Modelling mathematics for educational research and practice

a comparison of two theoretical approaches

verfasst von: Reinhard Hochmuth, Jana Peters, Frode Rønning, Carl Winsløw
Abstract: The production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within Subject Matter Didactics (Stoffdidaktik). The second is the notion of praxeology from the Anthropological Theory of the Didactic, which originated in France. After presenting the genesis and interpretation of these notions as theoretical modelling tools, we provide a detailed case study of actual models produced with these tools, concerning the notion of limits and derivatives. Furthermore, we identify similarities and differences of both models in how they can support didactical research and practice, for instance, by identifying important phenomena or problems. We conclude that the two approaches offer important, different and, to some extent, complementary positions and perspectives.
Organisationseinheit(en): Institut für Didaktik der Mathematik und Physik
Externe Organisation(en): Norwegian University of Science and Technology (NTNU)
Københavns Universitet
Typ: Artikel
Journal: Educational studies in mathematics
Anzahl der Seiten: 16
ISSN: 0013-1954
Publikationsdatum: 05.11.2024
Publikationsstatus: Elektronisch veröffentlicht (E-Pub)
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Ausbildung bzw. Denomination, Allgemeine Mathematik
Elektronische Version(en): https://doi.org/10.1007/s10649-024-10368-8 (Zugang: Offen)

BibTeX

@article{a625b7da282c4c0eabd873dc05790a8f,
title = "Modelling mathematics for educational research and practice: a comparison of two theoretical approaches",
abstract = "The production and use of explicit models of mathematics are important elements of research in Didactics of Mathematics. In this paper, we present and compare two different European approaches to didactical modelling. The first, centred around the notion of basic idea (Grundvorstellung), arose in German-speaking countries as a development within Subject Matter Didactics (Stoffdidaktik). The second is the notion of praxeology from the Anthropological Theory of the Didactic, which originated in France. After presenting the genesis and interpretation of these notions as theoretical modelling tools, we provide a detailed case study of actual models produced with these tools, concerning the notion of limits and derivatives. Furthermore, we identify similarities and differences of both models in how they can support didactical research and practice, for instance, by identifying important phenomena or problems. We conclude that the two approaches offer important, different and, to some extent, complementary positions and perspectives.",
keywords = "Anthropological Theory of the Didactic, Basic ideas, Networking of theoretical frameworks, Praxeologies, Subject Matter Didactics",
author = "Reinhard Hochmuth and Jana Peters and Frode R{\o}nning and Carl Winsl{\o}w",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",
year = "2024",
month = nov,
day = "5",
doi = "10.1007/s10649-024-10368-8",
language = "English",
journal = "Educational studies in mathematics",
issn = "0013-1954",
publisher = "Springer Netherlands",
}