KNOWLEDGE based Support in Problem-oriented Mathematical Tutoring Systems

A special type of ITS, called Problem-oriented Tutoring System (PTS), has been designed to train the skill of solving mathematical interpolation problems, i.e. problems, in which a start state has to be transformed into a goal state by stepwise applications of operators from a given operator set. Classes of interpolation problems occur in many subject areas of the mathematics curriculum in Secondary Schools. Examples are the transformation of arithmetic and algebraic terms, the solving of equations and the solving of geometric proof problems. Because some modules of an PTS are domain independent and a PTS needs only a rather simple student model, the costs for development are comparatively low. The concept of a PTS is explained and exemplified with reference to the tutorial systems GEOPROOF and GEOCON, developed and completely implemented by the author to support the solving of geometrical proof and construction problems. First classroom experiences with GEOPROOF are reported.