Avaliando o conhecimento algébrico do estudante através de redes bayesianas dinâmicas: um estudo de caso com o sistema tutor inteligente PAT2Math

Abstract

Students learn more through personalized instruction, because the teacher can focus on each learner. Being a impracticable strategy in terms of cost, Intelligent Tutoring Systems (ITS) offers a feasible alternative. By using Artificial Intelligence techniques, these systems are able to adapt themselves to the students, providing individualized instruction. Such adaptation is provided by the Student Model, which is able to assess and map the knowledge of each student. In the literature there are several studies that deal with knowledge evaluation in ITS, some of them are related to algebra. These studies present a Bayesian Network modeling, probabilistic structures that are widely used because of their interesting results concerning the evaluation of the student knowledge. However, in this studies, the network structure only models algebraic concepts, or only model a relationship between algebraic operations and its main properties and common misconceptions. These studies do not aim to represent the relationship between concepts and algebraic operations and how the former can be interfering, in a positive or negative way, on the learning of the second one. For example, in algebra, there are key concepts, such as the unknown and equality among sides of the equation, which directly interferes with the understanding of some algebraic operations. If a student does not understand these concepts, he would hardly be able to apply correctly the related operations in every situation. Thus, it is desirable that the inference model be able to identify if the student understands such concepts. In addition, another limitation of the related work of algebraic student models refers to how they deal with the evidence. As these studies use the assessment items for evidence, for each new exercise, it is necessary to insert a new node in the network, and establish relationships with each concept addressed by this item. This makes the network design laborious and dependent on each ITS exercise. In this context, this work proposes an algebraic student model that, in addition to infer the student knowledge of algebraic concepts (as unknown, equality, inverse operation), skills (algebraic operations) and common misconceptions, defines the relationship between concepts and skill. An initial focus of this study will be the 1st degree equations. For the inference model we use the Dynamic Bayesian Networks (DBN), in which the evidences are the operations applied by the student to solve each equation step. In this structure of DBN, each time slice corresponds to a resolution step, which makes the proposed model independent of the ITS exercises. Thus, the proposed inference model can be used in every algebraic equation, without need to make changes in the network, as occurs with other works.In order to verify the inference capacity of the network, evaluations were conducted. From the resolution history of the students, that interact with PAT2Math, the evidences for the network were obtained; and from the post-test data, solved by the same students, the percentages to compare with the results of the network were obtained. As the results aren’t very satisfactory, we applied the threshold rule, every variable that exceeded this value are instantiated. The network were evaluated under the threshold of 96% and 98%. The proposed DBN has shown more accurate inference with the 96% threshold, in which the differences between the results of the network and the percentages of the post-test remained mostly with ceiling of 5%.