Engaging Students in a Visual and Conceptual Approach to Taylor Series

Autor/inn/en	Soosloff, Elisa; Huey, Maryann; Alexander, Daniel S.
Titel	Engaging Students in a Visual and Conceptual Approach to Taylor Series
Quelle	In: PRIMUS, 33 (2023) 9, S.981-996 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Huey, Maryann)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1051-1970
DOI	10.1080/10511970.2023.2193967
Schlagwörter	Mathematics Instruction; Visual Aids; Prior Learning; Teaching Methods; Graphs; Mathematical Concepts; Concept Formation; Mathematical Logic; College Mathematics; Calculus; Active Learning + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Anschauungsmaterial; Vorkenntnisse; Teaching method; Lehrmethode; Unterrichtsmethode; Grafische Darstellung; Concept learning; Begriffsbildung; Mathematical logics; Mathematische Logik; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Aktives Lernen
Abstract	In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as formulaic, which leads them to focus on procedural aspects. We share our instructional approach, which introduces students to graphs of polynomial functions that resemble transcendental functions. However, students are not told that they are approximating polynomials initially, and through carefully sequenced experiences, students gradually build an intuitive understanding of the Taylor series. With the goal of equipping instructors who wish to embark upon similar journeys, we describe the visual representations employed, the questions we pose to students, students' typical responses, and important topics for discussion. The activities described engage students in reasoning and sense-making throughout the learning process, which is essential for developing a robust understanding of Taylor series as well as other calculus topics. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01