Math Garden: A new educational and scientific instrument

This dissertation describes the research concerning the construction of a new educational and scientific instrument. This instrument, Math Garden, is a web application in which children can practice arithmetic by playing math games in which items are tailored to their ability level. At the same time, Math Garden enables studying arithmetical development with high frequency measurements. For these aims a new method for combining computer adaptive practice and testing was implemented. This method enables simultaneously tracking the development of the abilities of persons and the difficulties of items, and is an extension of the Elo rating system. Both response times and accuracy are used in the computation of the ability and item difficulty estimates. This dissertation includes research concerning the working of the system. It shows that the new computer adaptive method leads to reliable and valid ability and item difficulty estimates. For example, large proportions of variance in the item difficulties of addition, subtraction, and multiplication problems could be explained by a limited set of problem characteristics, and these estimates were robust over time. This supports the claim that this new method leads to stable and well interpretable item difficulty estimates. The dissertation also presents a classification method for classifying children’s arithmetical errors. Finally, the research within this dissertation supports the claim that both educational and scientific aims can be met within one instrument and that these fields (scientific research and education) may even benefit from each other.