Contrasting Cases of Calculus Students' Understanding of Derivative Graphs

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 proc...

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Bibliographic Details
Published in:Mathematical thinking and learning 2010-04, Vol.12 (2), p.152-176
Main Authors: Haciomeroglu, Erhan Selcuk, Aspinwall, Leslie, Presmeg, Norma C.
Format: Article
Language:English
Subjects:
Calculus
Cognition & reasoning
Cognitive Processes
College Mathematics
College Students
Comprehension
Critical thinking
Equations (Mathematics)
Graphs
Imagery
Interviews
Mathematical Logic
Mathematics Instruction
Pictorial Stimuli
Students
Studies
Teaching Methods
Thinking Skills
Visualization
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Summary: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.
ISSN:1098-6065
1532-7833
DOI:10.1080/10986060903480300