Seattle, Washington
June 14, 2015
June 14, 2015
June 17, 2015
978-0-692-50180-1
2153-5965
Educational Research and Methods
7
26.1666.1 - 26.1666.7
10.18260/p.25002
https://peer.asee.org/25002
1169
Jonathan C. Hilpert is an Educational Psychologist at Georgia Southern University.
Bachelor of Science in Applied Mathematics from Middle Georgia State College. Currently a graduate student in the Department of Mathematical Sciences at Georgia Southern University with a concentration in Applied Mathematics and research in Graph Theory.
Using Havel-Hakimi to graph classroom networksEngineering education research and ABET accreditation standards both emphasize theimportance of collaborative learning. Researchers have argued that classroomcollaborations can be studied as emergent systems, where the actions of individual agentsproduce an outcome that is not reducible to its individual parts. The underlying structureof an emergent system is a network. Networks can be graphically represented asinterconnected collections of nodes and edges, or in the context of the current studystudents working together in classrooms to learn and solve problems. Althoughresearchers have examined collaborative emergent systems in classrooms from aqualitative perspective, there is need for more advanced tools to examine how thenetwork structure of classrooms influences student learning and performance.In this paper, we use the Havel-Hakimi algorithm to visualize data collected fromstudents to investigate classroom networks. The Havel-Hakimi algorithm uses a recursivemethod to create a simple graph from a graphical degree sequence. In this case, thedegree sequence is a representation of each student in a classroom, and we use thenumber of peers with which a student studied or collaborated to determine the degree.We expand upon the Havel-Hakimi algorithm by coding a program in Python thatgenerates random graphs with the same degree sequence. In doing this, we can examineall potential possibilities of which students work with whom. Then, we use an edge-weight technique to determine which of those random graphs is the best fit to the real lifenetwork in the classroom. Once best fit has been determined, we analyze why theclassroom network looks this way and what it means. To do this, we use Gephi (popularnetwork analysis software) to calculate closeness, betweenness, and other significantmeasures of network characteristics.Our results will describe a useful technique for developing classroom graphs that canaccurately, graphically represent engineering classroom networks. We will show someexample graphs and conclude with a discussion of how these graphs may be related tostudent learning.
Hilpert, J. C., & Holliday, R. (2015, June), Using Havel-Hakimi to Graph Classroom Networks Paper presented at 2015 ASEE Annual Conference & Exposition, Seattle, Washington. 10.18260/p.25002
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