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Full-Text Articles in Physical Sciences and Mathematics
Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood
Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood
Graduate Theses, Dissertations, and Problem Reports
An individual’s knowledge of definite integrals can range from rote memorization to a strong foundational connection harkening back to its Riemann sum limit definition. In my research, I conducted seven task-based face-to-face interviews with Applied Calculus students. Through the use of real-life examples and guided reinvention, I analyzed ways in which these students, who all initially demonstrated rote memorization, could exhibit a Riemann sum based level of comprehension. This research was conducted in the confines of a student population with definite integral experience, but no formal instruction on limits. My results show that the lack of computational emphasis in class …
Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty
Analyzing Mathematicians' Concept Images Of Differentials, Timothy Shawn Mccarty
Graduate Theses, Dissertations, and Problem Reports
The differential is a symbol that is common in first- and second-year calculus. It is perhaps expected that a common mathematical symbol would be interpreted universally. However, recent literature that addresses student interpretations of differentials, usually in the context of definite integration, suggests that this is not the case, and that many interpretations are possible. Reviews of textbooks showed that there was not a lot of discussion about differentials, and what interpretations there were depended upon the context in which the differentials were presented. This dissertation explores some of these issues. Since students may not have the experience necessary to …