Representation Registers in the Solution of Calculus Problems
Author(s)
Elena Fabiola Ruiz Ledesma
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.
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.
Cite this paper
nullLedesma, E. (2011) Representation Registers in the Solution of Calculus Problems. Creative Education, 2, 270-275. doi: 10.4236/ce.2011.23036.
nullLedesma, E. (2011) Representation Registers in the Solution of Calculus Problems. Creative Education, 2, 270-275. doi: 10.4236/ce.2011.23036.
References
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[1] Arcavi, A., & Hadas, N. (2002). Computer mediated learning: An example of an approach. In F. Hitt (Ed.), Representations and mathematics visualization. International Group for the Psychology of Mathematics Education North American Chapter and Cinvestav-IPN. México. [2] Duval, R. (1998). Registros de representación semiótica y funcionamiento cognitivo del pensamiento. In: F. Hitt (Ed.), Investigaciones en Matemática Educativa II. Grupo Editorial Iberoamérica, 5, 101- 120. [3] Hitt, F. (2003). The role of the external representations in the constructions of mathematical concepts. L’educazione Matematica, 5, 205- 227. [4] Hitt, F. (2002a) Representations and mathematics visualization. International Group for the Psychology of Mathematics Education North American Chapter and Cinvestav-IPN. México. [5] Hitt, F. (2002b). Funciones en Contexto. México: Pearson Educación (Prentice Hall). [6] Hitt, F. (1994). Teachers’ difficulties with the construction of continuous and discontinuous functions. Focus on Learning Problems in Mathematics, 16, 10-20. [7] Plan y Programa de Estudios Cálculo Aplicado 2009 ESCOM. IPN. [8] Ruiz, E. F. (2010). Estrategias Didácticas en la ense?anza del Cálculo Diferencial e Integral en Ingeniería. Reporte técnico de proyecto de investigación registrado en la Secretaría de Investigación y Posgrado (SIP), del IPN con núm. de registro CGPI 20100398, México, IPN. [9] Ruiz, E. F. (2011). Indicadores teóricos para la Constricción de Conceptos del Cálculo Diferencial. Proyecto de investigación registrado en la Secretaría de Investigación y Posgrado (SIP), del IPN con núm. de registro CGPI 20110343. México, IPN.