Date of Award

2008

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)

Department

Teaching

Advisor

Robert Franzosa

Second Committee Member

Tod Shockey

Third Committee Member

William Bray

Abstract

This thesis describes results from an ongoing investigation of students' mathematics learning in general education courses. This work focuses in particular on first semester calculus students' ability to determine properties of a function's graph from a sign chart of the first derivative of the function. This thesis presents results of a qualitative study involving 136 students enrolled in MAT126 Calculus I in the fall of 2007 and ninety-nine students enrolled in MAT 126 in the spring of 2008. Both groups were given a test problem addressing the topic under investigation as part of their course final exam. The test problem is quantitatively analyzed and these results are supplemented with results from eleven follow-up interviews. The purpose of this study is to investigate more thoroughly calculus students' graphical and conceptual understanding. The results of this study indicate that students' graphical knowledge is weak for a variety of reasons, including students' preference for procedural knowledge, students' preference for algebraic functions, students' weakness graphing without an algebraic representation of a function, and students' unresolved cognitive conflict.

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