Learning qualitative and quantitative reasoning in a microworld for elastic impacts

From a psychological point of view efficient teaching by means of an intelligent tutoring system necessarily involves that the communication of knowledge is adapted to the requirements of the learner: to her cognitive abilities, her pre-instructional knowledge and her learning capabilities. To tackle these topics in a precise way, we have developed the artificial-intelligence-based microworld DiBi (disk billiard) and MULEDS, a multi-level diagnosis system. The microworld DiBi sets up a learning environment which simulates elastic impacts as a subtopic of classical mechanics. DiBi enables and supports reasoning on different levels of mental domain representation ordered along the dimension ‘qualitative/quantitative’. This way of representing the domain provides a basis for passive adaptation in an advanced way. Correspondingly, active adaptation is supported by MULEDS, wherein student modeling is realized by assessing the student’s correct and/or incorrect domain-specific knowledge at these different levels. Within this psychological perspective, the use of instructional tools, such as the microworld DiBi and the computerized diagnosis system MULEDS, aims at gradually supporting and guiding the student in the construction of more and more powerful an sound domain representations. The progression through these levels of domain representation will enable the student to solve the problems posed by the domain in a flexible way.