Fall term of 2006, a web-assisted undergraduate mathematics course was taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers I. The course goals were: To foster a deep understanding of critical mathematical content; and to promote the development of mathematical communication and collaboration concepts, skills, and dispositions. Outside of regular class periods, students participated in an ongoing asynchronous mathematical dialogue using an asynchronous communication network--"WebCT" threaded discussion forum. A modified rubric from the Interaction Analysis Model (Gunawardena, Lowe, and Anderson, 1997) was utilized to code the cognitive level of student postings on "WebCT." The focus of this study was to explore changes in students' level of higher-order thinking and knowledge construction in asynchronous threaded discussions, the emergence of communication patterns and structures in the network, and relationships between role centrality and concept centrality in student discourse. It employed multiple analysis techniques by employing both content analysis and social network analysis to pursue its research foci. Results revealed that students did not post consistently at high, middle, or low levels, the level of student discourse from topic to topic increased over time as fewer low- and middle-level messages were posted relative to high-level messages, and student(s) with the highest role centrality were the same students who contributed the ideas with the highest content centrality. Also, a slightly weaker relationship was found in which students with lesser role centrality were lesser (but meaningful) contributors of central concepts. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]