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ERIC Number: EJ880351
Record Type: Journal
Publication Date: 2010
Pages: 25
Abstractor: As Provided
Reference Count: 30
ISSN: ISSN-1098-6065
Contrasting Cases of Calculus Students' Understanding of Derivative Graphs
Haciomeroglu, Erhan Selcuk; Aspinwall, Leslie; Presmeg, Norma C.
Mathematical Thinking and Learning: An International Journal, v12 n2 p152-176 2010
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.)
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A