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Creativity in Mathematics and Task Types

Integrating research and applied knowledge: From understanding the logical structure of the task to realizing potential in a heterogeneous classroom.

Creativity Metrics
Task Types
Classroom Teaching

Mathematical Creativity

Mathematical creativity is the learner’s ability to propose original, diverse, and flexible solutions to problems, while deviating from routine algorithmic thinking. It expresses a deep understanding of mathematical structure and enables the discovery of new ways of acting, even when dealing with complex problems (Leikin, 2009, 2013, 2016).

Mathematical creativity is not solely an innate trait, but a talent that can be developed. Evaluation models focus on three key dimensions that combine convergent and divergent thinking:

Fluency

The ability to generate a large number of solutions or ideas. This metric indicates the speed of access to knowledge resources.

Flexibility

The ability to switch between different mathematical approaches and representations. This metric indicates the depth of understanding of mathematical connections.

Originality

The rarity of the solution and the use of unconventional insights. This metric indicates independent thinking and deep insight.

Distinguishing between Expertise and Creativity

Following the discussion on the cognitive mechanisms of expertise, the applied and pedagogical level raises the question of how it integrates with creativity. Research highlights the complex relationship between these two traits. It has been found that not every expert is necessarily creative. While expertise is based on mastery of skills and existing knowledge, creativity requires mental daring, formulating new problems, and deviating from known procedures (Elgrably & Leikin, 2021; Leikin & Elgrably, 2022).

Mathematical creativity is perceived as a talent that can be nurtured through learning environments that combine convergent and divergent thinking, using tasks that challenge the learner to go beyond the obvious solution.

Task Types

Research conducted at Range Center presents a broad theoretical and empirical infrastructure that establishes the nature of mathematical tasks as a shaping factor in cognitive processes and the development of creativity and giftedness. At the heart of the research work is the distinction between different task types, primarily open tasks.

These tasks allow for the exploration of diverse answer spaces and develop fluency and originality (Leikin, 2009, 2013, 2019). This distinction has been reinforced in comparative studies that examined learner populations with different cognitive profiles.

Multiple Solution Strategy Tasks (MST)

These tasks require solving a single problem in multiple ways. The emphasis is on using different strategies (e.g., algebraic vs. geometric or graphical solutions) to promote mental flexibility and understanding of the connections between different representations (Leikin & Lev, 2013).

Multiple Solution Outcome Tasks (MOT)

Tasks with multiple outcomes that challenge the learner to explore an open answer space and reach a complete set of solutions. These tasks allow for the diagnosis of fluency and originality (Guberman & Leikin, 2013; Leikin, 2013)..

Problem Posing (PP)

Creating new problems from a given situation or from mathematical exploration. The emphasis is on developing creativity, conceptual understanding, and independent learning initiative, while combining problem-solving processes with posing new problems (Cai et al., 2026; Elgrably & Leikin, 2021; Guberman & Leikin, 2013).

Investigation Problems

Tasks in which the learner investigates a mathematical situation without a rigid definition of a solution path. The learner is required to discover properties, develop a set of hypotheses, and even reach generalizations. The investigation is seen as a foundation upon which the ability to pose new problems (PPI) is built and flexible thinking is exercised (Leikin & Elgrably, 2020).

Insight Problems

These tasks emphasize a transition from routine thinking to mathematical insight. The solution relies not only on technical algorithms but on understanding the deep structure, completing missing information, analyzing complex situations, and breaking fixed thinking patterns, thereby increasing the level of complexity and creativity required from the learner (Leikin & Guberman, 2023).

Potential for Development by Task Type

Relative assessment of the impact of tasks on creativity metrics according to research findings:

Classroom Activity: From Lab to Field

The connection between the logical structure of the assignment and learner abilities forms the scientific basis for adjusting the learning challenge in heterogeneous classrooms, and leads directly to the informed use of tasks within pedagogical intervention programs (Leikin & Lev, 2013; Leikin et al., 2016).

Creativity-Oriented Activity

It has been found that the systematic integration of open tasks in mathematics lessons contributes not only to the development of creativity but also to deepening students’ conceptual knowledge (Leikin, 2014; Levav-Waynberg & Leikin, 2012). At the center of the work stands the issue of mathematical curiosity, as a factor driving learning and growth (Leikin et al., 2025). Lesson design is influenced by a combination of conceptual components, socio-mathematical norms, and the use of technological tools. Researchers point out that a creative planning process does not necessarily guarantee a creative product, and that there is a significant cognitive distinction between the two (Leikin & Elgrably, 2022). This allows teachers to create a higher level of challenge adapted to heterogeneous classrooms through the transformation of closed textbook problems into open investigation tasks (Leikin & Grossman, 2013).

Problem Posing (PP)

This experience has been found to improve proof and mathematical formulation skills. The ability to formulate new problems from investigation (PPI) helps in merging knowledge and understanding mathematical structure (Cai et al., 2026; Elgrably & Leikin, 2021).

Technological Environments (DGE)

Dynamic geometry environments allow students with different potential levels to engage in problem-solving at varying depths using scaffolding (Leikin et al., 2023; Klein & Leikin, 2020).

Teaching in a Heterogeneous Classroom

The continuous connection between task characterization, empirical findings, and field application allows Range Center to offer evidence-based models that promote excellence in the education system (Leikin & Guberman, 2023; Waisman et al., 2012, 2023).

Fostering excellence and creativity in the classroom requires the teacher to integrate as a designer of a creative environment, recognizing that developing expertise and creativity are intertwined processes that depend on the quality of tasks and the complex interaction between individual abilities and challenges (Leikin, 2016, 2019, 2021, 2023).

🧩 Diagnosis and Development

Identifying abilities through fluency, flexibility, and originality.

⚖️ Self-Regulation

Adjusting the level of individual challenge to the learner’s needs.

🚀 Realizing Potential

Maximizing high abilities among all learners.

🌱 Growth

Improving individual achievements through stepped tasks.

👦 Social Norms

Fostering a discourse of investigation and multiple solutions

Cai, J., Leikin, R., & Robison, V. (2026). New Advances and Directions of Mathematical Problem-Posing Research. Research in Mathematical Problem Posing: New Advances and Directions, 1-15. https://doi.org/10.1007/978-3-032-05493-7_1

Elgrably, H., & Leikin, R. (2021). Creativity as a function of problem-solving expertise: Posing new problems through investigations. ZDM–Mathematics Education, 53(4), 891-904. https://doi.org/10.1007/s11858-021-01228-3

Guberman, R., & Leikin, R. (2013). Interesting and difficult mathematical problems: changing teachers’ views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56. https://doi.org/10.1007/s10857-012-9210-7

Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: what do teachers do and feel? Educational Studies in Mathematics, 105(3), 349–365. https://doi.org/10.1007/s10649-020-09983-y

Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101574. https://doi.org/10.1016/j.ijer.2020.101574

Leikin, R., & Elgrably, H. (2022). Strategy creativity and outcome creativity when solving open tasks: focusing on problem posing through investigations. ZDM–Mathematics Education, 54(1), 35-49. https://doi.org/10.1007/s11858-021-01319-1

Leikin, R., & Grossman, D. (2013). Teachers modify geometry problems: from proof to investigation. Educational Studies in Mathematics, 82(3), 515-531. https://doi.org/10.1007/s10649-012-9460-4

Leikin, R., & Guberman, R. (2023). Creativity and challenge: Task complexity as a function of insight and multiplicity of solutions. In R. Leikin (Ed.), Mathematical challenges for all (pp. 325-342). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-031-18868-8_17

Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference?. Zdm, 45(2), 183-197. https://doi.org/10.1007/s11858-012-0460-8

Leikin, R., Waisman, I., & Leikin, M. (2016). Does solving insight-based problems differ from solving learning-based problems? Some evidence from an ERP study. ZDM Mathematics Education, 48(3), 305-319. https://doi.org/10.1007/s11858-016-0767-y

Leikin, R., Klein, S., Ovodenko, R., Gurevitch, I., Dinur, S., & Leen, Y. (2023). Math-Key Program: Opening mathematical minds by means of open tasks supported by dynamic applets. In R. Leikin (Ed.), Mathematical challenges for all (pp. 93–113). Springer. https://doi.org/10.1007/978-3-031-18868-8_6

Leikin, R., Pitta-Pantazi, D., Cai, J., Hsu, H.-Y., Felmer, P., Gödeke, P., Karp, A., Koichu, B., Krawitz, J., Robison, V., Schukajlow, S., & Zazkis, R. (2025). Curiosity in mathematics: Theoretical, methodological and practical lenses. In C. Cornejo, P. Felmer, D. M. Gómez, P. Dartnell, P. Araya, A. Peri, & V. Randolph (Eds.), Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: General Contributions (pp. 151-180). PME.

Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Sense Publishers.

Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight. Psychological Test and Assessment Modeling, 55(4), 385–400.

Leikin, R. (2014). Challenging mathematics with multiple solution tasks and mathematical investigations in geometry. In Y. Li, E. A. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 59-71). Springer. https://doi.org/10.1007/978-3-319-04993-9_5

Leikin, R. (2016, August). Interplay between creativity and expertise in teaching and learning of mathematics. In Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 19-34). Szeged, Hungary: PME.

Leikin, R. (2019). Openness and constraints associated with creativity-directed activities in mathematics for all students. In N. Amado, S. Carreira, & N. Amado (Eds.), Broadening the scope of research on mathematical problem solving (pp. 387–396). Springer. https://doi.org/10.1007/978-3-319-99861-9_17

Leikin, R. (2019). Stepped tasks: Top-down structure of varying mathematical challenge. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Problem solving in mathematics instruction and teacher professional development (pp. 167–186). Springer Nature Switzerland AG. https://doi.org/10.1007/978-3-030-29215-7_9

Leikin, R. (2021). Characterisation of mathematics teacher educators’ knowledge in terms of teachers’ professional potential and challenging content for mathematics teachers. In M. Goos & K. Beswick (Eds.), The learning and development of mathematics teacher educators (pp. 109–121). Springer. https://doi.org/10.1007/978-3-030-62408-8_6

Leikin, R. (2023). Introduction to Mathematical Challenges for All Unraveling the Intricacy of Mathematical Challenge. In: Leikin, R. (eds) Mathematical Challenges For All . Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-18868-8_1

Levav-Waynberg, A., & Leikin, R. (2012). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31(1), 73–90. https://doi.org/10.1016/j.jmathb.2011.11.001

Waisman, I., Shaul, S., Leikin, M., & Leikin, R. (2012). General ability vs. expertise in mathematics: An ERP study with male adolescents who answer geometry questions. In Proceedings of the 12th International Congress on Mathematical Education (pp. 1290–1299). COEX.

Waisman, I., Leikin, M., & Leikin, R. (2023). Brain activity associated with logical reasoning in geometry in students with different levels of ability. Journal for Research and Study in Mathematics Education, 10, 45–59.