Abstract
The definition of ‘definition’ cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of concept definition and concept image, conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to construct definitions. This paper will deal with ‘definition construction processes’ and aims more specifically at proposing a new approach to the study of the formation of mathematical concepts. I shall demonstrate that the study of the defining and concept formation processes demands the setting up of a general theoretical framework. I shall propose such a tool characterizing classical points of view of mathematical definitions as well as analyzing the dialectic involving definition construction and concept formation. In that perspective, a didactical exemplification will also be presented.
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Ouvrier-Buffet, C. Exploring Mathematical Definition Construction Processes. Educ Stud Math 63, 259–282 (2006). https://doi.org/10.1007/s10649-005-9011-3
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DOI: https://doi.org/10.1007/s10649-005-9011-3