Representation Registers in the Solution of Calculus Problems

Elena Fabiola Ruiz Ledesma

doi:10.4236/ce.2011.23036

Abstract

This article is derived from the research project registered under number 20110343 (Ruiz, 2011), and developed in Escuela Superior de Cómputo del Instituto Politécnico Nacional (IPN) (School of Computer Sciences of the National Poly-technical 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 know ledge 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 give the calculus courses, and a diagnostic questionnaire is 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.

Highlights

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, on solving the optimization problems worked on in the Calculus Learning Unit for second year Engineering students
Does solving problems motivate your learning of Calculus? Explain why
What is your basis for solving optimization problems? Explain

Summary

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, on solving the optimization problems worked on in the Calculus Learning Unit for second year Engineering students. As pointed out by Duval (1998), 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. 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. On building mathematics concepts, Duval, 1998 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

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