The non-derivability points of a function and their importance in the understanding of the derivative concept

Edelmira Rosa Badillo Jimenez, Claudio Fuentealba, Gloria Sánchez-Matamoros

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)


© 2018, Faculdade de Educacao da Universidade de Sao Paulo. This study analyzes the importance of the treating non-derivability points in addressing the derivative schema. To do this, we have considered the framework proposed by APOS theory, through the use and logical connections that university students established between mathematical elements and representation modes when solving tasks on derivative concept. To achieve the aim, we devised two instruments: the first was a questionnaire consisting of three tasks proposed in different representation modes, in whose resolution the use of mathematical constituent elements of the concept of derivative was necessary, this instrument was applied to 40 students that participated in the study. The second instrument corresponded to a clinical interview focused on the analysis of student answers regarding the treatment performed in non-derivability points in successive derivatives. This clinical interview was applied to 5 of the 9 students classified in the level of development Trans-derivative. The results of analysis corroborate that the coherence of the schema is fundamental to identify a addressed schema, in addition, they show the important role played by the analysis of the non-derivability points in the connection and transit between derivatives of different orders, especially from the graphic representation mode, which favors addressing the derivative schema.
Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalEducacao e Pesquisa
Issue number4
Publication statusPublished - 1 Jan 2018


  • APOS theory
  • Derivada
  • Derivative
  • Esquema
  • Non-derivability points
  • Puntos de no-derivabilidad
  • Schema
  • Tematización
  • Teoría APOE
  • Thematization


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