The Understanding of the Derivative Concept in Higher Education
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Claudio Fuentealba 1 * , Edelmira Badillo 2, Gloria Sánchez-Matamoros 3, Andrea Cárcamo 1
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1 Facultad de Ciencias de la Ingeniería, Universidad Austral de Chile, Valdivia, CHILE2 Departament de Didàctica de la Matemàtica i de les Ciències Experimentals, Universitat Autònoma de Barcelona, Barcelona, SPAIN3 Departamento de Didáctica de las Matemáticas, Universidad de Sevilla, Sevilla, SPAIN* Corresponding Author

Abstract

The aim of this work was to identify and characterize the levels of development of derivative schema. In order to do so, a questionnaire to 103 university students with previous instruction in Differential Calculus was applied. The questionnaire was composed of three tasks. For the identification of the levels of development of schema and their subsequent characterization, we consider the framework proposed by the APOS theory. In particular, this framework was operationalized through the establishment of 27 variables that allowed for the breakdown of the resolution protocols from the questionnaire into discrete elements. In this way, we obtained a vector associated with each of these variables. The identification of students assigned to each level of development of schema was carried out by a cluster analysis. Subsequently, we performed a statistical analysis of frequencies and implicative, with the 27 variables, which allowed to characterize the levels of development identified.

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2019, Volume 15, Issue 2, Article No: em1662

https://doi.org/10.29333/ejmste/100640

Publication date: 10 Dec 2018

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