Undergraduate Students’ Connections Between the Embodied, Symbolic, and Formal Mathematical Worlds of Limits and Derivatives: A Qualitative Study Using Tall’s Three Worlds of Mathematics

FieldValue
dc.contributor.authorSmart, Angela
dc.date.accessioned2013-06-14T15:43:51Z
dc.date.available2013-06-14T15:43:51Z
dc.date.created2013
dc.date.issued2013
dc.identifier.urihttp://hdl.handle.net/10393/24247
dc.identifier.urihttp://dx.doi.org/10.20381/ruor-3048
dc.description.abstractCalculus at the university level is taken by thousands of undergraduate students each year. However, a significant number of students struggle with the subject, resulting in poor problem solving, low achievement, and high failure rates in the calculus courses overall (e.g., Kaput, 1994; Szydlik, 2000; Tall, 1985; Tall & Ramos, 2004; White & Mitchelmore, 1996). This is cause for concern as the lack of success in university calculus creates further barriers for students who require the course for their programs of study. This study examines this issue from the perspective of Tall’s Three Worlds of Mathematics (Tall, 2004a, 2004b, 2008), a theory of mathematics and mathematical cognitive development. A fundamental argument of Tall’s theory suggests that connecting between the different mathematical worlds, named the Embodied-Conceptual, Symbolic-Proceptual, and Formal-Axiomatic worlds, is essential for full cognitive development and understanding of mathematical concepts. Working from this perspective, this research examined, through the use of calculus task questions and semi-structured interviews, how fifteen undergraduate calculus students made connections between the different mathematical worlds for the calculus topics of limits and derivatives. The analysis of the findings suggests that how the students make connections can be described by eight different Response Categories. The study also found that how the participants made connections between mathematical worlds might be influenced by the type of questions that are asked and their experience in calculus courses. I infer that these Response Categories have significance for this study and offer potential for further study and educational practice. I conclude by identifying areas of further research in regards to calculus achievement, the Response Categories, and other findings such as a more detailed study of the influence of experience.
dc.language.isoen
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectmathematics education
dc.subjectmultiple representations
dc.subjectuniversity calculus
dc.subjectcognitive development
dc.subjectThree Worlds of Mathematics
dc.subjectconnecting representations
dc.subjectembodiment
dc.titleUndergraduate Students’ Connections Between the Embodied, Symbolic, and Formal Mathematical Worlds of Limits and Derivatives: A Qualitative Study Using Tall’s Three Worlds of Mathematics
dc.typeThesis
dc.contributor.supervisorSuurtamm, Christine
dc.embargo.termsimmediate
dc.degree.namePhD
dc.degree.leveldoctorate
dc.degree.disciplineÉducation / Education
thesis.degree.namePhD
thesis.degree.levelDoctoral
thesis.degree.disciplineÉducation / Education
CollectionThèses, 2011 - // Theses, 2011 -

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