The understanding of the derivative concept in higher education

Claudio Fuentealba, Edelmira Badillo, Gloria Sánchez-Matamoros, Andrea Cárcamo

Research output: Contribution to journalArticleResearch

18 Citations (Scopus)


© 2019 by the authors. 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.
Original languageEnglish
Article numberem1662
JournalEurasia Journal of Mathematics, Science and Technology Education
Publication statusPublished - 1 Jan 2019


  • Calculus
  • Cluster analysis
  • Derivative schema
  • Implicative analysis
  • Levels of development


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