William Hall’s Thesis Defense
ORAL THESIS DEFENSE
William L. Hall, Jr.
MST Candidate
Thesis Advisor: Robert Franzosa
Monday, June 7
2:00 p.m.
102 Bennett Hall
Language and Area: Barriers to Student Understanding of Integration
Research has shown that many students have a computationally-based understanding of integration and they usually associate integration with area. One of the factors which may be impacting student understanding is the linguistic ambiguity of mathematical phrases as the everyday language on their mathematics understanding is called “semantic contamination” and it appears that this may be affecting student understanding of integration. 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 defining the terms “definite integral” and “indefinite integral”. Students were apt to define the definite integral as finding an area under the curve and some even extend this area representation to the indefinite integral. It was observed that, much like in previous research, students seem to lack the requisite ability to understand graphical area and instead rely on physical area. This reliance on physical characteristics poses significant problems for student understanding of integration. Interviews also demonstrate that semantic contamination is a significant issue in integration as students defined the definite integral as “more precise” than the indefinite integral which was seen as “vague”. Implications for instruction in calculus, including how to utilize linguistic ambiguity as an instructional tool for developing quality mathematical discourse are discussed.