Students' Challenges with Polar Functions: Covariational Reasoning and Plotting in the Polar Coordinate System

Autor/in	Habre, Samer
Titel	Students' Challenges with Polar Functions: Covariational Reasoning and Plotting in the Polar Coordinate System
Quelle	In: International Journal of Mathematical Education in Science and Technology, 48 (2017) 1, S.48-66 (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2016.1220027
Schlagwörter	Mathematics Achievement; Mathematics Activities; Problem Solving; Geometry; Calculus; Task Analysis; Cognitive Style; Cognitive Processes; Graphs; Mental Computation; Questionnaires; Pretests Posttests; Interviews; Trigonometry; College Students; International Schools; Foreign Countries; Lebanon + Suchen Sie Ihr Suchwort? Mathmatics sikills; Mathmatics achievement; Mathematical ability; Mathematische Kompetenz; Problemlösen; Geometrie; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Aufgabenanalyse; Cognitive styles; Kognitiver Stil; Cognitive process; Kognitiver Prozess; Grafische Darstellung; Kopfrechnen; Fragebogen; Interviewing; Interviewtechnik; Trigonometrie; Collegestudent; International school; Internationale Schule; Ausland; Libanon
Abstract	Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the corresponding plot in the Cartesian plane. In particular, it examines how students coordinate the covariation in the polar coordinate system with the covariation in the Cartesian one. The research, which was conducted in a sophomore level Calculus class at an American university operating in Lebanon, investigates in addition the challenges when students synchronize the reasoning between the two coordinate systems. For this, the mental actions that students engage in when performing covariational tasks are examined. Results show that coordinating the value of one polar variable with changes in the other was well achieved. Coordinating the direction of change of one variable with changes in the other variable was more challenging for students especially when the radial distance r is negative. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01