In this paper we present a category-theoretical characterization of mathematical objects as synthetic objects within a transitory epistemology. This allows us to take into account pragmatic and dynamic issues as in the definitions of mathematical object in mathematics education research and in the historical evolution of mathematical practice. We discuss the relations of such objects to mathematical objects considered from an objective, set-theoretical perspective, as well as the implications of the categorytheoretical characterization for teaching and learning mathematics.
Mathematical objects within a transitory epistemology / M. Asenova - In: History and Epistemology in Mathematics Education / [a cura di] E. Barbin, R. Capone, M.N. Fried, M. Menghini; H. Pinto, F.S. Tortoriello. - Roma : Nuova Cultura, 2023. - ISBN 9788833656014. - pp. 237-242 (( Intervento presentato al 9. convegno European Summer University of History and Epistemology in Mathematics Education tenutosi a Salerno nel 2023.
Mathematical objects within a transitory epistemology
M. Asenova
2023
Abstract
In this paper we present a category-theoretical characterization of mathematical objects as synthetic objects within a transitory epistemology. This allows us to take into account pragmatic and dynamic issues as in the definitions of mathematical object in mathematics education research and in the historical evolution of mathematical practice. We discuss the relations of such objects to mathematical objects considered from an objective, set-theoretical perspective, as well as the implications of the categorytheoretical characterization for teaching and learning mathematics.
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