Empirical results of the implementation of a proposal for teaching the concept of the Definite Integral of functions of one variable at the Higher Education Level
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Abstract
Observed results of the implementation of an innovation for the teaching of Calculus at the Higher level are reported. After the discussion of three problems involving the Definite Integral (arc length, area under the curve and volume of a solid of revolution), the students were evaluated. It was found that some manage to establish the Definite Integral with which the exact value of the surface area of a particular solid of revolution is determined. Among other issues, it was observed that a significant fraction of the group has deficiencies in their algebra skills, which causes them not to be able to establish said Definite Integral.
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References
Alanís, J. y Soto, E. (2012). La Integral de funciones de una variable: Enseñanza Actual. El Cálculo y su Enseñanza, 3(1), 1-6.
Artigue, M. (1995). La enseñanza de los principios del Cálculo: Problemas epistemológicos, cognitivos y didácticos. En Artigue, M., Douady, R., Moreno, L. Gómez, P. (Eds.). Ingeniería Didáctica en Educación Matemática. México: Grupo Editorial Iberoamericano. 97-140.
Chappell, K.K., y Killpatrick, K. (2003). Effects of concept-based instruction on students’ conceptual understanding and procedural knowledge of Calculus. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 13(1), 17-37.Cordero, F. (2003). Reconstrucción de significados del Cálculo Integral: La noción de acumulación como una argumentación. México, DF: Grupo Editorial Iberoamérica, SA de CV.
Mahir, N. (2009). Conceptual and procedural performance of undergraduate students in integration. International Journal of Mathematical Education in Science and Technology, 40(2), 201-211.
Maggelakis, S. y Lutzer, C. (2007). Optimizing student success in Calculus. PRIMUS: Problems, Resources and Issues in Mathematics Undergraduate Studies, 17(3), 284-299.
Muñoz, O.G. (2000). Elementos de enlace entre lo conceptual y lo algorítmico en el Cálculo Integral. Revista Latinoamericana de Investigación en Matemática Educativa, 3(2), 131-170.
Petterson, K., y Scheja, M. (2008). Algorithmic contexts and learning potentiality: A case study of students’ understanding of Calculus. International Journal of Mathematical Education in Science and Technology, 39(6), 767-784.
Salinas, P. y Alanís, J.A. (2009). Hacia un nuevo paradigma en la enseñanza del Cálculo dentro de una institución educativa. Revista Latinoamericana de Investigación en Matemática Educativa, 12(3), 355-382.
Salinas, P., Alanís, J.A. y Pulido, R. (2011). Cálculo de una variable: Reconstrucción para el aprendizaje y la enseñanza. Didac, 56-57(62-69).
Salinas, P., Alanís, J.A., Garza, J., Pulido, R., Santos, F., y Escobedo, J. (2012). Cálculo Aplicado: Competencias matemáticas a través de contextos. México, DF: CENGAGE Learning.
Soto, E., Alanís, J. (2014). Antecedentes y surgimiento de la Integral acorde a Leibniz. Eureka, 31(4), 7-23.
Steen, L.A. (2003). Analysis 2000: Challenges and opportunities. En D. Couray, D. Furinghetti, F., Gispert, H., Hodgson, B.R., Schubring, G. (Eds.), One Hundred Years of L’Enseignement Mathèmatique: Moments of Mathematics Education in the Twentieth Century. Monograph No. 39 (pp. 91-210). Génova: L’Enseignement Mathèmatique.
Thompson, P.W., Byerley, C., y Hatfield, N. (2013). A conceptual approach to Calculus made posible by technology. Computers in the Schools, 30, 124-147.