The field of artificial intelligence and education, in which AI techniques and methodologies are used to build sophisticated intelligent educational systems, is developing rapidly. In this paper we present an intelligent educational system for teaching high school and college students how to analyze and draw graphs of mathematical functions. The system, named SEDAF, has been developed in a knowledge engineering environment and runs on a Lisp-machine workstation. We illustrate the various modules constituting SEDAF: the user interface; an expert module, capable of solving problems in the subject domain; a diagnosis module, which points out possible reasons for students' errors; a student modeling module, capable of building an explicit representation of the learning status of the student; and a remedial subsystem, called a therapy module, constituted by means-ends tutorial rules that execute teaching actions on the base of the status of the student model. The goal of the presentation is to stress the innovative aspects of the architecture of SEDAF, in particular the use of metalevel knowledge to embed in the system the teaching expertise that allows the system to personalize its behavior to the specific student and to pursue a didactic plan.