@article{437d3df0934340b5ba26db72173d5f70,

title = "Meta-mathematical aspects of definitions",

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{\textquoteright} processes of constructing definitions. We argue that awareness of meta-mathematical aspects improves students{\textquoteright} conception of mathematical definitions.",

keywords = "Construction of definition, Definition, High-school, Inflection point, Meta-mathematics, Tangent",

author = "Nava Gilboa and Tommy Dreyfus and Ivy Kidron",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature B.V.",

year = "2023",

month = nov,

doi = "10.1007/s10649-023-10252-x",

language = "אנגלית",

volume = "114",

pages = "461--481",

journal = "Educational Studies in Mathematics",

issn = "0013-1954",

publisher = "Springer Netherlands",

number = "3",

}