Social Network Methods for Assigning Students to Teams

Abstract

Teachers often group students into teams to organize their classrooms and network informed interventions hold great promise as a way to facilitate positive peer influence and promote the diffusion of intervention effects. Yet thus far, relatively little research has explored how teachers or prevention scientists can best use social network information to assign students to teams. The goal of the present study was to identify and compare seven methods that use different data sources and assignment algorithms to create teams of students. To test these methods, we used survey data from 247 5th through 8th grade students in three rural schools that assessed students’ social networks, sociability, values and interests, and bonding to school. To create teams, we first identified popular students (i.e., those who received the highest number of peer nominations) who also had school bonding scores in the normal range and formed 4-person teams around them, applying different methods to assign students to teams. In all but one method, we placed at-risk students (i.e., those who had the lowest school bonding scores) in teams only during the final round of team creation. Team assignments were compared against three criteria: (1) team-level bonding to school, (2) patterns of affiliation among teammates, and (3) shared values and interests. Two methods, one that used only social network data and one that used social network data in combination with students’ values and interests, yielded the most promising outcomes. The most positive results were obtained when a pruning algorithm akin to the one proposed by Girvan and Newman (2002) was used to select which dyads to join as teammates; this pruning method joined more weakly linked students first, maximizing their potential to find suitable matches. These methods for team assignment hold promise for designing network informed school-based interventions.

Social networks shape behaviors ranging from substance use (Fujimoto et al. 2012; Mercken et al. 2010; Pearson & Michell 2000; Osgood et al. 2013; Rulison et al., 2019), to delinquency (Haynie 2001; Kreager et al. 2011), to school performance and adjustment (Molloy et al. 2011; Shin & Ryan 2014). Thus, there has been an increasing interest in developing interventions that use social networks to accelerate behavior change (Valente 2012; Whitlock et al. 2014; Wyman et al. 2010). Yet relatively little research has explored how teachers or program developers can use social network information to structure teams proactively so that they can promote positive friendships and facilitate positive behaviors and attitudes. Instead, most research in this area has focused on developing methods to identify existing friendship groups or cliques (Frank 1995; Gest et al. 2007; Girvan & Newman 2002; Johnson 1967; Kindermann & Gest 2009; Newman & Girvan 2004; Urberg et al. 1995; Wasserman & Faust 1994). The goal of the present study is to identify, explore, and compare multiple methods that prevention scientists and teachers could use to assign students to teams.

Social relationships influence a wide variety of psychosocial and behavioral outcomes. In schools, social relationships are often enhanced when students are assigned to sit and work with other students. Sometimes these assignments are purposeful and are designated as teams. On other occasions, students may simply be placed in proximity for extended periods of time. The rationale for developing a method for assigning students to teams is to facilitate the development of positive social relationships that avoid potential negative outcomes that may otherwise ensue.

Teachers and program developers face several competing priorities when structuring teams. On the one hand, friendships are an important part of development, allowing children to learn intimacy and trust (Szcześniak et al. 2012). Placing students into teams may facilitate the development of prosocial friendships, which in turn can increase bonding to school (Vaquera & Kao 2008) as well as provide opportunities for conventional norms to be transmitted (Gest et al. 2011). Haynie (2001) notes that closely knit or dense networks are more likely to influence behavior than less cohesive networks. On the other hand, some closely knit friendship groups can work at cross-purposes to programmatic goals. Dishion and colleagues (Dishion et al. 1999; Dishion et al. 1996; Poulin et al. 2001) found that when deviant adolescents were grouped together, they established norms that exacerbated pre-existing tendencies and they modeled and reinforced each other’s deviant talk and behavior. Delinquent students are often enmeshed within groups of other delinquent students, making it difficult to intervene with naturally occurring friendship groups (Lonardo et al. 2009). Using existing friendship groups as the basis of structuring teams thus has the potential to work both for and against the purposes of education.

Few studies of school-based interventions have used social network information to form teams. One study of a smoking prevention program (Valente et al, 2003), compared three methods for creating teams: (1) teachers created teams; (2) peer leaders (i.e., students who received the most friendship nominations) were identified, and the remaining students were randomly assigned to teams; and (3) peer leaders were identified and the remaining students were assigned to teams where they were directly connected to a peer leader, or, if there was no direct link, they were assigned to teams where they had identified another team member as a friend. Students assigned to teams using social network data (the third method) reported that they liked the program more, had improved attitudes toward the program, improved reported self-efficacy to refuse offers to smoke cigarettes, and decreased intentions to smoke. These findings suggest that using social networks to create teams improved program outcomes.

In another study, Van den Berg and colleagues (Braun et al. 2020; Van den Berg & Stoltz 2018) tested a sociometric method for organizing classroom seating to improve relations among students who initially disliked each other. In this method, researchers identified “target pairs” of students who nominated each other as least liked and who rated each other as not likable generally. Then, they created seating charts that reduced the physical distance between these pairs of students by 25% to 50% as measured using a Euclidean classroom seating chart metric. Compared to students in control classrooms, students in treatment classrooms saw greater improvements in their likability ratings. Further, compared to control students, students in the treatment condition reported less victimization; however, there was no change in friendship patterns. Interestingly, relational aggression increased among students in the treatment condition (Braun et al. 2020). Further, the status of students who sat next to children with externalizing problems declined (Van den Berg & Stoltz 2018).

Prior to conducting the current study, we asked teachers and administrators to identify their goals of team formation. To start, they noted that teams should serve to improve at-risk students’ feeling of connectedness to school and facilitate positive attitudes and behaviors such as increasing anti-substance use attitudes (Hansen & Hansen, 2016). In particular, they identified improving students’ bonding to school as an important goal, as higher school bonding is related to better academic performance and increased likelihood of staying in school (Maddox & Prinz, 2003). To accomplish this goal, at-risk students should be in teams with peers who can positively influence them. Prior research (Dishion et al., 1999) suggests that at-risk youth should be disaggregated to reduce the potential for negative influence.

Teachers also indicated that they preferred to avoid placing close friends together on teams; they shared anecdotes in which close friends were difficult to control and undermined teachers’ efforts. Further, it seemed logical that placing students into teams where the other students were already close friends might make it difficult for at-risk students to form new relationships with, or be positively influenced by, their team members. Instead, teachers preferred teams where students were acquaintances, so they had some level of affiliation to build upon, but were not yet close friends. To further support the development of friendships between students within a team, teachers believed that team members should share similar values and interests, as people who have qualities in common are more likely to form positive and lasting relationships than those who do not (McPherson et al., 2001).

Taken together, these goals suggest three criteria that we could use to evaluate team creation methods. The first criterion is to assess how well team creation methods disaggregate at-risk youth, so as to protect against iatrogenic effects and ensure that each team had prosocial students who might positively influence their at-risk peers. The second criterion is to assess how well each method created teams of students whose members were acquainted but not extremely close or cliquish. The third criterion is to assess how well teams members share similar interests and values, and thus have a basis upon which to form new relationships.

In the current study, we propose seven different team creation methods that teachers and program developers could potentially use and we evaluate how well each method achieves the criteria described above. We believe that a successful team creating method should consider social relations (as measured through social network analysis) as well as the psychosocial qualities of group members (as measured by team members’ values and interests). Specifically, we compare methods that use: (1) social network data only (SN), (2) within group similarity of values and interests (VI), or (3) the combination of social network and values and interests data (ALL). We also compare two algorithms for processing data. The first algorithm is a “clustering” approach that joins students to teams using a nearest neighbor procedure (i.e., those who are most similar are joined first). The second algorithm is a “pruning” approach that joins students to teams using a method adapted from Girvan and Newman (2004). This algorithm sequentially eliminates unqualified students (e.g., those who are least similar) until one pair remains and then joins them into a team. Each of these methods initially sequester students with low school bonding scores and then add them to teams as a last step. We compare these six novel methods (three sources of data by two algorithms) with each other. Each of these methods use students’ bonding with school as a strategy for disaggregating at-risk students. We also include a seventh method to form teams of close friends without considering students’ bonding scores. This latter method, modeled after the strategy used by Valente et al., (2003), is intended to serve as a manipulation check to assess the value of including bonding in team formation.

We had three hypotheses. We expected that, without disaggregating low school bonding students, they would typically prefer to be with others like them. Therefore, our first hypothesis was that all novel methods that sequester low school bonding students until the final step of team formation would create more heterogeneous teams in terms of bonding compared to the method that allowed close friends to form teams without considering their school bonding. In addition, clustering algorithms join most ideally suited students together first whereas pruning algorithms join more weakly linked students first, maximizing their potential to find suitable matches. Therefore, our second hypothesis was that pruning algorithms would have higher overall affiliation, more shared interests, and more heterogenous bonding scores compared to teams formed using clustering algorithms. Finally, because more information may make team formation more sensitive to similarities among students, our third hypothesis was that methods that use both social network indices and values and interests would meet the proposed criterion better than methods that use only one set of variables.

Methods

Participants

Nine classes of students from three rural schools in the Rocky Mountain region of the United States participated in the study. There was one 8th grade class (25 students), three 7th grade classes (94 students), three 6th grade classes (68 students), and two 5th grade classes (60 students). The average class size was 27.7 students (Range: 21 to 34 students). Gender was equally represented: 49.0% were male; 51.0% were female. Students lived in stable, racially homogenous communities, comprised of 89% to 94% White residents.

Survey Procedures and Measures

School staff uploaded students’ names to an online social network and attitude survey. The survey required students to identify themselves at login, which then identified them within the survey as “egos” and remaining students in their grade as “alters”. After students completed the survey, school staff forwarded de-identified data (ID numbers only) to the research staff.

Each student viewed the names of classmates in their grade and selected classmates they had “talked with (more than saying hello) or done something with in the past 30 days.” This prompt is similar to that used in studies that ask students to list their friends (e.g., Haas et al., 2010; Mercken et al., 2010; Osgood et al., 2013). The goal of asking the question in this way was to establish whether face-to-face interaction had occurred (Adams, 1967; Wasserman & Faust, 1994). The survey did not impose a limit on the number of classmates that students could select. We computed degree centrality for each student as the total number of nominations made and received divided by the number of students in their grade minus 1. For each classmate that a student selected, they also indicated how much time they had spent with him/her in the past 30 days: (1) less than an hour, (2) one to two hours, (3) two to five hours, (4) five to ten hours, and (5) more than ten hours. We coded missing data (when a student was not selected in response to the first prompt) as (0) to indicate no time had been spent together. Several students whose names were on class rosters withdrew from school before the survey was administered; we removed any friendship nominations to these students prior to analysis.

Students indicated how much they valued (1) acceptance, (2) achievement, (3) adventure, (4) character, (5) creativity, (6) education, (7) faith, (8) fame, (9) fitness, (10) independence, (11) inner strength, (12) peace, (13) stewardship, (14) talent, and (15) wealth. Response categories were “not at all”, “somewhat important”, and “very important”. Students also indicated how much they were interested in (1) singing or playing a musical instrument, (2) participating in plays or drama, (3) reading books or magazines, (4) doing arts, crafts, or hobbies, (5) playing sports or attending sporting events, (6) doing things to improve their fitness, (7) thinking about fashion and style, (8) playing computer, board, or fantasy games, (9) doing outdoor activities, (10) doing things with animals, and (11) doing things with engines, machines, or technology. Response categories were “low interest”, “some interest”, and “high interest”.

Finally, the survey measured school bonding by asking students how much they agreed with the following statements: (1) I am accepted at this school; (2) I feel like I belong at this school; (3) The teachers at this school like me; (4) I wish I did not attend this school; (5) This school is a pretty good school to go to; (6) I like the teachers at this school; and (7) I have no interest in school. Response categories ranged from 1=strongly disagree to 4=strongly agree. To make the findings easier for teachers and administrators to understand, we rescaled the initial scores of 1–4 to 0, 3.333, 6.667, and 10 respectively. We reverse coded items 4 and 7 and averaged all items (α = .805).

Classification of Students

Based on the survey data, we classified students into the following three categories:

At-risk Students

We operationalized at-risk for school disengagement as having low school bonding. To ensure that there was one at-risk student per team, we ranked students within each class based on their school bonding scores and selected the x students with the lowest scores, where x = the number of teams in that class.

Low-risk/Highly Popular Students (Seeds)

To identify high-centrality students that we could use as “seeds” to start the team formation process, we ranked the remaining students based on number of inbound nominations and identified x low-risk/highly popular students per class.

Average Students

We classified the remaining half of each class as “average.”

Table 1 displays average bonding scores and degree centrality for each category of students separately by class. By design, at-risk students had the lowest bonding scores and seeds had the highest degree centrality. Interestingly, in three classes, School A Grade 7, School B Grade 6, and School C Grade 5, students reported fewer friendships overall, making distinctions among students less clear.

Table 1. Key Descriptive Measures for Three Groups of Students within Each Grade and School.

			Average Bonding Score†			Average Degree Centrality
School	Students	Grade	Seed	Average Student	At-Risk	Seed	Average Student	At-Risk
A	26	5	7.54	8.57	6.11	0.70	0.51	0.53
C	34	5	7.98	7.59	4.35	0.39	0.26	0.24
A	22	6	7.53	7.36	2.95	0.80	0.49	0.51
B	25	6	8.97	8.69	6.98	0.41	0.41	0.38
C	23	6	6.91	7.14	4.36	0.65	0.45	0.53
A	32	7	7.14	7.41	4.88	0.17	0.12	0.10
B	30	7	8.57	8.06	6.74	0.69	0.47	0.47
C	33	7	7.44	7.40	3.51	0.65	0.45	0.52
C	25	8	7.46	7.51	5.08	0.72	0.59	0.63

^†We coded Bonding to School as a 0–10 scale, where a score of 0 reflected no bonding and a score of 10 reflected the greatest amount of bonding.

Dyadic Indices

Our algorithms (described in more detail in the following section) required us to identify pairs of students to join together; therefore, these algorithms required a single score for each dyad. Using students’ survey responses, we derived the following dyadic social network indices. Except for dyad values and interests distance, we calculated all indices in Excel.

To achieve our goal of creating teams of students who spent some (but not too much) time together, we first computed dyad affiliation by calculating the average amount of time that students in each possible pair reported spending together. Scores ranged from 0 (neither student named the other) to 5 (both students reported 10+ hours together). We wished to create teams that were balanced in terms of the overall popularity of team members. We specifically wished to avoid creating some teams whose members were highly popular and other teams whose members were relatively unpopular. Therefore, we decided to also consider popularity as part of our criteria. To do so, we first the degree centrality (i.e., number of nominations made and received divided by the number of students in their grade minus one) for each pair of students in the class. We then computed dyad sociability score as the product of dyad centrality and dyad affiliation. Several of our team creation algorithms relied on identifying students who were connected but not overly friendly (i.e., lowest non-zero value). To achieve this condition, we set dyad sociability to missing whenever both students reported no affiliation with each other. For a given dyad, a high score meant the members were both popular and spent a lot of time together whereas a lower score meant that although the two students had a relationship, on average they were less popular and spent less time with each other. These lower scores were considered more ideal, as they indicated pairs of students who were acquainted but likely not close friends (yet) and who would be open to influence from each other.

To achieve our goal of creating teams of students who shared values and interests, we calculated a dyad values and interests distance score by calculating Euclidean distances across all value and interest items using the Hierarchical Cluster Analysis procedure in SPSS version 20 (IBM Corp., 2011). Much like physical distance, dyads have more in common when there is less distance between them. A score of 0 indicates that two students share exactly the same values and interests. The greater the score, the more distant or discrepant their ratings are.

As noted earlier, we also expected the best approach would be for algorithms to consider both social network ties and shared interests. To create a single dyadic measure that captured both of these constructs, we calculated the product of sociability and distance by multiplying dyad sociability and dyad values and interests distance. When dyad sociability was missing, this score was also missing. A lower score meant dyad members interacted less (i.e., lower sociability) but were more similar (i.e., less distant) in values and interests. We used this measure to identify dyads whose members were acquainted (but not too close) and who also shared values and interests.

Team Formation Methods

School principals indicated that teams of four students were optimal for allowing schools to organize team activities because classroom seating charts typically had students’ desks grouped in fours. We adhered to this team size except when the number of students in a class was not divisible by four. Overall, we created 60 teams. Of these, 51 (85.0%) included four students, one (1.7%) included three students, and 8 (13.3%) included five students.

We used seven methods to form these teams. The first six methods were novel methods that used one of three different data sources and one of two different algorithms for joining students to teams. For all six novel methods, we used a three-round process. The goal of the process was to create teams that balanced status and risk. To start, we identified and sequestered the x highest at-risk students in the class, where x = the number of teams in the class; this approach ensured that at-risk students were spread across teams. During round 1, we identified the x highest status students among those who were left to use as “seeds” to build our teams around; this approach ensured that lower risk popular students were spread across teams . We then joined an average student with each high-centrality seed using the algorithms described below. Once joined, we averaged the scores for the students in this two-person team and removed the “team” from further consideration for the rest of the round. During round 2, we joined the remaining average students with these existing two-person teams, and then averaged the scores for all currently joined students. During the last round, we added at-risk students to teams. We then compared these methods to the Close Friends method, adapted from the method used by Valente et al. (2003). We followed a similar three round process for this method, except that we did not sequester at-risk students.

Data Used for Creating Teams

We formed teams based on (1) Social Network data only (SN) to create teams based on low (but not zero) levels of sociability, (2) Dyad values and interest distance (VI) to create teams of students who shared similar interests and values (i.e., close scores), and (3) the product of sociability and distance (ALL) to create teams of students who had low sociability (i.e., were connected but did not currently interact much) who shared similar values and interests and thus had potential on which to build future relationships.

Algorithms for Creating Teams

We joined students into teams using one of two algorithms: Cluster and Prune.

The first algorithm, Cluster, joined “nearest cases” first. Specifically, we determined which students to join together based on which pair had the smallest non-zero score on a particular data source (i.e., dyad sociability, dyad values and interests, or the product of sociability and distance). Once a pair was joined, we reviewed the remaining students and joined the pair with the next smallest non-zero score. In round 1, we continued until all seeds had been joined with an average student to form two-student teams. In rounds 2 and 3, we used team averages to find students to join with teams. This algorithm is ideal for identifying pairs that can be joined early in the process but leads to less ideal matches for pairs that are joined later.

Because the Cluster algorithm has the potential to bias teams that join late, we developed a second algorithm, Prune. Specifically, we adapted an algorithm used by Girvan and Newman (2002; Newman & Girvan, 2004) in which least desirable links (i.e., those with the largest values) were eliminated one at a time until a single remaining link remained. For example, in round 1, we created a matrix that contained the dyad scores for each seed and average student and eliminated the largest values one at a time until, for a given seed, a value for only one average student remained. We joined the seed and average student into a team and continued eliminating the largest values until another seed was paired with only one average student. During subsequent rounds, we recalculated the matrix values for teams and remaining un-joined students and repeated the process. The result of this process is that those pairs that would otherwise have least desirable matches are typically joined first, thus balancing the degree of desirability across all matches.

Team Creation Methods

Taken together, these three data sources (social network data only, dyad values and interest distance, and the product of sociability and distance) and two algorithms (cluster and prune) resulted in six methods for creating teams: (1) SN_Cluster, (2) SN_Prune, (3) VI_Cluster, (4) VI_Prune, (5) ALL_Cluster, and (6) ALL_Prune.

For comparison purposes, we compared the six novel methods above with a seventh method that can be used when individual-level characteristics (e.g., bonding, values and interests) are unknown. Specifically, we created Teams of Close Friends (CF), using dyad sociability to create teams that shared a high degree of interaction among team members. We selected seeds based on degree centrality while ignoring their risk status based on bonding. Thus, some at-risk students now became seeds and the remaining at-risk students were merged with average students, allowing them to join teams during any round of team formation. We used the prune algorithm, except that we defined least desired links as pairs with the smallest dyad sociability scores (i.e., we put students into pairs who interacted frequently).

All seven methods are summarized in Table 2.

Table 2. Team Formation Strategies, Data and Algorithms Used for Joining Students to Teams.

Method†	Dyadic Data Used	A student is joined to a team when:
SN_Cluster	Sociability	the dyad with the strongest sociability score is found
SN_Prune	Sociability	pairs with the largest dyad sociability scores are eliminated, until only one pair remains
VI_Cluster	Values/Interests	the dyad with the least distance is found
VI_Prune	Values/Interests	Smallest distance on values/interests links are eliminated, leaving only one link
ALL_Cluster	Sociability×Values/Interests	the dyad with the combined strongest sociability and values/interests distance is found
ALL_Prune	Sociability×Values/Interests	strongest sociability and least distance on values/interests links are eliminated, leaving only one link
CF	Sociability	weakest sociability links are eliminated, leaving only one link

^†For all methods except CF, students with the lowest school bonding scores were sequestered until the final round of team formation.

Evaluation Criteria

We used three criteria to evaluate the potential of the seven team creation methods.

1. Bonding.

To evaluate how well each method disaggregated at-risk students, we computed the average within-team and between-team standard deviations for bonding across all teams. We then identified the teams with the lowest and highest bonding scores in each classroom and report the average scores for these teams, along with the average disparity (highest – lower scores) across classrooms. Low disparity scores indicate bonding is relatively similar across teams. High disparity scores indicate some teams consisted of low bonded students whereas others were composed of highly bonded students.

2. Affiliation.

To evaluate the extent to which each method created teams among peers who are acquainted but not extremely close, we computed the average team affiliation scores across all teams and the average within team standard deviation of affiliation across all teams. As with bonding, we identified the least and most affiliated teams in each classroom and report the average scores for these teams, along with the average disparity across classrooms. Low disparity scores indicate pre-existing friendship patterns are relatively similar across teams within the classroom whereas higher disparity scores indicate an imbalance across teams.

3. Shared Values and Interests.

To evaluate the extent to which each method created teams of peers who share similar interests and values, we computed the average values and interests distance scores across all teams and the average within team standard deviation of distance across all teams. We then identified teams with the lowest and highest scores in each classroom and report the average scores for these teams, along with the average disparity across classrooms. As with bonding and affiliation, low disparity scores indicate that most teams in the classroom are similar in terms of average shared values and interests whereas high disparity scores indicate that teams are imbalanced.

Results

Bonding

Table 3 presents the outcomes for bonding for each team creation method. Overall, teams created using CF had the smallest within-team variability and the greatest between team variability in bonding. Therefore, some teams created by CF consisted primarily of students who were highly bonded to school whereas other teams consisted primarily of students who scored low on the bonding measure. By contrast, the six experimental methods that disaggregated low bonding students by sequestering them until the last stage of team formation and adding one at-risk student per team resulted in teams with lower between-team variability. The largest difference with CF as measured by the effect size difference was attributable to the SN_Prune method.

Table 3. Performance of Each of Seven Team Creation Methods on Achieving Goals for Bonding.

Method	Average Within-Team Standard Deviation	Average Between-Team Standard Deviation	Average Scores of the Least Bonded Team per Class	Average Scores of the Most Bonded Team per Class	Disparity	ES†
SN_Cluster	1.59	0.47	6.38	7.81	1.43	1.47
SN_Prune	1.61	0.41	6.45	7.70	1.25	1.82
VI_Cluster	1.59	0.48	6.37	7.87	1.50	1.34
VI_Prune	1.57	0.46	6.41	7.77	1.36	1.59
ALL_Cluster	1.59	0.48	6.38	7.88	1.50	1.34
ALL_Prune	1.59	0.49	6.41	7.86	1.45	1.42
CF	1.42	0.73	5.71	8.04	2.33

Bonding to School was constructed to form a 0–10 scale, with a score of 10 reflected greatest bonding and a score of 0 reflecting no bonding.

^†Disparity effect sizes for each experimental method compared to CF.

Affiliation

The four methods that emphasized low levels of affiliation (i.e., ALL_Prune, ALL_Cluster, SN_Prune, and SN_Cluster) all produced teams that spent the least amount of time together per week (average affiliation scores < 1; see Table 4). Of these, the two that used the prune algorithm (i.e., ALL_Prune and SN_Prune) had more consistent results than the two that used the cluster algorithm (i.e., All_Cluster and SN_Cluster which had lower within team standard deviations). Indeed, when effect sizes were calculated, SN_Prune and ALL_Prune were the only two methods that produced positive outcomes compared to CF. CF, the method that emphasized high levels of affiliation, produced teams that spent the most time together per week (average within-team affiliation scores > 2). VI_Prune and VI_Cluster, which ignored affiliation information, had moderate within-team affiliation scores and high within-team standard deviation and disparity scores.

Table 4. Affiliation with Teammates for Each of Seven Team Creation Methods.

Method	Average Within-Team Affiliation Scores	Average Within-Team Standard Deviation	Average Least Affiliated Team per Class	Average Most Affiliated Team per Class	Disparity	ES†
SN_Cluster	0.95	0.57	0.34	2.11	1.77	−0.81
SN_Prune	0.95	0.28	0.56	1.37	0.81	1.49
VI_Cluster	1.65	0.70	0.73	2.90	2.17	−1.39
VI_Prune	1.43	0.73	0.48	2.60	2.12	−1.26
ALL_Cluster	0.93	0.52	0.39	1.92	1.52	−0.33
ALL_Prune	0.97	0.34	0.48	1.50	1.02	0.86
CF	2.30	0.44	1.66	3.02	1.36

Affiliation scores vary between 0 (no time spent together) and 5 (more than 10 hours spent together).

^†Disparity effect sizes for each experimental method compared to CF.

Shared Values and Interests

As shown in Table 5, VI_Prune and VI_Cluster methods produced teams of students who were most similar to each other (i.e., lowest scores on average dyadic distance) in terms of shared values and interests. However, of the two VI methods, only VI_Prune had a positive effect size when compared to CF. As above, the method that used the prune algorithm (i.e., VI_Prune) produced teams that had less variability than the method that used the cluster algorithm (i.e., VI_Cluster), with VI_Cluster producing the teams with highest disparity in terms of shared interests and values.

Table 5. Degree to which Members of Teams Created Using Seven Methods Shared Values and Interests.

Method	Average Within-Team Distance	Average Within-Team Standard Deviation	Average Distance for Least Similar Team per Class	Average Distance for Most Similar Team per Class	Disparity	ES†
SN_Cluster	4.46	0.53	5.91	3.46	2.45	0.21
SN_Prune	4.31	0.55	5.45	2.98	2.47	0.18
VI_Cluster	3.94	0.60	5.80	2.77	3.03	−0.77
VI_Prune	3.98	0.46	5.44	3.08	2.36	0.40
ALL_Cluster	4.39	0.56	6.44	3.47	2.97	−0.70
ALL_Prune	4.34	0.54	5.86	3.12	2.74	−0.30
CF	4.28	0.59	5.62	3.05	2.57

Note: The Values and Interests Distance score is the team average Euclidean distance, which consists of the distances for all team members summed across all 15 values and all 11 interests. A value of zero (0) would indicate that teammates gave identical answers to all 26 questions. The maximum Euclidean distance for any pair of students in this project is 10.198, which would occur if they expressed maximum disagreement on all 26 questions.

^†Disparity effect sizes for each experimental method compared to CF

Discussion

Teachers often group students into teams to organize classrooms and learning tasks. Prevention scientists are beginning to recognize the potential of using structured teams for intervention delivery, to facilitate peer influence, and promote diffusion of intervention effects. Little work has considered what methods should be used to create these teams. Therefore, we identified seven methods that prevention scientists and teachers could use to create teams: six novel methods (using three sources of data x two algorithms for joining students into teams), and a method that used affiliation data alone without information about students’ characteristics. We evaluated these methods in terms of how well each method (1) disaggregated at-risk students (i.e., students with low bonding scores), (2) created teams of peers who were acquainted but did not spend too much time together so that students were not overly cliquish, and (3) created teams whose members shared interests and values to support the development of new relationships.

The first criterion that we used to evaluate each method was how well they disaggregated at-risk students (i.e., defined here as students with low school bonding scores). Disaggregation is evident when there is more variability of bonding within teams (i.e., large within team standard deviation); in addition, when there is heterogeneity within teams, there is a potential for positive peer influence with respect to bonding to occur within the team (Burt & Rees, 2015; Jonkmann, et al., 2009). Consistent with our first hypothesis, all six novel methods that sequestered the highest risk students in the class until the last round of team formation created heterogeneous teams (i.e., moderate within-team variability for bonding), suggesting that they successfully disaggregated at-risk students. Notably, the process of sequestering at-risk students mattered much more than the data source or algorithm used, as all six novel methods produced relatively comparable results. By contrast, the CF method did not sequester at-risk students prior to team formation and instead focused only on existing relationships. As a result, there was lower variability within teams, meaning that at-risk students were often placed in teams with each other. When at-risk students are grouped together, students can reinforce each other’s negative tendencies, leading to iatrogenic effects (Dishion et al., 1999). Therefore, we do not recommend using the CF method exactly as it has been used before. Instead, if researchers wish to create teams of tightly knit students, we recommend that they sequester at-risk students as an initial step so that these students are not inadvertently placed in teams together. Taking advantage of the fact that most at-risk adolescents have a mix of both at-risk and prosocial friends (Espelage et al. 2021; Hektner et al. 2000; Vitaro et al. 1997; Weerman & Bijleveld 2007), the at-risk students should then be inserted into teams with whom they have other, more prosocial, friends.

The second criterion that we used to evaluate each method was how well each method created teams among peers who are acquainted but not extremely close. We found that teams formed using SN_Prune, ALL_Prune, SN_Cluster, ALL_Cluster had similarly low levels of affiliation. These methods yielded lower overall levels of affiliation than would have happened had close relationships had been used as the basis of team formation, as was the case with CF. The two methods that used dyad’s shared values and interests as part of the team creation process (VI_Cluster and VI_Prune) had moderate levels of affiliation on average. SN_Prune and ALL_Prune performed best in terms of limiting the disparity between least and most affiliated teams. These findings suggest that team formation methods that included social network information and used the prune algorithm were most successful at meeting the second criterion.

The third criterion that we used to evaluate the team creation methods was the extent to which each method created teams of students who shared values and interests. We used the cumulative Euclidean distance between pairs of students to identify dyads who were more similar (i.e., less distance in their scores). We found that VI_Prune had the lowest observed within team variability and the lowest disparity across teams, indicating that this method identified teams with the greatest overall homophily in terms of values and interests (i.e., dyads on the team were more similar to the other dyads in terms of their shared values and interests).

In sum, our goal was to test experimental methods to create teams that could increase school bonding among students who otherwise were at-risk for success in school by creating teams that disaggregate at-risk students (to maximize the potential for positive influence and minimize the potential for negative influence) that built on existing relationships among pairs of students who shared values and interests. Of the six experimental methods, SN_Prune offers the greatest potential to meet these goals. ALL_Prune also produced positive bonding and values and interests outcomes. SN_Prune joined students into teams using social network data. ALL_Prune used a similar approach but balanced social network data with data about students’ shared values and interests. It is interesting that, even though SN_Prune did not specifically take values and interests into account, dyads on these teams nonetheless had high levels of shared values and interests even when there were low levels of affiliation. Although parsimony suggests that using only social network data may be sufficient, including values and interests data for team formation may lead to desired outcomes and be recommended in some situations. For instance, using values and interest data would be useful when placing new students at a school in a team or when teams are created at the beginning of the school year, especially when the students have not been together in the past (e.g., multiple elementary schools feeding into one middle school).

Consistent with our second hypothesis, the most promising methods used the prune algorithm. This algorithm eliminated least viable links between seeds and potential teammates and progressed until only one match for a team remained. This algorithm is akin to, but not identical to the algorithm proposed by Girvan and Newman (2002). It is appropriate for using scaled data and was adapted because the nature of the data being considered did not include edge betweenness. The benefit of using the prune compared to the cluster algorithm was that it minimized within-team variability (i.e., created more heterogenous groups).

Limitations and Future Directions

This project used specialized software to collect and analyze social network data. The software is not yet publicly available. This limits the immediate availability of these methods and represents only a first step toward using social network data for team formation. The end goal would be to create a user-friendly software program that both collects the needed social network data and applies the best algorithms in the background and then provides suggested teams for teachers or program implementers to use. We see our work of attempting to identify the best way(s) to create teams that meet specific goals as an important first step toward this end goal.

This research was limited in the number and character of the classes included. We examined nine classes of 21–34 students across three schools located within rural communities. Thus, this study was very much a pilot study. Results may change should analyses be replicated on other populations with larger numbers of classes and students. We did not consider race/ethnicity or gender in our methods or in our criteria for evaluating teams as creating diverse teams was not one of our goals, but researchers who wish to create heterogeneous teams could adapt the algorithms to consider these variables. Future research should also explore how these methods work when different sized teams are desired, and using data collected at the beginning rather than at the end of the school year.

Future research needs to document the longitudinal outcomes of these team creation methods. Ideally, each method should be implemented and evaluated in a randomized field trial using changes in targeted outcomes (e.g., increase at-risk students’ friendships to less risky peers; increases in school bonding). For example, when compared to a control group, we hypothesize that classes that adopt a structured team assignment approach would experience greater increases in bonding to school. Other outcomes, such as the effect of team creation methods on anti-social behaviors, bullying, and substance use, should also be explored.

Future research should also explore whether there are developmental differences in how well these methods work for creating teams. Notably, we were able to apply the methods equally across all four grades, as there were no apparent grade-related challenges to completing the survey and bonding was relatively consistent across grades (the correlation between grade and bonding score, r = −.071, was not significant). There was a positive correlation between grade and the number of inbound links (r = .330; p < .001), which suggests that, on average, older students reported having more classmates with whom they interacted, but the differences were small enough that they did not interfere with our ability to identify seeds or create teams.

Conclusion

As school-based network interventions are developed, methods for forming teams need to be evaluated. Methods are needed that meet a priori criteria. In this study, we examined multiple team formation methods with the goal of creating teams that disaggregated at-risk students and that were composed on students who were friendly (but not cliquish) and who shared interests and values to potentially facilitate future relationships. Algorithms that combined students using a process akin to that defined by the Girvan-Newman algorithm (2002) generally met these criteria, as did algorithms that either used social network data or that used social network data in combination with values and interests data. Methods that use social network and personal interests and values hold promise for creating school-based teams.