Contrasting Cases of Calculus Students' Understanding of Derivative Graphs

Autor/inn/en	Haciomeroglu, Erhan Selcuk; Aspinwall, Leslie; Presmeg, Norma C.
Titel	Contrasting Cases of Calculus Students' Understanding of Derivative Graphs
Quelle	In: Mathematical Thinking and Learning: An International Journal, 12 (2010) 2, S.152-176 (25 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1098-6065
Schlagwörter	Graphs; Cognitive Processes; Calculus; Visualization; Mathematics Instruction; Comprehension; Mathematical Logic; Teaching Methods; Thinking Skills; Pictorial Stimuli; Imagery; Interviews; Equations (Mathematics); College Students; College Mathematics + Suchen Sie Ihr Suchwort? Grafische Darstellung; Cognitive process; Kognitiver Prozess; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Visualisation; Visualisierung; Mathematics lessons; Mathematikunterricht; Verstehen; Verständnis; Mathematical logics; Mathematische Logik; Teaching method; Lehrmethode; Unterrichtsmethode; Denkfähigkeit; Fantasieanregung; Metaphorik; Interviewing; Interviewtechnik; Equations; Mathematics; Gleichungslehre; Collegestudent
Abstract	This study adds momentum to the ongoing discussion clarifying the merits of visualization and analysis in mathematical thinking. Our goal was to gain understanding of three calculus students' mental processes and images used to create meaning for derivative graphs. We contrast the thinking processes of these three students as they attempted to sketch antiderivative graphs when presented with derivative graphs. These students constructed different and idiosyncratic images and representations leading to different understandings of derivative graphs. Our results suggest that the two students whose cognitive preferences were strongly visual or analytic and who did not synthesize visual and analytic thinking experienced different difficulties associated with their preferred modes for mathematical representation and thinking. Even the student who did synthesize these modes to some extent, to good effect, experienced difficulty when he did not do so. We discuss pedagogical implications for these results in a final section. (Contains 2 tables and 15 figures.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10