#### Presentation Title

Graphs of Classroom Networks

#### Location

Room 1909

#### Session Format

Paper Presentation

#### Research Area Topic:

Natural & Physical Sciences - Mathematics

#### Co-Presenters, Co- Authors, Co-Researchers, Mentors, or Faculty Advisors

Faculty Advisors: Dr. Jonathan Hilpert and Dr. Colton Magnant

#### Abstract

Researchers have argued that classroom collaborations can be studied as emergent systems, where the actions of individual agents produce an outcome that is not reducible to its individual parts. The underlying structure of an emergent system is a network. Networks can be graphically represented as interconnected collections of nodes and edges, or in the context of the current study students working together in classrooms to learn and solve problems. Although researchers have examined collaborative emergent systems in classrooms from a qualitative perspective, there is need for more advanced tools to examine how the network structure of classrooms influences student learning and performance.

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation the students in a classroom, and we use the number of peers with which a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in Python that generates random graphs with the same degree sequence. In doing this, we can examine some of the potential possibilities of which students work together. Then, we use an edge-weight technique to determine which of those random graphs is the best fit to the real life network in the classroom. Once best fit has been determined, we attempt to analyze why the classroom network looks this way and what it means.

Our results will describe a useful technique for developing classroom graphs that can accurately, graphically represent engineering classroom networks. We will show some example graphs and conclude with a discussion of how these graphs may be related to student learning.

This work was supported by the National Science Foundation (NSF) under NSF TUES Type 1 REC-1245081.

#### Keywords

Havel-Hakimi, Graph theory, Classroom network

#### Presentation Type and Release Option

Presentation (Open Access)

#### Start Date

4-24-2015 1:30 PM

#### End Date

4-24-2015 2:30 PM

#### Recommended Citation

Holliday, Rebecca, "Graphs of Classroom Networks" (2015). *Georgia Southern University Research Symposium*. 70.

https://digitalcommons.georgiasouthern.edu/research_symposium/2015/2015/70

Graphs of Classroom Networks

Room 1909

Researchers have argued that classroom collaborations can be studied as emergent systems, where the actions of individual agents produce an outcome that is not reducible to its individual parts. The underlying structure of an emergent system is a network. Networks can be graphically represented as interconnected collections of nodes and edges, or in the context of the current study students working together in classrooms to learn and solve problems. Although researchers have examined collaborative emergent systems in classrooms from a qualitative perspective, there is need for more advanced tools to examine how the network structure of classrooms influences student learning and performance.

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation the students in a classroom, and we use the number of peers with which a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in Python that generates random graphs with the same degree sequence. In doing this, we can examine some of the potential possibilities of which students work together. Then, we use an edge-weight technique to determine which of those random graphs is the best fit to the real life network in the classroom. Once best fit has been determined, we attempt to analyze why the classroom network looks this way and what it means.

Our results will describe a useful technique for developing classroom graphs that can accurately, graphically represent engineering classroom networks. We will show some example graphs and conclude with a discussion of how these graphs may be related to student learning.

This work was supported by the National Science Foundation (NSF) under NSF TUES Type 1 REC-1245081.