Tanja Käser

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a childs individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities.

Beyond Knowledge Tracing: Modeling Skill Topologies with Bayesian Networks

Modeling and predicting student knowledge is a fundamental task of an intelligent tutoring system. A popular approach for student modeling is Bayesian Knowledge Tracing BKT. BKT models, however, lack the ability to describe the hierarchy and relationships between the different skills of a learning domain. In this work, we therefore aim at increasing the representational power of the student model by employing dynamic Bayesian networks that are able to represent such skill topologies. To ensure model interpretability, we constrain the parameter space. We evaluate the performance of our models on five large-scale data sets of different learning domains such as mathematics, spelling learning and physics, and demonstrate that our approach outperforms BKT in prediction accuracy on unseen data across all learning domains.

Modelling and optimizing the process of learning mathematics

This paper introduces a computer-based training program for enhancing numerical cognition aimed at children with developmental dyscalculia. Through modelling cognitive processes and controlling the level of their stimulation, the system optimizes the learning process. Domain knowledge is represented with a dynamic Bayesian network on which the mechanism of automatic control operates. Accumulated knowledge is estimated to select informative tasks and to evaluate student actions. This adaptive training environment equally improves success and motivation. Large-scale experimental data quantifies substantial improvement and validates the advantages of the optimized training.

Cluster-Based Prediction of Mathematical Learning Patterns

This paper introduces a method to predict and analyse students’ mathematical performance by detecting distinguishable subgroups of children who share similar learning patterns. We employ pairwise clustering to analyse a comprehensive dataset of user interactions obtained from a computer-based training system. The available data consist of multiple learning trajectories measured from children with developmental dyscalculia, as well as from control children. Our online classification algorithm allows accurate assignment of children to clusters early in the training, enabling prediction of learning characteristics. The included results demonstrate the high predictive power of assignments of children to subgroups, and the significant improvement in prediction accuracy for short- and long-term performance, knowledge gaps, overall training achievements, and scores of further external assessments.

When to stop?: towards universal instructional policies

The adaptivity of intelligent tutoring systems relies on the accuracy of the student model and the design of the instructional policy. Recently an instructional policy has been presented that is compatible with all common student models. In this work we present the next step towards a universal instructional policy. We introduce a new policy that is applicable to an even wider range of student models including DBNs modeling skill topologies and forgetting. We theoretically and empirically compare our policy to previous policies. Using synthetic and real world data sets we show that our policy can effectively handle wheel-spinning students as well as forgetting across a wide range of student models.

Towards a Framework for Modelling Engagement Dynamics in Multiple Learning Domains

In this paper, we explore the possibility of a general framework for modelling engagement dynamics in software tutoring, focusing on the cases of developmental dyslexia and developmental dyscalculia. This project aims at capturing the similar engagement state patterns for the two learning disabilities. We start by presenting a model of engagement dynamics in spelling learning, which relates input behaviour to learning and explains the dynamics of engagement states. Predictive power of extracted features is increased by incorporating domain knowledge in the pre-processing. The introduced model enables the prediction of focused and receptive states, and of forgetting. In the second part, we extend the model to a more general framework, which takes into account the similarities and dissimilarities of the two studied cases. Finally, we define desirable properties of a general engagement dynamics model, while analysing the reusability of the introduced spelling model.

Dynamic Bayesian Networks for Student Modeling

Intelligent tutoring systems adapt the curriculum to the needs of the individual student. Therefore, an accurate representation and prediction of student knowledge is essential. Bayesian Knowledge Tracing (BKT) is a popular approach for student modeling. The structure of BKT models, however, makes it impossible to represent the hierarchy and relationships between the different skills of a learning domain. Dynamic Bayesian networks (DBN) on the other hand are able to represent multiple skills jointly within one model. In this work, we suggest the use of DBNs for student modeling. We introduce a constrained optimization algorithm for parameter learning of such models. We extensively evaluate and interpret the prediction accuracy of our approach on five large-scale data sets of different learning domains such as mathematics, spelling learning, and physics. We furthermore provide comparisons to previous student modeling approaches and analyze the influence of the different student modeling techniques on instructional policies. We demonstrate that our approach outperforms previous techniques in prediction accuracy on unseen data across all learning domains and yields meaningful instructional policies.

Modelling and Optimizing Mathematics Learning in Children

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic Bayesian network which incorporates domain knowledge and enables the operation of an online system of automatic control. The system identifies appropriate tasks and exercise interventions on the basis of estimated levels of accumulated knowledge. Student actions are evaluated and monitored to extract statistical patterns which are useful for predictive control. The training system is adaptive and personalizes the learning experience, which improves both success and motivation. Comprehensive testing of input data validates the quality of the obtained results and confirms the advantage of the optimized training. Pilot results of training effects are included and discussed.

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children.

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the childs individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6–8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.

Stealth Assessment in ITS - A Study forźDevelopmental Dyscalculia

Intelligent tutoring systems are adapting the curriculum to the needs of the student. The integration of stealth assessments of student traits into tutoring systems, i.e. the automatic detection of student characteristics has the potential to refine this adaptation. We present a pipeline for integrating automatic assessment seamlessly into a tutoring system and apply the method to the case of developmental dyscalculia DD. The proposed classifier is based on user inputs only, allowing non-intrusive and unsupervised, universal screening of children. We demonstrate that interaction logs provide enough information to identify children at risk of DD with high accuracy and validity and reliability comparable to traditional assessments. Our model is able to adapt the duration of the screening test to the individual child and can classify a child at risk of DD with an accuracy of 91i?ź% after 11i?źmin on average.