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The aim of this paper is to present a novel approach to model a knowledge domain for teaching material in a tutorial-like system. In this approach, the tutorial-like system is capable of presenting teaching material within a Socratic model of teaching. The corresponding questions are of a multiple choice type, in which the complexity of the material increases in difficulty. This enables the tutorial-like system to present the teaching material in different chapters, where each chapter represents a level of difficulty that is harder than the previous one. We attempt to achieve the entire learning process using the learning automata (LA) paradigm. In order for the domain model to possess an increased difficulty for the teaching environment, we propose to correspondingly reduce the range of the penalty probabilities of all actions by incorporating a scaling factor mu. We show that such a scaling renders it more difficult for the student to infer the correct action within the LA paradigm. To the best of our knowledge, the concept of modeling teaching material with increasing difficulty using an LA paradigm is unique. The main results we have obtained are that increasing the difficulty of the teaching material can affect the learning of normal and below-normal students by resulting in an increased learning time, but it seems to have no effect on the learning behavior of fast students.