Analysis tasks based on a theorem in Nonlinear Approximation theory

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)1113-1132
Seitenumfang20
FachzeitschriftInternational Journal of Mathematical Education in Science and Technology
Jahrgang53
Ausgabenummer5
Frühes Online-Datum20 Okt. 2021
PublikationsstatusVeröffentlicht - 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.

ASJC Scopus Sachgebiete

Zitieren

Analysis tasks based on a theorem in Nonlinear Approximation theory. / Hochmuth, Reinhard.
in: International Journal of Mathematical Education in Science and Technology, Jahrgang 53, Nr. 5, 2022, S. 1113-1132.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Hochmuth, R 2022, 'Analysis tasks based on a theorem in Nonlinear Approximation theory', International Journal of Mathematical Education in Science and Technology, Jg. 53, Nr. 5, S. 1113-1132. https://doi.org/10.1080/0020739X.2021.1978572
Hochmuth, R. (2022). Analysis tasks based on a theorem in Nonlinear Approximation theory. International Journal of Mathematical Education in Science and Technology, 53(5), 1113-1132. https://doi.org/10.1080/0020739X.2021.1978572
Hochmuth R. Analysis tasks based on a theorem in Nonlinear Approximation theory. International Journal of Mathematical Education in Science and Technology. 2022;53(5):1113-1132. Epub 2021 Okt 20. doi: 10.1080/0020739X.2021.1978572
Hochmuth, Reinhard. / Analysis tasks based on a theorem in Nonlinear Approximation theory. in: International Journal of Mathematical Education in Science and Technology. 2022 ; Jahrgang 53, Nr. 5. S. 1113-1132.
Download
@article{e2afa34ad1c445908615b2dc283e6240,
title = "Analysis tasks based on a theorem in Nonlinear Approximation theory",
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",
author = "Reinhard Hochmuth",
note = "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. ",
year = "2022",
doi = "10.1080/0020739X.2021.1978572",
language = "English",
volume = "53",
pages = "1113--1132",
number = "5",

}

Download

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 -

Von denselben Autoren