Modeling and Optimizing Computer-Assisted Mathematics Learning in Children

Arithmetic abilities are essential in modern society. However, many children suffer from difficulties in learning mathematics, ranging from mild to severe numeracy problems. The prevalence of developmental dyscalculia is about 3%−6% in German speaking countries. Children with developmental dyscalculia often develop anxiety and aversion against thesubject and experience difficulties in school and later in profession. Despite the relatively high prevalence, few targeted interventions for children with developmental dyscalculia exist and only a fraction of these programs is computer-based. In this thesis, we present a complete loop in the data-driven development of an intelligent tutoring system for mathematics learning that overcomes the limitations of previous work.This process consists of three steps: The development of a first training environment, its evaluation in user studies and the data-driven validation and improvement of the system. We first develop Calcularis, a computer-based training program for children with difficulties in learning mathematics. The curriculum and concepts of the system are theory-based: The program transforms current neuro-cognitive findings into the design of different instructional games. A Bayesian network student model representing different mathematical skills and their dependencies, and a non-linear control algorithm ensure adaptationof the training to the mathematical abilities of the individual child. Furthermore, the program features a bug library allowing recognition and remediation of specific errors. In a second step, we evaluate Calcularis in two user studies to prove its effectiveness. Based on the input data collected in these studies, we performa data-driven validation andimprovement of the program in the third step. We assess student model and controller properties and analyze the quality of our model via logistic regression. The data-driven investigations lead to the development and extensiveanalysis of techniques for model validation. We improve prediction accuracy of the student model by introducing aconstrained latent structured predictionmethod for efficientparameter learning in Bayesian networks. By applying a clustering and classification approach, we are able to predict the mathematical characteristics of the children. Moreover, we also explore the possible addition of an engagement model to Calcularis. Finally, we develop a data-driven diagnosis tool for developmental dyscalculia based only on input data. The integration of this tool into Calcularis closes the loop of data-driven development.