Details
| Original language | English |
|---|---|
| Pages (from-to) | 1113-1132 |
| Number of pages | 20 |
| Journal | International Journal of Mathematical Education in Science and Technology |
| Volume | 53 |
| Issue number | 5 |
| Early online date | 20 Oct 2021 |
| Publication status | Published - 2022 |
Abstract
The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year of study, which are less compartmentalized and allow for an extended acquisition of rationales of advanced mathematical practices and concepts. Against this background, subject-specific potentials of advanced mathematics are examined in this contribution. The Anthropological Theory of the Didactic (ATD) serves as the theoretical framework and in the analyses notions from its 4T-model are applied. Structural observations in praxeological terms are illustrated by examples chosen from a presentation of a classical result in Nonlinear Approximation. At the specific focus of the praxeological analyses are aspects for bridging and extending concepts within and across Analysis. On this basis, tasks designed for first-year university Analysis courses are analysed in detail. Moreover, general characteristics of the methodological approach realized in this contribution are discussed.
Keywords
- Advanced mathematics, Analysis tasks, de-compartmentalization, Nonlinear Approximation, praxeologies, rationales
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
- Social Sciences(all)
- Education
- Mathematics(all)
- Applied Mathematics
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In: International Journal of Mathematical Education in Science and Technology, Vol. 53, No. 5, 2022, p. 1113-1132.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Analysis tasks based on a theorem in Nonlinear Approximation theory
AU - Hochmuth, Reinhard
N1 - Funding Information: The writing of this paper benefited from discussions within the Erasmus+ project PLATINUM (\\platinum.uia.no). The author is grateful for all the critical enquiries by partners about the practicality of the systematic framework for task analysis presented here.
PY - 2022
Y1 - 2022
N2 - The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year of study, which are less compartmentalized and allow for an extended acquisition of rationales of advanced mathematical practices and concepts. Against this background, subject-specific potentials of advanced mathematics are examined in this contribution. The Anthropological Theory of the Didactic (ATD) serves as the theoretical framework and in the analyses notions from its 4T-model are applied. Structural observations in praxeological terms are illustrated by examples chosen from a presentation of a classical result in Nonlinear Approximation. At the specific focus of the praxeological analyses are aspects for bridging and extending concepts within and across Analysis. On this basis, tasks designed for first-year university Analysis courses are analysed in detail. Moreover, general characteristics of the methodological approach realized in this contribution are discussed.
AB - The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year of study, which are less compartmentalized and allow for an extended acquisition of rationales of advanced mathematical practices and concepts. Against this background, subject-specific potentials of advanced mathematics are examined in this contribution. The Anthropological Theory of the Didactic (ATD) serves as the theoretical framework and in the analyses notions from its 4T-model are applied. Structural observations in praxeological terms are illustrated by examples chosen from a presentation of a classical result in Nonlinear Approximation. At the specific focus of the praxeological analyses are aspects for bridging and extending concepts within and across Analysis. On this basis, tasks designed for first-year university Analysis courses are analysed in detail. Moreover, general characteristics of the methodological approach realized in this contribution are discussed.
KW - Advanced mathematics
KW - Analysis tasks
KW - de-compartmentalization
KW - Nonlinear Approximation
KW - praxeologies
KW - rationales
UR - http://www.scopus.com/inward/record.url?scp=85117583374&partnerID=8YFLogxK
U2 - 10.1080/0020739X.2021.1978572
DO - 10.1080/0020739X.2021.1978572
M3 - Article
AN - SCOPUS:85117583374
VL - 53
SP - 1113
EP - 1132
JO - International Journal of Mathematical Education in Science and Technology
JF - International Journal of Mathematical Education in Science and Technology
SN - 0020-739X
IS - 5
ER -