Learning Integrals Based on Adding Up Pieces across a Unit on Integration

Autor/inn/en	Stevens, Brinley N.; Jones, Steven R.
Titel	Learning Integrals Based on Adding Up Pieces across a Unit on Integration
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 9 (2023) 1, S.118-148 (31 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Jones, Steven R.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-022-00204-w
Schlagwörter	Mathematics Skills; Calculus; Mathematical Concepts; Addition; Mathematics Instruction + Suchen Sie Ihr Suchwort? Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht
Abstract	Recent research on integration has shown the importance of quantities-based meanings for integrals. However, this research body is still in need of detailed empirical accounts of "how" students develop such understandings across an entire unit on integration. This paper contributes by providing one such account, based on a quantities-based orientation called "adding up pieces" (AUP). Our study examines how three separate pairs of students learned definite integrals and integral functions within interview settings over four consecutive interview-lessons, meant to correspond to four consecutive in-class sessions. The first interview developed the partition, target quantity, and sum structure for definite integral, which were solidified in the second interview. The third and fourth interviews extended this AUP structure to a variable upper bound, output, and function structure for integral functions in preparation for the Fundamental Theorem of Calculus (FTC). (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01