An Investigation of the Relationships between Conceptualization of Limits and Proof Comprehension

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dc.contributor.advisorSorto, M. Alejandra
dc.contributor.authorHerrera, Christine A.
dc.contributor.committeeMemberWhite, Alexander
dc.contributor.committeeMemberStrickland, Sharon
dc.contributor.committeeMemberCory, Beth
dc.date.accessioned2016-06-13T19:11:19Z
dc.date.available2016-06-13T19:11:19Z
dc.date.issued2016-05
dc.description.abstractThis study investigates eighteen Real Analysis students’ informal and formal understanding of the mathematical concept of limits and the relationship on their comprehension of limit proofs. This study utilizes Tall and Vinner’s (1981) notion of concept image and concept definition. The framework examined students’ conceptualization of limit by eliciting their mental images, associated properties, processes, and example space (Watson & Mason, 2005). The study analyzed surveys on the conceptualizations of limits of sequences and limits of functions, class observations, and task-based interviews to explore the different varieties of conceptual understanding held by Real Analysis students. From the data emerged two cognitive categorization of participants’ thinking. Those whose concept image held serious potential conflict factors with the formal definitions of limits and those who had resolved their serious potential conflict factors by the end of the semester, called the cognitive conflict and cognitive resolution groups, respectively. The students were given an end-of-semester proof comprehension assessment that was designed based on Mejia-Ramos, Fuller, Weber, Rhoads, and Samkoff’s (2012) model for assessments for advanced mathematics’ proof comprehension. The analysis showed that Real Analysis students with cognitive resolution had a better local understanding of limit proofs. However, both cognitive groups had difficulty generating examples that illustrated the main ideas of the limit proofs.
dc.description.departmentMathematics
dc.formatText
dc.format.extent314 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationHerrera, C. A. (2016). <i>An investigation of the relationships between conceptualization of limits and proof comprehension</i> (Unpublished dissertation). Texas State University, San Marcos, Texas.
dc.identifier.urihttps://hdl.handle.net/10877/6051
dc.language.isoen
dc.subjectLimits
dc.subjectLimits of sequences
dc.subjectLimits of functions
dc.subjectReal analysis
dc.subjectUndergraduate mathematics
dc.subjectProof
dc.subjectProof comprehension
dc.subjectConcept image
dc.subjectConcept definition
dc.subjectExample space
dc.subject.lcshMathematical analysisen_US
dc.subject.lcshMathematics--Study and teachingen_US
dc.titleAn Investigation of the Relationships between Conceptualization of Limits and Proof Comprehension
dc.typeDissertation
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics Education
thesis.degree.grantorTexas State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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