Keywords

2.1 Introduction

Nowadays, the global situation is undergoing profound and complex changes (Xi, 2022). To meet these challenges and seek further development, many countries/jurisdictions and international organisations have gradually attached importance to developing students’ “21st-century skills” in the field of basic education, going beyond traditional subject knowledge and to focus on contemporary competencies and literacies for Education 4.0 (Griffin et al., 2012; World Economic Forum, 2020). As a future-oriented education reform, various countries/jurisdictions and organisations have highlighted the key capabilities and core competencies necessary for students’ learning, working, and living in the twenty-first century, such as collaboration and problem-solving, in their educational objectives and learning contents for cultivating practical and innovative talents with global competitiveness (Deng and Peng, 2019; UNESCO, 2021). Integrating “21st-century skills” into the national education system and various learning areas, such as science, art, humanities, and mathematics, has become the main practice in many countries (OECD, 2018). Mathematics, the “queen of science,” is the basis of science and an important part of school curricula. Realising the development of students’ “21st-century skills” in mathematics learning and promoting practical and innovative talents have become the main trends in mathematics curriculum reform (Sun et al., 2019).

School classrooms are the main place for talent training and curriculum implementation. Classroom learning is an important carrier for promoting students’ development and achieving educational goals. The sample of Chinese 15-year-old students’ average collaborative problem-solving (CPS) performance (OECD, 2017a), junior high school’s role in connecting the preceding and the following, and junior high school students’ unique physical and mental development create a singular learning environment. Focusing on junior middle school mathematics classroom teaching and learning, promoting the transformation and innovation of teaching methods, and carrying out mathematical problem-solving-based collaborative learning (MPSCL) meets the requirements of contemporary learning theory, creates an autonomous, cooperative, inquiry-based learning environment, and reflects current development trends. MPSCL provides a carrier for realising the above educational goals and has become an active exploration of how to strengthen the educational function of mathematics classroom learning and teaching in the new era and build a high-quality education system (Sun and Guo, 2020). However, MPSCL still faces many theoretical and practical difficulties. Changing teaching methods and improving learning quality are still in the exploratory stage. For example, the widely used collaborative learning approach is inefficient; the learning process is a mere formality, and students’ poor collaborative learning performance leads to low teaching and learning quality (Li, 2019; Wang, 2019).

To fully understand students’ MPSCL performance, the quality of student groups’ problem-solving solutions was assessed based on the research project data and found wanting. High-performance groups completed the mathematical problem-solving task requirements and produced nice solutions, while low-performance groups completed less than half of the task requirements or provided solutions that were less than half as accurate. To some extent, this result confirms the ineffectiveness of collaborative learning in mathematics classrooms and students’ poor collaborative problem-solving performance (Sun, 2004). Therefore, by examining and comparing high- and low-performance groups, it is necessary and important to study this team-based learning process further; in particular, how to optimise MPSCL and improve students’ learning performance and learning quality have become important problems that need to be solved.

Learning science is closely related to curriculum, teaching, and learning. It guides curriculum, teaching, and learning development based on the latest research achievements and is the key to ensuring that curriculum reform is scientific, forward-looking, and effective (Peng and Liu, 2019; Chi et al., 1994). With the development of social constructivism and socio-cultural cognition, learning is the social negotiation of knowledge, and establishing a learning community to carry out collaborative knowledge building (CKB) has become a new learning metaphor and has attracted much attention (Ma, 2004). CKB provides a critical perspective for understanding problem-solving-based collaborative learning.

As a key term in constructivist learning theory, knowledge construction is the core concept of the constructivist knowledge view and epistemology. Knowledge construction theory holds that humans cannot directly understand objective reality as it is independent of how they perceive it. The perceptions and experiences from which humans construct their understanding of objective reality are mediated by their existing knowledge and experience. Learning is just the process through which humans adapt to their experience world. When human experience differs from cognition, the unbalanced result triggers the process of human adaptability (learning); reflection on successful adaptive operation produces new or revised concepts (Von Glasersfeld, 1982).

Since the rise of constructivist learning theory in the 1980s, educational theorists and practitioners’ different perspectives on constructivist theory have led to diverse understandings of “knowledge construction.” Although the concepts of “radical constructivism” and “social constructivism” provide some directions for understanding “knowledge construction,” there are various views on knowledge construction in these categories. Therefore, knowledge construction has a diversified development orientation in educational research. Different perspectives have produced different emphases in knowledge construction research, leading to many different research aspects, such as mechanism, teaching, and evaluation.

Compared with traditional knowledge “transmission-reception” classroom teaching and learning, knowledge construction theory fundamentally guides education to reconstruct its teaching activities, promotes students to enter a cultural atmosphere of creating knowledge, and emphasises that knowledge construction is a process of information transmission and meaning understanding through language interaction, which needs to be realised in a specific learning environment. Therefore, a large amount of research in the field of Computer Supported Cooperative Learning (CSCL) has addressed knowledge construction themes, including knowledge construction principles, knowledge construction community, collaborative knowledge construction, and so on (Scardamalia and Bereiter, 1994). Thus, we will focus on individual knowledge acquisition in knowledge construction in a learning community. Stahl pointed out that individual independent learning does not necessarily result in a problem-solving task being properly solved. Jointly building knowledge and meaning through cooperation makes it possible to better deal with problem-solving tasks by making learning enter the socialisation process.

In a learning community, students must cooperate to complete problem-solving tasks jointly and create new intelligent products. In this process, group members need to share their personal views in the learning community, establish different perspectives on problem-solving based on their different personal backgrounds, promote mutual understanding and cooperation through mutual exchange of and consultation on knowledge and experience, promote problem-solving, and realise the continual improvement of small members’ views and ideas, so as to create new public knowledge and improve and optimise each group member’s personal knowledge structure. Therefore, CKB emphasises building knowledge in solving practical problems, pays attention to learners’ creation and sublimation of knowledge through team interaction, and develops valuable views, ideas, strategies, and methods for the learning community.

As the main learning body, students establish various relationships through interactive behaviours, such as raising questions, expressing opinions, providing resources, etc. Educational data-mining technology, in-depth analysis of relationship networks and contents in interactive behaviour, and analyses of information flow and meaning sharing can help teachers, students, and other stakeholders more deeply understand the collaborative problem-solving learning process and promote knowledge discovery, knowledge production, knowledge sharing, and knowledge innovation. With the transformation and upgrading of the current global economy from traditional manufacturing to knowledge and scientific and technological innovation, school education and teaching should pay more attention to information interactions and how knowledge is acquired, generated, and innovated in the cooperative problem-solving process, promote the development of high-quality classroom teaching, and take this as the carrier to develop students’ collaborative problem-solving ability and other necessary core competencies for citizens in the twenty-first century.

However, few studies focus on students’ face-to-face group collaboration and problem-solving from this perspective, analyse or explain this learning process, or mine students’ problem-solving-based collaborative learning data in a micro way to trace and compare high- and low-performance groups’ CKB behaviour processes.

Therefore, this study aims to optimise students’ MPSCL process and improve learning efficiency and quality. The following questions are addressed in this research:

  1. 1.

    What is the CKB process when junior high school students participate in MPSCL activities in mathematics classrooms?

  2. 2.

    Are there any differences in CKB between high- and low-performance groups that produce different quality mathematical problem-solving solutions?

This research used design-based principles, controlling for the influence of external macro factors and investigating the students’ micro-level CKB process in comparing high- and low-performance groups’ mathematics problem-solving to provide research support for improving classroom teaching and learning for talent training.

2.2 Methodology

Studying students’ MPSCL from the CKB perspective is an effective way to understand team-based interactive processes and evaluate this learning quality to support academic analysis and teaching improvement. This section details the study’s main concepts, research design, sample learning task, participants, research methods, and technical road.

2.2.1 The Main Concepts

  1. 1.

    Collaborative/Cooperative learning is a teaching theory and strategy based on the theories of psychology, sociology, and educational technology and aimed at promoting students’ all-around development. It takes group activities as its basic organisational form, teacher–student and student–student classroom interactions as its driving force, and group performance as its basis for evaluating teachers’ and students’ goals, interactions, and roles (Wang, 2002). Collaborative learning emphasises that group members have shared task goals and realise joint learning through meaning negotiation, the division of labour, and collaboration.

  2. 2.

    MPSCL includes team collaboration and problem-solving processes (OECD, 2017b) taking place in school mathematics classrooms under specific space–time conditions, with group members (usually four-person groups) jointly participating in learning activities to solve a given problem (learning task) through meaning negotiation, the division of labour, and collaboration and complete its transformation from its real state to its ideal goal. Here, problems refer to open, comprehensive, and complex mathematical problems with realistic situations.

  3. 3.

    Knowledge construction, the core concept of constructivist learning theory, originates from the philosophical position that humans cannot directly understand objective reality and can only build their understanding of the world from their perceptions and experiences mediated by their previous knowledge. Therefore, learning is a process by which humans adapt their experience world (Jonassen & Kwon, 2001). Knowledge construction is a process and result based on junior high school students’ existing knowledge and experience, relying on mathematical problem-solving, realising the improvement of old and new knowledge and experience, and creating new meaning.

  4. 4.

    Collaborative knowledge building. The research on the learning process has increasingly focused on the social essence of knowledge construction, emphasising that it is affected by the learning community (Hung and Der-Thanq, 2000). It focuses academic attention on the impacts of environment and society on individual cognition. Thus, different from individual knowledge construction, CKB emphasises the social process of learning and believes that learning is constructed by individuals’ cognitive processes and meaning negotiations between individuals and groups. In this research, CKB reveals that against the background of MPSCL, students use personal cognition to interact with their learning community members to build public knowledge through meaning negotiation, and division of labour, which realises the deepening of group members’ cognition and the development of high-order thinking. Mathematical problem-solving realises individuals’ meaningful learning, and collaboration makes rich individual knowledge construction and reliable results.

2.2.2 Research Design

This study’s discussion of students’ MPSCL from a CKB perspective began with a quality evaluation of groups’ collaborative mathematical problem-solving results, selecting high- and low-performance groups as participants. Second, it developed an analytic framework and research tools. Finally, it traced students’ MPSCL process from the micro level to analyse their collaborative knowledge building. The research design map is shown in Fig. 2.1.

Fig. 2.1
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The design map of CKB research

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2.2.3 Sample Learning Task

Design-based methods were used to conduct an experimental investigation, taking the mathematical problem “Xiao Ming’s Apartment” as an example (see Appendix Task 1). The main reasons for choosing this problem as a learning task and conducting a case study are as follows:

First, this problem (the design of Xiao Ming’s apartment) has a realistic situation. It requires students to draw a possible graphical representation of Xiaoming’s apartment and mark each room's possible functions, length, and width. This situation is closely related to pupils’ future-oriented social life and is rooted in each student’s real-life experience. The concept of apartment exists in students’ cognitive schema, and their pre-knowledge and experience can provide a carrier for group collaboration, mathematical problem-solving, and learning.

Second, it is an open-ended problem. Because it has no unique solution, any solution that meets the task requirements and conforms to scientific facts and mainstream values is correct and reasonable. Therefore, the problem provides enough space for group collaboration, mathematical problem-solving, and learning.

Third, the difficulty of this problem is in line with the cognitive abilities of and can be solved by junior high school students. The mathematical knowledge, activity experience, and mathematical competencies involved in solving this problem are within the scope of junior high school students’ physical and mental development, in line with the characteristics of students’ cognitive development at this stage. Students can successfully complete the mathematical problem-solving task.

Fourth, it is representative for students to experience a mathematical process—identify key mathematical concepts from a real-world situation, extract primary mathematical knowledge, and bring the results back to real life for evaluation and reflection after mathematical activities such as abstraction, modelling, and problem-solving.

2.2.4 Research Participants

  1. 1.

    Pilot study: Evaluation of students’ collaborative problem-solving solutions. To understand the quality of collaborative mathematical problem-solving solutions, a two-dimensional evaluation framework for the completion and correctness of CPS solutions was constructed, and an evaluation table was developed, based on the existing literature on project-based learning, problem-based learning, and cooperative learning achievement evaluation (see Table 2.1). Through several rounds of discussion and revision with experts in the field of mathematics education and repeated coding verification combined with sample data, the reliability and validity of the evaluation framework and research tools were ensured to accurately evaluate the quality groups’ CPS solutions.

    Table 2.1 Solution quality evaluation form
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    Fig. 2.2
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    An example of a high-quality solution

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    Fig. 2.3
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    An example of a medium-quality solution

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    Fig. 2.4
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    An example of a low-quality solution

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  2. 2.

    Based on the pilot study “evaluation of students’ collaborative problem-solving solutions,” which provides the specific criteria, high- and low-performance student groups were selected as research participants. The researcher and a graduate student majoring in mathematics education independently rated the collaborative problem-solving solutions of 29 groups in three classes. In addition, where the scores of the two were inconsistent, a professor in mathematics education was invited to score the cases again to ensure quality evaluation results. On this basis, six high-performance and six low-performance groups were selected, as shown in Table 2.2.

    Table 2.2 Research participants
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Here, the score refers to the latest competency-oriented mathematics test results of the sample students (Guo et al., 2015), which is essential evidence teachers use to group students based on the principle of “homogeneity between groups and heterogeneity within groups.”

2.2.5 Research Method

This research adopted a mixed research paradigm. Literature review, video observation, content analysis, statistical analysis, social network analysis, and comparative study were comprehensively used to conduct this research.

  1. 1.

    Literature review. A literature review informed the whole research process, helping the researcher recognise the history and current situation of CKB research and other relevant research, clarify the academic positioning of this research, and learn from existing research ideas and methods to provide references for the research design. At the same time, the research’s results were incorporated into existing academic contexts for understanding and interpretation, and its innovations, shortcomings, and future research direction were clarified.

  2. 2.

    Video observation. Video observation of the 12 groups’ collaborative learning processes was conducted to capture a realistic view of student group collaboration and mathematical problem-solving, understand the students’ communication, discussion status, and interactive learning processes, and (combined with content analysis) make the interactive learning data coding more stable and objective (Man and Clarke 2019).

  3. 3.

    Content analysis. The coding unit was each student’s interactive dialogue sentences in the 12 groups. Each student’s interactive content was marked to indicate whether it conformed to and reflected the coding system’s definition of the index to ensure a detailed and objective description of the process and mechanism of students’ CKB.

  4. 4.

    Statistical analysis. Based on content analysis, the encoded data are further quantified to describe the junior high school students’ CBK behaviour processes. The statistical analysis methods in this research mainly involved descriptive statistical analysis, with the targeted goal of describing the basic form of the research data.

  5. 5.

    Social network analysis (SNA). Social network analysis is mostly used in the CSCL field to study the connections between social actors and the structural functions of these connections (Zheng, 2010). The interaction processes of the students in each group were analysed using SNA to understand the team interaction of students’ CKB.

  6. 6.

    Comparative study. Comparative study was used to understand the similarities and differences in the high- and low-performance groups’ CKB behaviour processes to further analyse students’ MPSCL performance and characteristics and understand their CKB.

2.2.6 Analytical Framework

Based on Pólya’s (1945) and Schoenfeld’s (1992) mathematical problem-solving process models, and referring to Gunawardena et al.’s (1994) and Stahl’s (2000) knowledge-building interaction models, a preliminary analysis framework was formed. The framework was modified by incorporating sample data and repeated observation and refinement to create a three- and six-stage coding system for junior high school students’ CKB levels (see Table 2.3).

Table 2.3 Coding system of CKB process
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The CPS learning process involves knowledge transmission and acceptance and interactions between students for knowledge construction. Based on the mathematical problem-solving process model and referencing Jiang and colleagues’ coding schema for evolutionary knowledge construction in an information technology environment (Jiang et al., 2019), the viewpoints coding system was further constructed by repeatedly observing the sample data, as shown in Table 2.4.

Table 2.4 Coding system of CKB viewpoints
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2.2.7 Research Implementation and Data Processing

Taking Grade 7 students in T School District of B city as an example, an MPSCL activity was carried out in six classes of three schools in the second semester of Grade 7. Students’ process data were recorded and transcribed into text by means of classroom video recording and students’ dialogue tape recording. Twelve groups of interactive text data were formed with a total of 3244 interactive dialogues and more than 90,000 words of transcripts for coding analysis. Based on the basic steps of learning analytics (Li et al., 2012) and CKB interactive analysis (Shaffer et al., 2016), this study designed a process for analysing junior middle school students’ CKB, as shown in Fig. 2.5.

Fig. 2.5
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CKB analysis process

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2.2.8 Description of Reliability and Validity

The validity guarantee of this research is based on two aspects. First, it relied on research theories and models that have high international and domestic recognition and are based on a large body of previous research to form a preliminary framework for coding junior middle school students’ CKB. Second, based on the repeated exploration of research data, the preliminarily determined coding system was modified and improved, then submitted to senior experts and scholars in mathematics education for review and revision to obtain expert validity support.

In this research, repeated coding ensured coding consistency. Based on the initial coding, two high- and low-performance groups were randomly selected to verify the coding. Coding consistency between the groups was over 90%, indicating good coding stability.

2.3 Results

The following research results were formed through quantitative and qualitative analysis of the high- and low-performance groups’ mathematical problem-solving data.

2.3.1 General CKB Situation

  1. 1.

    High-performance groups. The number of sentences and proportion distribution of high-performance groups is shown in Table 2.5. The CKB discussion refers to the substantive and constructive discussion carried out by students to solve the mathematical problems of “Xiaoming’s Apartment.” It includes 1408 interactive sentences, accounting for 89.33% of the total, indicating that the students in high-performance groups gave full play to their collective wisdom, contributed their personal views and knowledge when participating, negotiating, and discussing, and integrated their collective strength to promote solutions to mathematical problems. Further analysing the CKB process in each high-performance group revealed differences in the proportion between the number of sentences and irrelevant discussions. For example, Group 03aS5 students spoke the most in discussions while Group 02aS1 students spoke the least, a difference of 203 sentences.

    Table 2.5 Number of sentences and proportion distribution of high-performance groups
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    In addition, tracking the irrelevant discussions of each high-performance group identified four types of irrelevant discussions. The first was discussions about completing the formalised CPS learning task requirements. For example, the teacher asked students in each group to fill in their names on the task paper based on the grouping list, and the students said something about this. The second type was irrelevant discussions deriving from the CKB process (deviation topic discussions), which accounted for a large proportion of all discussions. The third type was irrelevant discussions caused by differences of opinion among team members, while the fourth included irrelevant discussions while implementing the solution, such as discussing who drew well or asking others for a pencil, ruler, eraser, etc.

  2. 2.

    Low-performance groups. The low-performance groups’ sentence and proportion distributions are shown in Table 2.6. There were 1358 CKB sentences in low-performance groups, accounting for 82.91% of the total, indicating that the students in low-performance groups were jointly building knowledge in the mathematical problem-solving process and integrated their collective strength to promote mathematical problem-solving. Further analysis showed differences in each low-performance group’s number of CKB sentences and proportion of irrelevant discussions. For example, Group 03aS2 communicated and discussed the most (388 sentences), while 04aS4 had the fewest communications and discussions (166 sentences).

    Table 2.6 Number of sentences and proportion distribution of low-performance groups
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    In addition, there were three types of irrelevant discussions in the low-performance groups. The first concerned completing the formal CPS task requirements, such as communications about controlling problem-solving time. The second group of irrelevant discussions derived from the CKB process, accounting for a large proportion. Finally, group members had some irrelevant discussions when implementing mathematical problem solutions, such as discussing whose academic performance was good, looking for pencils and rulers, etc.

  3. 3.

    Comparison of the groups’ general CKB situations. The sentence and proportion distribution between the high- and low-performance groups is shown in Table 2.7. There were 1593 sentences CKB spoken by high-performance groups, only 57 fewer than were spoken by low-performance groups (1650). This shows there was little difference in the total amount of CKB communication and discussion between the high- and low-performance groups. The proportion of CKB discussions in the high-performance group was 6.42% higher than in the low-performance group, indicating the former had a relatively more CKB around the mathematical problems of “Xiaoming’s Apartment” and a somewhat more efficient mathematical problem-solving process.

    Table 2.7 Number of sentences and proportion distribution of high- and low-performance groups
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    In addition, the high- and low-performance groups had similar types of irrelevant discussion content, i.e., content related to completing the formalised CPS learning task requirements, topic deviations (e.g., when discussing the design scheme for “Xiaoming’s apartment”), or implementing mathematical problem solutions.

2.3.2 Trajectory of CKB

  1. 1.

    High-performance groups. In solving collaborative problems, the high-performance groups generated 1187 views, averaging 197.83 per group and 49.45 per capita. The high-performance groups’ cumulative view distribution is shown in Table 2.8. Shared views accounted for the highest proportion, mainly because team members sought mathematical problem information, shared their views on the problem, and explained their views. The discussion view was mainly used to find and explore inconsistent views, concepts, or statements, discuss problems, clarify or distinguish meanings, similarities, and differences in terms and views, integrate views, and deepen understanding. The proportion of sublimated views was relatively low, mainly because the group members summarised and sublimated the fragmented and scattered views in the negotiation and discussion process, which changed their knowledge structure and thinking mode and became their final basis for forming and optimising mathematical problem solutions.

    Table 2.8 Number of views and the percentage of high-performance groups
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  2. 2.

    Low-performance groups. The low-performance group generated 1340 views, averaging 223.33 per group and 55.83 per capita. The distribution of the low-performance groups’ views is shown in Table 2.9. First, shared views accounted for up to 55.83% of the total, highlighting that each student could freely advance opinions and suggestions and state their personal views and ideas. Second, the discussion view accounted for 36.34%, mainly involving the evolution of existing views, the integration of similar or related views, the demise of naive, wrong, or meaningless views, and the emergence of new views. Finally, the sublimation view accounted for 10.75%, which was relatively low.

    Table 2.9 Number of views and the percentage of low-performance groups
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  3. 3.

    The comparison of CKB trajectory. The number of views in different groups is shown in Table 2.10. Low-performance groups contributed more views than high-performance groups, showing a higher level of thinking divergence (to a certain extent). In detail, the percentage of shared views was 17.11% lower in the high-performance group than in the low-performance group, the discussion view was 5.23% lower, and the sublimation view was 19.43% higher. In addition, there were differences in the evolution of views between the high- and low-performance groups. The high-performance group showed a better spiral, while the low-performance group had a messy view of evolution.

    Table 2.10 Number of views of high- and low-performance groups
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2.3.3 Level of CKB

  1. 1.

    High-performance groups. CKB level is a macro description of the process quality for students’ interactive learning and reflects the effect of constructing knowledge together in the learning community (Shi, 2011). Table 2.11 shows the number and proportion distribution of talking sentences from high-performance groups, divided by their CKB level. There were 260 deep-level sentences (16.32%), 604 middle-level sentences (37.92%), and 559 shallow sentences (35.09%). This shows that the high-performance groups could reach a deep-seated CKB level, showing that MPSCL had some effect. Each group had high-order interactive dialogues, promoted in-depth processing of views, and promoted the CKB process.

    Table 2.11 The number and proportion distribution of CKB level of high-performance groups
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    Detailed analysis of the above results revealed that although each high-performance group’s CKB reached a deep level, the proportion of deep-level sentences was not high. Medium-level CKB dominated interactive dialogue, but some groups (e.g., 02aS1, 03aS4, and 03aS7) had mainly shallow-level interactions. The high-performance groups’ interactive dialogue data were coded and counted based on the CKB stage, as shown in Table 2.12. The high-performance groups’ CKB reached the deep-seated “reflection and evaluation of achievements” stage. For example, Group 03aS5 had the highest CKB and a higher proportion of deep-level CKB, indicating its CKB had a good effect.

    Table 2.12 The number and proportion distribution of CKB level at each stage of high-performance groups
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  2. 2.

    Low-performance groups. The number and proportion distribution of the low-performance groups’ CKB levels is shown in Table 2.13. On average, the groups had 74 deep-level CKB interactions (5.41%), 670 medium-level (48.98%), and 614 shallow-level (44.88%). This shows that the low-performance group also reached deep-level CKB, with high-order interactive dialogue in each group, indicating their collaborative learning on the topic of “Xiaoming’s apartment” had an effect.

    Table 2.13 The number and proportion distribution of CKB level of low-performance groups
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    Although the low-performance group reached deep-level CKB, the proportion was low; overall, medium-level CKB dominated, with some groups (e.g., 02aS2 and 04aS4) being dominated by shallow-level CKB. This shows that low-performance groups’ deep-level CKB was not sufficient, and their collaborative learning process was not efficient. The number and proportion distributions for CKB levels at each stage are shown in Table 2.14. The low-performance groups’ CKB reached the deep-seated “Reflection and evaluation of achievements” stage. For example, Group 03aS2 had the most dialogue sentences, but a relatively low proportion of deep-seated knowledge building.

    Table 2.14 The number and proportion distribution of CKB level at each stage of low-performance groups
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  3. 3.

    Comparison of the groups’ CKB levels. The proportion distribution of the different groups’ CKB levels is shown in Table 2.15. Although all groups’ CKB reached a deep level, medium-level CKB dominated overall, accounting for the highest proportion in both the high- and low-performance groups. At the same time, the high-performance groups’ had a much higher proportion of deep-seated CKB (10.91%), indicating that the low-performance groups’ deep-seated CKB was insufficient.

    Table 2.15 The high- and low-performance groups’ number and proportion distribution of CKB level
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    Table 2.16 shows the number and proportion distribution of CKB levels at each stage. Although the students in the high- and low-performance groups reached the stage of “Reflection and evaluation of achievements,” the low-performance groups’ proportions of “content verification and adjustment,” “consensus reaching and application,” and “reflection and evaluation of achievements” stages were much lower than in the high-performance groups. At the same time, students in the low-performance groups had a greater proportion of different views (8.8% higher) than their peers in the high-performance group.

    Table 2.16 The high- and low-performance groups’ number and proportion distribution of CKB level at each stage
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2.3.4 Team Interaction of CKB

  1. 1.

    High-performance groups. MPSCL in high-performance groups led to the emergence of interactive groups. Most group members spoke actively in the CKB process, promoting the circulation and generation of knowledge among groups. Group 01aS2’s social network relationship is shown in Fig. 2.6, as an example. S1 and S4 continually communicated around the “Xiaoming’s apartment” design task, negotiating views, exchanging meanings, and forming a subgroup of two people.

    Fig. 2.6
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    01aS2 CKB social network relationship

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    Based on the students’ speech frequency, high-performance group members showed better participation, with average CKB-related speech frequencies of 66.38 and 59.29. This interactive group had a variety of team interaction modes, including two-person and three-person interactive subgroups. The smaller the number of subgroups, the less balanced the group members’ speeches. For example, the number of speeches in Group 01aS2 is shown in Fig. 2.7. The group featured a typical two-person interactive subgroup. S4 and S1 talked the most (140 and 119 sentences, respectively), while S3 spoke the least (11). Part of Student 3’s speech had nothing to do with mathematical problem-solving, and the relevant content they did offer was at a shallow level, showing insufficient participation in interactive learning.

    Fig. 2.7
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    Number of speeches of 01aS2

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  2. 2.

    Low-performance groups. Low-performance groups’ CKB also promoted the emergence of interactive groups. Most group members could actively speak and contribute knowledge to the learning community. Group 01aS1’s social network relationship is shown in Fig. 2.8, as an example. S1 and S3 constantly exchanged views and discussed the design of “XiaoMing’s Apartment,” forming a two-person subgroup.

    Fig. 2.8
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    01aS1 CKB social network relationship

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    The students in the low-performance group also showed good participation with average CKB-related speaking frequencies of 68.75 and 57. There were diverse group interaction modes, including two-person and three-person interaction subgroups. For example, the number of speeches in Group 01aS1 is shown in Fig. 2.9. The group featured a typical two-person interactive subgroup, with S1 and S3 interacting a lot (150 and 105 sentences, respectively), while S4 spoke the least (47). Some of S4’s speeches had nothing to do with mathematical problem-solving, and the CKB-related content they offered was at a shallow level, indicating insufficient participation in interactive learning.

    Fig. 2.9
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    Number of speeches of 01aS1

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  3. 3.

    Comparison of teams’ CKB interactions. The data show that the high- and low-performance groups’ CKB promoted the emergence of interactive groups. Most group members spoke actively, participated in exchanges, and contributed their personal knowledge to the learning community, promoting the generation and flow of information among group students. For example, S1 and S3 (in Group 01aS1) had continual communication and dialogue around mathematical problems, negotiating views, exchanging meanings, and forming a two-person subgroup.

    Comparative analyses of the speech frequencies in the high- and low-performance groups revealed that students’ interaction groups in the high- and low-performance groups had diverse interaction modes—mainly two-person and three-person interaction subgroups. Some individual students rarely participated in MPSCL activities, rarely interacted with other group members, and played the role of listener. For example, Student 4 in Group 02aS6 almost never spoke in the group cooperative mathematics problem-solving process, showing insufficient participation in interactive learning.

2.4 Discussion

This research has investigated the similarities and differences in high- and low-performance junior high school student groups’ CKB behaviour processes by assessing the groups’ CPS quality to better understand the students’ CKB. This section expounds on the main findings.

Existing studies have researched CKB from different perspectives. One is to explore students’ CKB based on the problem-solving-based collaborative learning task, as different learning tasks affect group students’ CKB differently. The second is to explore CKB from the perspective of learning resources and learning environment, as students’ willingness and ability to propose personal thoughts and views depend on having good learning resources and learning environments. The third is to explore the CKB based on students’ knowledge and experience. When dealing with new problems, students must establish a conceptual system to have an opportunity to succeed; this concept is not simply passed from teachers to students, but must be understood by students themselves. In addition, students’ mathematical competencies, emotions, attitudes, values, and “21st-century skills” (represented by critical thinking, innovative thinking, and collaborative problem-solving) will affect the CKB process. The fourth perspective explores CKB based on each group member’s active participation and meaningful interaction, as group power is the fundamental factor to accelerate the process of group CKB and promote the generation of intelligent products (Diez-Palomar et al., 2021).

Although the collaborative problem-solving-based learning task, learning resources and learning environment, students’ knowledge and experience, and mathematical competencies, emotions, attitudes, values, and “21st-century skills” affect student groups’ CKB. However, by examining and comparing high- and low-performance groups CKB, it is necessary to unlock the black box of this comprehensive and critical learning behaviour processes in determining whether a problem can be successfully solved. At present, few studies focus on students’ face-to-face group collaboration and problem-solving in real classrooms from the CKB perspective, nor analyse and explain students’ MPSCL from this perspective. Therefore, this research focused on a junior high school mathematics classroom, paying attention to students’ collaborative learning processes and results and using design-based principles to investigate students’ micro-level CKB behaviour processes by comparing high- and low-performance groups’ mathematical problem-solving. Its findings are discussed below.

First, although there was a proportion of irrelevant discussion in both the high- and low-performance groups, CKB-related discussions predominated; that is, students could closely focus on the mathematical problems of “Xiaoming’s apartment,” giving full play to their collective wisdom, contributing their personal views and knowledge through participation, negotiation, and discussion, and integrating collective strength to promote the mathematical problem’s solution. The high- and low-performance groups had similar types of irrelevant discussions, such as irrelevant discussions related to completing the formalised CPS task requirements, derived by group members in the CKB process (deviated topic discussions), or generated by group members when implementing the mathematical problem-solving solutions. In addition, there were some differences in the high- and low-performance groups’ general CKB processes. For example, the high-performance groups had slightly fewer MPSCL information interactions (1593) than those in the low-performance group (1650). However, the high-performance groups had a higher proportion of CKB-related discussions than the low-performance groups (less than 6.42%), indicating a higher proportion of CKB related to “Xiaoming’s apartment” and fewer irrelevant discussions, macroscopically reflecting the high-performance group’s more efficient CKB.

Second, the junior high school students’ CKB went through six stages: information sharing and understanding, discovery and clarification of differences, content negotiation and co-construction, content verification and adjustment, consensus achievement and application, and reflection on and evaluation of achievements. There were many kinds of view evolution paths and similarities in the view evolution paths of the high- and low-performance groups. In particular, shared views predominated in both groups, followed by discussion views and then sublimation views. Specifically, the high-performance groups’ shared views accounted for 38.72% of the total, followed by discussion views (31.11%) and sublimation views (a relatively low 30.18%). The low-performance groups’ shared views accounted for 55.83% of the total, followed by discussion views (36.34%) and sublimation views (10.75%). In addition, there were some differences in the two groups’ CKB evolution paths. For example, the proportion of sublimated views in the high-performance group was much higher than in the low-performance group. Students in the high-performance group showed a better view evolution spiral, indicating the low-performance groups’ deep-seated interactions were deficient, and their view evolution process lacked continuity.

Third, although the junior high school students’ CKB reached a deep level and there was interactive discussion in the “reflection and evaluation of achievements” stage, most discussions were at a medium or shallow level, indicating that each group’s collaborative learning in the “Xiaoming’s apartment” theme had a certain effect, and their high-level thinking participation was insufficient. In addition, there were differences in the high- and low-performance groups’ CKB levels. For example, students in high-performance groups had a much higher proportion of deep knowledge construction than students in low-performance groups (10.91%), especially in the “consensus reaching and application” and “achievement reflection and evaluation” stages. The proportion of high-performance group students in the “divergence and clarification of views” and “content negotiation and co-construction” stages is 8.8%, lower than in the low-performance group. This further proves the dilemma of insufficient in-depth interactive learning and the high proportion of different views among students in the low-performance group.

Fourth, generally, the junior high school students’ participation in CKB was good. They could solve mathematical problems through active speech and communication to form interactive groups, generate information, and make it flow between different individuals, indicating that both the high- and low-performance groups carried out MPSCL. Most group members spoke actively, participated in communications, and contributed personal knowledge to the learning community, promoting the generation and flow of information among groups. At the same time, the interaction groups had a variety of interaction modes, mainly including two-person and three-person interaction subgroups. There was also a phenomenon in which individual students rarely participated or interacted with group members, such as in high-performance Group 01aS2 and low-performance Group 02aS6.

2.5 Conclusion

As the above outline indicated, this chapter has considered MPSCL’s unique teaching value for integrating “21st-century skills” and promoting practical and innovative talents, aiming at investigating junior high school students’ CKB process based on a comparison of high- and low-performance groups’ mathematical problem-solving for promoting student groups learning efficiency and performance.

Junior high school students could carry out CKB with mathematical problem-solving as the core. CKB-related discussions accounted for over 80% of all discussions in both the high- and low-performance groups. Student groups’ CKB went through six stages and there were many kinds of view evolution paths with shared views accounting for the highest proportion, followed by discussion views and sublimation views, respectively. CKB reached the deep level, but the proportion was low. The junior high school students mainly had medium- and shallow-level CKB discussions, accounting for over 35% of the total. Generally, the junior high school students’ participation was good and had a variety of interactive modes, mainly including two-person and three-person interactive subgroups. Some students rarely participated in the intra-group collaborative knowledge building process or interacted with other group members.

However, there were some differences in the high- and low-performance groups’ CKB processes. Specifically, high-performance groups had slightly fewer MPSCL information interactions, a higher proportion of CKB-related discussions, and fewer irrelevant discussions than low-performance groups. The high-performance groups had fewer views than the low-performance groups but a much higher proportion of sublimation views and showed a better view evolution spiral, while low-performance group students’ view evolution was relatively chaotic. High-performance groups had a higher proportion of deep-level CKB, a higher proportion of students in the “information sharing and understanding” and “content verification and adjustment” stages, and a lower proportion of students in the “different and clear views” and “content negotiation and co-construction” stages.

Since the twenty-first century, achieving the integration and development of “twenty-first century skills”, such as collaboration/cooperation and problem-solving in mathematics education, and promoting the cultivation of practical and innovative talents has become a global education concern(Cao and Sun, 2019; OECD, 2017a, 2017b). As practical and innovative talents, their significant characteristics are reflected in their specialised knowledge structure in specific fields, their capabilities to deeply represent real-world problems, identify problem meaning patterns, and design flexible problem-solving strategies, which require deep-level knowledge building(Sawyer, 2012; EU, 2008). An experimental survey of junior high school student groups’ MPSCL and examining their CKB based on the comparison of high- & low-performance groups’ mathematical problem-solving in the classroom, we had a certain understanding of students’ CKB process. These CKB characteristics could provide evidence for enhancing MPSCL, especially for teachers’ design of new learning task, guidance for students’ collaboration/cooperation, and problem-solving. From this perspective, further research is needed to explore student groups CKB addressing different collaborative problem-solving tasks, expanding student groups, and understanding how to promote the occurrence of higher-order thinking during MPSCL.