Teaching Derivatives Concepts with Computational Techniques

**Jaqueline Maria da Silva**, *Universidade Federal dos Vales do Jequitinhonha e Mucuri (Brazil)*

**Deborah Faragó Jardim**, *Universidade Federal dos Vales do Jequitinhonha e Mucuri (Brazil)*

**Ana Carolina Carius**, *Instituto Federal do Rio de Janeiro (Brazil)*

Abstract

The Federal University of Jequitinhonha and Mucuri Valleys (UFVJM) mission is to produce and spread knowledge and innovation by integrating teaching, research and extension services as propellers of regional and national development. In this context it is a great challenge to teach Mathematics in the Interdisciplinary Science and Technology Bachelor (STB) course with students with so many social and structural problems.

The students that arrive as freshman in the STB have a great lack of mathematical and physical concept. It is very important that these students can to describe and understand natural phenomena that need mathematical representation. These are fundamental reasons to motivate teaching carefully the fundamental Calculus concepts in STB course.

This work presents a teaching strategy for Differential and Integral Calculus using technology as an important modeling teaching tool, particularly, using the GeoGebra software to improve the learning process by the students and also their modeling thinking. We believe that the technology can provide a better understanding of some mathematical concepts and ideas that are still abstract to the students.

Researchers who follow the didactics of mathematics line search to adapt teaching methodologies through a sequential structure for the learning process, focusing on work in the classroom and challenging activities as a stimulus in the production and construction of the mathematical knowledge. The Didactic Engineering, for example, proposed by researchers in France, follows this thinking. The work proposed here is part of a step sequence presented by the Didactic Engineering and uses technology to encourage and propose challenges to students in the classroom, enhancing the work of the students and the teaching activity. By analyzing the characteristics of mathematical teaching and learning cases, two viewpoints have been presented on teaching this course in this work, namely what should the instructor teach (i.e., the teaching goal) and what should be learnt by the students (i.e., the orientation of the learning).

References:

[1] Jardim, D. F., da Silva, J. M., Pereira, M. M., Soares Júnior, E. A., Nepomucena, T. V. Estudando Limites com o Geogebra. Revista Vozes dos Vales. N. 08. Ano IV. 2015.

[2] Silva, J. M., Souza, F. S., Carius, A. C. and Jardim, D. F. Mathematical Modeling and the Differential and Integral Calculus Teaching Challenges. ICMTA – 17. Modelling perspectives: looking in and across boundaries. Conference Contributions. Notthingham. 2015.

[3] D’Ambrosio, U. Mathematical Modeling as a Strategy for Building-Up Systems of Knowledge in Different Cultural Environments. In: Stillman, G. and Blum, W. and Bibemgut, M. S. and (Eds), Mathematical Modeling in Education Research and Practice. New York: Springer, 2015. Chapter 2. Page 35-44.

[4] Artigue, M. Ingénierie didactique. Recherches en Didactique des Mathématiques, vol. 9, n°3, pp. 281-307. La Pensée Sauvage. 1990.

[5] Silva, J. M., Jardim, D. F., Carius, A. C. O ensino e a aprendizagem de conceitos de Cálculo usando modelos matemáticos e ferramentas tecnológicas. Revista de Ensino de Engenharia. v. 35, n. 2, p. 70-80, 2016.

[6] D’Ambrosio, U. Educação matemática: Da teoria à prática. 14ª. ed. São Paulo: Papirus. 2009.

[7] Morrison, F. The Art of Modeling Dynamics Systems. Forecasting for Chaos, Randomness, and Determinism. Nova Jersey: John Wiley & Sons. 1991.

[8] Kaiser, G., Sriraman, B. A global survey of international perspectives on modelling in mathematics education. ZDM_The International Journal on Mathematics Education. 2006. 38(3), 302–310.

[9] Araujo, J. L., Campos, I. S. (2015). Negotiating the Use of Mathematics in a Mathematical Modeling Project. In: Stillman, G. and Blum, W. and Bibemgut, M. S. and (Eds). Mathematical Modeling in Education Research and Practice. New York: Springer. Cap.23, p. 283-292.

[10] Palharini, B., Almeida, L. M. W. Mathematical Modelling Tasks and the Mathematical Thinking of Students. In: Stillman, G. and Blum, W. and Bibemgut, M. S. and (Eds). Mathematical Modeling in Education Research and Practice. New York: Springer. 2015. Chapter.17, p. 219-228.