A view from the ETC-OSA networking of theories on the role of mathematical connections in understanding the derivative

Keywords: Understanding, Extended Theory of Connections, Onto-semiotic Approach, Derivative, Graph

Abstract

The question is answered: Given the algebraic expression of , what connections ensure the student an understanding of  that allows him to sketch the graph of and explain its relationship with that of ? To do this, interviews and a task were applied to a group of students, in which they had to sketch the graph of  and explain its relationship with that of the derivative, and their mathematical activity was analyzed using the ETC-OSA articulation as a theoretical reference. The students who showed an understanding that allowed them to solve the task established connections of: different representations, meaning, part-whole, implication and feature. On the other hand, the failure to establish certain connections is a plausible explanation for why some students do not solve the task.

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Author Biographies

Camilo Andrés Rodríguez-Nieto, Universidad Autónoma de Guerrero

Doctor en Ciencias con Especialidad en Matemática Educativa por la Universidad Autónoma de Guerrero (UAGro), México. Profesor catedrático en la Universidad del Atlántico (UA), Colombia. Coordinador del Semillero de investigación CETMEM adscrito al Grupo de Investigación Horizontes en Educación Matemática (GIHEM) de la UA.

Flor Monserrat Rodríguez-Vásquez, Universidad Autónoma de Guerrero

Doctora en Educación Matemática. Profesora en el programa de Doctorado y maestría en Matemática Educativa de la Universidad Autónoma de Guerrero, Chilpancingo, Guerrero (UAGro), México.

Vicenç Font Moll, Universidad de Barcelona

Doctor en filosofía y ciencias de la Educación. Profesor en el programa de doctorado en Didáctica de las Ciencias, las Lenguas, las Artes y las Humanidades de la Universitat de Barcelona (UB), España.

Armando Morales-Carballo, Universidad Autónoma de Guerrero

Doctor en Ciencias con Especialidad en Matemática Educativa. Profesor titular de la Facultad de Matemáticas de la Universidad Autónoma de Guerrero (UAGro), México

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Published
2021-07-24
How to Cite
RODRÍGUEZ-NIETO, C. A.; RODRÍGUEZ-VÁSQUEZ, F. M.; FONT MOLL, V.; MORALES-CARBALLO, A. A view from the ETC-OSA networking of theories on the role of mathematical connections in understanding the derivative. Revemop, v. 3, p. e202115, 24 Jul. 2021.
Section
Enfoque Ontosemiótico: abordagens teóricas, metodológicas e práticas