Representation for interactive exercises

Interactive exercises play a major role in an adaptive learning environment ActiveMath. They serve two major purposes: training the student and assessing his current mastery, which provides a basis for further adaptivity. We present the current state of the knowledge representation format for interactive exercises in ActiveMath. This format allows for representing multi-step exercises, that contain different interactive elements. The answer of the learner can be evaluated semantically. Various types of feedback and hint hierarchies can be represented. Exercise language possesses a construction for specifying additional components generating (parts of) the exercise. One example of such component is a Randomizer, which allows for authoring parametrized exercises. Another example is so-called Domain Reasoner Generator, that automatically generates exercise steps and refined diagnosis upon the learner's answer. This turns ActiveMath system into an ITS as soon as some Domain Reasoner is connected to it. Finally, several tutorial strategies can be applied to the same exercise. This strategies control feedback and the way the exercise is navigated by the learner, and can adapt to the learner.