Student Understanding of the Sign of Negative Definite Integrals in Mathematics and Physics

Autor/inn/en	Bajracharya, Rabindra R.; Sealey, Vicki L.; Thompson, John R.
Titel	Student Understanding of the Sign of Negative Definite Integrals in Mathematics and Physics
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 9 (2023) 1, S.62-91 (30 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Bajracharya, Rabindra R.) ORCID (Sealey, Vicki L.) ORCID (Thompson, John R.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-022-00202-y
Schlagwörter	Physics; Knowledge Level; Mathematical Concepts; Scientific Concepts; Calculus; College Students + Suchen Sie Ihr Suchwort? Physik; Wissensbasis; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Collegestudent
Abstract	In a study of student understanding of negative definite integrals at two institutions, we administered a written survey and follow-up clinical interviews at one institution and found that "backward integrals", where the integral was taken from right to left on the x-axis, were the most difficult for students to interpret. We then conducted additional interviews focused on backward integrals at a second institution. Our analysis uses the concept image framework and a recent categorical framework for mathematical sense making. We found that students were most successful using the Fundamental Theorem of Calculus to determine the sign of an integral when a symbolic expression was provided. When considering a definite integral in a graphical context, students often had difficulty if they viewed the integral as a spatial area, stating that area must always be positive. Some students were able to conceptualize [delta]x or dx as a difference or change and thus a signed quantity; when these students were able to view the area as a sum of smaller pieces, they were more successful in justifying a negative backward integral. Students who used amounts or similar images often had difficulty making sense of the negative sign. Even more progress was made when students either invoked or were asked explicitly about a specific physical context to be represented by the backward integral, other than spatial area. The context provided a meaning to the difference represented by [delta]x or dx and thus to the sign of that difference and the definite integral. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01