Preparing Oral Examinations of Mathematical Domains with the Help of a Knowledge-Based Dialogue System

A conception of discussing mathematical material in the domain of calculus is outlined. Applications include that university students work at their knowledge and prepare for their oral examinations by utilizing the dialogue system. The conception is based upon three pillars. One central pillar is a knowledge base containing collections of mathematical objects: theorems and their proofs, concepts, and task types. Manifold attributes complement the object specifications including attributes related to categorization, to didactics, to applications, to transition to other objects, and to error handling. The second pillar consists of question types, of dialogue strategies, and of a user model. To formulate the answers a restricted natural language is used. The selection and the order of the questions may be controlled by an explicit specification or implicitly by the choice of a dialogue strategy including an exploration dialogue, a spot check dialogue, or a problem solving dialogue. The third pillar consists of procedural knowledge to monitor and verify the answers. For that, techniques of the fields of theorem proving and of formula manipulation are employed.