Identification and characterization of the development sub-levels of the derivative schema
Abstract
The results of the research related to the learning process of the derivative notion show that its understanding is very complex and that only a significant number of students acquire a partial comprehension of the concept. In this context, this research presents an exploratory/confirmatory analysis in which we identify and characterize, through mixed analysis methods, the different sub-levels of development of the derivative schema that university students previously instructed in Differential Calculus managed to reach. The results show how useful these methods are in this study, since they made it possible to identify the 9 sub-levels of development and to characterize 5 of them according to the dominant variables and their associated mathematical elements.Keywords
Derivative schema, Development sub-level, Cluster analysis, Implicative analysis, APOS theoryReferences
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M. y Weller, K. (2014). APOS theory: A framework for research and curriculum development in mathematics education. Berlin: Springer.
Asiala, M., Cottrill, J., Dubinsky, E. y Schwingendorf, K. (1997). The Development of Students’ Graphical Understanding of the Derivate. Journal of Mathematics Behavior, 16(4), 399-430. https://doi.org/10.1016/S0732-3123(97)90015-8
Baker, B., Cooley, L. y Trigueros, M. (2000). A calculus graphing schema. Journal for research in mathematics education, 31(5), 557-578. https://doi.org/10.2307/749887
Balzarini, M. G., González, L., Tablada, M., Casanoves, F., Di Rienzo, J. A. y Robledo, C. W. (2008). Manual del Usuario. Córdoba, Argentina: Editorial Brujas.
Cisterna, F. (2005). Categorización y triangulación como procesos de validación del conocimiento en investigación cualitativa. Theoria, 14(1), 61-71.
Font, V., Trigueros, M., Badillo, E. y Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107-122. https://doi.org/10.1007/s10649-015-9639-6
Fuentealba, C., Sánchez-Matamoros, G., Badillo, E. y Trigueros, M. (2017). Thematization of derivative schema in university students: nuances in constructing relations between a function’s successive derivatives. International Journal of Mathematical Education in Science and Technology, 48(3), 374-392. https://doi.org/10.1080/0020739X.2016.1248508
García, M., Llinares, S. y Sánchez-Matamoros, G. (2011). Characterizing thematized derivative schema by the underlying emergent structures. International journal of science and mathematics education, 9(5), 1023-1045. https://doi.org/10.1007/s10763-010-9227-2
Johnson, D. (1998). Applied multivariate methods for data analysts. Duxbury Resource Center.
Lerman, I., Gras, R. y Rostam, H. (1981). Élaboration et évaluation d'un indice d'implication pour des données binaires. Mathématiques et sciences humaines, 75, 5-47.
Meel, D. (2003). Modelos y teorías de la comprensión matemática: Comparación de los modelos de Pirie y Kieren sobre el crecimiento de la comprensión matemática y la Teoría APOE. Relime, 6(3), 221-278.
Piaget, J. y García, R. (1983). Psicogénesis e Historia de la Ciencia. México, España, Argentina, Colombia: Siglo Veintiuno Editores, S.A.
Rocco, T., Bliss, L., Gallagher, S. y Pérez-Prado, A. (2003). Taking the next step: Mixed methods research in organizational systems. Information Technology, Learning, and Performance Journal, 21(1), 19-29.
Sánchez-Matamoros, G., García, M. y Llinares, S. (2006). El desarrollo del esquema de derivada. Enseñanza de las Ciencias, 24(1), 85-98.
Sokal, R. y Rohlf, F. (1962). The comparison of dendrograms by objective methods. Taxon, 11(2), 33-40.
Trigueros, M. y Escandón, C. (2008). Los conceptos relevantes en el aprendizaje de la graficación. Revista Mexicana de Investigación Educativa, 13(36), 59-85.
Trigueros, M. ( ). La noción de esquema en la investigación en matemática educativa a nivel superior. Educación Matemática, 17(1), 5-31.
Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. En E. Dubinsky, A. Schoenfeld y J. Kaput (Eds.), Research in collegiate mathematics education. IV (pp. 103-127). Washington DC: American Mathematical Society Mathematical Association of America.
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