The Influence Of Dynamic Visualization On Undergraduate Calculus Learning
Sutton, Julie Marie Skinner
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The urgent need in the United States to produce an additional one million graduates in the areas of science, technology, engineering and mathematics and previous research into why students choose to abandon their quest to earn such degrees motivates exploration of the appropriate use of technology that engages students in the first-year calculus classroom. Technology enhances our capacity to incorporate visualization into the teaching of mathematics, yet research suggests that high school mathematics students who prefer to visualize when solving mathematics tasks are not the “super stars” of their classrooms. In this qualitative study, nine students, five of whom prefer to visualize when solving mathematics tasks, completed a series of four individual interviews focusing on topics covered in their calculus course. Four of the nine students used dynamic visualization software (DVS) during interview sequences whereas the remaining five students participated in analogous static interviews. Research questions guiding the study design focus on how student interactions with DVS result in differences in student views of derivative as a rate of change at a point, if students exploring mathematical relationships using DVS hold multi-representational views of derivative when compared to their peers who were not offered DVS as a learning tool, and how exploration with DVS influences student understanding of the Extreme Value Theorem and the relationship between continuity and differentiability. Using grounded theory, results suggest that focusing features must accompany DVS exploration in the undergraduate calculus classroom. In addition, results raise questions about accurate assessment of transfer of knowledge when DVS is presented as a learning tool and not made available during testing. There were several instances where DVS exploration clarified mathematical relationships. Although findings suggest a higher incidence of this for visualizers, DVS exploration also enhanced the reasoning of those students who prefer not to visualize when solving mathematics tasks.