Analysis Tasks Based on a Theorem in Nonlinear Approximation Theory

Autor/in	Hochmuth, Reinhard
Titel	Analysis Tasks Based on a Theorem in Nonlinear Approximation Theory
Quelle	In: International Journal of Mathematical Education in Science and Technology, 53 (2022) 5, S.1113-1132 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Hochmuth, Reinhard)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2021.1978572
Schlagwörter	Undergraduate Students; Mathematics Instruction; Task Analysis; Teaching Methods; Mathematical Concepts; Advanced Courses; Anthropology; Models; Calculus + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Aufgabenanalyse; Teaching method; Lehrmethode; Unterrichtsmethode; Fortgeschrittenenunterricht; Anthropologie; Analogiemodell; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung
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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01