The basis step in the construction of the principle of mathematical induction based on APOS theory

Isabel García-Martínez, MARCELA CECILIA PARRAGUEZ GONZALEZ

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5 Scopus citations

Abstract

Using APOS theory as the framework along with a case study from a perspective within the methodological design of APOS theory, this study presents a cognitive model of the Principle of Mathematical Induction (PMI) in higher education. Based on evidence from university classrooms and the result of an initial measurement, the genetic decomposition designed by Dubinsky and Lewin for this concept was reformulated, introducing and defining the basis step in the PMI as a mental process. Using this reformulated genetic decomposition, the productions of four university students are analysed in order to support or refute the constructions it proposes. The results show that the reformulated genetic decomposition is viable and that the inclusion of the basis step as a mental process was seen in the cognitive model of the PMI shown by the students. The instruments used provide activities for a teaching sequence for the PMI at university level.

Original languageEnglish
Pages (from-to)128-143
Number of pages16
JournalJournal of Mathematical Behavior
Volume46
DOIs
StatePublished - 1 Jun 2017

Keywords

  • APOS
  • Genetic decomposition
  • Principle of mathematical induction
  • University education

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