On the role of student understanding of function and rate of change in learning differential equations

Kuster Jr, George Emil

On the role of student understanding of function and rate of change in learning differential equations

dc.contributor.author	Kuster Jr, George Emil	en
dc.contributor.committeechair	Wawro, Megan	en
dc.contributor.committeemember	Wagner, Joseph F.	en
dc.contributor.committeemember	Zietsman, Lizette	en
dc.contributor.committeemember	Johnson, Estrella	en
dc.contributor.committeemember	Ulrich, Catherine L.	en
dc.contributor.department	Mathematics	en
dc.date.accessioned	2016-07-23T08:00:26Z	en
dc.date.available	2016-07-23T08:00:26Z	en
dc.date.issued	2016-07-22	en
dc.description.abstract	In this research, I utilize the theoretical perspective Knowledge In Pieces to identify the knowledge resources students utilize while in the process of completing various differential equations tasks. In addition I explore how this utilization changes over the course of a semester, and how resources related to the concepts of function and rate of change supported the students in completing the tasks. I do so using data collected from a series of task-based individual interviews with two students enrolled in separate differential equations courses. The results provide a fine-grained description of the knowledge students consider to be productive with regard to completing various differential equations tasks. Further the analysis resulted in the identification of five ways students interpret differential equations tasks and how these interpretations are related to the knowledge resources students utilize while completing the various tasks. Lastly, this research makes a contribution to mathematics education by illuminating the knowledge concerning function and rate of change students utilize and how this knowledge comes together to support students in drawing connections between differential equations and their solutions, structuring those solutions, and reasoning with relationships present in the differential equations.	en
dc.description.degree	Ph. D.	en
dc.format.medium	ETD	en
dc.identifier.other	vt_gsexam:8671	en
dc.identifier.uri	http://hdl.handle.net/10919/71827	en
dc.publisher	Virginia Tech	en
dc.rights	In Copyright	en
dc.rights.uri	http://rightsstatements.org/vocab/InC/1.0/	en
dc.subject	Differential equations	en
dc.subject	Knowledge in Pieces	en
dc.subject	Undergraduate Mathematics Education	en
dc.title	On the role of student understanding of function and rate of change in learning differential equations	en
dc.type	Dissertation	en
thesis.degree.discipline	Mathematics	en
thesis.degree.grantor	Virginia Polytechnic Institute and State University	en
thesis.degree.level	doctoral	en
thesis.degree.name	Ph. D.	en