Date of Award

2010

Level of Access

Campus-Only Thesis

Degree Name

Master of Science (MS)

Department

Teaching

Advisor

Natasha Speer

Second Committee Member

Robert Franzosa

Third Committee Member

William Bray

Abstract

Research has shown that many students are adept at solving integration exercises and that they tend to associate the definite integral with finding the area under a curve. However, student understanding of underlying concepts and their computation skills of integration problems tend to break down in difficult examples such as the use of fractional exponents or negative area. One of the factors that may be impacting student understanding of integration is linguistic ambiguity, which refers to the influence of students' knowledge of everyday language on their understanding of mathematical terms. In this study, twenty-five students in an introductory calculus course were interviewed about their knowledge of integration. Participants were asked to discuss various integration problems, both definite and indefinite, as well as define the terms "definite integral" and "indefinite integral." Students were apt to describe both the definite and indefinite integral with the process of finding an area under the curve. Additionally, students seem to have significant issues understanding area under the curve as an abstract representation and instead tended toward a concept of area that was reliant on physical characteristics, such as area of land. Findings from interview data also demonstrates that students struggle with the linguistic ambiguity of integration terms. For example, students defined the definite integral as "more precise" than the indefinite integral, which some saw as "vague." Implications for instruction in calculus, including how to utilize the linguistic ambiguity of terms as an instructional tool for developing quality mathematical discourse are discussed.

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