Date of Award

Spring 2017

Project Type

Dissertation

Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

First Advisor

Karen Graham

Second Advisor

Sharon McCrone

Third Advisor

Maria Basterra

Abstract

Little is known about the difficulty students have with sequences and series in second semester calculus courses. In my dissertation, I investigate the misconceptions students had about sequences and series as they worked through problems typically seen in a second semester calculus course.

The dissertation begins with a rationale for studying student understanding of sequences and series. Next, I state my goals for the study as research questions. A conceptual framework is then developed for discussing student misconceptions in terms of an optimal concept map. Then, a three-phase methodology is given. In the first phase of the study, I collected data on student solutions to exam problems involving determining the convergence of sequences and series. In phase two, students were interviewed and asked how they would go about solving similar problems. Finally, in phase three, students were given multiple-choice questions on sequences and series.

The results of this study show that students lack the prerequisite skills needed to be successful in second semester calculus. In addition, students have difficulty selecting which series test to use when investigating series convergence, why the assumptions of such tests are important, and what the conclusions in series tests tell them.

The dissertation concludes with a discussion of errors versus misconceptions, how this study contributes to the existing literature on sequences and series, limitations of the study, and implications for further research.

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