Understanding introductory students’ application of integrals in physics from multiple perspectives

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dc.contributor.author Hu, Dehui
dc.date.accessioned 2013-08-06T18:23:55Z
dc.date.available 2013-08-06T18:23:55Z
dc.date.issued 2013-08-06
dc.identifier.uri http://hdl.handle.net/2097/16190
dc.description.abstract Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that students often encounter in math classes. Research in physics education has reported students’ lack of ability to transfer their calculus knowledge to physics problem solving. In the past, studies often focused on what students fail to do with less focus on their underlying cognition. However, when solving physics problems requiring the use of integration, their reasoning about mathematics and physics concepts has not yet been carefully and systematically studied. Hence the main purpose of this qualitative study is to investigate student thinking in-depth and provide deeper insights into student reasoning in physics problem solving from multiple perspectives. I propose a conceptual framework by integrating aspects of several theoretical constructs from the literature to help us understand our observations of student work as they solve physics problems that require the use of integration. I combined elements of three important theoretical constructs: mathematical resources or symbolic forms, which are the small pieces of knowledge elements associated with students’ use of mathematical ideas; conceptual metaphors, which describe the systematic mapping of knowledge across multiple conceptual domains – typically from concrete source domain to abstract target domain; and conceptual blending, which describes the construction of new learning by integrating knowledge in different mental spaces. I collected data from group teaching/learning interviews as students solved physics problems requiring setting up integrals. Participants were recruited from a second-semester calculus-based physics course. I conducted qualitative analysis of the videotaped student conversations and their written work. The main contributions of this research include (1) providing evidence for the existence of symbolic forms in students’ reasoning about differentials and integrals, (2) identifying conceptual metaphors involved in student reasoning about differentials and integrals, (3) categorizing the different ways in which students integrate their mathematics and physics knowledge in the context of solving physics integration problems, (4)exploring the use of hypothetical debate problems in shifting students’ framing of physics problem solving requiring mathematics. en_US
dc.description.sponsorship National Science Foundation grant 0816207 en_US
dc.language.iso en_US en_US
dc.publisher Kansas State University en
dc.subject Problem solving en_US
dc.subject Mathematics en_US
dc.subject Integration en_US
dc.title Understanding introductory students’ application of integrals in physics from multiple perspectives en_US
dc.type Dissertation en_US
dc.description.degree Doctor of Philosophy en_US
dc.description.level Doctoral en_US
dc.description.department Department of Physics en_US
dc.description.advisor N. Sanjay Rebello en_US
dc.subject.umi Mathematics Education (0280) en_US
dc.date.published 2013 en_US
dc.date.graduationmonth August en_US

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