Theoretical elements for analyzing the development of variational thinking in students.
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Abstract
This paper presents an advance of an investigation on the development of variational thinking in engineering students during their first calculus course, through the integration of different digital tools. In particular, we show an effort to adapt the theoretical framework presented by Carlson et al. (2002) and by Thompson (1994), called Covariational Reasoning applied to the modeling of dynamic events, in order to make it congruent with the vision with which we developed this research; the five major mental actions constituting covariational reasoning are described and exemplified, from the study of activities of emptying and filling containers, as well as movement, in which in addition to the tabular, graphical, analytical and verbal representations, a fifth modality is included: digital representation.
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References
Carlson, M., Jacobs, S., Coe, E., & Hsu, E. (2003). Razonamiento covariacional aplicado a la modelación de eventos dinámicos: Un marco conceptual y un estudio. EMA, 121-156.
Imaz, C. Moreno, L.(2010) Génesis y la enseñanza del calculo, las trampas del rigor. Editorial: TRILLAS
Thompson, P. W. (1994). Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics, 26(2-3), 229–274.
Thompson, P. W., Byerley, C., & Hatfield, N. (2013). A conceptual approach to calculus made possible by technology. Computers in the Schools, 30, 124-147.