Simulation as a resource in the Calculus Solving Problem Elena Fabiola Ruiz Ledesma Departamento de Posgrado Escuela Superior de Cómputo Instituto Politécnico Nacional México, D.F. efruiz@ipn.mx Juan Jesús Gutiérrez García Departamento de Posgrado Escuela Superior de Cómputo Instituto Politécnico Nacional México, D.F. jjggarc@gmail.com Abstract— This article is derived from the research project and developed at School of Computer Sciences of the National Polytechnic Institute of Mexico. The article reports on the problems found among engineering students with respect to their resistance to using different representation registers when solving optimization problems in the Calculus Learning Unit. Use of such registers could help the students to build mathematics knowledge and to solve calculus problems. As a didactic strategy, simulations are used in an electronic environment in order to support the students by fostering their use of tabular, graphical and algebraic representation registers. Interviews are undertaken of six of the professors who gave the calculus courses, and a diagnostic questionnaire was applied to 68 students prior to and after working with the proposal. As for the theoretical framework, the work reported by Duval and Hitt is salient in this report, particularly their emphasis of the fact that working on activities by way of one single representation system is not sufficient. From the first responses provided by the students, one can conclude that the algebraic register is preferred by the majority of students. It is however used in a mechanical fashion without affording any meaning to the content of the problem and to the process of solving it. Another conclusion reported is that implementing tasks in the classroom in which the mathematics activity requires coherent use of different representations is necessary. Keywords—simulation, representation register, Calculus, Solving problem. I. INTRODUCTION The study reported in this article uses the reference of a cognitive focus based on the registers of semiotic representation of Duval and their effect on the learning of mathematics notions, particularly on solving the optimization problems worked on in the Calculus Learning Unit for second year engineering students. Hence first a review was undertaken of aspects of the representation registers, after which the three registers used in the study reported in this article, namely the graphical, tabular and algebraic registers, are documented. II. THEORETICAL ASPECTS A. Background As pointed out in [1], the semiotic representations are representations that employ signs, which can be expressed in natural language or in algebraic formulae or in graphs or in geometric figures. However those semiotic representations are the means through which a person can externalize his/her mental representations in order to make them visible or accessible to others. Those semiotic representations also make communication possible. Duval [1] focuses on and establishes the fundamental importance of issues the likes of: • The ability to change registers of semiotic representation, which is necessary in the learning of mathematics. • The importance of coordinating different registers of semiotic representation. He explains that many of the difficulties experienced by students can be described and explained as a lack of coordination among representation registers. • Considering conceptual knowledge (comprehension) as the invariant of multiple semiotic representations. • Based on different representation registers, defining specific independent variables for cognitive contents and organizing didactic proposals in order to develop coordinated representation registers. On building mathematics concepts, Duval [1] establishes that given that each representation is partial vis-à-vis the concept it represents, interaction among different representations of the mathematics object must be considered absolutely necessary for its formation. As for the work per se of the graphical, tabular and algebraic representation registers, as well as of the problem, as is pointed in [2]-[4], who underscores that visualization enables statements to be understood and activities to be carried out, and although it does not lead to the correct Comisión de Operación y fomento de Actividades Académicas. INTERNATIONAL JOURNAL OF SYSTEMS APPLICATIONS, ENGINEERING & DEVELOPMENT DOI: 10.46300/91015.2021.15.25 Volume 15, 2021 E-ISSN: 2074-1308 172