Details
| Original language | English |
|---|---|
| Pages (from-to) | 153–168 |
| Number of pages | 16 |
| Journal | Educational studies in mathematics |
| Volume | 118 |
| Issue number | 2 |
| Early online date | 5 Nov 2024 |
| Publication status | Published - Feb 2025 |
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
ASJC Scopus subject areas
- Social Sciences(all)
- Education
- Mathematics(all)
- General Mathematics
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In: Educational studies in mathematics, Vol. 118, No. 2, 02.2025, p. 153–168.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Modelling mathematics for educational research and practice
T2 - a comparison of two theoretical approaches
AU - Hochmuth, Reinhard
AU - Peters, Jana
AU - Rønning, Frode
AU - Winsløw, Carl
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2025/2
Y1 - 2025/2
N2 - 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.
AB - 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.
KW - Anthropological Theory of the Didactic
KW - Basic ideas
KW - Networking of theoretical frameworks
KW - Praxeologies
KW - Subject Matter Didactics
UR - http://www.scopus.com/inward/record.url?scp=85208179277&partnerID=8YFLogxK
U2 - 10.1007/s10649-024-10368-8
DO - 10.1007/s10649-024-10368-8
M3 - Article
AN - SCOPUS:85208179277
VL - 118
SP - 153
EP - 168
JO - Educational studies in mathematics
JF - Educational studies in mathematics
SN - 0013-1954
IS - 2
ER -