In the era of artificial intelligence, the significance of creativity has become increasingly evident, along with a shift in its forms and manifestations. In particular, group creativity has emerged as a dominant paradigm, as collaborative creative processes are now widely observed across various domains. This perspective is particularly relevant in mathematics education. Research has firmly established the importance of fostering creativity in mathematics, identifying it as a key educational objective (Harpen & Sriraman, 2013; Schoevers, Kroesbergen, & Maria, 2018). While research underscores its significance, existing studies primarily focus on individual mathematical creativity (e.g., Silver, 1997;  Leikin & Lev, 2013; Bal-sezerel & Sak, 2022), with limited attention to how collaborative mathematical creativity unfolds in classroom settings. Some scholars have begun to explore the nature of GMC and its instructional implications. These studies examine how students collaboratively construct collective mathematical understandings and how group interactions foster mathematical problem-solving (e.g., Martin, Towers, & Pirie, 2006; Aljarrah & Towers, 2023; Levenson & Molad, 2022; Schindler & Lilienthal, 2022). 

However, research on the assessment of GMC remains in its early stages. Studies on the assessment of mathematical creativity have generally lagged behind research on its conceptualization and teaching. Assessments of mathematical creativity, often based on problem-solving or problem-posing tasks, still primarily focus on divergent thinking (Leikin & Sriraman, 2022). These assessments typically use the three indicators of fluency, flexibility, and originality (e.g., Levenson & Molad, 2022; Silver, 1997; Zainudin et al., 2019), with an emphasis on evaluating the outcomes of students’ thinking. Guided by sociocultural theories of creativity, which emphasize the interaction between creative perspectives and actions, this study constructs the core elements of GMC from a process-oriented perspective. It integrates the strands of group collaboration and mathematical creativity as foundational components of the framework. Therefore, this study seeks to address the following two sub-questions: (1) How is GMC conceptualized? (2) What are the key dimensions of the GMC assessment framework, and how are they defined? The assessment framework developed in this study can offer valuable theoretical support for mathematics teachers in assessing and nurturing students' GMC and provide valuable insights for fostering group creativity across disciplines.

Sociocultural theory of creativity (Glăveanu, 2020) serve as the foundational theoretical lens for defining GMC in this study. Unlike psychological perspectives that focus on internal cognitive mechanisms, sociocultural theory define creativity as emerging from interactions between individuals and their environment. This theory explains how creators engage in co-creative processes within a group, shaped by the interaction and development of perspectives and actions. Shifts in perspective reflect fundamental changes in one’s thinking about phenomena, which in turn lead to creative actions (Glăveanu, 2020). For GMC, the term “perspective” specifically refers to the mathematical perspective—a lens through which students observe, interpret, and make sense of the real world mathematically. 

Drawing on sociocultural theory, this study positions the interaction and development of mathematical perspectives as the central driver of GMC. Through dialogue, negotiation, and evaluation of perspectives, students are able to use mathematical thinking tools to emerge with mathematical creativity during the collaboration process. This process consists of two interwoven dynamics: The Group Collaboration Dynamic defines the “actors” (student groups) and “actions” (how they collaborate to generate group creativity), which focuses on how group generate new ideas and solutions through dialogue, coordinate, and co-evaluate; The Mathematical Creativity Dynamic defines the “artifacts” of GMC, which explores how group produce creative mathematical outputs (e.g., new insights mathematically, new mathematical connections, and alternative mathematical strategies) through mathematical thinking tools (e.g., abstraction, reasoning, and transformation).

This study adopts a qualitative research approach, drawing on multiple data sources, including student videos, worksheets, artifacts, and expert interview recordings. The data were analyzed using a combination of the Critical Incident Technique (CIT), interaction analysis, artifact analysis, and text analysis. The research process consisted of three key phases: (1) theoretical construction of the assessment framework, (2) student investigation, and (3) expert interviews. First, grounded in the sociocultural theory of creativity, this study developed the "Volcanic Model" and an assessment framework for GMC. To refine this framework, an empirical analysis was conducted on elementary students' performance in open-ended mathematical collaboration activities. Using the preliminary framework as an "observational lens," this study examined the collaborative interactions of student groups at different proficiency levels (two students per group, totaling six students). The aim was to provide empirical validation of student performance corresponding to the framework’s observation criteria, as well as to refine the framework by identifying new key indicators or modifying/removing those misaligned with students’ cognitive processes. In studies of group creativity processes—such as the collaborative emergence of ideas—interaction analysis is a widely recognized method (Sawyer & DeZutter, 2009). This study specifically captured students' "mini-c" key events and applied interaction analysis to examine patterns of group creativity. Finally, in-depth expert interviews were conducted with ten scholars specializing in mathematics education and creativity research. A combination of purposive and convenience sampling ensured a diverse yet relevant selection of experts. The interview data were subjected to text analysis to extract key themes from expert feedback, facilitating a rigorous and iterative refinement of the final assessment framework.

This study, based on sociocultural theories of creativity and drawing from existing research, develops the “Volcanic Model” of group mathematical creativity by combining two interrelated dynamics: group collaboration and mathematical creativity dynamics. The “Volcanic Model” comprises three dimensions and six components: (1) Dialogue and Understand: Describe the mathematical perspective of problem-solving and engage in open dialogue with others' perspectives; Clarify misunderstandings of one's own perspective and express new, generalized insights mathematically. (2) Coordinate and Connect: Engage in perspective-taking to explore mathematical strategies from different perspectives, and negotiate disagreements within the group; Embrace differences and discover new mathematical connections between different strategies through conjecture, analogy, and induction. (3) Co-evaluate and Transform: Evaluate existing mathematical strategies within the group to align with a common goal; Utilize feedback from others to shift fixed perspectives, reconsider the problem and generate alternative strategies. These dimensions reflect the emergent nature of GMC. A new assessment framework for GMC is developed based on the above “Volcanic Model”, refining both student performances and assessment examples. Specifically, the "Dialogue and Understand" element can be seen as the "Preparation and Incubation" stage. During this stage, students engage in dialogue as the primary collaborative action, expressing new mathematical understandings characterized by mathematical formulations detached from specific contexts. The "Coordinate and Connect" element corresponds to the "Illumination" stage. In this stage, coordination is the central collaborative action, through which students discover new mathematical connections aimed at establishing intrinsic relationships between abstract mathematical objects. The "Co-evaluate and Transform" element represents the "Verification" stage. In this stage, students engage in co-evaluation as the primary collaborative action, shifting their fixed perspectives to generate alternative strategies. This transformation emphasizes mathematical conversion thinking, with a strong focus on overcoming cognitive biases and establishing long-range connections.

Aljarrah, A., & Towers, J. (2023). The Emergence of Collective Mathematical Creativity Through Students’ Productive Struggle. Canadian journal of science mathematics and technology education, 22, 856-872. Bal-Sezerel, B., & Sak, U. (2022). Mathematical Creativity Test (MCT) development for middle school students. Turkish Journal of Education, 11(4), 242-268. Glăveanu, V. P. (2020). A sociocultural theory of creativity: Bridging the social, the material, and the psychological. Review of General Psychology, 24(4), 335-354. Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201-221. Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM-Mathematics Education, 45(2), 183-197. Leikin, R., & Sriraman, B. (2022). Empirical research on creativity in mathematics (education): from the wastelands of psychology to the current state of the art. ZDM-Mathematics Education, 54(1), 1-17. Levenson, E. S., & Molad, O. (2022). Analyzing collective mathematical creativity among post high‑school students working in small groups. ZDM-Mathematics Education, 54(1), 193-209. Martin, L. C., Towers, J., & Pirie, S. E. B. (2006). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning, 8(2), 149-183. Sawyer, R. K., & DeZutter, S. (2009). Distributed creativity: How collective creations emerge from collaboration. Psychology Aesthetics Creativity Arts, 3(2), 81–92. Schindler, M., & Lilienthal, A. J. (2022). Students’ collaborative creative process and its phases in mathematics: an explorative study using dual eye tracking and stimulated recall interviews. ZDM-Mathematics Education, 54(1), 163-178. Schoevers, E. M., Kroesbergen, E. H., & Maria, K. (2018). Mathematical creativity: a combination of domain-general creative and domain-specific mathematical skills. The Journal of creative behavior, 54(2), 242-252. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM-Mathematics Education, 97(3), 75-80. Walsh, C. S., Chappell, K., & Craft, A. (2017). A co-creativity theoretical framework to foster and evaluate the presence of wise humanising creativity in virtual learning environments (VLEs). Thinking Skills & Creativity, 228-241. Zainudin, M., Subali, B., & Jailani. (2019). Construct Validity of Mathematical Creativity Instrument: First-Order and Second-Order Confirmatory Factor Analysis. International Journal of Instruction, 12(3), 595-614.