The increasing availability of digitized campus administrative data provides researchers with the opportunity to systematically quantify how co-presence in classes shapes individual students' educational outcomes. Social network analysis is appropriate for this purpose through the construction of course co-enrollment network and network-based statistical models. This study intends to explore different ways to construct the course co-enrollment network and evaluate their capacity to capture meaningful student connections through courses. We specifically compare a simple unweighted co-enrollment network and a weighted network based on course characteristics along two dimensions: the relationship between network indices and students' academic performance, and the degree to which students with stronger weighted ties with each other experience more peer influence on individual performance than peers who are less connected through course co-enrollment.
Course-taking experience is a critical part of undergraduate students’ college life. Exposure to peers
who take the same course might significantly impact individual academic achievement. The
demographic composition (in regard to gender, ethnicity, etc.) of classmates shapes the socio-cultural
contexts of students’ academic experience, and the direct (such as group work) and indirect (such as
presentations) interactions with peer students exert intangible influence on individual outcomes from
time to time
With the availability of campus administrative data, researchers are able to evaluate this important peer influence at scale. Among a few different methodological traditions, social network analysis (SNA) is appropriate for this purpose because it is one of the most used methods to study relational data and can explicitly model how students are connected through the course co-enrollment network as well as the effects of network properties on individual-level outcomes.
Studies applying SNA to course co-enrollment networks have found that network statistics such as
degree and density contribute to explaining students’ educational outcomes
Social network analysis (SNA) has been used in studying educational contexts for a long time
As various campus-wide data become digitally available from the administrative end, some other
aspects of peer influence become measurable on a larger scale and at low cost. A prominent example is
course transcript data which can be used to construct course co-enrollment networks. Course
coenrollment captures the most important academic relations between students and their fellow students,
but only a handful of studies in the field of higher education have examined how the structure of
coenrollment network relates to students’ connections and behavior
Different network constructions represent researchers’ understanding of the relation(s) being
modeled. In friendship networks, the existence of a tie depends on students’ self-reports of their best
friend(s), which assumes that perceived intimacy between friends has a significant effect on individual
students. Ties could also be constructed based on students’ direct interactions. The discussion forum
network, for example, usually defines a tie as a student’s response to another student’s post. Networks
in the context of small groups such as study groups or orientation groups are also based on the
assumption that students affect each other through direct interaction. Another type of network is
copresence networks which define ties as students’ physical presence in the same space during the same
time, such as networks constructed based on campus network data, course co-enrollment, and campus
activity participation
In the case of course co-enrollment network, it can either be constructed as a two-mode
coursestudent network or be projected as two one-mode networks separately (student-student and
coursecourse network). The network structure and tie definition could also be affected by the time span, node
inclusion criteria and other research-specific concerns
Researchers have applied SNA to explore how network-level features and node-level indices could
help understand the connection between students’ social relations and their educational outcomes as
well as how such relations form and evolve in contexts. Network-level indices such as density,
betweenness centralization, clustering coefficient, and two-mode bi-component structure are used to
examine overall how students are connected to each other, and how certain classes or students play
critical linking roles
This study investigates different ways to construct course co-enrollment networks with course-level information from university administrative data. We specifically focus on weighting network ties by different pieces of course information such as course type, class size, and meeting schedule. The assumption is that co-enrolling in a course means different levels and effects of peer exposure in different course contexts. For example, students may have more in-depth connections in small seminars than in large lectures, in classes with more frequent meeting schedules than in courses with fewer opportunities to meet. This course-relevant information would affect the strength of students’ connection through the course co-enrollment network.
RQ 1:
What are the different ways of constructing co-enrollment networks weighted by course information from campus administrative data?
To further validate which construction approach more effectively captures students’ connection in different course contexts, we employ two modeling perspectives. We first examine the predictive power of local network statistics on individual outcomes in each network construction. The assumption is that a stronger predictive relationship would indicate a more valid network construction.
RQ 2:
Is the relationship between network indices and students’ academic performance in an unweighted baseline co-enrollment network different from that in a weighted network?
We also examine how individual students' academic performance correlates with each other in each network construction through network autocorrelation models. We assume that in a valid co-enrollment network, peers with heavier weights on their connections have stronger correlations in their performance.
RQ 3:
How does the autocorrelation model fit on a weighted co-enrollment network compared to an unweighted baseline network?
The data used in constructing the course co-enrollment network come from the administrative data from a large four-year public university in the United States. The administrative data includes studentlevel courses-taking records and grades, and the course-level information for full-time undergraduate students across multiple years. This context carries good representative value for research on coenrollment networks for a few reasons. First, the large public university includes a variety of majors and schools that are commonly in place at other institutions. Second, students come from very different family backgrounds including those that are traditionally underrepresented. Third, courses at the university have a variety of class size and delivery format, providing sufficient variations in course contexts and the corresponding network constructions. In this study we restrict our analysis to the data from 2015 to 2020 in order to follow the complete college experience of students from the 2015 and 2016 cohort. We only include course enrollment records for students who completed a course and got a valid grade.
The course co-enrollment network is constructed as a one-mode network that each node represents one student (Zhou et al., 2007). Students have ties with other students if they enrolled and completed the same class. The network is an m*m matrix that m equal to the total number of students in that term excluding students who were only in courses with only one student or students who failed all classes.
Each cell in the matrix presents the weight of the tie of row m student and column n student. If they went to and completed the same class then their cell would be filled with 1 instead of 0. If row m student and column n student enrolled and completed more than one class, the cell would be filled with the total overlapping courses they had.
In the baseline network, the existence of ties between two students solely depends on whether they completed the same courses together, but in reality not all ties are equal. Considering the differences in course contexts, we further add the edge weight based on the combination of different aspects of courselevel information. The specific course features we use include: • Course types, including lecture, seminar, lab, and discussion. Different types correspond to different edge weights in the co-enrollment network based on the chance of interaction they generally offer to students. The order from the most to the least weighted course type is seminar, discussion, lab, and lecture; • Course schedule (meeting times). Courses that meet more often correspond to larger edge weight than courses with fewer meetings (Srinivasan et al., 2006); • Class size. Smaller courses lead to larger edge weight because the chance of interaction between students there is higher than in larger classes; • Courses level (upper-division vs. lower division). Upper-division courses are weighted heavier than lower-division courses since they generally expect more engagement from students. 4.3.
The network autocorrelation model enables us to analyze the social influence process among people
in an interdependent network
In this study, students’ term GPA would be the endogenous outcome variable, and the covariates include students’ cumulative GPA before the term and demographic characteristics (gender, race, firstgeneration college student status, low-income status). In the baseline network, the weight matrix is defined as described in Section 4.2.1; in the weighted network, the weight matrix is further computed from the weighted ties following Section 4.2.2. By comparing the model fit on these different network constructions, we can evaluate if incorporating more course information could capture more accurate strength of students’ influence to each other in the course co-enrollment.
This proposed study is contextualized in a specific usage of campus administrative data: understanding students’ connection and peer influence through course co-enrollment. We focus on finding the optimal approach to constructing co-enrollment networks from both student transcripts and course-level metadata, largely because these administrative records only reflect co-presence and the actual peer exposure and influence needs to be inferred. While the two analytical perspectives we take (network statistics in relation to individual outcome; network autocorrelation model) aim at evaluating the different network constructions, the results in turn could provide insights into how college students’ academic connection with each other varies with course characteristics. For policymakers, this is informative for them to better tailor academic and curricular policies to the goal of promoting student success.
This material is based upon work supported by the National Science Foundation under Grant No.153500 and the Andrew W. Mellon Foundation under Grant No.1806-05902.
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