Theses and Dissertations from UMD
Permanent URI for this communityhttp://hdl.handle.net/1903/2
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Applying Mathematics to Physics and Engineering: Symbolic Forms of the Integral(2010) Jones, Steven Robert; Campbell, Patricia F; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A perception exists that physics and engineering students experience difficulty in applying mathematics to physics and engineering coursework. While some curricular projects aim to improve calculus instruction for these students, it is important to specify where calculus curriculum and instructional practice could be enhanced by examining the knowledge and understanding that students do or do not access after instruction. This qualitative study is intended to shed light on students' knowledge about the integral and how that knowledge is applied to physics and engineering. In this study, nine introductory-level physics and engineering students were interviewed about their understanding of the integral. They were interviewed twice, with one interview focused on and described as problems similar to those encountered in a mathematics class and the other focused on and described as problems similar to those found in a physics class. These students provided evidence for several "symbolic forms" that may exist in their cognition. Some of these symbolic forms resembled the typical interpretations of the integral: an area, an addition over several pieces, and an anti-derivative process. However, unique features of the students' interpretations help explain how this knowledge has been compiled. Furthermore, the way in which these symbolic forms were employed throughout the interviews shows a context-dependence on the activation of this knowledge. The symbolic forms related to area and anti-derivatives were more common and productive during the mathematics interview, while less common and less productive during the physics interview. By contrast, the symbolic form relating to an addition over several pieces was productive for both interview sessions, suggesting its general utility in understanding the integral in various contexts. This study suggests that mathematics instruction may need to provide physics and engineering students with more opportunities to understand the integral as an addition over several pieces. Also, it suggests that physics and engineering instruction may need to reiterate the importance, in physics and engineering contexts, of the integral as an addition over several pieces in order to assist students in applying their knowledge about the integral.Item AN EXAMINATION OF THE RELATIONSHIP BETWEEN PARTICIPATION IN ACADEMIC-CENTERED PEER INTERACTIONS AND STUDENTS' ACHIEVEMENT AND RETENTION IN MATHEMATICS-BASED MAJORS(2006-03-27) Howell, Kadian M.; Milem, Jeffrey F.; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This mixed-method study employed quantitative and qualitative methods to examine the nature of first-year undergraduate students' experiences learning mathematics with peers through interactions that have an academic focus and how participation in these experiences (in and outside of math classrooms) relate to students' academic success in precalculus and calculus courses and their retention in mathematics- and science-based programs. Quantitative and qualitative results provided evidence that students have different experiences learning mathematics in-class and outside of class by race/ethnicity, gender, and ability (determined by students' first semester math course). Descriptive statistics and correlation analyses revealed that in both of these contexts first semester math course had the strongest relationship to students' level of participation in ACPIs. ANOVAs and multiple comparisons revealed differences in students' participation in in-class ACPIs by race/ethnicity and ability. Regression analyses revealed that the math course in which students enrolled for their first semester and for their second semester was predictive of students' math course grades during each of those semesters. Students' level of participation in ACPIs did not predict their academic achievement in mathematics or their retention in undergraduate math- and science-based programs after one year. Qualitative analyses resulted in the following assertions (1) When students struggle with learning mathematics their primary resource is the course text. (2) Students recognize the benefit of learning mathematics with other students both in- and outside of class, but they do not do it outside of class! and (3) Formally-organized, out-of-class interactions with undergraduates, TAs, faculty, and professors in math- and science-based programs have a strong influence in helping students to connect with others in these programs. Students report that this can influence their persistence in undergraduate math- and science-based programs. Results of this study provided information about students' learning experiences that can be valuable to undergraduate math and math education faculty and university administrators who are interested in improving undergraduate mathematics education.