visualization of the problem space to maximally support teachers and game developers in designing and refining CAP-enabled games. Two case studies demonstrate practical applications of the proposed instruments on empirical data. Future research directions are proposed to address potential drawbacks.