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.
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This research has been partially supported by the Israel Science foundation under grant numbers 1743/19 and 1815/16.
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Gilboa, N., Dreyfus, T. & Kidron, I. Meta-mathematical aspects of definitions. Educ Stud Math 114, 461–481 (2023). https://doi.org/10.1007/s10649-023-10252-x
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DOI: https://doi.org/10.1007/s10649-023-10252-x