Categorizing and promoting reversibility of mathematical concepts

Martin A. Simon; Melike Kara; Nicora Placa; Hakan Sandir

doi:10.1007/s10649-016-9697-4

Categorizing and promoting reversibility of mathematical concepts

Martin A. Simon, Melike Kara, Nicora Placa, Hakan Sandir

Teaching and Learning

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	137-153
Number of pages	17
Journal	Educational Studies in Mathematics
Volume	93
Issue number	2
DOIs	https://doi.org/10.1007/s10649-016-9697-4
State	Published - Oct 1 2016

Keywords

Mathematical concepts
Reflective abstraction
Reversibility
Task design

ASJC Scopus subject areas

General Mathematics
Education

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AB - 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.

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Categorizing and promoting reversibility of mathematical concepts

Abstract

Keywords

ASJC Scopus subject areas

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