Investigating Interaction Patterns in Educational Forums: A Social

Networks Analysis Approach

O. Ferreira-Pires, M. E. Sousa-Vieira, J. C. L´opez-Ardao and M. Fern´andez-Veiga

Department of Telematics Engineering, University of Vigo, Spain

Keywords:

Online Social Learning Environments, Forums, Social Networks Analysis.

Abstract:

Social networks analysis allows to study and understand the structural properties of a wide spectrum of natural

or artiﬁcial systems. In the ﬁeld of education, online social networks arise quite naturally in the virtual class-

rooms as an inherent part of the learning activities. In this work we focus in forums participation, modeling

and investigating the social relationships taking place during an undergraduate course on computer networks.

Our ﬁndings show signiﬁcant correlations among the patterns of engagement and the structure of the networks

and the students’ achievements.

1 INTRODUCTION

During the recent years, the structure of several natu-

ral and artiﬁcial complex systems has been analyzed,

and as a result many of the structural properties of

these objects have been discovered (Barab´asi, 2016).

The examples are pervasive,from biological networks

to online social networks, or from the Internet AS

topology to the Bitcoin transactions. Nevertheless,

despite the signiﬁcant progress made in the structural

understanding of massive networks the ultimate goal

is to translate this physical or logical structure, which

has no meaning in itself, to functional predictions or

behavior of the system under study.

In the ﬁeld of education, online social networks

(OSNs) arise quite naturally when information tech-

nology is used in the classroom as an inherent part of

the learning activities. The network is just a depiction

of the existence and strength of interaction among the

students, or among the students with the instructors.

It has long been recognized that the structure of such

interactions is key to a deep comprehension of the in-

formation ﬂow within the students’ group, and that in

the end it can be used to measure the quality of the

learning process and to infer students’ performance

directly from their pattern of interactions.

In this paper, we discuss the results of struc-

tural social networks analysis (SNA) conducted on a

class of college students. Traditionally, information

technology-based learning activities have not been re-

garded as pure academic activities, but this view is

shifting and giving way to the introduction of infor-

mal learning-oriented tasks embedded into the course

design (Cross, 2006). In our case, we use a software

platform based on Moodle, especially built for en-

couraging online participation of the students to de-

sign, carry out and evaluate a set of online learning

tasks and games. After logging the activity during

a full year, we have performed a thorough network

analysis with the aim to understand the information

ﬂow within this controlled group of students. In this

work we focus on the participation in forums, model-

ing the social relationships taking place in each one of

the three forums of the virtual classroom as suitable

social graphs. Our ﬁndings include the detection of

signiﬁcant correlations among the pattern of activity

and the structure of the network and the ﬁnal results.

The rest of the paper is organized as follows. Sec-

tion 2 summarizes some recent related work. The

methodology employed in the course under study is

reported in Section 3. Section 4 contains the main re-

sults of the SNA applied to the datasets. Finally, some

concluding remarks are included in Section 5.

2 RELATED WORK

In the last decade, a signiﬁcant research effort has

been done on understanding how the interpersonal in-

teractions in OSNs shape, reinforce and enhance the

learning process. Datasets were mined in order to dis-

cover the most inﬂuential students or to ﬁnd out how

collaboration among groups of students arise, and the

impact of relationships on learners’ performance. In

other words, whether the structure of the community

to which a student belongs while he/she is engaged in

the learning environment has any substantial correla-

tion on his/her performance. In this Section, we pro-

Ferreira-Pires, O., Sousa-Vieira, M., López-Ardao, J. and Fernández-Veiga, M.

Investigating Interaction Patterns in Educational Forums: A Social Networks Analysis Approach.

DOI: 10.5220/0007721600880099

In Proceedings of the 11th International Conference on Computer Supported Education (CSEDU 2019), pages 88-99

ISBN: 978-989-758-367-4

vide a chronological review of representative papers.

A more extensive compilation can be found in (Dado

and Bodemer, 2017).

The focus of the study reported in (Laat et al.,

2007) is to highlight the advances that social net-

work analysis can bring, in combination with other

methods, when studying the nature of the interac-

tion patterns within a networked learning community

and the way its members share and construct knowl-

edge. Structural analysis of student networks has been

done in (Dawson, 2008) too, where the authors ex-

plore the relationships between a student’s position in

the social learning network and their reported sense

of community. The ﬁndings suggest that the posi-

tion is indicative of both their degree of perceived

sense of community and of the nature of the aca-

demic and social support the student requires for fu-

ture progression through the course. A complemen-

tary work (Haythornthwaite, 2008) studies learning

communities from a social network perspective, in-

cluding what relations are evident in these communi-

ties, how media affect online relationships formation

and what beneﬁts can arise from successfully main-

taining learning networks. In (Manca et al., 2009)

authors highlight the importance of a good under-

standing of the communication ﬂows that really occur

among users in educational online forums, in order to

detect signiﬁcant postings to be included in social net-

works analysis. (Rienties, 2009) examines the impact

of academic motivation on the type of discourse con-

tributed and on the position of the learner in the so-

cial learning network, concluding that highly intrin-

sically motivated learners become central and promi-

nent contributors to cognitive discourse; in contrast,

extrinsically motivated learners contribute on average

and are positioned throughout the social graph. (Heo

et al., 2010) investigates the patterns and the quality

of online interactions during project-based learning,

showing its correlation with project scores. The iden-

tiﬁcation of social network analysis indices that are

actually related to the experiences of the learning pro-

cess is addressed in (Toikkanen and Lipponen, 2011),

showing that some popular measures such as density

or degree centrality are meaningful or not depend-

ing on the characteristics of the course under study.

The structure of two distributed learning networks is

given in (Cadima et al., 2012) in order to understand

how it could enhance students’ success. In (Hommes

et al., 2012), the authors study the inﬂuence of so-

cial networks, motivation, social integration and prior

performance on learning, proposing degree central-

ity as a key predictor for students learning. In addi-

tion to structural properties, the inﬂuence of cognitive

styles and linguistic patterns of self-organizing groups

within an online course is the focus of (Vercellone-

Smith et al., 2012).

More recently, the work (Shea et al., 2013) ex-

amines relationships between online learner self- and

co-regulation. Here, the results indicate that students

with high levels of learner presence occupy more ad-

vantageous positions, suggesting that they are more

active and more sought after in networks of inter-

action. (Stepanyan et al., 2014) discusses the pat-

terns of network dynamics within a multicultural on-

line collaborative learning environment. The study

tests a set of hypothesis concerning tendencies to-

wards homophily/heterophily and preferential attach-

ment, participant roles and group work in the course

under study. In (Xie et al., 2014) social network

analysis techniques are used to examine the inﬂu-

ence of the moderator’s role on online courses. The

main conclusion is that when students are assigned

to the moderator position their participation quantity,

diversity and interaction attractiveness increases sig-

niﬁcantly, and their lack of participation inﬂuences

the group interaction. A theoretical model is devel-

oped in (Chung and Paredes, 2015) to investigate the

association between social network properties, con-

tent richness in academic learning discourse and per-

formance, concluding that these factors cannot be

discounted in the learning process and must be ac-

counted for in the learning design. In (Gaggioli et al.,

2015), the relationship between social network posi-

tion, creative performance and ﬂow in blended teams

is investigated. The results indicate that social net-

work indices, in particular those measuring central-

ization and neighbors’ interactions, can offer valuable

insight into the creative collaboration process. (Lin

et al., 2015) compares the impact of social-context

and knowledge-contextawareness on quantitativeand

qualitative peer interaction and learning performance,

showingthat with the ﬁrst one the community had sig-

niﬁcantly better learning performance, likely related

to the more extensive and frequent interactions among

peers. (Siqin et al., 2015) investigates the discourses

involving student collaboration in ﬁxed groups and

opportunistic cooperation. They ﬁnd that activelypar-

ticipating and contributinghigh-levelideas were posi-

tively correlated with students’ domain of knowledge.

The existence of a positive relationship between cen-

tralization and cohesion and the social construction of

knowledge in discussion forums is the main conclu-

sion in (Tirado et al., 2015). In (Putnik et al., 2016)

the authors present a new model for students’ eval-

uation based on their behavior during a course, and

its validation through an analysis of the correlation

between social network measures and the grades ob-

tained by the students. Finally, (Jan and Viachopou-

Investigating Interaction Patterns in Educational Forums: A Social Networks Analysis Approach

los, 2018) investigate the inﬂuence of learning design

and tutor interventions on the formation and evolution

of communities of learning, employing SNA to study

three differently designed discussion forums.

Related to our previous work within this area of

research, (Sousa et al., 2017) pays detailed attention

to the characterization of informal learning activities.

To this end, we used one custom software platform,

SocialWire, for discovering what factors or variables

have measurable correlation with the performance of

the students. The dataset was ﬁrst collected along

three consecutive editions of an undergraduate course

on computer networks. Later, we also measured the

extent and strength of social relations in a online so-

cial network used among students of a master level

course on computer networks (Sousa et al., 2018).

The dataset comprised again a period of three aca-

demic years. As these papers discuss, in addition to

the quantity of interactions among participants, suc-

cessful prediction of performance is possible when

the quality of interactions can also be observed, or

inferred on the basis of the network structure.

In this work we use a similar approach, but ap-

plied to the analysis of forums engagement. It is the

ﬁrst time that we encourage and reward quality par-

ticipation in this activity in the undergraduate course

on computer networks under study.

3 EDUCATIONAL CONTEXT &

DATASET

We have taken as our educational environment the

2017/2018 edition of a course on Computer Net-

works directed to undergraduates of the second year

in the Telecommunications Engineering bachelor de-

gree. This course has a weekly schedule that spans 14

weeks. Overall, the classroom activities are organized

as follows:

• Lectures (2 hours each), that mix descriptive con-

tent (the Internet architecture, basic principles and

concepts, anatomy of the main protocols) with

some elementary mathematical details for analyz-

ing network performance.

• Laboratory sessions (2 hours each), organized in

small study groups. These are complementary

sessions where the students solve written exer-

cises, work hands-on with real networking equip-

ment and make a small programming assignment.

The course activities are supported by a tailored

Moodle site to which the students and teachers be-

long, and wherein general communication about the

topics covered takes place. To encourage networked

learning and collaborative work, each year different

activities are planned and carried out in the platform.

The students may gain different points by completing

or participating in these activities, and the resulting

rankings are eventually made public to the group. In

the edition forming the basis for this work, the follow-

ing online activities were proposed:

1. Homework tasks, to be worked out previously to

the in-class or the laboratory sessions. With this

activity teachers successfully encourage the stu-

dents to prepare some of the material in advance.

2. Quizzes, proposed before the midterm exams.

Quizzes are just practice exams for self-training.

3. Collaborative participation in forums. Three sep-

arate forums were created in Moodle to allow the

students to post questions, doubts or puzzles re-

lated to the organization of the course (organiza-

tion forum), the content of the in-class lectures or

the laboratory sessions (lessons forum), and the

programming assignments (programming forum).

4. Optional activities, such as collaborative edition

of a glossary of terms related to the subject,

games, peer assessment of tasks, etc.

The maximum score of tasks and quizzes is mea-

sured in so-called merit points, and represents the to-

tal score gained from engagement in online activities

during the continuous assessment. It is also possible

to obtain extra merit points by doing some optional

activities in order to compensate for bad scores or late

submissions of some of the tasks or quizzes.

The participation in forums, the answers to doubts

or the act of sharing interesting resources are also

rewarded with points granted by the teachers or the

classmates; speciﬁcally, each post can be voted in a

discrete scale: 3 points (lessons forum), 5 points (pro-

gramming forum) or 11 points (organization forum).

As new points are obtained, the karma level of each

student increases, depending on the average of the

points obtained in each forum, the difference with the

average of the points obtained by the class in each fo-

rum, the total number of points obtained and the total

number of posts voted by the student. The weighs of

the lessons, programming and organization forums to

the karma level are 75%, 15% and 10%, respectively.

Finally, the use of the virtual classroom is also re-

warded by the automatic scoring of different actions

carried out in the platform related to the normal activ-

ity unfolded along the term, like viewing resources,

posting new threads, replying to posts, etc. The so-

called experience points are awarded in a controlled

environment, with their maximum values and their

frequency set by the teachers.

CSEDU 2019 - 11th International Conference on Computer Supported Education

Figure 1: Forums activity graphs. LG (top-left), PG (top-right) and OG (bottom).

The accomplishment of some tasks, the karma lev-

els and the experience points are ultimately converted

into certain beneﬁts helpful to pass the subject: bonus

points for the grades, more time for the assignments,

tips in the ﬁnal exam, etc.

Though this course may be passed with a single

ﬁnal examination covering all the material (provided

the programming assignment meets the minimum re-

quirements), students are encouraged to follow the

continuous assessment path. The weight of the con-

tinuous assessment is 50%, and the remaining 50% is

awarded as the result of a ﬁnal exam held on two dif-

ferent dates (last week of May and ﬁrst week of July,

non-exclusive). The continuous assessment weight is

split into a 20% for the programming assignment, a

20% from the midterm exam and a 10% of the ﬁnal

grade comes out from the points gathered by engaging

in the social activities described previously,devised as

a tool to increase the level of participation.

To ﬁnish our description, in this edition 136 stu-

dents followed the course. 129 students which fol-

lowed the continuous assessment and 65 of these ﬁ-

nally passed. Only 7 students were not stuck to con-

tinuous assessment, and 2 of them were able to pass.

Remarkably, one of the two had a very active partici-

pation in the three forums.

4 ANALYSIS OF THE DATASETS

We applied standard SNA (Newman, 2010) tech-

niques and tools to mine the data collected in the fo-

rums activity. As explained in the introduction, we

model the social relationships taking place in each

one of the three forums as graphs, termed hereafter

lessons graph (LG), programming graph (PG) and or-

ganization graph (OG). Our intent is to explain the

basic structural properties of such graphs as conse-

quences of the social interactions among its agents.

For such purpose, we recorded the events that took

place in each forum: users who posted new threads,

users who replied, and the average valuations they re-

ceived. This information is represented as a graph

where two nodes —the users— are connected by an

edge if one has given a reply to an entry posted by the

other. Self-edges represent new threads. The weight

of each edge is equal to the average points obtained

by the reply or the new thread post.

An illustration is given in Figure 1, where every

node is a student identiﬁed by his/her position in the

ordered list of ﬁnal grades. The node with label 0 cor-

responds to the instructors. Light green nodes belong

to students that passed the subject at the ﬁrst oppor-

tunity (May), while dark green is for students who

Investigating Interaction Patterns in Educational Forums: A Social Networks Analysis Approach

Table 1: Summary of basic structural parameters of each graph.

LG PG OG

Density

without self-edges 0.0564 0.0525 0.0764

with self-edges 0.0718 0.0666 0.0971

Reciprocity 0.4091 0.3171 0.2857

Transitivity 0.1151 0.1687 0.2201

Number of cliques

Size

2 70 69 78

3 20 32 52

4 0 5 10

5 0 0 1

6 0 0 0

Degree

In 0.1525 0.1564 0.2543

Out

without self-edges 0.5733 0.6298 0.7387

with self-edges 0.5663 0.5817 0.6941

Closeness 0.6432 0.6487 0.7579

Betweenness

Directed 0.4949 0.2275 0.4335

Undirected 0.7202 0.6637 0.6957

Eigenvector Unweighted

without self-edges 0.8355 0.8206 0.8209

with self-edges 0.8384 0.8109 0.8078

Assortativity

Degree −0.0616 −0.2551 −0.1472

Nominal 0.0955 −0.0805 0.0154

passed after the second opportunity (July), and grey

is for those students who dropped off the course or

failed the subject in the end. The width of each edge

is proportional to its weight.

4.1 Graph Level Measures

In SNA, the static or dynamic structure of a graph re-

veal key aspects of the collective and individual be-

havior of the agents. Next, we brieﬂy report some of

the typical descriptive measures of a graph, and their

values in our datasets. Notice that for some measures

we consider simpliﬁed versions of the graphs, where

the weight of each edge is the sum of the weights of

all the edges between the underlying pair of nodes.

Moreover, including self-edges means including the

opening of new forum threads in the analysis.

4.1.1 Density

The density of a graph refers to the number of edges

that exist, reported as a fraction of the total possible

number of edges, with values ranging from 0 (spars-

est) to 1 (densest). The results in Table 1 show that the

density values are small and only a bit higher in the

organization graph. This fact simply reﬂects the def-

inition of the links; since only a part of the students

provide replies of each post, we would not expect a

dense graph of interactions.

4.1.2 Reciprocity

Reciprocity accounts for the number of mutual ex-

changes of information in the network. In the studied

graphs, these exchanges happen in the form of posts-

replies pairs. In mutual collaboration, either part re-

ceives at least one reply from the other part. Table 1

also lists the average reciprocity in the networks. The

results obtained are noticeable, since they are mea-

suring an interactive activity as the participation in

forums. The smaller value of the OG is due to the

fact that many of the questions raised in this forum

are solved with a single answer, in many cases by the

teachers. This also happens in the PG, in which some

of the doubts, mainly related to the speciﬁcations of

the tasks, are also solved by the teachers.

4.1.3 Transitivity

A broader form of collaboration is transitivity, the

fraction of closed loops with three nodes in the graph.

The global transitivity coefﬁcient has been computed

for the datasets. The results obtained are shown in Ta-

ble 1 again, and conﬁrm that transitivity is moderate.

However, this is not entirely unexpected, since in fo-

rums there is beneﬁt in acquiring or propagating infor-

mation through third parties. Our data are consistent

with this observation and, consequently, transitivity is

quite small. Notice the opposite order of the values of

reciprocity and transitivity of the three networks.

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Figure 2: Degree centralities. LG (left), PG (middle) and OG (right).

4.1.4 Cliques

A clique is a maximal complete subgraph of a given

graph. So, a clique represents a subcommunity where

each member interacts with any other member. 2-

cliques and 3-cliques are related to the measures dis-

cussed in the last paragraphs. Table 1 lists the number

of cliques in the graphs by their size. We can see that

large cliques are not very likely.

4.1.5 Centrality

Many different measures of centrality have been de-

veloped, that capture different features of nodes’ po-

sition in a graph, the following ones being some of the

most commonly used:

• Degree centrality: measures how connected a

node is, just counting its neighbors.

• Closeness centrality: measures how easily a node

can reach other nodes, computing the inverse of

the average length of the shortest paths to all the

other nodes in the graph.

• Betweenness centrality: tries to capture the im-

portance of a node in terms of its role in con-

necting other nodes, computing the ratio between

the number of shortest paths that a node lies on

and the total number of possible shortest paths be-

tween two nodes.

• Eigenvector centrality: a measure based on the

premise that a node’s importance is determined by

how important or inﬂuential its neighbors are. The

scores arise from a reciprocal process in which the

centrality of each node is proportional to the sum

of the centralities of the nodes it is connected.

For the case of degree centrality, we considered

separately the in-degree centrality, which is the num-

ber of replies a student receives, and two measures of

the out-degree centrality: (1) the number of replies

given by a student in the graphs without self-eldges,

and (2) the number of new threads opened and replies

given by a student in the graphs with self-edges (we

consider this last measure due to the fact that these

are the interactions that can be voted by the rest of

the class). The results in Table 1 reveal that the in-

degree centrality values are only moderate, but the

out-degree centrality is noticeable, indicating a non-

homogeneous distribution of the replies submitted by

the participants, mainly in the OG. A subset of few

nodes act as very active participants in forums (the

subset includes the teachers, obviously). Neverthe-

less, more nodes act as generators of new threads and

recipients of information.

As for the closeness centrality, the high values

shown in Table 1 are again indicative of the existence

of few very active contributors. In the case of the be-

tweenness centrality, the high values observed in Ta-

ble 1 suggest that in the three networks few nodes act

as bridges between different parts of the graph. These

results are coherent with the reduced number of artic-

ulation points in each network: ﬁve in the LG (0, 4,

23, 76 and 105), seven in the PG (0, 5, 9, 15, 33, 90

and 127) and four in the OG (0, 33, 53 and 73).

Finally, for the eigenvector centrality, we consid-

ered the undirected version and tested different con-

ﬁgurations of the graphs built up from the datasets

(weighted or not, with or without self-loops). Ta-

ble 1 shows that all the measured centrality values

are noticeable, meaning again that not all nodes act as

Investigating Interaction Patterns in Educational Forums: A Social Networks Analysis Approach

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Figure 3: Quantity and quality of interactions. LG (left), PG (middle) and OG (right).

sources or recipients of information in the same way.

4.1.6 Assortativity

The assortativity coefﬁcient measures the level of ho-

mophyly of a graph, based on some labeling assigned

to the nodes. It is positive if similar nodes tend to con-

nect to each other, and negative otherwise. Table 1

lists the degree assortativity and the case of nominal

assortativity where each student is labeled according

to his/her ﬁnal grade, considering in both cases the di-

rected graphs. For the nominal assortativity we have

obtained low values, suggesting randomness in the re-

lationships. For the degree assortativity, the negative

values obtained suggest relationships between the less

and the most active students, as it is desirable.

4.2 Per Student Behavior

Due to the fact that global level measures can hide

some characteristics of the graphs, it might be inter-

esting to study the distribution of the participation of

the students in each forum. Next, we brieﬂy report the

results of such analysis.

4.2.1 Individual Centralities

In Figures 2 and 3 we depict the histograms of indi-

vidual degree centralities and number of new threads

or replies, which are good indicators of the students’

activity. The tail of the empirical out-degree and

number of replies distributions accumulates a non-

negligible probability. This is consistent with the

view that some nodes concentrate a signiﬁcant part

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Figure 4: Closeness centralities. LG (left), PG (middle) and OG (right).

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0.8

0 0.1 0.2 0.3 0.4 0.5 0.6

undirected betweenness

Frequency

0.2

0.4

0.6

0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

undirected betweenness

Frequency

Figure 5: Betweenness centralities. LG (left), PG (middle) and OG (right).

of the activity of the graphs. Notice that the content

of teachers concentrates more that 36, 43 and 49 in-

teractions with more than 20 students in each one of

the three graphs. Among the students, the most active

ones (4, 5, 90) interact with several others. In addition

to the intensity of interactions, another factor is their

quality. Figure 3 shows the histograms of the aver-

age points obtained for posting new threads or replies

(remember the different limits of the scales used in

each forum, 3, 5 and 11, respectively). In general,

new threads and replies are positively voted, espe-

cially those of the lessons and programming forums.

It is important to highlight that a 70% of the best con-

tributors (those students whose posts always received

the maximum score) ﬁnally passed the course.

The alternative measures of centrality produce

similar, consistent ﬁndings. For example, the individ-

ual closeness centralities exhibit non-negligible tails

in their histograms, see Figure 4, revealing the exis-

tence of a small number of very active students (4, 5,

15, 23, 36, 90), close to many others. And for the

betweenness centralities, Figure 5 shows with the his-

tograms that the higher values are correlated to the

articulation points of each graph, listed previously.

Finally, Figure 6 depicts the histograms of the in-

dividual eigenvector centralities, taking into account

the undirected version of the graphs, weighted or not.

Again, we can observe the non-negligible probability

of the tails of the distributions (teacher and students

4, 5, 10, 25, 33, 90).

Next, in order to check the relationship among

the patterns of participation in the forums and the

achievements of the course, we have measured the

statistical correlations between the features under

study in this section and the ﬁnal grades. The sample

correlations

ρ were computed and the linear regres-

sion statistical test was used to quantify such correla-

tions. This test checks the statistical signiﬁcance of

a linear ﬁt of a response variable on one factor vari-

able. The estimated linear coefﬁcient is denoted by

β. Under the null hypothesis (meaning that there is

no such linear dependence) the test statistic follows a

t-distribution, so high values are very unlikely to ob-

serve empirically (James et al., 2013).

The result, in Table 2, shows a statistically signif-

icant positive dependence (

ρ > 0.2) between almost

all the considered factors and the students’ perfor-

mance. Moreover, in order to understand the relation-

Investigating Interaction Patterns in Educational Forums: A Social Networks Analysis Approach

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

weighted eigenvector (with self-edges)

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

weighted eigenvector (with self-edges)

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

weighted eigenvector (with self-edges)

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

unweighted eigenvector (with self-edges)

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

unweighted eigenvector (with self-edges)

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

unweighted eigenvector (with self-edges)

Frequency

Figure 6: Eigenvector centralities. LG (left), PG (middle) and OG (right).

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20 25 30 35 40 45

crossclique #

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50

crossclique #

Frequency

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60 70 80

crossclique #

Frequency

Figure 7: Crossclique numbers in the students’ networks. LG (left), PG (middle) and OG (right).

ship among the differents roles that each student plays

in each network, in Table 3 we show some correla-

tions that suggest a balanced behavior, as desirable.

Finally, in order to check the analogies among the dif-

ferent networks, in Table 4 we show some correlations

that suggest that many students show a similar pattern

of participation in the three forums.

4.2.2 Crossclique Number

The crossclique number counts the number of cliques

a node belongs to. Figure 7 depicts histograms of this

measure for the three networks. In the LG, students

with values higher than 10 are only 4, {4, 25, 53, 90}.

In the PG, the students with values higher than 20 are

just 3, {4, 5, 90}. Finally, in the OG, students with

values higher that 20 are {4, 10, 21, 36, 90}. Addition-

ally, the results in Table 2 indicate that in the three

graphs there is a statistically signiﬁcant positive de-

pendence (again,

ρ > 0.2) between membership to

many subgraphs and the students’ performance. Fi-

nally, values in Table 4 also suggest similarities re-

lated to this feature among the three forums.

5 CONCLUSIONS

In this paper, we have reviewed the extent to what

structural properties of networks can help to explain,

and ultimately predict, the behavior and performance

of students in online social learning environments, es-

pecially the ones which integrate support for informal

learning activities. Provided these informal activities

are well designed to capture the students’ interest and

engage them in participation, the structure of the col-

laboration networks reﬂects and contains useful, sta-

tistically signiﬁcant information to identify the indi-

vidual patterns of engagement, the communities, as

well as the correlation between network position or

activity and the academic performance of students.

The work presented here focuses on the study of

participation in the forums, modeling and investigat-

ing the social relationships developed during a typical

undergraduate course. We have found evidence that

quality participation in this activity is signiﬁcantly

correlated with the ﬁnal outcome of the course, but

it is necessary to continue encouraging and reward-

ing it in order to increase the degree of involvement

CSEDU 2019 - 11th International Conference on Computer Supported Education

Table 2: Correlation between individual features in each graph and student’s performance.

May Final

Lessons Graph

ρ (

β,t, P(> |t|))

ρ (

β,t, P(> |t|))

in degree 0.2189 (0.5149, 2.5591, 1.16· 10

−2

) 0.2768 (0.6411,3.3351, 1.11· 10

−3

)

out degree 0.2401 (0.6325, 2.8192, 5.57· 10

−3

) 0.2393 (0.6352,2.8531, 5.01· 10

−3

)

number new threads 0.1927 (0.8942, 2.2401, 2.68· 10

−2

) 0.2593 (1.1634,3.1082, 2.31· 10

−3

)

number replies 0.1646 (0.3818, 1.9032, 5.93· 10

−2

) 0.1834 (0.4176,2.1613, 3.25· 10

−2

)

points new threads 0.1992 (0.3783, 2.318, 2.21· 10

−2

) 0.2514 (0.4611, 3.0081, 3.14· 10

−3

)

points replies 0.1772 (0.1572, 2.0542, 4.21· 10

−2

) 0.2025 (0.1751,2.3943, 1.81· 10

−2

)

directed betweenness 0.2089 (20.3111, 2.4361, 1.62· 10

−2

) 0.1727 (17.0614, 2.0301, 4.44· 10

−2

)

undirected betweenness 0.2206 (20.3111, 2.5802, 1.11· 10

−2

) 0.2011 (17.0614, 2.3762, 1.89· 10

−2

)

closeness 0.2901 (4.2911, 3.4552, 7.43· 10

−4

) 0.2956 (4.2402,3.5823, 4.77· 10

−4

)

weighted eigenvector 0.1702 (4.4565,1.9713, 5.09· 10

−2

) 0.1179 (3.0696,1.3756, 1.71· 10

−1

)

unweighted eigenvector 0.2572 (6.9747,3.0356, 2.91· 10

−3

) 0.2366 (6.3358,2.8191, 5.55· 10

−3

)

crossclique number 0.2488 (0.2601, 2.9291, 4.01· 10

−3

) 0.2665 (0.2742,3.2012, 1.71· 10

−3

)

Programming Graph

ρ (

β,t, P(> |t|))

ρ (

β,t, P(> |t|))

in degree 0.2585 (0.5633, 3.0521, 2.76· 10

−3

) 0.2425 (0.5227,2.8941, 4.44· 10

−3

)

out degree 0.2226 (0.4688, 2.6041, 1.03· 10

−2

) 0.2066 (0.4418,2.4453, 1.58· 10

−2

)

number new threads 0.2035 (0.6394, 2.3701, 1.93· 10

−2

) 0.1989 (0.6028,2.3501, 2.02· 10

−2

)

number replies 0.3172 (0.6326, 3.8141, 2.11· 10

−4

) 0.2708 (0.5383,3.2574, 1.42· 10

−3

)

points new threads 0.1963 (0.1333, 2.2834, 2.41· 10

−2

) 0.1928 (0.1271,2.2753, 2.45· 10

−2

)

points replies 0.3186 (0.1462, 3.8321, 1.97· 10

−4

) 0.2733 (0.1251,3.2891, 1.28· 10

−3

)

directed betweenness 0.1835 (23.9093, 2.1294, 3.52· 10

−2

) 0.1754 (23.2548, 2.0632, 4.12· 10

−2

)

undirected betweenness 0.1981 (23.9093, 2.3051, 2.28· 10

−2

) 0.1922 (23.2548, 2.2681, 2.49· 10

−2

)

closeness 0.3488 (4.9687, 4.2442, 4.14· 10

−5

) 0.3604 (5.0941,4.4732, 1.63· 10

−5

)

weighted eigenvector 0.1286 (3.8211,1.4798, 1.41· 10

−1

) 0.1439 (4.3298,1.6845, 9.46· 10

−2

)

unweighted eigenvector 0.2105 (4.2566,2.4567, 1.54· 10

−2

) 0.2639 (5.3481,3.1671, 1.91· 10

−3

)

crossclique number 0.2117 (0.1331, 2.4713, 1.48· 10

−2

) 0.2109 (0.1333,2.4987, 1.37· 10

−2

)

Organization Graph

ρ (

β,t, P(> |t|))

ρ (

β,t, P(> |t|))

in degree 0.2035 (0.4045, 2.3712, 1.92· 10

−2

) 0.2022 (0.4069,2.3912, 1.82· 10

−2

)

out degree 0.2331 (0.4814, 2.7321, 7.17· 10

−3

) 0.1767 (0.3692,2.0782, 3.96· 10

−2

)

number new threads 0.2107 (0.8142, 2.4582, 1.53· 10

−2

) 0.2176 (0.8351,2.5821, 1.09· 10

−2

)

number replies 0.1691 (0.3196, 1.7623, 5.25· 10

−2

) 0.1505 (0.2824,1.7624, 8.03· 10

−2

)

points new threads 0.2015 (0.0847, 2.3461, 2.05· 10

−2

) 0.2171 (0.0907,2.5742, 1.12· 10

−2

)

points replies 0.1911 (0.0481, 2.2193, 2.82· 10

−2

) 0.1806 (0.4052,2.1263, 3.53· 10

−2

)

directed betweenness 0.1712 (32.9823, 1.9812, 4.97· 10

−2

) 0.1243 (24.1481, 16.6465, 1.49· 10

−1

)

undirected betweenness 0.2076 (32.9823, 2.4201, 1.69· 10

−2

) 0.1681 (24.1483, 1.9743, 5.05· 10

−2

)

closeness 0.2259 (3.0287, 2.6453, 9.17· 10

−3

) 0.2181 (2.9128,2.5863, 1.08· 10

−2

)

weighted eigenvector 0.1371 (3.5669,1.5773, 1.17· 10

−1

) 0.2111 (5.3343,2.4994, 1.37· 10

−2

)

unweighted eigenvector 0.2111 (4.9496,2.4632, 1.51· 10

−2

) 0.2526 (5.9487,3.0234, 3.01· 10

−3

)

crossclique number 0.2428 (0.1109, 2.8546, 5.02· 10

−3

) 0.2094 (0.0971,2.4802, 1.44· 10

−2

)

Table 3: Correlation between number of new threads and replies posted per student in each forum.

ρ (

β,t, P(> |t|))

Lessons Graph 0.4707 (0.2388,6.176, 7.35· 10

−9

)

Programming Graph 0.6794 (0.4456, 10.719, 2.01· 10

−16

)

Organization Graph 0.5637 (0.2757, 7.9021, 8.92· 10

−13

)

of students. We believe that this study contributes to

a better understanding of the learning experience and

possibly to devise more effective designs of this aca-

demic activity.

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Investigating Interaction Patterns in Educational Forums: A Social Networks Analysis Approach

Table 4: Correlation between individual features in different forums.

Lessons - Programming Graphs

ρ (

β,t, P(> |t|))

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−12

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out degree 0.5517 (0.4444, 7.6582,3.37· 10

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number new threads 0.2354 (0.1591, 2.8041, 5.81· 10

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number replies 0.6396 (0.5584, 9.6332,2.01· 10

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unweighted eigenvector 0.5813 (0.4399, 8.2711, 1.17· 10

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crossclique number 0.5664 (0.3479, 7.9562,6.61· 10

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ρ (

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)

number new threads 0.3133 (0.3967, 3.8191, 2.04· 10

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closeness 0.8826 (0.8342, 21.7434,2.01· 10

−16

)

weighted eigenvector 0.4458 (0.3913, 5.7654, 5.36· 10

−8

)

unweighted eigenvector 0.6331 (0.7416, 9.4684, 2.01· 10

−16

)

crossclique number 0.6445 (0.4724, 9.7651,2.01· 10

−16

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