Abstract
The purpose of this chapter is to present the integration of SimCalc into a new approach to calculus. This is the way in which the freshman course of math at ITESM, Mexico is currently being taught. SimCalc offers, through movement, the image of the derivative (velocity) and its antiderivative (position). This feature allows integrating SimCalc into a teaching approach in the classroom that puts together both core subjects of calculus: derivative and integral. Its mediator role is translated into contextual versions of these concepts at an early stage of the course. Then, situated proofs in this environment are produced and from there, new approaches to develop meaning about the mathematics of variation and change emerge. I describe elements of our experience in the classroom; since it is there, in the classroom, where the students have lived their experience and have triggered a symbolization process that includes body gestures to visual images. The learning objective is set to interpreting the graph of a function through the behavior of its derivative.
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References
Duval, R. (2002). Representation, vision and visualization: cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt (Ed.), Representations and mathematics visualization (pp. 311–336). México: Cinvestav-IPN.
Duval, R. (2006a). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1/2), 103–131.
Duval, R. (2006b). Un tema crucial en la educación matemática: La habilidad para cambiar el registro de representación. La Gaceta de la Real Sociedad Matemática Española, 9(1), 143–168.
Duval, R. (2008). A crucial issue in mathematics education: the ability to change representation register. Regular Lecture. In M. Niss (Ed.), Proceedings of the 10th international congress on mathematical education (pp. 1–17). Denmark: IMFUFA, Department of Science, Systems and Models, Roskilde University.
Hegedus, S. J., & Moreno-Armella, L. (2009). Intersecting representation and communication infrastructures. ZDM, 41(4), 399.
Hegedus, S. J., & Moreno-Armella, L. (2010). Accommodating the instrumental genesis framework within dynamic technological environments. For the Learning of Mathematics, 30(1), 26–31.
Hegedus, S. J., & Penuel, W. R. (2008). Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures. Educational Studies in Mathematics, 68(2), 171–183.
Moreno-Armella, L., & Hegedus, S. J. (2009). Co-action with digital technologies. ZDM, 41(4), 505.
Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: historical and representational perspectives. Educational Studies in Mathematics, 68(2), 99–111.
Moreno-Armella, L., & Sriraman, B. (2005). Structural stability and dynamic geometry: some ideas on situated proofs. ZDM, 37(3), 130.
Moreno-Armella, L., & Sriraman, B. (2010). Symbols and mediation in mathematics education. Theories of mathematics education. In B. Sriraman & L. English (Eds.), Theories of mathematics education: advances in mathematics education (pp. 213–232). Berlin: Springer.
Noss, R., & Hoyles, C. (2004). The technological presence: shaping and shaped by learners. In Plenary paper of the 10th international congress on mathematical education. Recuperado el 29 de Mayo, 2009, http://www.icme-organisers.dk/tsg15/Noss&Hoyles.pdf.
Noss, R., Hoyles, C., Mavrikis, M., Geraniou, E., Gutierrez-Santos, S., & Pearce, D. (2009). Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalization. ZDM, 41(4), 493.
Salinas, P., & Alanís, J. A. (2009). Hacia un nuevo paradigma en la enseñanza del Cálculo. Revista Latinoamericana de Investigación en Matemática Educativa, 12(3), 355–382.
Salinas, P., Alanís, J., & Pulido, R. (2010). Cálculo de una variable: Reconstrucción para el aprendizaje y la enseñanza. Didac, 56–57, 62–69.
Salinas, P., Alanís, J. A., Pulido, R., Santos, F., Escobedo, J. C., & Garza, J. L. (2011). Cálculo Aplicado: Competencias Matemáticas a través de contextos. Tomo I. México: Cengage Learning.
Wells, G. (2007). Semiotic mediation, dialogue and the construction of knowledge. Human Development, 50(5), 244–274.
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Salinas, P. (2013). Approaching Calculus with SimCalc: Linking Derivative and Antiderivative. In: Hegedus, S., Roschelle, J. (eds) The SimCalc Vision and Contributions. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5696-0_21
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DOI: https://doi.org/10.1007/978-94-007-5696-0_21
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