Conjecturing process for the mean value theorem for derivatives: An approach from the detection of invariants in mobile devices with GeoGebra

Authors

DOI:

https://doi.org/10.17981/cultedusoc.12.1.2021.05

Keywords:

Mobile learning, Conjecturing process, GeoGebra, Mean value theorem for derivatives

Abstract

This article presents the results of a research project whose main objective was to describe the mediating role of GeoGebra’s “Graphing Calculator” mobile application on the conjecturing processes of the mean value theorem for derivatives by the use of some dragging tools, which combines dynamic geometry and infinitesimal calculus. By means of a qualitative case study, involving students from aeronautical engineering, research efforts were carried out looking forward to get evidence that allow the judgement of a hypothesis involving a positive influence of a mobile learning strategy on conjecturing processes in the context of a calculus course. The results obtained allowed us to conclude significant advances in the conjecturing process of the above-mentioned theorem for the solving-problems process in engineering. The discussion of how this type of digital resources, through a dynamic geometry environment in mobile devices, could favor the learning of calculus, is also addressed.

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Author Biographies

Vladimir Alfonso Ballesteros-Ballesteros, Fundación Universitaria Los Libertadores. Bogotá, D.C. (Colombia)

Professor, dedicated to Mathematics Education and Science Education. Dean, Faculty of Engineering and Basic Sciences, Fundación Universitaria Los Libertadores (Colombia). https://orcid.org/0000-0002-6920-789X

Óscar Iván Rodríguez-Cardoso, Profesor, Fundación Universitaria Los Libertadores. Bogotá, D.C. (Colombia)

Graduate in Mathematics, Universidad Pedagógica Nacional (Colombia). Specialist in Applied Mathematics, Universidad Sergio Arboleda (Colombia). Master in Education, Fundación Universitaria los Libertadores (Colombia). Candidate for PhD in Educational Sciences, Universidad Distrital Francisco José de Caldas (Colombia). Professor of Mathematics and Statistics, Fundación Universitaria Los Libertadores (Colombia). https://orcid.org/0000-0003-1203-4999

Sébastien Lozano-Forero, Fundación Universitaria Los Libertadores. Bogotá, D.C. (Colombia)

Mathematician, Universidad Nacional (Colombia). Master in Statistics, Universidade Federal de Pernambuco (Brazil). Specialist in Applied Statistics, Fundación Universitaria Los Libertadores (Colombia). Professor of Statistics, Universidad del Rosario (Colombia) and Fundación Universitaria Los Libertadores (Colombia). Statistical Consultant of the National Institute of Health (Colombia). https://orcid.org/0000-0002-9551-165X

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Published

2020-12-02

How to Cite

Ballesteros-Ballesteros, V. A., Rodríguez-Cardoso, Óscar I., & Lozano-Forero, S. (2020). Conjecturing process for the mean value theorem for derivatives: An approach from the detection of invariants in mobile devices with GeoGebra. CULTURA EDUCACIÓN Y SOCIEDAD, 12(1), 63–84. https://doi.org/10.17981/cultedusoc.12.1.2021.05