Intelligent tutors and artificial intelligence: Problems in the construction of geometric figures

Abstract

Our purpose is to illustrate, through the conception and realization of an ITS for the construction of geometric figures, an approach to the expression of the pedagogical contract based on first order logic. It is critical for the contract to be very precise as well as understandable and explanable throughout. This requires the teacher to define the specification of the goal to be attained and the context using tools with a precise semantics. The means of expression available to the student for constructing a solution must also possess a clear semantics. We show that a methodology associating a formula in a logic language which is common to the specification and to the solution makes it possible to give a first concrete definition of a given contract. We can then better grasp both the requirements for the contract not accounted for in a first stage and the constraints of implementation and efficiency. Certain points which still require improvement—e.g., the exact meaning of negation and the non particularity of constructions—are brought to light. Finally, we present the results of experiments with exercises typically found in geometry textbooks.