Ali Bicer , Jung Colen , Mi Yeon Lee

DOI:10.7468/jksmed.2025.28.3.233 Vol.28(No.3) 233-237, 2025

This special issue explores mathematical creativity across diverse contexts including curriculum materials, instructional practices, teacher preparation, professional development, and classroom interactions. Grounded in the perspective that mathematical creativity is a dynamic ability to generate new ideas, processes, or products that are novel to learners, the issue brings together theoretical and empirical studies that examine how creativity can be fostered through curriculum design, open-ended tasks, problem posing, puzzle-based learning, collaborative proving, and inquiry-based instruction. The eight contributions highlight creativity as both an individual and collective endeavor, demonstrating that it can be nurtured from elementary classrooms to higher education and in teacher professional development. At the same time, the papers critically address challenges in assessment, systemic barriers, and teacher preparation and development. Collectively, this issue makes the case that creativity is not peripheral but central to mathematics education that positioning exploration, curiosity, and innovation as essential for advancing student learning and reshaping instructional practice.

mathematical creativity, creative thinking in mathematics, creativity-directed practices

Shin-chan Wen , Qiaoping Zhang

DOI:10.7468/jksmed.2025.28.3.239 Vol.28(No.3) 239-261, 2025

Cultivating students’ creativity to develop their problem-solving abilities has become a critical goal in mathematics education. However, evidence-based studies are limited, especially in the field of gifted mathematics education. Such research not only helps determine the effectiveness of different curriculum materials in fostering students’ mathematical creativity but also documents successful practices for future reference and enhancement. This study employed a case study approach to put theoretical strategies into practice for enhancing mathematical creativity among gifted primary school students. Drawing on the five core principles of mathematical creativity and a problem-solving model, a curriculum incorporating challenging and open-ended mathematical problems was designed and implemented. The study lasted 10 weeks and involved 21 gifted fifth grade students from a primary school in Taiwan. Data were collected through classroom observations and video recordings, followed by qualitative analysis. The findings suggest that, in terms of classroom design, collaborative learning and reflective practices can enhance students’ mathematical creativity. In terms of mathematics question design, the integration of open-ended problems and multistep tasks can substantially increase the diversity and originality of students’ problem-solving strategies. This study puts theoretical insights into practice. It provides practical implications for the development of curricula material that aims to foster mathematical creativity in primary education and highlights the pivotal role of creativity in pedagogical practice.

mathematical creativity, case study, gifted education, open-ended problems

Mark Applebaum , Viktor Freiman

DOI:10.7468/jksmed.2025.28.3.263 Vol.28(No.3) 263-297, 2025

This article explores puzzle-based learning (PBL) to develop creative thinking in pre-service mathematics teachers (PTs). Through a case study involving a magic square puzzle, PTs engaged in trial-and-error, pattern recognition, and collaborative reflection, moving from surface-level problem-solving to deeper mathematical inquiry. Guided by Polya's framework of "looking back," PTs revisited and refined their initial strategies, leading to a "feeding forward" process where each solution attempt informed further questioning, exploration, and refinement. The study highlights how PBL fosters essential 21st-century skills, such as adaptive reasoning and reflective practice, preparing future educators to guide their students through similarly complex, open-ended problems. We conclude that integrating puzzles into teacher education programs can enhance PTs’ problem-solving abilities and equip them with strategies to foster a culture of inquiry and creative thinking in their future classrooms.

mathematical creativity, prospective teachers, magic squares, solving problems

Ryan D Fox , Anna M Payne

DOI:10.7468/jksmed.2025.28.3.299 Vol.28(No.3) 299-318, 2025

One opportunity to increase mathematical creativity among prospective elementary teachers (PETs) is to encourage their creation of multiple solution paths and algorithms to typical questions found in mathematics curricula and tasks. In this study, we asked prospective elementary teachers currently enrolled in mathematics teaching methods courses in two separate regions of the United States to complete a survey about generating multiple solutions to two two-digit whole-number multiplication questions and to reflect on a mathematics teacher educator showing them via video recordings three approaches each to two multi-digit whole-number multiplication questions. In this report, we will focus on the PETs’ generation of multiple solutions to the multiplication questions. Although most PETs included an algorithm commonly taught in American mathematics textbooks at the elementary level, many study participants expressed the same solution in different ways. The expression of familiar ideas in new ways affords mathematics teacher educators to use their limited time in mathematics methods classes to present PETs familiar content (how to teach multiplication) and new-to-them content (mathematical creativity). By doing so, PETs will be able to enter the classroom well-prepared to use their creative knowledge in their mathematics teaching.

Pedagogical knowledge, multiplication, algorithms, mathematical creativity

Jung Y Colen , Amy Lein

DOI:10.7468/jksmed.2025.28.3.319 Vol.28(No.3) 319-338, 2025

This paper showcases the development and implementation of a year-long, job-embedded professional development (PD) program designed for a small private elementary school. Utilizing an action research framework of planning, acting, observing, and reflecting, the PD aimed to enhance teachers' pedagogical content knowledge (PCK) and foster their mathematical creativity, ultimately facilitating students' creative thinking in mathematics. The findings suggest the importance of sustained, iterative support in PD to cultivate teachers' confidence and ability to implement creative pedagogies, thereby transforming mathematics education to value inquiry and creative reasoning.

Professional development, mathematical creativity, pedagogical content knowledge, action research, teacher education

Hyunkyung Kwon

DOI:10.7468/jksmed.2025.28.3.339 Vol.28(No.3) 299-319, 2025

There is growing recognition of the importance of fostering creativity in education, particularly in mathematics. Creativity supports not only problem-solving but also innovation and critical thinking, essential for academic and future success. Despite this, mathematics is often seen as rigid and abstract, causing anxiety or disinterest among students. In reality, mathematics requires imagination and innovation. Thus, it is crucial to prepare preservice teachers to teach mathematics creatively. However, many lack the necessary skills and positive perceptions due to limited exposure to mathematical creativity in their own education. This study explored how cooperative learning strategies―where students work collaboratively―affect preservice teachers’ perceptions of creativity. Forty-three preservice teachers enrolled in a mathematics methods course participated in the study, which used a mixed-methods design. Data were collected through pre- and post-surveys, including Likert scale items and open-ended questions. Analyses included descriptive statistics, paired-sample t-tests, and Cohen’s d to determine the magnitude of change, along with thematic analysis for qualitative insights. Results revealed a statistically significant improvement (d = 0.63, p < 0.05) in participants’ perceptions of creativity following their engagement in group work. Additionally, preservice teachers expressed a strong interest in incorporating creativity-enhancing strategies into their future teaching practices. These findings suggest that collaborative learning approaches can effectively enhance preservice teachers’ appreciation of creativity, with potential long-term impacts on their instructional methods. The study advocates for integrating cooperative learning in teacher preparation programs to foster creative, confident mathematics educators equipped to inspire future generations of problem solvers.

Mathematical creativity, collaborative learning, preservice teachers, mathematics education

Amanda Lake Heath

DOI:10.7468/jksmed.2025.28.3.361 Vol.28(No.3) 299-327, 2025

Working creatively and producing mathematical ideas collaboratively is a cornerstone of the professional work of mathematicians, thus it is critical to engage undergraduate students in these practices for them to grow from novice to expert in the mathematical community. Very little, however, is known about how undergraduate students perceive themselves and their classmates as creative through collaborative activities. In this study, I use a lens of participatory intersubjectivity to explore a single case of three undergraduate students from the United States engaged in in-class collaborative mathematical proving. Written individual narrative data and group stimulated-recall interview data were used to investigate how students experienced creativity at both the individual and collective levels during their collaboration. Results indicate that the collaborative team engaged in a proving process characterized by the emergence of two distinct initial ideas for approaching the proving task, a decision to pursue one of these ideas, and an eventual divergence by one group member from her peer’s idea to revisit her initial intuition for the proof. Moreover, the individual reflections of each group member indicate that different moments of the collaborative proving process facilitated the students’ creative contributions to the proof. I describe potential instructional implications as well as directions for future research on instruction to foster collaborative creativity and more robustly understand collaborative mathematical creativity as a construct.

Creativity, collaboration, intersubjectivity, proof

Yanhui Xu

DOI:10.7468/jksmed.2025.28.3.391 Vol.28(No.3) 391-406, 2025

This paper highlights the role of multiple solutions to a problem and posing new problems in cultivating students' creative thinking in mathematics. Based on a model of cultivating students’ creativity by one problem with several solutions, changes, and applications in an inquiry-based mathematics classroom, the study analyzes one expert Chinese mathematics teacher who takes a simple plane geometry problem as an example to guide students how to find different solutions and pose new problems in inquiry-based classroom. These activities can be used to cultivate students’ creative thinking ability in mathematics.

Plane geometry problem, different solutions, problem-posing, creative thinking ability, inquiry-based classroom

Anne N Waswa , Kevin C Moore

DOI:10.7468/jksmed.2025.28.3.407 Vol.28(No.3) 407-434, 2025

Mathematical creativity is a multifaceted psychological construct, necessitating innovative research techniques to enhance its integration into mathematics education. Though existing studies primarily focus on teachers’ personal conceptions of mathematical creativity, there is a pressing need to identify their actual creative practices during problem-solving (PS) and problem-posing (PP) activities. Understanding these authentic acts of creativity is crucial for evaluating how teachers’ thinking and enactment of mathematical concepts reflect their creativity and influence their instructional practices. In this paper, a theoretical and methodological approach to studying mathematical creativity in action by integrating two theoretical approaches to outline mental operations that underpin creative characteristics is proposed. We illustrate the application of our theory and methodology using examples from a specific study of pre-service teachers’ (PSTs’) PS activities. Our approach aims to fill the gap in understanding mathematical creativity as it unfolds, providing insights into cognitive processes and contextual factors affecting mathematical creativity, and ultimately informing the evolution of practices in mathematics education research and practice.

Mathematical creativity, theory, methodology, pre-service teachers