Categorizing and promoting reversibility of mathematical concepts

Martin Simon, Melike Kara, Nicora Placa, Hakan Sandir

Research output: Contribution to journalArticle

Abstract

Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We discuss uses of the typology and how reversibility can be understood as the result of reflective abstraction. Finally, we describe two strategies for promoting reversibility that have distinct uses in terms of the types of reverse concepts they engender. We share empirical results which led to our postulation of these strategies and discuss their theoretical basis.

Original languageEnglish (US)
Pages (from-to)137-153
Number of pages17
JournalEducational Studies in Mathematics
Volume93
Issue number2
DOIs
StatePublished - Oct 1 2016

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Reversibility
Reverse
typology
abstraction
Concepts
Distinct
Strategy

Keywords

  • Mathematical concepts
  • Reflective abstraction
  • Reversibility
  • Task design

ASJC Scopus subject areas

  • Mathematics(all)
  • Social Sciences(all)

Cite this

Categorizing and promoting reversibility of mathematical concepts. / Simon, Martin; Kara, Melike; Placa, Nicora; Sandir, Hakan.

In: Educational Studies in Mathematics, Vol. 93, No. 2, 01.10.2016, p. 137-153.

Research output: Contribution to journalArticle

Simon, Martin ; Kara, Melike ; Placa, Nicora ; Sandir, Hakan. / Categorizing and promoting reversibility of mathematical concepts. In: Educational Studies in Mathematics. 2016 ; Vol. 93, No. 2. pp. 137-153.
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