Computer adaptive practice of Maths ability using a new item response model for on the fly ability and difficulty estimation

In this paper we present a model for computerized adaptive practice and monitoring. This model is used in the Maths Garden, a web-based monitoring system, which includes a challenging web environment for children to practice arithmetic. Using a new item response model based on the Elo (1978) rating system and an explicit scoring rule, estimates of the ability of persons and the difficulty of items are updated with every answered item, allowing for on the fly item calibration. In the scoring rule both accuracy and response time are accounted for. Items are sampled with a mean success probability of .75, making the tasks challenging yet not too difficult. In a period of ten months our sample of 3648 children completed over 3.5 million arithmetic problems. The children completed about 33% of these problems outside school hours. Results show better measurement precision, high validity and reliability, high pupil satisfaction, and many interesting options for monitoring progress, diagnosing errors and analyzing development.