In recent years, the research on commognitive conflict has tended to extend in a broad sense, viewing commognitive conflict as a state produced by discrepancies between an individual’s cognitive structure and the environment or between various components within that structure (Lee et al., 2003). Commognitive conflicts, which are cognitive conflicts that arise during communication, exist in the communication of different vocabulary usage, rules of evidence, etc. (Sfard, 2008). From a cognitive perspective, the heterogeneity of a team’s knowledge gives rise to diverse cognitive conflicts, which, in turn, facilitates the activation of more flexible cognitive mechanisms. These mechanisms enable the fusion of divergent cognitive schemata, ultimately leading to the creation of new cognitive constructions (Perry-Smith and Shalley, 2014). As the communicative interaction between people with different knowledge structures generates new patterns of knowledge connection, creative friction or creative chaos emerges (Zhang and Ni, 2006), stimulating various types of information exchange and the discovery of new solutions.

Sociocultural theory academics’ research on the social interaction view of individual mental development has offered a theoretical and empirical basis for the assessment of commognitive conflict. Vygotsky (1962) originally proposed that learners acquire knowledge most effectively through interaction, dialog, and negotiation in social, authentic learning situations that promote the holistic development. This not only improves the competency and learning performance of the students, but also stimulates the cognitive growth of the group through cooperation and interaction. When students are confronted with socially authentic problem situations, they participate in the CPS process through interaction, dialog, negotiation, and other learning styles. At this time, members’ heterogeneous knowledge structures communicate with each other, and while they build complementary knowledge within the team, they also generate varying degrees of commognitive conflicts. And the proportion of commognitive conflicts in CPS was significantly higher than the traditional cooperative learning (Liang et al., 2017).

Sfard (2007) created the theory of commognition and categorized its levels and components based on various student-teacher and student–student communication dialogs. She developed the commognitive vision of mathematics as a type of discourse—as a defined form of communication, made distinct by its vocabulary, visual mediators, routines, and the narratives it produces. However, the theory has not yet codified the level of discourse and developed a more detailed description of the forms of conflicts, which is a challenging and innovative aspect of the study. Although commognitive theory has areas that need refinement, its applications are very broad and can serve as an effective research lens for different fields, and its potential has not yet been fully explored (Presmeg, 2016).

Due to the widespread application of commognitive theory, which has also received considerable attention from academics, the theory has been refined in practice. Regarding knowledge constructs for commognitive conflict, Gyoungho (2007) proposed a structural map of knowledge and beliefs that points to the students’ cognitive conflict analysis. This serves as a reference for the classification of knowledge content for commognitive conflicts.

Therefore, this paper argues that the commognitive version of discourse can be classified into conceptual, procedural, and contextual knowledge dimensions. In this way, we would able to observe how students collaborate to solve problems through classroom and to record the commognitive conflicts that arise during the learning process of interaction, dialog, and negotiation among members. If students can effectively manage commognitive conflicts, they will be able to foster cognitive development at both individual and group level. Moreover, this ability will also enhance their critical thinking skills and creative abilities.

In terms of problem-solving research and practice, scholars have constructed mature models to study and understand the process of problem solving. These models provide frameworks and guidelines for approaching problems effectively. Polya (1973) proposed a problem-solving model consisted of four-step process, which emphasizes the importance of understanding the problem thoroughly, strategic thinking, and critical reflection and helps develop effective problem-solving skills. Subsequent scholars have adapted and expanded upon Polya’s problem-solving model to cater to various needs and situations (Yu, 2008; Cao et al., 2016; Wei, 2019). For example, Schoenfeld (1985) divided the paradigm of problem-solving into six phases: preparation, exploration, strategy formulation, execution, evaluation and inquiry. In the “Inquiry” module, commognitive conflict refers to the cognitive conflicts that students may encounter while engaging in an inquiry-based learning process. When learners encounter these conflicts, they are presented with opportunities for deeper understanding and critical thinking. However, these researches have primarily focused on individual student problem solving of closed problems as the primary case study, and none of the models directly address commognitive conflict. When students’ pairs or groups solve mathematical problems in open environments, the cognitive model of CPS will become more sophisticated, and major commognitive conflict will occur.

In a study involving students’ commognitive conflict processes, Lewis and Mayer (1987) constructed a model on the process of comparing problem comprehension, arguing that students have a preference for the order of information provided in a problem and prefer problems that are in the same order. When students do not agree on the relational terms in solving comparison problems and the required arithmetic operations, comprehension errors occur and commognitive conflict arises. This type of conflict due to students’ preference for the order of problems will most likely present explicit commognitive conflict during CPS.

In terms of discourse analysis of commognitive conflict in CPS, Barron (2000), on the other hand, focuses on group-level characteristics of CPS, providing targeted strategies for examining cooperative group learning and providing explanations for the variability in the outcomes of collaborative activities. By recording and coding the quality of communication in the study groups, the characteristics of group interaction, problem-solving goal congruence are analyzed and the groups are classified into high quality and low quality problem solving. Iiskala et al. (2011) explore how metacognition becomes a socially shared phenomenon in their study of conversational episodes and characteristics during collaborative mathematical problem solving among high achieving students’ pairs. These researches provide a powerful reference for the discourse analysis of commognitive conflict in CPS.

In the context of commognitive conflict visualization, Ding (2009) visualized the knowledge refinement in CPS work. The study used a behavioral sequential approach to map students’ pairs and personal knowledge refinement curves in CPS. This visualization study of commognitive conflict in CPS offers valuable insights and ideas.

Overall, the majority of research on commognitive conflict in CPS has focused on the cognitive processes of individuals in problem solving and discourse conflict, whereas the visualization of commognitive conflict content classification and discourse is lacking. Therefore, our research utilized the SOLO theory to select student pairs of high-quality, medium-quality, and low-quality, and conducted a comprehensive investigation into identifying, visualizing, and diagnosing the commognitive conflicts during CPS. The statistical profile, discourse diagnosis, and visual analysis of commognitive conflict in CPS enable teachers to gain a deeper understanding of how students encounter commognitive conflicts and how different quality student pairs approach problem-solving. As a result, this provides teachers with timely and targeted guidance to support their students effectively, thereby enhancing students’ CPS skills. Moreover, the process of discourse analysis and visualization also offers a learning-oriented and innovative approach, providing a script for technology-assisted feedback practices.

Year 7, which is the present focus of the international CPS assessment, was selected prior to Year 8 in consideration of the exploratory nature of the project. The research segment, problem tasks, and research environment are all mostly consistent with the Australian partner side. 32 student pairs, consisting of a total of 64 seventh-grade students from the LH middle school in an urban area of the TZ district in BJ city, with moderate educational quality, were selected as the sample for the CPS recordings.

At the same time, the student outcomes were evaluated using the SOLO (Structure of the Observed Learning Outcome) five-level classification evaluation method (Biggs and Collis, 1982), which took into account the characteristics of the open-ended mathematical and contextual problems used in the project. The SOLO theory classifies observable learning outcomes into five levels: prestructural, unistructural, multistructural, relational and extended abstract structure. This resulted in the selection of the typical cases with the high quality, medium quality and low quality outcomes, as shown in Table 1.

The study utilized open-ended contextualized mathematical problems that better provoke commognitive conflict in communication (Clarke and Helme, 1998) from the Sino-Australian SEL project. The mathematical problem task is “Households and Age,” in which student pairs will collaborate to solve the problem, calculate the age of each person, and associate the social relationships of five people, as shown in Table 2. The student competencies examined in this task include the pedagogical problem-solving cycle involved in the International Institute for Frontier Mathematics Education, which promotes individual and group reflection on a dialectical cycle (Lu, 2017). Additionally, the study categorized the knowledge dimensions of commognitive conflict as conceptual, procedural, and contextual, and then examined and visually presented the features of the knowledge dimensions of the students’ pairs.

Conforming to the specifications of the data collection classroom environment for the Sino-Australian Student Collaborative Mathematics Problem Solving Project, the study environment was built in a school-filmed classroom with which the children were quite familiar. Each group of 4–6 students in the videotaped classroom sat around a multi-tabled collocation table. The participants performed three tasks: individually, in pairs and in groups. In this paper, we only analyze the task conducted in pairs. A video camera was set up to capture the entire activity, and wireless microphones, such as left and right channels, were used to gather sound. Each group of students received pens, task sheets, rough draft paper, and other tools so they could complete the mathematical tasks. The study utilized 12 min of data from the problem-solving session involving pair participation. Figure 1 depicts the information in detail.

During mathematical problem solving, student performance was videotaped, and the discourse was coded and analyzed. In this paper, we present a visual presentation and qualitative analysis of students’ performance in commognitive conflict during CPS. We analyze the differences in knowledge dimensions, the time and frequency of occurrences, as well as the diagnosis and visualization of commognitive conflict. The study coded the knowledge dimensions of commognitive conflict, identifying and classifying the types of conflict segments and recording the length of conflict for each segment. This resulted in statistics on the number, type, and average duration of conflict for 32 pairs of commognitive conflict groups. Two coders were utilized to confirm the validity of the coding results, and the consistency coefficient of the results was 0.913. Inconsistencies in coding were reviewed and deemed consistent by the coders.

To further analyze different quality student pairs’ commognitive conflict, the study used Nvivo12 software and 3D visualization block diagrams to visualize the data and thus present a more visual representation of commognitive conflict in CPS.

The study first encoded the commognitive conflicts of 32 student pairs and conducted an overall statistical analysis of the number of conflicts, average conflict duration, proportion of different types of conflicts, and resolution rate among student pairs. By coding and counting students’ pairs commognitive discourse, it was found that students’ commognitive conflicts were mainly concentrated in procedural and contextual knowledge, accounting for 47.5% and 46.50%, respectively. Conceptual knowledge accounted for only 6%. In terms of problem solving percentage, the problem solving percentage of procedural knowledge was 31%, and the solving rate was 65.3%; the contextual knowledge was 26%, and the solving rate was 55.9%. The percentage of problem solving based on conceptual knowledge was 6%, and the resolution rate was 100%. In terms of average conflict duration, the longest time was required to solve procedural knowledge, with an average of 52.77 s for one conflict. In contextual knowledge, the time for unresolved conflicts was 49.61 s, in which students were aware of the differences in their respective different mathematical contexts and therefore chose to postpone the conflicts. The details are shown in Table 3.

As it can be seen in Table 3, it is evident that the conceptual knowledge conflicts have the lowest percentage and the highest resolution rate, which indicates that students have a good grasp of the basic concepts of such problems.

To further analyze the commognitive conflicts among student pairs in CPS, the study selected high-quality, medium-quality, and low-quality case pairs using the SOLO theory. Visual analysis was then conducted on the quantity, occurrence, duration, and resolution status of commognitive conflicts in student pairs, as shown in Table 4.

Similarities and differences were discovered in the total number of occurrences, duration, and resolution status of commognitive conflicts among student pairs. The similarity lies in the total number of commognitive conflicts, with 8–9 conflicts occurring within a 12-min period. The difference is that each pair has its own characteristics in terms of the occurrence, duration, and resolution status of commognitive conflicts. The commognitive conflicts among high-quality student pairs emerged early and were resolved relatively quickly, with 7 out of 8 conflicts being resolved, while medium-quality pairs resolved 5 out of 8 and low-quality student pairs resolved only 3 out of 9, and the first two periods took longer. The information presented in the visualization diagram in Table 4 can also be expressed as the information shown in Table 5.

In terms of the categories of commognitive conflicts, different student pairs have fewer conflicts in the conceptual knowledge dimension. This is because the conceptual knowledge content of this mathematical task is not difficult, such as ‘the total age of five people, the age of seventh grade, and the age of the remaining four people’. When conflicts arise, students are more likely to resolve them. The commognitive conflicts mainly focus on the procedural and contextual dimensions, which is consistent with the conclusions obtained in Table 3. In high-quality student pairs, all procedural dimension conflicts have been resolved, while unresolved conflicts still exist in the middle and low-quality pairs. Therefore, the study will perform further discourse diagnosis and 3D block diagram visualization analysis on the procedural and contextual knowledge dimensions conflict, and reveal the characteristics and patterns associated with these conflicts.

After selecting procedural dimensional commognitive conflict fragments, such as high quality P14-4S, medium quality P4-3S and low quality P2-2S and performing discourse visualization diagnosis, it was discovered that the procedural commognitive conflict is primarily manifested in the discourse of mathematical results after calculation errors by pairs. Table 6 takes the commognitive conflict fragments of the procedural knowledge dimension as an example and performs discourse diagnose from the beginning to the end of the conflict. This approach is also applicable throughout the entire study.

Discourse diagnosis helps the research to identify and analyze the linguistic, semantic, and interaction features of discourse, and reveal the underlying patterns and dynamics of how student pairs solve the procedural commognitive conflict. For example, in the high-quality student pairs, the discourse diagnosis reveals that Girl 14B had a commognitive conflict with Girl 14A’s calculation of 34 and further questioned the follow-up operation, which diagnosed as the cause and found of conflict. Girl 14B corrected the commognitive conflict after Girl 14A pointed to the draft document and made her explanations clear. She also suggested using 125 minus 34 and continuing to move backward, which was accepted by Girl 14A. The entire procedure, which took only 40 s, resolved the problem and even reversed some forward progress.

The study selected different quality cases of contextual knowledge dimension commognitive conflict fragments and conducted 3D block diagram visualization analysis and diagnosis. This 3D block diagram is adapted from Lee’s structure of cognitive conflict. In research tasks, contextual knowledge is mainly divided into school mathematics knowledge and life experience. On the dimension of procedural knowledge, it is divided into arithmetic, mathematics quantitative certainty, and interval uncertainty. In terms of conceptual knowledge dimension, it involves basic mathematical concepts and other knowledge, consistent with the previous text. The path characteristics of commognitive conflicts can be intuitively seen from the 3D block diagram, as shown in Table 7.

The 3D diagram allows for an intuitive visualization of the paths taken by student pairs in commognitive conflicts. Taking high-quality P14-5S fragments as an example, the conflict paths are as follows: 1-BA → 2-B → 3-A → 4-BA → 5-A. The specific process is described as follows:

1-BA represents student 14B, who based their judgment on life experience and considered the possibility that children are 12 years old. Meanwhile, student 14A revised 13 years old. 2-B indicates that student 14B, while considering the reasonableness of the gap between parents’ age and child’s age, concluded that the other two children should be siblings. 3-A indicates that student 14A experienced a communication cognitive conflict in response to the 2-B judgment made by student 14B. This conflict arose due to student 14A’s narrow focus on mathematical quantification in school mathematics. 4-BA represents student 14B’s explanation for their 2-B judgment. After student 14A confirmed the explanation, they performed calculations to determine the validity. 5-A indicates that when student 14A was recording the results, they considered the uncertain nature of mathematics and added descriptive elements such as “examples” in the column.

Research has revealed distinct path characteristics for commognitive conflicts among student pairs of different quality levels. In the case of the high-quality student pair (P15-5S), the process path for the emergence, negotiation, and resolution of commognitive conflicts follows a path of “life experience → school mathematics → life experience.” They also consider both the certainty and uncertainty aspects of mathematical problems. Similarly, the medium-quality student pair (P4-8S) follows a path of “life experience → school mathematics → life experience.” They take into account the age range in real life, which is then transformed into mathematical certainty, leading them to conclude that the five individuals have a shared rental agreement. Although their thinking is somewhat biased toward the life context, their logic remains reasonable. On the other hand, the low-quality student pair (P2-8S) only experiences the path of “life experience → school mathematics.” They fail to fully convert the discussed problems into the realm of school mathematics. Despite considering the interval uncertainty, their analysis lacks accuracy and depth.

In the 3D visualization diagnosis of commognitive conflict, the study mainly draws on Gyoungho Lee’s three-dimensional viewable framework (Lee and Yi, 2013); however, Lee’s related research mainly reveals static cognitive conflict and has not yet used the theory to analyze dynamic cooperative problem solving. This research uses the 3D analysis framework to present a dynamic path for commognitive conflicts and also refine the use of the analysis framework. Table 7 shows that the different quality commognitive conflict in CPS has a distinct pathway, the high- and medium-quality student pairs showing a “life experience-school mathematics-life experience” problem solving process. In this process, students make full use of their existing life experiences and mathematical knowledge, improve their own mathematical knowledge during the commognitive conflict with their pairs, and internalize and recreate based on their existing mathematical knowledge. This also coincides with Freudenthal’s theory of mathematics education—the idea of mathematical reality, mathematization and recreation (Freudenthal, 1973). It demonstrates that students may increase mathematics learning and create their own mathematical and life experiences by effectively resolving commognitive conflicts in CPS.

Existing commognitive theories give a detailed classification of commognitive conflict levels and elements, but research on content classification and visualization of discourse levels is lacking. In this study, we classify and visualize the knowledge dimensions of commognitive conflict in order to provide a theoretical and practical foundation for broader application. Future advancements can be made in the precise classification of commognitive conflict, the refinement of discourse analysis, and the development of visualization tools.

The visual analysis of the commognitive conflicts of different quality student pairs revealed significant differences in the duration, amount, and resolution of conflict, especially in the procedural and contextual knowledge dimensions. Thus, teachers need to encourage students to focus and resolve commognitive conflicts and make appropriate instructional interventions, which facilitate the development of students’ CPS from low to high quality. The commognitive conflict in CPS, when coupled with timely and targeted feedback, empowers teachers by fostering student engagement, deepening understanding, enabling personalized instruction, and so on. When students receive immediate responses to their contributions, it reinforces their engagement and participation. Furthermore, timely and personalized feedback provides guidance and clarifies misconceptions, helping students refine their understanding and address their unique challenges. Therefore, the dynamic coding and visualization of commognitive conflict in CPS can more effectively identify the types and manifestations of commognitive conflict in problem solving and thus provide a basis for teachers to provide targeted instructional interventions.

During the research, we investigate explicit indicators of CPS, such as commognitive conflict categories, the occurrence and the average conflict duration etc., which are conducive to automatic identification and data analysis in the context of the rapid development of artificial intelligence (AI) for speech recognition. As AI technologies have the potential to reduce the workload for teachers and test developers (Yunjiu et al., 2022), their further development in the application of commognitive theory can provide directions and scripts for AI-assisted teaching, particularly in commognitive conflict discourse recognition and diagnosis in the future.

At the same time, computerized automated evaluation, at a time when AI development such as speech recognition is becoming more and more mature, has been able to begin to intelligently perform automated diagnostic analysis. Therefore, a more in-depth visualization study of commognitive conflict in CPS can provide ideas and references for future AI-empowered teaching and learning.

In this paper, intelligent diagnosis and visual analysis are carried out according to the commognitive conflict of students’ pairs in CPS, which provides an innovative solution for visual presentation of teaching feedback. Visual studies of commognitive conflict can provide teachers with rich data that informs their decision-making. For example, when the visual diagram shows the low quality student pairs, by analyzing visual data, teachers gain insights into the quality of students’ interactions, and determine when and how to provide targeted instructional interventions. Its further development can provide analysis framework and case reference for teachers or even computer automation to evaluate students’ pairs problem solving level. This solution of intelligent diagnosis and visual analysis is intended to provide a deeper understanding of how students respond to feedback practices of commognitive conflicts in CPS in the future teaching, and to shift to more applicable results. This, in turn, promotes the development of individuals in the social interaction and communication. Therefore, in the future, it is necessary to strengthen research on the diagnosis and visualization of commognitive conflict in CPS which will provide scripts for future artificial intelligence, offer data support for targeted, timely, and personalized assistance.