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Py D.,
Nicolas P. (1990)
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Abstract This paper presents MENTONIEZH, an Intelligent Tutoring System in geometry, which coaches and corrects a student during a problem solving session. Most of the time, geometry I.T.S.s concentrate upon the way to coach a student who demonstrates. Now, we think that geometry problem solving is not limited to proof writing. At school, pupils, who practise with paper and pencil, begin with drawing a scheme, investigating it, and sometimes adding objects. So, we are interested in the integration of a preliminary phase. During this phase, the pupil draws the figure corresponding to the problem, and the system corrects it. We present the languages used by the pupil and the teacher to describe the statement's hypotheses. Then, we translate the two formulae into a common logical language, in order to be able to compare them. We study the possibility of reducing this representation, by deducing equalities of objects. At last, we perform the comparison, which evaluates whether the pupil's figure is both proper and not particular, in regard to the specification the teacher gave. Concerning the second phase, we want to take into account the fact that the most natural proof, according to a pupil, is not necessarily the straightest one, neither the one choosed by a teacher. So, we are interested in designing a tutor which accepts a correct but not optimal proof. That is the reason why we need to recognize the student's intention, which may be formalized as plans, the actions of which are theorem applications, in order to provide the student with well-adapted assistance, and to avoid too much directiveness. A plan recognition method is presented, which deduces, from the problem's space research and the student's inputs, the underlying intention, and can also detect intention shifting. Otherwise, the system relies on the classical architecture of an I.T.S. The expert of the domain, a set of geometry rules together with an inference engine, can solve exercises in different ways and distinguish the student's erroneous or unuseful inferences. At last, we describe implemented parts of the system, its evaluation, and compare with related works about I.T.S. in geometry. |