Vector Line Integrals in Mathematics and Physics

Autor/inn/en	Dray, Tevian; Manogue, Corinne A.
Titel	Vector Line Integrals in Mathematics and Physics
Quelle	In: International Journal of Research in Undergraduate Mathematics Education, 9 (2023) 1, S.92-117 (26 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Dray, Tevian) ORCID (Manogue, Corinne A.)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2198-9745
DOI	10.1007/s40753-022-00206-8
Schlagwörter	Visual Aids; Teaching Methods; Science Instruction; Comparative Analysis; Textbooks; Undergraduate Students; Mathematics Instruction; Advanced Courses; Content Analysis; Learning Trajectories; Scaffolding (Teaching Technique); Correlation; Geometric Concepts; Algebra + Suchen Sie Ihr Suchwort? Anschauungsmaterial; Teaching method; Lehrmethode; Unterrichtsmethode; Teaching of science; Science education; Natural sciences Lessons; Naturwissenschaftlicher Unterricht; Textbook; Text book; Schulbuch; Lehrbuch; Mathematics lessons; Mathematikunterricht; Fortgeschrittenenunterricht; Inhaltsanalyse; Korrelation; Elementare Geometrie
Abstract	"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly but not entirely correlated with these two disciplines. These textbook approaches are compared to existing characterizations for (single-variable) integration in the theory literature, notably "adding up pieces" (or "multiplicatively-based summation"), which is generalized here to chop, "multiply, add; accumulation from rate; quantitatively-based summation;" and a new characterization, parametric integrals. A review of upper-division textbooks establishes key features of an upper anchor in the learning trajectory. In conclusion, a hypothetical learning trajectory is presented, designed to scaffold student acquisition of rich concept images for vector line integrals. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01