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Tanja Käser, Markus Gross
Content
Introduction
Developmental dyscalculia is a specific learning disability affecting the acquisition of arithmetic skills. Genetic, neurobiological, and epidemiological evidence indicates that developmental dyscalculia, like other specific learning disabilities, is a brain-based disorder, although poor teaching and environmental deprivation have also been implicated in its aetiology. The prevalence of developmental dyscalculia in Germany and Switzerland is about 6%.
We develop a novel software, that trains underlying skills such as subitizing, strengthens the understanding of number representation accoring to the tipple code model, and introduces arithmetic operations. Behind the sceens, a Bayes net adjusts the learning to the student's individual skills.
Training Software
The software both trains mathematical functions as well as different number representations (see below). Different game forms are available. There are two main games: The "Landing Game" trains the representation of numbers on the number line, which is the most advanced form of representation. The "Calculator" trains mathematical operations. Additionally, there are several support games training subitizing, estimation, the transfer of spoken numbers to arabic numberals, ordering, the crossing of tens, etc. If a student displays difficulties in one of the main games, the software turns to the support game most suitable to train the necessary skills.
The support game to train estimation.
All the games permanently use the different number representations. In order to do so, we use modern 3D graphics and animation. Especially for representing the number line and morphing one representations seemlessly into another representation, there is nothing more suitable than computer graphics.
(The training software is developped together with the ETH spin-off Dybuster in a project sponsored in parts by CTI.)
Number Processing
The three different number representations (spoken, arabic and internal number lines) and the translation between them form the basis of number processing. Therefore, we develop a special number design to enhance these representations and at the same time facilitate numerical understanding.
The number "848" represented as a combination of colors and a topology.
The number 53 displayed in 3D to facilitate establishing the mental number line.
Student Modelling
In order to offer optimal learning conditions, the software adapts to the needs of a specific user. At the beginning of the training, all users start with the same game. After each input, the software estimates the actual knowledge state of the user and displays a new task adjusted to this state. In this way, the velocity of advancement can be adapted to each user and specific problems of a user can be recognized and addressed.
In order to do so, the software holds an internal representation of the userŐs knowledge. In our case, the knowledge is modeled using a dynamic Bayes net. This net consists of a directed acyclic graph representing different mathematical skills and the dependencies between them. If, for example, a user is proficient in the number range 0 to 100, the Bayes net will start prompting tasks in the range 0 to 1,000. If a student fails in the range 0 to 1,000, the Bayes net will return to the range 0 to 100.
UserStudies
To validate the effectiveness of our approach, we run several user studies. The studies started in 2011. You can find more about the studies here: Link to user studies.
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