Development of Group Cognition in Online Collaborative Problem-Solving Processes

Abstract

Group cognition is a cognitive science concept that studies how groups think, learn, and work. Most research investigates group cognition as a qualitative-oriented phenomenon. From a quantitative perspective, this research proposes a measure equation of group cognition, conducts empirical research during online collaborative problem-solving, and uses multiple quantitative methods to examine group cognition complemented with qualitative microanalysis. Specifically, social network analysis, behavioral pattern analysis, and quantitative content analysis are used to measure three groups’ group cognition. Results show that only one group successfully develops group cognition through synergistic coordination of social, behavioral, and cognitive activities. Students in the other two groups either take separate responsibilities to cooperate or have unequal participations, which indicates an inadequacy of group cognition. The extent that three groups develop group cognition is consistent with the order of groups’ final performance scores. Research analytical and pedagogical implications are provided to advance research and practice of group cognition.

Keywords

Group cognition computer-supported collaborative learning collaborative problem-solving mixed methods knowledge building

Introduction

In computer-supported collaborative learning (CSCL), small groups of students engage in higher-level cognitive activities (e.g., ill-structured problem solving) to create knowledge and relevant artifacts through sustained interactions, communications, and actions (Dillenbourg, 1999; Goodyear et al., 2014; Roschelle & Teasley, 1995). Since CSCL emphasizes the importance of small groups’ collaborative process, a critical research trend focuses on small groups’ cognition, e.g., how groups think, know, and learn as a strand of the cognitive science research (Cooke et al., 2013; Fiore et al., 2010; Stahl, 2006). In the past decades, varied concepts have been proposed to describe groups’ cognitive inquiry from social psychology, cognitive science, sociocultural learning, or organizational development perspectives. Those concepts include Distributed Cognition (Salomon, 1993), Collective Mind (Weick & Roberts, 1993), Intersubjective Meaning Making (Matusov, 1996), Team Mental Model (Carley, 1997), Socially Shared Distributed Cognition (Yoo & Kanawattanachai, 2001), Shared Cognition (Cannon-Bowers & Salas, 2001), Group Cognition (Stahl, 2005), MacroCognition-in-Teams (Fiore et al., 2010), Interactive Team Cognition (Cooke et al., 2013), Collaborative Cognitive Load (Kirschner et al., 2018), etc. Moreover, many recent work has started to focus on the collaborative cognitive load, group-level metacognition, or group performance from the group perspective (e.g., Dindar et al., 2020; Kuhn et al., 2020; Ouyang, Chen, Yang, et al., 2021; Zheng et al. 2021). Most of those work define and investigate group cognition from the qualitative, phenomenological perspective (e.g., Fiore et al., 2010; Matusov 1996; Stahl, 2005). Some researchers start to conduct quantifiable measurements of group cognition at different granularities (e.g., Amon et al., 2019; Fiore et al., 2010; Medina & Stahl, 2020). As the education field has promoted multilevel analyses for a better understanding of collaborative learning (Janssen et al., 2013; Medina & Stahl, 2020; Stahl, 2009), a quantitative measure of group cognition is necessary to complement qualitative understanding of group cognition. To achieve this purpose, this research first develops an operationalizable working definition of group cognition, then proposes a quantifiable measure equation to calculate group cognition, and finally empirically examines group cognition in China’s higher education context with mixed methods that integrate quantitative measurements and qualitative explanations.

Review of the Relevant Literature

Although varied concepts are proposed to describe groups’ cognitive inquiry, they all emphasize that group cognition is an irreducible cognitive structure on the group level, which has its own collective characteristic, change, and development. Consistent with the complex adaptive system theory, a group is a complex system, comprised of a set of elements and interdependent relationships of elements within the system (Byrne & Callaghan, 2014; Hilpert & Marchand, 2018). Here we elaborate three main research groups’ work conducted in the past decade to describe the group-level attributes of the development of group cognition (as a general term). First, Nancy Cooke’s research team proposes the concept of Interactive Team Cognition, which emphasizes the understanding of how teams process information, coordinate, and behave as a unit (Cooke et al., 2000, 2013, 2017). They propose that team cognition is an interactive activity rather than a final product, which should be measured and studied at the team level rather than the individual level. The interaction, collaboration, and communication among group members have laid the foundation for group behavior and cognitive development; in turn, the development of team cognition also provides a changing context for the formation of individual-level behavior and cognition. The group’s cognitive development may foster or constrain the individual’s cognitive inquiry (Cooke et al., 2013). Second, Gerry Stahl’s research team proposes the concept of Group Cognition based on research findings from the Virtual Math Teams (VMT) project (Çakır et al., 2009; Medina & Stahl, 2020; Stahl, 2009). Stahl (2009) designs an online mathematics system for groups of students to collaboratively solve mathematic problems online. In this system, groups of students construct and manipulate graphical objects, communicate with peers about their ideas through online texting, and make joint meanings to solve mathematical problems (Stahl, 2006; 2009; 2014). The key to develop a successful group cognition is how students make their chat posts and drawing actions intelligent to each other, organize a sequence of social, indexical, and semantic references, and achieve a coherence of knowledge development (Çakır et al., 2009; Stahl, 2006, 2009). Third, Stephen Fiore’s research team proposes the concept of MacroCognition-in-Teams, which focuses team cognition on the knowledge building process, particularly how individuals and teams generate new knowledge for addressing unique problems during collaborative problem-solving (Fiore, 2008; Fiore et al., 2010; Newton et al., 2018). They propose that MacroCognition-in-Teams generates from the coordinated interactions between the individual knowledge building and group knowledge building processes. Individual knowledge building includes individual information gathering, information synthesis, and the development of knowledge products; team knowledge building includes team information exchange, knowledge sharing, solution generation, team evaluation and negotiation, and team plan and regulation. The coordination of those two dimensions triggers the development of internalized team knowledge (the collective knowledge held in the individual minds of team members) and externalized team knowledge (facts or concepts explicitly agreed upon by team members). Although those concepts argue that group cognition is a complex, multidimensional, and multilevel phenomenon which cannot be simply attributed to the aggregation of individuals’ contributions (Akkerman et al., 2007; Ludwig, 2015; Stahl, 2009), very few studies have proposed operationalizable working definition of group cognition to ground further analysis of empirical research.

Based on the review of relevant literature published recently, we identify primary elements of group cognition and provide an operationalizable working definition of group cognition accordingly, which underpins the further proposal of a measure equation. The development of group cognition requires students to effectively organize, coordinate, and contribute to social, behavioral, and cognitive activities in order to ultimately build group knowledge, solve collective problems and achieve collective accomplishments (Akkerman et al., 2007; Çakır et al., 2009; Stahl, 2006). This collaborative interaction of group cognition consists of at least three elements, i.e., multimodal interaction (social), referential behavior (behavioral), and idea-centered discourse (cognitive). First, on the social dimension, the multimodal interaction is built through students’ verbal-in-interaction, text-in-interaction, and graphics-in-interaction (Zemel & Koschmann, 2013). The multimodal interaction is a prerequisite for the development of group cognition (Altebarmakian & Alterman, 2019), because collaborative work cannot be successfully completed with a low level of interactions between students (Stahl, 2009). Second, on the behavioral dimension, students develop referential behavior to coordinate their own behaviors on knowledge artifacts and the behaviors of others (Fiore et al., 2010; Stahl, 2017; Zemel & Koschmann, 2013). Third, on the cognitive dimension, to solve the collective problems, the group proposes, uptakes, negotiates and assesses knowledge within group members. The idea-centered discourse starts with the individual learner’s cognitive inquiry, followed with the rise-up of individual inquiry to the group’s knowledge negotiation, and finally the collective knowledge building as a group (Borge & Mercier, 2019; Damşa, 2014; Ouyang & Chang, 2019). More importantly, group cognition is an integrative, sequential, and coordinated phenomenon, where social, behavioral, and cognitive activities take place synergistically, intertwine inseparably, and influence each other. The group collectively build knowledge as a whole through multimodal interactions and actions, references of each other’s behaviors and discourses, and accumulations and negotiations of knowledge as a group (Damşa, 2014; Fiore et al., 2010; Stahl, 2009). Based on the review, we initially define group cognition as an intertwining social-behavioral-cognitive phenomenon, developing through members’ multimodal interaction, referential behavior, and idea-centered discourse to accumulate group knowledge in order to solve complex problems. This definition serves as an operationalizable working definition to underpin the proposal of a measure equation (see the following section), which is used as the analysis methods of this empirical research.

Moreover, to analyze the complex, multi-level characteristics, relevant work has used both qualitative and quantitative methods to reveal the interactions that can be attributed as group cognition during collaborative learning. First, earlier work of group cognition has used qualitative, ethnographic approaches (e.g., conversation or discourse analysis) to examine micro-level turn-taking relevancies between interactional, behavioral, and cognitive activities during a short time period of collaborative learning (Stahl, 2009). Based on the case study research method, Damşa (2014) used in-depth qualitative analysis to investigate the nature of productive interactions, the joint efforts to co-construct knowledge and the shared epistemic agency that emerged during groups’ problem-solving processes over time. From a qualitative perspective, those studies focus on the fine-grained microanalysis to reveal the moment-to-moment details of how members coordinate their interactions, discourses, and behaviors to build knowledge and relevant artifacts (Stahl, 2009). An advantage of qualitative analysis is that it can examine the inherent, delicate organization of prior, current, and subsequent practices of group members. With the development of learning analytics and educational data mining techniques, recent work has used quantifiable models and methods to analyze group cognition. For example, in terms of the concept of distributed cognition, Amon et al. (2019) used multidimensional recurrence quantification analysis to examine fine-grained collective patterns of regularity across team members’ speech rate, body movement, and team interaction during collaborative problem solving. Moreover, based on the interactive team cognition model, Gorman et al. (2020) used mixed quantitative models and techniques (including discrete recurrence, non-linear prediction algorithm, average mutual information) to detect real-time changes in team cognition in the form of communication reorganization patterns during collaborative training. An important advantage of quantitative approaches is that they can be applied in large size of data or long discourse sequences to investigate the structures, patterns, or orderings based on standardized procedures (Cohen et al., 2013). Complementing with each other, qualitative and quantitative methods together can provide a more holistic, multilevel, and multidimensional analysis of group cognition to reveal the characteristics of collaborative interactions at the group level rather than the individual level (Borge & Rose, 2021; Janssen et al., 2013; Suthers et al., 2013). Echoing this research trend, this work uses a mixed method to analyze groups’ development of group cognition based on quantifiable measurements, complemented with the qualitative, fine-grained microanalysis of groups’ social-behavioral-cognitive fragments. In the following sections, we introduce the measure equation of group cognition, elaborate the analytical methods, procedures, and results, and provide relevant implications.

The Measure Equation of Group Cognition

According to the operationalizable working definition, group cognition is developed when group members share individual ideas and perspectives, make joint meanings, and build group knowledge and artifacts through interactions, behaviors, and discourses. The conceptual framework is comprised of multimodal interaction, referential behavior, and idea-centered discourse, that have closely interrelated relationships (Figure 1). To measure group cognition mathematically, a corresponding equation (see Eq. (1)) is proposed based on the working definition. The equation is primarily comprised of group members’ accumulation of knowledge (i.e., $S_{kn}$ ) over a time duration, with three coefficients (i.e., $c_{int}$ , $c_{beh}$ , and $c_{cog}$ ) that represent the group’s social, behavioral and cognitive characteristics, respectively.
$S_{gc} = \lg (c_{int} \cdot c_{beh} \cdot c_{cog} \cdot \frac{S_{kn}}{time duration})$
(1)
where $c_{int}$ , $c_{beh}$ , and $c_{cog}$ are normalized into the range from 0.0 to 1.0 to make sure that three coefficients play equal roles in the final result; $S_{gc}$ is standardized by the logarithm of 10 to make the results more explainable.

Figure 1.
The Conceptual Framework of Group Cognition.

First, in Eq. (1), $S_{kn}$ is a cumulative score of group knowledge during a time duration that represents the quality and efficiency of a group’s development of cognition ( $\frac{S_{kn}}{time duration})$ . Group knowledge is accumulated from individual learner’s cognitive inquiry, knowledge negotiations with peers, to knowledge building at the group level. More importantly, the group’s development of knowledge is grounded upon group members’ interactions with each other, built through their communicative discourses, and reflected on their knowledge artifacts (e.g., concept maps, write-ups, graphical objects). In other words, multimodal interaction (social), referential behavior (behavioral), and idea-centered discourse (cognitive) are critical media for the group members to communicate, demonstrate, and build knowledge. Correspondingly, three coefficients, i.e., $c_{int}$ , $c_{beh}$ , and $c_{cog}$ are used to represent a group’s social, behavioral, and cognitive characteristics 0, respectively. $c_{int}$ is the group-level indicator of interactive characteristics (e.g., activeness, balance, and distribution). A group is more likely to successfully develop group cognition with a more active, mutual interaction between members. $c_{beh}$ is the group-level indicator of behavioral characteristics related to knowledge artifacts (e.g., concept map) in order to externalize group knowledge. A group is more likely to demonstrate and enrich knowledge with a more frequent behavior related to the knowledge artifact. $c_{cog}$ is the group-level indicator of the knowledge-related, idea-centered discourse, representing the group’s ability to construct the group-level knowledge based on individual cognitive inquiry. The group is more likely to build collective knowledge when members are able to connect, deepen, and rise above peer’s ideas to make new meanings. Overall, those three coefficients are conditions for group members to accumulate knowledge over a time duration as they develop group cognition. Details of analysis methods and procedures of these components of the equation are presented in the following section.

Methodology

Research Purposes and Questions

The main purpose of the empirical research is to initially propose, apply, and justify the equation of group cognition based on an operationalizable working definition. To achieve this purpose, we design and facilitate an online collaborative problem-solving (CPS) activity in China’s higher education and then analyze the empirical research data based on the proposed measure of group cognition. Our research question is: Whether, to what extent, and how did three groups build group cognition during the CPS processes?

Research Context, Participants, and Procedures

The research context was an online, synchronous CPS activity in China’s higher education context. CPS has been widely used as a collaborative learning activity to foster group cognition, because CPS stresses a group’s higher-order, cognitive accomplishments, development of problem-solving skills, as well as the creation of knowledge and artifacts (Damşa, 2014; Fiore et al., 2017; Hmelo-silver, 2004). In this research, the CPS activity was designed as one of the learning activities in a graduate-level course titled Distance and Online Education, offered in the Spring semester 2020 by the Educational Technology (ET) program at a top research-intensive university in China. The course instructor (the first author) designed and facilitated the CPS activity, aiming to engage small groups (triads) to solve authentic problems instructors faced in the distance and online education during COVID-19. A research consent form was sent through the ET program’s social media (WeChat groups) to invite students to participate in the research. Ten participants voluntarily participated and agreed with the data collections; one participant (who was very inactive and made few contributions) withdrew the participation in the middle of the semester, which was excluded from the research (see Table 1).

Table 1.
Participants’ Information.

Participant Gender Age Status

Group A A1 Female 32 Graduate

A2 Male 41 Part-time graduate student

A3 Female 36 Full-time Ed.D. student

Group B B1 Female 24 Full-time Master student

B2 Male 25 Potential graduate student

B3 Male 31 Full-time Ph.D. student

Group C C1 Female 24 Potential graduate student

C2 Female 27 Full-time Master student

C3 Male 23 Full-time Master student

The collaborative learning environment was a completely online learning setting supported with the online platform Huiyizhuo (https://www.huiyizhuo.com/). Huiyizhuo provides functions such as text chatting, audio and video communication, concept map, note and comment, resource sharing, etc. In the CPS process, group members first communicate through the audio and text chatting to determine how to proceed the problem; then, groups share resources, continued communications and construct concept map to demonstrate their problem-solving processes; and finally write up the groups’ solution proposals (see Figure 2). The concept map serves as the main medium for participants to interpret the problems, discuss and negotiate understandings, identify misunderstandings and reach the group consensus of the solution.

Figure 2.
A Group’s Screenshot on the Huiyizhuo Platform.

Data Collection

The original data includes computer screen videos, audio recordings, texting chatting content, as well as Huiyizhuo clickstream files (about 1.5 hours/group). We deliberately choose the data from Week 4 to investigate group cognition, since the problem in Week 4 is to design an online activity for a mechanical engineering course. The topic is new to all participants such that they have the similar level of prerequisite knowledge. Although several participants (e.g., A2, A3) have some teaching experiences while others (e.g., B2, B3, C2) have educational technician working experiences, they are all new to instructional design of online teaching; therefore, we consider them as equal participants in this research regardless of their previous experiences. In addition, after three weeks’ practices, the participants are familiar with their group members, able to fully use the online platform’s functions, and familiar with the collaborative workflow.

The Analytical Approaches

An overall analytical framework of process data was proposed, supported with mixed methods to analyze social, behavioral, and cognitive dimensions (see Table 2). Mixed methods, including social network analysis, behavioral pattern analysis, and quantitative content analysis is used to measure the components in Eq. (1).

Table 2.
The Analytical Framework and Methods.

Dimension Approaches Purposes Data source

Multimodal interaction (Social) Social network analysis (SNA) of interaction data To analyze the social dimension of peer interactions through verbal discourse and online behaviors Computer screen videos, audio recordings, and texting chatting content

Referential behavior (Behavioral) Click stream analysis (CSA) of behavior data and lag-sequential analysis To analyze the behavioral patterns of group online behaviors Computer screen videos and Huiyizhuo clickstream files

Idea-centered discourse (Cognitive) Quantitative content analysis (QCA) of discourse data To analyze the individual-level and group-level knowledge Audio recordings and texting chatting content

First, on the social dimension, social network analysis (SNA) is used to analyze the multimodal interaction network that represents student interactions through verbal communication (i.e., one student responds to others through audio), texting (i.e., one student replies to others through text), and knowledge artifact (i.e., one student builds on or modifies others’ work of the concept map). The original data is transformed into the directed, weighted student-student network dataset. In the networks, the direction represents who responds to whom and builds on whose work (i.e., bi-directional); tie weight represents the frequency of responses, replies and build-on work a participant makes to others (i.e., interaction frequency). In Eq. (1), the original $c_{int}$ (before normalization) is the inverse of a coefficient of variation (ICV) of the interaction, namely the inverse of the standard deviation of the student-student interaction frequency divided by the mean of student-student interaction frequency. With the same mean, the smaller the standard deviation is, the larger the ICV value is. In other words, a larger ICV indicates a more active, balanced, distributed interaction between group members. The final value of $c_{int}$ is normalized into the range from 0.0 to 1.0 for three groups. It is worth mentioning that we calculate other group-level SNA metrics (e.g., connectivity, Opsahl’s clustering coefficient, centralization) that could be used as $c_{int}$ here; but the results of these metrics are all the same for three groups due to the small number of participants (N = 3). We decide to use ICV because it is the most generalizable measure regardless of the number of participants in a group. In addition, the group-level SNA metrics, including density, interaction, average degree, reciprocity, and outdegree/indegree centralization are also calculated to complement ICV values (see Table 3) (Opsahl, 2009; Ouyang, 2021; Ouyang & Scharber, 2017; Shu & Gu, 2018).

Table 3.
Descriptions of Network-Level Metrics.

Metrics Description

Density Ratio of the number of existing ties to the number of all possible ties

Interaction The total number of interaction frequencies, as well as each student’s interaction frequency to others

Average degree Average value of the sum of degree

Inverse coefficient of variation (ICV) The inverse of the standard deviation of student-student interaction frequency divided by its mean

Reciprocity Ratio of symmetric dyads to non-null dyads

Outdegree/indegree centralization The extent to which outdegree/indegree is concentrated within a small number of nodes

Second, on the behavioral dimension, we use the behavioral pattern analysis to analyze the students’ online behaviors from the computer clickstream videos, and then use the lag-sequential analysis (LsA) to examine the referential behavior related to the construction of knowledge artifact. The first author codes students’ online behaviors in terms of the time frame, identifies six online behaviors, and asks other authors to double check the accuracy of the codes (see Table 4). The quantity of each behavior code is calculated and the LsA approach (lag = 1) is used to examine the direct strength of the transition between behaviors (Chen et al., 2017). Yule’s Q measure (standardized measure ranging from –1 to +1) is used to calculate the strength because it controls for the base numbers to maintain the best explanatory power among all sequential measures (Chen et al., 2017). Yule’s Q values, which are smaller than zero, are all neglected. In Eq. (1), $c_{beh}$ represents the strength of referential behavior transferred to concept mapping (CM), by calculating the sum of Yule’s Q values from TU, RM, PC, CM, OG, and OB to CM (see Table 7 in the next section). The behaviors with a quantity below 5% of the total quantity are all excluded, because the inclusion of rarely-occurred behavior would cause large Yule’s Q value which is meaningless. A larger $c_{beh}$ represents students are more likely to make frequent behaviors transitioned to concept mapping. The final value of $c_{beh}$ is normalized into the range from 0.0 to 1.0 for three groups.

Table 4.
Six Types of Online Behaviors.

Code Description

Task understanding (TU) A student moved the mouse to the task area to read and understand the task

Resource management (RM) A student searched, shared or managed resources

Peer communication (PC) A student used the texting message or audio to communicate with peers

Concept mapping (CM) A student created, modified or commented on the concept map

Organization (OG) A student organized the arrangements, or addressed the technique issues

Observation (OB) A student moved the mouse over the platform to observe without any operations

Table 7.
Three Groups’ Social, Behavioral, and Cognitive Measurement Values.

Group A Group B Group C Group A Group B Group C Group A Group B Group C

Social Behavioral Cognitive

Density 22.70 28.20 42.80 1st beh. (freq.) PC (129) PC (218) PC (388) 1st cog. (freq.) GS (57) GM (64) GS (130)

Interaction 137 169 257 2nd beh. (freq.) CM (87) CM (132) CM (102) 2nd cog. (freq.) GM (29) GS (65) GM (98)

Avg. degree 45.70 56.30 85.70 3rd beh. (freq.) OB (82) OB (71) OB (75) 3rd cog. (freq.) GD (1) GD (9) GD (3)

Recip. 0.85 0.93 0.86 1st CM Trans. CM->CM (0.55) CM->CM (0.68) CM->CM (0.25) Overall kn. freq. 136 189 325

out/indegree cent. 10.83/6.83 3.83/7.83 26.12/26.67 2nd CM Trans. OB->CM (0.13) OB->CM (0.03) OB->CM(0.04) Group-level kn. freq. 87 138 237

original $c_{int}$ (ICV) 1.23 2.40 0.75 original $c_{beh}$ 0.68 0.71 0.29 original $c_{cog}$ 0.64 0.73 0.73

Third, on the cognitive dimension, quantitative content analysis (QCA) is used to analyze the individual-level and group-level knowledge. We transcribe the audio and texting recordings in term of the time framework, identify the unit of analysis as unit of idea (i.e., a sentence that represented an idea or a question), and use a predefined framework to analyze the transcripts (Ouyang & Chang, 2019) (see Table 5). Because group knowledge is built accumulatively from individual to group, the framework includes individual knowledge (capturing the individual knowledge inquiry in the initial ideas), and group knowledge (capturing the group knowledge advancement through peer responses) (see Table 5). The first author trains five raters to obtain a deep understanding of the framework; then six raters (including the first author) independently code the transcript data and reach an inter-rater reliability, i.e., Krippendorff’s alpha of 0.795. In Eq. (1), the original $c_{cog}$ is calculated as the percentage of the group-level knowledge codes (GS, GM, GD) on the overall occurrences of knowledge codes (see Table 7 in the next section). A larger percentage indicates that the group members connect and deepen peer’s ideas more frequently. The final value of $c_{cog}$ is normalized into the range from 0.0 to 1.0 for three groups.

Table 5.
The Code Framework for Quantitative Content Analysis (Adapted From Ouyang & Chang, 2019).

Level Code Description

Individual Knowledge Superficial (IS) A participant shares information without explicit statement of his/her own ideas

Medium (IM) A participant states his/her own ideas without explanations, or support of resources

Deep (ID) A participant states his/her own ideas with detailed explanations, support of resources, or experiences

Group Knowledge Superficial (GS) A participant simply repeats another participant’s idea, or presents (dis)agreements, or asks questions without argumentations, explanations or elaborations of the idea

Medium (GM) A participant argues, extends, and builds on another participant’s idea with explicit argumentations or elaborations, support of new information and resources

Deep (GD) A participant connects, synthesizes, and rises up ideas interpreted by the other two participants to construct new ideas, reach a consensus, or make a decision

Finally, as the operationalizable working definition of group cognition shows, group cognition is mainly identified as the knowledge building conducted interactively by the group, as opposed to being simply provided by individuals in the group. Therefore, we calculate a group’s accumulated knowledge over a time duration as a weighted knowledge score (i.e., $S_{kn} =$ N_IS * 0.5 + N_IM * 1 + N_ID * 1.5 + N_GS * 2 + N_GM * 2.5 + N_GD * 3), where the gradually increasing weights are assigned, referring to the measurement of externalized team knowledge demonstrated in knowledge artifacts (Fiore et al., 2010). The weighted score $S_{kn}$ is divided by the time duration to record the efficiency for a group to build knowledge.

We initially test the equation and the measures of components to three types of social-behavioral-cognitive fragments from our dataset (see Table 6). These three types include the whole CPS process (time duration about 1.5 hours), the medium-sized fragments with at least one occurrence of the deep-level group knowledge (time duration about 0.15 hour), and the small-sized fragments without any GD (time duration about 0.04 hour). The requirement is that all members must participate in the fragment. Based on the equation, for the whole CPS process, Groups A, B, and C have the group cognition scores ( $S_{gc}$ ) of 0.75, 1.28, and 0.60, respectively. For the medium-sized fragments, Groups A, B, and C have the group cognition scores ( $S_{gc}$ ) of 0.86, 1.51, and 0.90, respectively. For the small-sized fragments, Groups A, B, and C have the group cognition scores ( $S_{gc}$ ) of 1.19, 1.41, and 1.37, respectively (see Table 6). These results indicate similar orderings of three groups, which initially implies a certain level of justification of the equation. Furthermore, we focus on the medium-sized fragment of each group that best represents its group cognition, since it includes at least one occurrence of the deep-level group knowledge (GD). We explain the measures of group cognition, use a qualitative microanalysis to examine fine-grained details, and justify the quantitative measure by a complementary of qualitative explanations.

Table 6.
The Measurement Values of the Equation for Three Groups.

Group $c_{int}$ $c_{beh}$ $c_{cog}$ $S_{kn}$ Time (hour) $S_{gc}$

The whole process Group A 0.28 (1.23) 0.41 (0.68) 0.30 (0.64) 236.5 1.45 0.75 (5.62)

Group B 0.55 (2.40) 0.42 (0.71) 0.35 (0.73) 373.5 1.57 1.28 (19.23)

Group C 0.17 (0.75) 0.17 (0.29) 0.35 (0.73) 594.5 1.50 0.60 (4.01)

The medium-sized fragment Group A 0.14 (0.91) 0.48 (0.68) 0.31 (0.75) 42.0 0.12 0.86 (7.29)

Group B 0.73 (4.64) 0.30 (0.43) 0.34 (0.82) 64.5 0.15 1.51 (32.02)

Group C 0.13 (0.79) 0.22 (0.32) 0.35 (0.85) 79.0 0.10 0.90 (7.91)

The small-sized fragment Group A 0.41 (1.53) 0.33 (1.00) 0.26 (0.50) 23.5 0.053 1.19 (15.60)

Group B 0.37 (1.41) 0.33 (1.00) 0.30 (0.57) 25.0 0.036 1.41 (25.44)

Group C 0.22 (0.82) 0.33 (1.00) 0.44 (0.86) 30.5 0.042 1.37 (23.20)

Note. $c_{int}$ , $c_{beh}$ , and $c_{cog}$ are normalized into the range from 0.0 to 1.0, respectively. The values in parentheses are original measurements from the approaches abovementioned, which are not used in the final calculation. $S_{gc}$ is standardized by the logarithm of 10 to make the results more explainable for three groups than the original results (in parentheses).

Moreover, we evaluated the groups’ final performance of the concept map artifacts and the solution write-ups in terms of the following standards. Adapting a previous assessment approach (Novak & Cañas, 2008), we assessed the concept map in terms of three dimensions for the nodes included, i.e., propositions, hierarchy, and examples (S_cm = N_prop + N_hier + N_exam). In addition, we referred to the superficial, medium, and deep levels in the idea-centered discourse coding scheme (see Table 5) to analyze the groups’ write-up scores, coded as information sharing, solution proposal and solution elaboration, respectively (S_wu = N_sup * 1 + N_med * 2 + N_deep * 3). The unit of analysis was a sentence separated by a semicolon or a period in the write-up that represented a complete idea. Two trained raters scored the concept maps and write-ups independently and reached an agreement if there were differences. Finally, each group was assigned a final score by adding the concept map score and the write-up score and then the final score was multiplied by ICV of student contribution to concept map and write-up, i.e., S_final = (S_cm + S_wu) * ICV.

Results

Overall Group Cognition Development

Based on the equation, Group B has the highest score of group cognition ( $S_{gc}$ = 1.28), followed by Group A with the middle-level score ( $S_{gc}$ = 0.75), and Group C with the lowest score ( $S_{gc}$ = 0.60) for the whole CPS process (see Table 6). The three groups’ final performances followed the same order: Group B had a final performance of 184, followed by Group C with a final performance score of 94, and Group A with a final performance score of 69. Among three groups, Group B is the group that successfully builds mutual, balanced peer interactions (reflected by the highest value of $c_{int}$ ), takes actions to demonstrate group knowledge on the concept map (reflected by the highest value of $c_{beh}$ ), and frequently develops the group-level knowledge based on individual cognitive inquiry (reflected by the highest value of $c_{cog}$ ). On the contrary, although Group C also frequently builds group knowledge (reflected by the highest value of $c_{cog}$ ), Group C neither successfully forms the mutual, balanced, student-student interaction (reflected by the lowest value of $c_{int}$ ), nor does it effectively make referential behaviors to the concept map (reflected by the lowest value of $c_{beh}$ ). Therefore, Group C gains the lowest score of group cognition according to the equation, although it accumulates the highest knowledge score. Furthermore, the radar graphs of individual contributions show that Group B’s students make the most balanced social, behavioral, and cognitive contributions, while Group C’s students make contributions in the most unbalanced way since most contributions are made by two students (see Figure 3).

Figure 3.
The Radar Graphs of Students’ Social, Behavioral, and Cognitive Contributions in (a) Group A, (b) Group B, and (c) Group C.

Group A

We analyze the social, behavioral and cognitive characteristics developed in Group A. First, on the social dimension, the network analysis results show that Group A has the lowest interaction, consistent with the density and average degree results; therefore, it is the least active group among three groups (see Table 7). Group A has an original ICV value of 1.23, ranked at the middle of three groups, consistent with the out/indegree centralizations (see Table 7). Group A has the middle level of distribution among three groups. Second, on the behavioral dimension, among all six types of behaviors (frequency = 324), the most frequent behavior is peer communication (PC; frequency = 129), followed by concept mapping (CM; frequency = 87), and observation (OB; frequency = 82) (see Table 7). Excluding RM and OG with a low frequency (below 5% of all behavior frequency), the transition occurs from CM->CM (Yule’s Q = 0.55), followed by OB->CM (Yule’s Q = 0.13) (see Table 7). This result indicates that students use the concept map intensively to demonstrate their ideas and occasionally observe others’ operations before making changes. The original $c_{beh}$ is 0.68 before normalization. Third, on the cognitive dimension, among all knowledge contributions ( $S_{kn}$ = 236.50; frequency = 136), the weighted score of the group-level knowledge (i.e., GS, GM, GD) is 189.50 (frequency = 87) (see Table 7). Therefore, the original $c_{cog}$ is 0.64 before normalization, indicating 64% of the occurrence of group-level knowledge out of the overall knowledge. Specifically, the superficial-level group knowledge (GS) score is 114 (frequency = 57), followed by the medium-level group knowledge (GM) score of 72.50 (frequency = 29), and the deep-level group knowledge (GD) of 3 (frequency = 1) (see Table 7).

Finally, regarding the medium-sized fragment, Group A has a group cognition score of 0.86 according to the equation, which is the lowest score among three groups (see Table 6). In this fragment (see Table 8 and Figure 4), Group A’s students discuss about design content of the activity. A3 first proposes a question for the whole group to think (line 1), which triggers a few rounds of discussion among three students about human-computer interaction (line 2–7), techniques (line 15), and vehicle types (line 17–28). Group A’s interaction pattern is more like a form of cooperative learning rather than collaborative learning (Dillenbourg, 1999). For example, A2 is the student who proposes, synthesizes, and deepens group knowledge for problem-solving (line 15; coded as cognitive: GD). A3 communicates with A2 by initiating questions (line 3, 23), repeating ideas (line 28), and proposing suggestions (line 17, 20). A1 does not elaborate her thinking but takes agency to modify the concept map by reflecting A2’s ideas on the concept map (line 19, 21, 27, 29). When A2 explains his ideas back and forth, A1 adds, deletes, and modifies the concept map accordingly. This fragment demonstrates that in Group A, the deep-level group knowledge is initiated and deepened by one student A2; another student A3 tends to propose questions, explore ideas, and make suggestions; the third student A1 takes agency to reflect others’ ideas on the concept map without adding new perspectives. Therefore, Group A’s students take separate responsibilities, which is more like Dillenbourg’s (1999) description of cooperative learning: students split and assemble their parts of work into a final output.

Table 8.
Selected Excerpts From Group A.

Line From To Content Coding

1 A3 / Another critical question for us to think is why we need to do the design… Cognitive

2 A2 A3 We can focus our design on the driving experience or the human-computer interaction… Social; Cognitive

…

7 A2 A3 … We can use the VR techniques… Since students are supposed to learn relevant theories, we can teach them about the difference of power transmission between the tradition vehicles and the new energy vehicles… Social; Cognitive

…

9 A1 A2 I think we’d better narrow down the topic you mentioned and make it more targeted. Social; Cognitive

10 A3 A1 OK, what is in your mind? Which topic do you suggest to narrow down to? Social; Cognitive

…

15 A2 / …we can focus on engineering design, which means how to make a better design to improve the efficiency of energy use… students are supposed to tell the differences of the manufacturing techniques between the tradition vehicles and the new energy vehicles… students can use VR or online experiments to experience the transmission techniques… Cognitive

16 A1 / Observation & Concept mapping Behavioral

17 A3 A2 Yes, I think your idea is very good. And we can specify it, for example, the different energy types. Social; Cognitive

…

20 A3 A2 Yes. Students can form groups to focus on different types of vehicles…We can let students learn the theories first, and then use the VR to simulate the operations in the virtual laboratory. What do you think? Social; Cognitive

21 A1 / Observation & Concept mapping Behavioral

…

Note. Refer to the whole fragment, including details of social, behavioral, and cognitive coding results.

Figure 4.
The Temporal Change of Students’ Social-Behavioral-Cognitive Contributions from Group A.Note. A1-all, A2-all, and A3-all are not counted as the student-student interaction in the measure; they are demonstrated only for the neatness of graph presentation (same below).

Group B

We analyze the social, behavioral, and cognitive characteristics developed in Group B. First, on the social dimension, Group B has the middle level of interaction, with the same ranks of density and average degree among three groups (see Table 7). However, it is the most mutually-interactive and equally-distributed group, with the highest value of ICV and reciprocity, and the lowest out/indegree centralization (see Table 7). Second, on the behavioral dimension, among all six types of behaviors (frequency = 485), the most frequent behavior is PC (frequency = 218), followed by CM (frequency = 132), and OB (frequency = 71). Excluding RM and TU with a low frequency, the transition occurs from CM->CM (Yule’s Q = 0.68), followed by OB->CM (Yule’s Q = 0.03). The original $c_{beh}$ is 0.71 before normalization. Like Group A, students use the concept map intensively to externalize knowledge. Third, on the cognitive dimension, among all knowledge contributions ( $S_{kn}$ = 373.5; frequency = 189), the weighted score of the group-level knowledge is 317 (frequency = 138) (see Table 7). Therefore, the original $c_{cog}$ is 0.73 before normalization, indicating 73% of the occurrence of group-level knowledge out of the overall knowledge. Specifically, GM score is 160 (frequency = 64), GS score is 130 (frequency = 65), and GD score is 27 (frequency = 9). Among three groups, Group B has the highest score of the deep-level group knowledge (see Table 7).

Finally, for the medium-sized fragment, Group B has a group cognition score of 1.51, which is the highest score among three groups (see Table 6). In this fragment (see Table 9 and Figure 5), Group B’s students discuss about design details of a collaborative small-group activity. B1 first initiates an idea about role assignment (line 1), which triggers an intensive discussion about grouping strategy (line 3-10), platform functions (line 12-22), mission card gamification (line 25-48; line 40 is coded as cognitive: GD) and learning evaluation (line 49-53). Group B’s collaboration is more like an exploratory participation pattern (Zemel et al., 2009), where group members contribute from multiple perspectives to construct knowledge and take joint actions to update knowledge through concept map. For example, B2 proposes an idea of group activity design (line 25), followed with B3’s specification of the idea (line 28), and B1’s further explanation of her understanding (line 32). Therefore, the discussion process involves an initiation of ideas or proposal from one student, an uptake of the ideas, and negotiation of solution strategies. In addition, students not only build on each other’s ideas sequentially to achieve group knowledge, but also take actions to refer to, build upon and update others’ ideas on concept map (line 2, 6, 20, 26, 53). For example, B3 modifies ideas in the concept map to reflect his own ideas and others’ ideas (line 2, 6, 20, 23, 33); B1 and B2 further update ideas in concept map created by B3 (line 8, 11, 13, 31). The microanalysis indicates that students form a mutual interaction to build on other ideas through verbal communication and artifact modification. Therefore, this fragment demonstrates an “exploratory participation” pattern where the group knowledge is articulated, raised up, and deepened by all students, reflected on the group’s concept map accordingly, and subsequently recognized and treated as a solution by three students.

Table 9.
Selected Excerpts From Group B.

Line From To Content Coding

1 B1 / Do we need to assign a role to students in the group? I think it would be inappropriate for all students to do the same thing… do we ask the students to form a group by themselves? Or form a group randomly? Cognitive

2 B3 / Concept mapping Behavioral

3 B3 B1 Random grouping? Why? Social; Cognitive

…

6 B3 / Concept mapping Behavioral

7 B2 B1 … I think we can let the instructor to assign the groups, if she knows students and their strengths. but I am afraid if we use random grouping, some groups may not be functioning if students are all not skillful at doing this work… Social; Cognitive

8 B1 B3 Concept mapping Social; Behavioral

…

13 B1 B3 Concept mapping Social;Behavioral

…

20 B3 / Concept mapping Behavioral

…

25 B2 B3 … the groups of students are required to complete their design of engine within the limited budget. Then, the instructor can evaluate students’ performance… Social;Cognitive

26 B2 / Observation Behavioral

27 B1 / Concept mapping Behavioral

28 B3 B2 … It is better to define the requirement specifically…I think we can specify some dimensions to evaluate the groups’ performance of engine assembling. Social;Cognitive

…

31 B2 B3 Concept mapping Social;Behavioral

32 B1 B2 It means that students form groups, and then the groups randomly receive their tasks. Social;Cognitive

33 B3 / Concept mapping Behavioral

…

40 B2 B3 It is like a mission card. When you open that card, you will find that you are in a specific group with an assigned role… Then the group will log in the online platform to assemble the engine… Social;Cognitive

…

53 B2 / Concept mapping Behavioral

Note. Refer to the whole fragment, including details of social, behavioral, and cognitive coding results.

Figure 5.
The Temporal Change of Students’ Social-Behavioral-Cognitive Contributions from Group B.

Group C

We analyze the social, behavioral, and cognitive characteristics developed in Group C. First, on the social dimension, Group C has the highest interaction frequency, with the same ranks of density and average degree among three groups. However, it is the most incohesive, centralized group among three groups, with the lowest ICV and the highest out/indegree centralizations (see Table 7). Like we discuss above (see Figure 3), most of the interactions occurs between two students in the group. Second, on the behavioral dimension, among all six types of behaviors (frequency = 680), the most frequent behavior is PC (frequency = 388), followed by CM (frequency = 102), and OB (frequency = 75). Excluding TU with a low frequency, the transition occurs from CM->CM (Yule’s Q = 0.25), followed by OB->CM (Yule’s Q = 0.04), resulting in an original $c_{beh}$ of 0.29. The result indicates that students do not use the concept map intensively to externalize knowledge. Third, on the cognitive dimension, among all knowledge contributions ( $S_{kn}$ = 594.50; frequency = 325), the weighted score of the group-level knowledge is 514 (frequency = 237) (see Table 7). Therefore, the original $c_{cog}$ is 0.73, indicating 73% of the occurrence of group-level knowledge out of the overall knowledge. Specifically, the GS score is 260 (frequency = 130), the GM score is 245 (frequency = 98), and the GD score is 9 (frequency = 3) (see Table 7). Among three groups, Group C has the highest score on the superficial-level and medium-level group knowledge.

Finally, in the medium-sized fragment, Group C has a group cognition score of 0.90 (see Table 6). Group C’s students discuss about using video conferencing as an in-class practical activity (see Table 10 and Figure 6). This process is similar with the description of expository participation (Zemel et al., 2009), where one student takes responsibilities to propose his own ideas and solutions without others’ critical contributions of the problem-solving. For example, the most active student C3 initiates an idea of video conferencing (line 27), feasibility of web cam (line 31), activity’s timing (line 34, 39), and concrete ways of activity (line 45). Simultaneously, C3 directly operates on the concept map to reflect ideas he proposes (line 35, 40, 46, 49, 55). Another student C2 occasionally expresses her understandings about C3’s ideas (line 36), proposes a couple of questions (line 42), and repeats C3’s ideas (line 44, 47). C1 is less engaged in the group as a free-rider, which indicates inequality of participation. In addition, C1 and C2 merely observe C3’s concept map operation without any modification (line 26, 29, 38, 41), indicating they accept the ideas and solutions proposed by C3 without argumentation, rise-above and build-on. Therefore, this fragment to some extent implies an “expository participation” pattern where most critical knowledge work is contributed by one active student C3 (line 23, 27, 31 coded as cognitive GD) as an authority in the group.

Table 10.
Selected Excerpts From Group C.

Line From To Content Coding

1 C3 / Another approach is the remote lab. A student can operate to control a real entity by using a remote computer… Cognitive

2 C1&C2 / Observation Behavioral

…

12 C1 / Is there a tool that allows all students to share the screen at the same time? Cognitive

…

23 C3 C1 … during the in-class activity, the instructor wants to know students’ practice process… Social;Cognitive

26 C1 / Observation Behavioral

27 C3 C2 Video conferencing is a simple way to teach online… Video conferencing is also used frequently in practice… Social;Cognitive

28 C2 C3 What you just mentioned that the instructor can monitor all students’ learning… it is in school’s computer labs… Social;Cognitive

29 C1 / Observation Behavioral

30 C1 C2 Yep… Social;Cognitive

31 C3 C2 So the situation is, every student needs to turn on the webcam… which may be difficult in real situations because the student can decide to turn it on or not… Social;Cognitive

…

36 C2 C3 These can all be put in the in-class activities actually… we can further describe them. Social;Cognitive

40 C3 / Concept mapping Behavioral

…

44 C2 C3 I mean the guidance of the video conferencing. Social;Cognitive

45 C3 C2 … Those parts like data simulation, virtual experiment and modeling are some concrete ways of practical activities… Social;Cognitive

…

48 C3 C2 Those are the strategies, right? Social;Cognitive

49 C3 / Concept mapping Behavioral

…

55 C3 / Concept mapping Behavioral

Note. Refer to the whole fragment, including details of social, behavioral, and cognitive coding results.

Figure 6.
The Temporal Change of Students’ Social-Behavioral-Cognitive Contributions from Group C.

Discussions and Implications

Viewing from the socio-cultural perspective, the development of group cognition requires students to synergistically coordinate social, behavioral, and cognitive activities in order to collectively solve problems, construct knowledge artifacts, and advance group knowledge (Akkerman et al., 2007; Ludwig, 2015; Stahl, 2009). Unlike most previous work that defines and investigates group cognition from the qualitative, phenomenological perspective, this research proposes a quantitative measure equation based on an operationalizable working definition to analyze group cognition, which is further complemented with the qualitative, temporal microanalysis of group fragments. Specifically, this research analyzes how three groups accumulate knowledge through multimodal interactions, referential behaviors, and idea-centered discourses during online collaborative problem-solving processes. The empirical research results indicate that only one group (i.e., Group B) successfully develops group cognition through equal, interdependent, and synergistic collaborations. Moreover, Group B maintains the highest group cognition score throughout, which is reflected by analytical results of three different sizes of group fragments. Consistent with the quantitative results calculated from the equation, qualitative microanalysis of group fragment indicates that students in Group B form a balanced, distributed peer interaction, use the concept map intensively and sequentially to externalize ideas, and had multiple occurrences of deep-level knowledge building within the group. Unlike Group B, students in Group A tend to take social, behavioral, and cognitive responsibilities separately, which is not an effective development of group cognition (Stahl, 2009). This cooperative learning characteristic results in a relatively low score of group cognition of Group A throughout. Like Group A, Group C does not successfully develop group cognition neither; but Group C has different collaborative characteristics from Group A. Group C has an unequal participation pattern, forms a scattered knowledge building discourse, and make discrete operations on the concept map. Since mutuality and equality have been theorized to be critical for a successful collaborative learning (e.g., Damon & Phelps, 1989), Group C does not successfully develop group cognition, which is consistent with the measured score calculated from the equation. In addition, the extent that three groups developed the group cognition was consistent with the order of groups’ final performance scores. Overall, the results indicate that a successful group cognition must be developed from all members’ active, equal participations: they need to make synergistic coordination of their social, behavioral, and cognitive contributions for achieving a shared goal.

From the analytical perspective, the proposed equation offers a rigorous analytical procedure to quantitatively measure group cognition, as previous studies in the cognitive science field have promoted (e.g., Rasenberg, Özyürek, & Dingemanse, 2020). This quantitative measure integrates students’ social interactions, behavioral sequences, and cognitive contributions to analyze group members’ accumulation of knowledge as the development of group cognition. Researchers can reproduce the analytical procedures to analyze collaborative interactions in the group level (Borge & Rose, 2021; Liu et al., 2021). Considering that quantitative measures would probably miss some nuances of collaboration (Zemel et al., 2009), qualitative fine-grained microanalysis is used to further explain the development of group cognition of selected social-behavioral-cognitive fragments. Group cognition equation is initially verified by the qualitative microanalysis results. Echoing the research trend of educational measurement (Borge & Rose, 2021; Creswell & Clark, 2017; Janssen et al., 2013; Puntambekar, 2013), the research takes a step forward to propose and use a rigorous procedure to quantitatively measure group cognition, complemented and justified with qualitative microanalysis results. Future quantitative measure of group cognition can be improved in the following three ways. First, future work should focus more on the measures of group’s social, behavioral, and cognitive characteristics. In this research, we test the measures of components in the equation on three different sizes of the dataset; results indicate the similar ordering of three groups, which implies a certain level of justification of the equation. But further examinations indicate that the equation result in a higher score for the small-sized, short sequences than the large-sized, long sequences. The significant differences come from the measures of three coefficients (i.e., $c_{int}$ , $c_{beh}$ , and $c_{cog}$ ). For example, within a small-sized sequence of behavior, the measure of referential behavior transferred to concept map could become a large value close to 1, which might be meaningless for the comparison of inter-group differences. Therefore, future research should focus on modifications of measurements for the group’s social, behavioral, and cognitive characteristics in order to better balance intra-group characteristics as well as inter-group differences. Second, since knowledge building at the group level is considered as the core element in the equation, future measure of group knowledge can consider to focus more on the nuance of group’s collective knowledge negotiation. For example, although the synergy of multimodal interaction, referential behavior, and idea-centered discourse is examined, the group’s knowledge accumulation process is calculated as a weighted score of individual contributions in the proposed equation; future work could examine, at a more micro level, how group members negotiate and contribute to one idea and further accept and demonstrate it on the knowledge artifact (e.g., concept map) afterwards. Third, because group cognition emphasizes that group knowledge exceeds that of all members’ personal understanding, future work should integrate students’ mental, perceived sense of knowledge, as a complementary, to understand the relations between individual knowledge acquisition and the group knowledge structure from a cognitive perspective (Akkerman et al., 2007; Kirschner et al., 2018; Schneider et al., 2020). Traditional qualitative methods (e.g., observation, interview, survey, reflection) can be used to understand students’ perceptions about individual and group knowledge before, during, and after the collaborative learning (e.g., Sun et al., 2021). Overall, this research argues that a mixed method, particularly a combination of the quantitative equation and qualitative microanalysis, serves as an appropriate method for making a better understanding of group cognition.

From the pedagogical perspective, the research results indicate that the development of group cognition is a new, challenging practice, for both students and instructors during collaborative problem solving (Fiore et al., 2017; Wiltshire et al., 2018). Simply putting students together in a group to work on collaborative tasks is no guarantee of the development of group cognition (Curşeu & Pluut, 2013); the practice of group cognition requires multiple conditions such as the communication and interpretation context, students’ shared intentionality and agency, social and cultural backgrounds, technological and pedagogical affordances, etc. (Borge & Mercier, 2019; Damşa, 2014; Stahl, 2007). Instructors should take advantage of instructional design, facilitation strategies, and technological supports to foster students’ practice of group cognition. First, during instructional design of collaborative learning activities, instructors can consider to provide students with choices to negotiate the collaborative purposes and procedures; when students view themselves as creators of the collaboration, they may be more prone to develop collective responsibility, joint actions and shared epistemic agency (Damşa, 2014; Ouyang, Chen, Cheng, et al., 2021; Ouyang & Chang, 2019). Students are more likely to form equal, interdependent participations with a shared, collective agency in the group, which is beneficial for students to develop group cognition. Second, instructors should be prepared to scaffold symmetrical, interdependent participation between students, particularly when some groups (e.g., Group A) or some group members (e.g., student C1 in Group C) show a low level of participation. Because the group cognition is dynamically influenced by the group’s social structures, dynamics, and changes (Damşa, 2014), one participant’s disengagement may significantly influence others’ participating motivation, which in turn influence the group’s productive collaboration (Altebarmakian & Alterman, 2019). Third, instructors should take advantage of the technologies and tools that have the functionalities to lower the barriers for equal, coordinated participation, to improve social- and cognitive-related group awareness, and to allow the real-time track of the group’s social learning processes (Chen et al., 2018; Damşa, 2014; Ouyang, Chen, & Li, 2021). Overall, these pedagogical implications have potential to foster students’ practice of group cognition.

Conclusion

The cognitive science of the small group—the group cognition theory—serves as a bridge between the psychological theories of individual mind and the social learning theories (Stahl, 2006). However, most research has conceptualized and investigated group cognition from the qualitative, phenomenological perspective. A researcher may see patterns in the data that others, even those with similar expertise, may not, due to cognitive biases regarding qualitative analysis results (Borge & Rose, 2021). The educational measurement field has argued a need to build rigorous quantitative methods and procedures to investigate collaborative interactions in the group level, that can be reproduced by others carrying out similar methods (Borge & Rose, 2021). More important, from a complex adaptive system perspective, a group system is an organic entity, comprised of a set of elements and complex relationships between them (Byrne & Callaghan, 2014; Hilpert & Marchand, 2018). Echoing this trend, this research provides a working definition of group cognition, proposes a quantitative equation to measure elements of group cognition through rigorous analytical procedures, and empirically investigates three groups’ development of group cognition. The results show that small groups of students have potential to synergistically coordinate their social, behavioral, and cognitive activities in order to develop a successful group cognition. Since the quantitative results are consistent with the qualitative observations as well as the final performance scores, the equation is initially justified. Based on the empirical research results, the relevant implications are provided for advancing the research and practice of group cognition.

There are several limitations of this research, which also guide future research and practice of group cognition. First, an advanced conceptualization of group cognition is needed to further consider the critical components of group members’ synergistic coordination of multimodal interactions, referential behaviors, and idea-centered discourses. Moreover, from a complex adaptive system theory, structural analysis can be considered in future research (Hibbeler & Kiang, 2015). Second, this research merely focuses on a small size of student sample, with a limited range of subjects’ demographic backgrounds and learning experiences. Future research should expand the sample size to further test, validate, or modify the group cognition measurement proposed. Third, only one group successfully develops group cognition; therefore, it is necessary for instructors to integrate the pedagogical and technological supports to foster group cognition by empowering collective agency, equal participation, and ownership for collaborative learning. Overall, this research develops a working definition and quantifiable measure of group cognition, and empirically examines group cognition in China’s higher education with mixed methods. The research results indicate that the development of group cognition is a new, challenging practice for both students and instructors, such that instructors should take advantage of instructional design, facilitation strategies, and technological supports to foster students’ practice of group cognition.

	Participant	Gender	Age	Status
Group A	A1	Female	32	Graduate
	A2	Male	41	Part-time graduate student
	A3	Female	36	Full-time Ed.D. student
Group B	B1	Female	24	Full-time Master student
	B2	Male	25	Potential graduate student
	B3	Male	31	Full-time Ph.D. student
Group C	C1	Female	24	Potential graduate student
	C2	Female	27	Full-time Master student
	C3	Male	23	Full-time Master student

Dimension	Approaches	Purposes	Data source
Multimodal interaction (Social)	Social network analysis (SNA) of interaction data	To analyze the social dimension of peer interactions through verbal discourse and online behaviors	Computer screen videos, audio recordings, and texting chatting content
Referential behavior (Behavioral)	Click stream analysis (CSA) of behavior data and lag-sequential analysis	To analyze the behavioral patterns of group online behaviors	Computer screen videos and Huiyizhuo clickstream files
Idea-centered discourse (Cognitive)	Quantitative content analysis (QCA) of discourse data	To analyze the individual-level and group-level knowledge	Audio recordings and texting chatting content

Metrics	Description
Density	Ratio of the number of existing ties to the number of all possible ties
Interaction	The total number of interaction frequencies, as well as each student’s interaction frequency to others
Average degree	Average value of the sum of degree
Inverse coefficient of variation (ICV)	The inverse of the standard deviation of student-student interaction frequency divided by its mean
Reciprocity	Ratio of symmetric dyads to non-null dyads
Outdegree/indegree centralization	The extent to which outdegree/indegree is concentrated within a small number of nodes

Code	Description
Task understanding (TU)	A student moved the mouse to the task area to read and understand the task
Resource management (RM)	A student searched, shared or managed resources
Peer communication (PC)	A student used the texting message or audio to communicate with peers
Concept mapping (CM)	A student created, modified or commented on the concept map
Organization (OG)	A student organized the arrangements, or addressed the technique issues
Observation (OB)	A student moved the mouse over the platform to observe without any operations

	Group A	Group B	Group C		Group A	Group B	Group C		Group A	Group B	Group C
Social				Behavioral				Cognitive
Density	22.70	28.20	42.80	1st beh. (freq.)	PC (129)	PC (218)	PC (388)	1st cog. (freq.)	GS (57)	GM (64)	GS (130)
Interaction	137	169	257	2nd beh. (freq.)	CM (87)	CM (132)	CM (102)	2nd cog. (freq.)	GM (29)	GS (65)	GM (98)
Avg. degree	45.70	56.30	85.70	3rd beh. (freq.)	OB (82)	OB (71)	OB (75)	3rd cog. (freq.)	GD (1)	GD (9)	GD (3)
Recip.	0.85	0.93	0.86	1st CM Trans.	CM->CM (0.55)	CM->CM (0.68)	CM->CM (0.25)	Overall kn. freq.	136	189	325
out/indegree cent.	10.83/6.83	3.83/7.83	26.12/26.67	2nd CM Trans.	OB->CM (0.13)	OB->CM (0.03)	OB->CM(0.04)	Group-level kn. freq.	87	138	237
original $c_{int}$ (ICV)	1.23	2.40	0.75	original $c_{beh}$	0.68	0.71	0.29	original $c_{cog}$	0.64	0.73	0.73

Level	Code	Description
Individual Knowledge	Superficial (IS)	A participant shares information without explicit statement of his/her own ideas
	Medium (IM)	A participant states his/her own ideas without explanations, or support of resources
	Deep (ID)	A participant states his/her own ideas with detailed explanations, support of resources, or experiences
Group Knowledge	Superficial (GS)	A participant simply repeats another participant’s idea, or presents (dis)agreements, or asks questions without argumentations, explanations or elaborations of the idea
	Medium (GM)	A participant argues, extends, and builds on another participant’s idea with explicit argumentations or elaborations, support of new information and resources
	Deep (GD)	A participant connects, synthesizes, and rises up ideas interpreted by the other two participants to construct new ideas, reach a consensus, or make a decision

	Group	$c_{int}$	$c_{beh}$	$c_{cog}$	$S_{kn}$	Time (hour)	$S_{gc}$
The whole process	Group A	0.28 (1.23)	0.41 (0.68)	0.30 (0.64)	236.5	1.45	0.75 (5.62)
Group B	0.55 (2.40)	0.42 (0.71)	0.35 (0.73)	373.5	1.57	1.28 (19.23)
Group C	0.17 (0.75)	0.17 (0.29)	0.35 (0.73)	594.5	1.50	0.60 (4.01)
The medium-sized fragment	Group A	0.14 (0.91)	0.48 (0.68)	0.31 (0.75)	42.0	0.12	0.86 (7.29)
Group B	0.73 (4.64)	0.30 (0.43)	0.34 (0.82)	64.5	0.15	1.51 (32.02)
Group C	0.13 (0.79)	0.22 (0.32)	0.35 (0.85)	79.0	0.10	0.90 (7.91)
The small-sized fragment	Group A	0.41 (1.53)	0.33 (1.00)	0.26 (0.50)	23.5	0.053	1.19 (15.60)
Group B	0.37 (1.41)	0.33 (1.00)	0.30 (0.57)	25.0	0.036	1.41 (25.44)
Group C	0.22 (0.82)	0.33 (1.00)	0.44 (0.86)	30.5	0.042	1.37 (23.20)

Line	From	To	Content	Coding
1	A3	/	Another critical question for us to think is why we need to do the design…	Cognitive
2	A2	A3	We can focus our design on the driving experience or the human-computer interaction…	Social; Cognitive
…
7	A2	A3	… We can use the VR techniques… Since students are supposed to learn relevant theories, we can teach them about the difference of power transmission between the tradition vehicles and the new energy vehicles…	Social; Cognitive
…
9	A1	A2	I think we’d better narrow down the topic you mentioned and make it more targeted.	Social; Cognitive
10	A3	A1	OK, what is in your mind? Which topic do you suggest to narrow down to?	Social; Cognitive
…
15	A2	/	…we can focus on engineering design, which means how to make a better design to improve the efficiency of energy use… students are supposed to tell the differences of the manufacturing techniques between the tradition vehicles and the new energy vehicles… students can use VR or online experiments to experience the transmission techniques…	Cognitive
16	A1	/	Observation & Concept mapping	Behavioral
17	A3	A2	Yes, I think your idea is very good. And we can specify it, for example, the different energy types.	Social; Cognitive
…
20	A3	A2	Yes. Students can form groups to focus on different types of vehicles…We can let students learn the theories first, and then use the VR to simulate the operations in the virtual laboratory. What do you think?	Social; Cognitive
21	A1	/	Observation & Concept mapping	Behavioral
…

Line	From	To	Content	Coding
1	B1	/	Do we need to assign a role to students in the group? I think it would be inappropriate for all students to do the same thing… do we ask the students to form a group by themselves? Or form a group randomly?	Cognitive
2	B3	/	Concept mapping	Behavioral
3	B3	B1	Random grouping? Why?	Social; Cognitive
…
6	B3	/	Concept mapping	Behavioral
7	B2	B1	… I think we can let the instructor to assign the groups, if she knows students and their strengths. but I am afraid if we use random grouping, some groups may not be functioning if students are all not skillful at doing this work…	Social; Cognitive
8	B1	B3	Concept mapping	Social; Behavioral
…
13	B1	B3	Concept mapping	Social;Behavioral
…
20	B3	/	Concept mapping	Behavioral
…
25	B2	B3	… the groups of students are required to complete their design of engine within the limited budget. Then, the instructor can evaluate students’ performance…	Social;Cognitive
26	B2	/	Observation	Behavioral
27	B1	/	Concept mapping	Behavioral
28	B3	B2	… It is better to define the requirement specifically…I think we can specify some dimensions to evaluate the groups’ performance of engine assembling.	Social;Cognitive
…
31	B2	B3	Concept mapping	Social;Behavioral
32	B1	B2	It means that students form groups, and then the groups randomly receive their tasks.	Social;Cognitive
33	B3	/	Concept mapping	Behavioral
…
40	B2	B3	It is like a mission card. When you open that card, you will find that you are in a specific group with an assigned role… Then the group will log in the online platform to assemble the engine…	Social;Cognitive
…
53	B2	/	Concept mapping	Behavioral

Line	From	To	Content	Coding
1	C3	/	Another approach is the remote lab. A student can operate to control a real entity by using a remote computer…	Cognitive
2	C1&C2	/	Observation	Behavioral
…
12	C1	/	Is there a tool that allows all students to share the screen at the same time?	Cognitive
…
23	C3	C1	… during the in-class activity, the instructor wants to know students’ practice process…	Social;Cognitive
26	C1	/	Observation	Behavioral
27	C3	C2	Video conferencing is a simple way to teach online… Video conferencing is also used frequently in practice…	Social;Cognitive
28	C2	C3	What you just mentioned that the instructor can monitor all students’ learning… it is in school’s computer labs…	Social;Cognitive
29	C1	/	Observation	Behavioral
30	C1	C2	Yep…	Social;Cognitive
31	C3	C2	So the situation is, every student needs to turn on the webcam… which may be difficult in real situations because the student can decide to turn it on or not…	Social;Cognitive
…
36	C2	C3	These can all be put in the in-class activities actually… we can further describe them.	Social;Cognitive
40	C3	/	Concept mapping	Behavioral
…
44	C2	C3	I mean the guidance of the video conferencing.	Social;Cognitive
45	C3	C2	… Those parts like data simulation, virtual experiment and modeling are some concrete ways of practical activities…	Social;Cognitive
…
48	C3	C2	Those are the strategies, right?	Social;Cognitive
49	C3	/	Concept mapping	Behavioral
…
55	C3	/	Concept mapping	Behavioral

Footnotes

Acknowledgments

The authors acknowledge assistances from Zixuan Chen, Mengting Cheng, Zifan Tang for their preliminary data cleaning and analysis work.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research is financially supported by the National Natural Science Foundation of China (62177041; 61907038) and 2021 University-level Educational Reformation Research Project for Undergraduate Education, Zhejiang University (zdjg21033).

ORCID iD

Fan Ouyang

Author Biographies

Fan Ouyang, PhD, is a research professor (tenure-track) of Educational Technology in the College of Education at Zhejiang University. Her research interests are computer-supported collaborative learning, learning analytics and educational data mining, online and blended learning, and artificial intelligence in education.

Tengjiao Ling, MS, was an associated research assistant under Fan Ouyang’s supervision when the research was conducted. Ling currently works in Xue Tong Science and Technology Ltd. as a data mining engineer. His research interests are computer-supported collaborative learning, learning analytics and educational data mining.

Pengcheng Jiao, PhD, is a research professor (tenure-track) of Ocean College at Zhejiang University. His research interests are advanced metastructures, mechanical metamaterials and soft robotics, and artificial intelligence in education.

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