### Fuzzy Models for Implementation of the Decision-Making Module in Networked Didactic Prototypes

#### Abstract

Representation and evaluation of knowledge are key concepts for the management of the domain module within an intelligent tutoring system. However, in order to develop more efficient education tools, not only should knowledge representation be considered as a base. One should go in depth into something more complex known as the representation of dependency between key knowledge concepts in a given domain, in such a way that the model is more robust and can be used to make decisions in didactic electronic devices, whose operation is similar to that of an intelligent tutoring system; which are connected, by the moment, to a local network, and later, the objective is to implement the concept of the internet of things in educational classrooms. The representation of dependency between key knowledge concepts in a given domain is supported by different pedagogical theories such as the Cognitive Load Theory (CLT), which computationally can be modeled through Fuzzy Cognitive Maps (FCM). FCMs help in the decision making process and allow us to represent such dependencies. The decision-making process is that the system can determine the types of problems that the student must solve, so that he can understand each of the topics of the domain. In this paper the results of the combination of fuzzy models (inference models and FCM) to identify cognitive skills and types of problems that help the student reach the appropriate levels in the domain of algebra topics and the differential calculus, are presented. The objective is to implement fuzzy models in electronic devices based on tangible interfaces. This tool is in an initial testing phase with students. Therefore, the results presented in this paper are experimental and are related, execution-wise, to map efficiency.

#### Keywords

Fuzzy cognitive maps, prototypes with tangible interfaces, automatic evaluation in algebra problem solving