Meta-mathematical aspects of definitions

Nava Gilboa*, Tommy Dreyfus, Ivy Kidron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The notion of definition is a central building block of mathematics. In addition to specific definitions, it is desirable that students learn about meta-mathematical aspects of definitions such as their role of classification, and about characteristics of definitions such as arbitrariness. We investigated how such meta-mathematical aspects emerge when students are led to construct a definition such as point of inflection or tangent line, and how the constructing process interacts with meta-mathematical aspects. We used Abstraction in Context as theoretical framework because of its suitability to analyze processes of knowledge construction. We found that meta-mathematical aspects of definitions influence and are influenced by students’ processes of constructing definitions. We argue that awareness of meta-mathematical aspects improves students’ conception of mathematical definitions.

Original languageEnglish
Pages (from-to)461-481
Number of pages21
JournalEducational Studies in Mathematics
Volume114
Issue number3
DOIs
StatePublished - Nov 2023

Funding

FundersFunder number
Israel Science Foundation1743/19, 1815/16

    Keywords

    • Construction of definition
    • Definition
    • High-school
    • Inflection point
    • Meta-mathematics
    • Tangent

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