Home \(\blacktriangleright\) Studies and Publications \(\blacktriangleright\) Scientific Basis and Research Infrastructure
Scientific Basis and Research Infrastructure
Theoretical Basis and Research Infrastructure
The extensive research conducted at Range Center is based on a broad, multidisciplinary, and integrative theoretical infrastructure that combines classical research traditions in mathematics education with contemporary developments in cognitive psychology, neuroscience, and creativity research. This infrastructure is documented through a series of review articles and comprehensive introductory chapters, which serve as a conceptual anchor for understanding the complexity of learning, teaching, and giftedness (Cai et al., 2026; Leikin, 2011, 2020, 2023; Leikin & Sriraman, 2022).
The works of Prof. Roza Leikin and her colleagues lay the foundations for the center’s central research tools (Sriraman & Leikin, 2016), while creating a synthesis of “state of the art” and updating central research questions, such as the relationship between creativity and giftedness in mathematics (Leikin, 2009, 2011).
In-depth Conceptual Distinction
The center distinguishes between mathematical potential, expertise, and general giftedness, relying on classical thinkers such as Krutetskii, Polya, Shulman, and Vygotsky, as well as on the development of modern models that link cognitive processes to learning outcomes (Leikin, 2006, 2007, 2009, 2019, 2021; Pitta-Pantazi & Leikin, 2018).
Creativity and Problem Solving
The review articles define criteria for assessing creativity (fluency, flexibility, and originality) and frameworks for analyzing open-ended tasks, such as Multiple solution Outcome Tasks (MOTs) and Multiple solution Strategy Tasks (MSTs), problem-posing tasks, insight tasks, and dynamic inquiry tasks (Leikin, 2015, 2026; Leikin & Cai, 2026; Leikin & Guberman, 2023; Leikin & Lev, 2013; Leikin & Pitta-Pantazi, 2013).
Applied Research
Neurocognitive Research in Mathematics
The center integrates research findings from the field of neurocognition to validate educational theories and deepen the understanding of learning and problem-solving processes (Leikin et al., 2013; Leikin et al., 2014; Leikin et al., 2025; Waisman et al., 2014). This integration enables science-practice bridges, based on an in-depth understanding of brain function when dealing with mathematical challenges. Research findings serve as a basis for developing learning environments adapted to the diverse cognitive abilities of students (Guberman & Leikin, 2013; Leikin, 2018, 2021; Leikin et al., 2023; Miller Markovitz et al., 2025; Sriraman & Leikin, 2016; Waisman et al., 2025).
Models of Teacher Knowledge
The center bases its activities on models of pedagogical content knowledge and the integration of formal and intuitive components (Leikin, 2006; Lev-Zamir & Leikin, 2011), as well as on theories of communities of practice and inquiry-based learning (Leikin & Levav-Waynberg, 2007; Leikin & Grossman, 2013). Strategies such as “What if not?”, emphasis on multiple solution methods, and utilizing educational challenges through tasks that guide toward different student learning are used (Leikin, 2018, 2019, 2023).
Transition from Applied Research to Pedagogical Practice
Pedagogical practice at Range Center relies not only on theory but on structured applied research. The pedagogical models we develop are based on a direct link between cognitive research and building a challenging learning environment.
Result-Oriented Research: Using Multiple solution Outcome and Strategy Tasks (MOTs, MSTs) to assess flexibility.
Supportive Environment: Implementing classroom norms that encourage mathematical daring.
Evidence-Based Feedback: Adjusting cognitive load according to neuroeducational research findings.
Theory and Cognitive Research
Applied Pedagogical Model
Classroom Practice and Thinking Development
The Learning Environment and the Mathematical Challenge
This section presents how a mathematical challenge is created in the classroom. Click on the various components to understand their impact on creating problem-based teaching adapted to different levels of students.
Teacher Guidance
Managing Teacher Challenges
Socio-Mathematical Norms
Socio-Mathematical Norms
Curiosity and Learner Abilities
The Role of Curiosity and the Learner
📚 References
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
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
Leikin, R., Cai, J. (2026). Research on Mathematical Creativity and Problem Posing: State of the Art and Future Development. In: Cai, J., Leikin, R. (eds) Research in Mathematical Problem Posing. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-032-05493-7_7
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., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in mathematics, 66(3), 349-371. https://doi.org/10.1007/s10649-006-9071-z
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM Mathematics Education, 45(2), 159-166. https://doi.org/10.1007/s11858-012-0459-1
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. https://doi.org/10.1007/s11858-022-01340-y
Leikin, R., Leikin, M., Waisman, I., & Shaul, S. (2013). Effect of the presence of external representations on accuracy and reaction time in solving mathematical double-choice problems by students of different levels of instruction. International Journal of Science and Mathematics Education, 11(5), 1049-1066. https://doi.org/10.1007/s10763-012-9388-z
Leikin, M., Waisman, I., Shaul, S., & Leikin, R. (2014). A comparative study on brain activity associated with solving short problems in algebra and geometry. In Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 121-128). PME
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., Hsu, H.-Y., Ansari, D., Abrahamson, D., Obersteiner, A., Miskin, M., & Waisman, I. (2025). Systematics review of the interdisciplinary exchange among mathematics education and neuroscience. ZDM – Mathematics Education, 57, 583–602. https://doi.org/10.1007/s11858-025-01705-z
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. (2006). Learning by teaching: The case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis & S. Campbell (Eds.), Number Theory in Mathematics Education: Perspectives and Prospects. (pp. 115-140). Mahwah, NJ: Erlbaum
Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. CERME 5, 2330-2339
Leikin, R. (2009). Bridging research and theory in mathematics education with research and theory in creativity and giftedness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 385–411). Sense Publishers
Leikin, R. (2011). The education of mathematically gifted students: Some complexities and questions. The Mathematics Enthusiast, 8(1), 167-188. https://doi.org/10.54870/1551-3440.1211
Leikin, R. (2015). Problem Posing for and Through Investigations in a Dynamic Geometry Environment. In F. M. Singer et al. (Eds.), Mathematical Problem Posing (pp. 373–391). Research in Mathematics Education. https://doi.org/10.1007/978-1-4614-6258-3_18
Leikin, R. (2018). Part IV: Commentary–characteristics of mathematical challenge in problem-based approach to teaching mathematics. In Teaching and learning secondary school mathematics: Canadian perspectives in an international context (pp. 413-418). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-92390-1_38
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. (2020). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (2nd ed., pp. 325-335). Springer International Publishing. https://doi.org/10.1007/978-3-319-77487-9_65-4
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. (2021). When practice needs more research: the nature and nurture of mathematical giftedness. ZDM-Mathematics Education, 53, 1579–1589. https://doi.org/10.1007/s11858-021-01276-9
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
Leikin, R. (2025). Creativity and curiosity (in mathematics) 2C or C2? Multiple facets, confluence and contrast. In R. Leikin et al. (Eds.), Mathematical Curiosity (Research in Mathematics Education). https://doi.org/10.1007/978-3-031-99082-3_3
Lev-Zamir, H., & Leikin, R. (2011). Creative mathematics teaching in the eye of the beholder: Focusing on teachers’ conceptions. Research in Mathematics Education, 13(1), 17–32. https://doi.org/10.1080/14794802.2011.550715
Miller Markovitz, L., Landau, G. M., & Leikin, R. (2025a). Characterization of STEM-motivated high school students: Focusing on intelligence, mathematical competencies, and creativity. Journal for the Education of the Gifted, 48(4), 382-403. https://doi.org/10.1177/01623532251372602
Pitta-Pantazi, D., & Leikin, R. (2018). Mathematical potential, creativity and talent. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.4334/9781325133562-20
Sriraman, B., & Leikin, R. (2016). Commentary on interdisciplinary perspectives to creativity and giftedness. In R. Leikin & B. Sriraman (Eds.), Creativity and Giftedness: Interdisciplinary Perspectives from Mathematics and Beyond (pp. 259–264). Springer. https://doi.org/10.1007/978-3-319-38840-3_16
Waisman, I., Leikin, M., Shaul, S., & Leikin, R. (2014). Brain activity associated with translation between graphical and symbolic representations of functions in generally gifted and excelling in mathematics adolescents. International Journal of Science and Mathematics Education, 12(3), 669–696. https://doi.org/10.1007/s10763-014-9516-0
Waisman, I., Leikin, R., & Leikin, M. (2025). Insight elements of mathematical problem solving in generally gifted and mathematical experts: ERP amplitudes in PO electrodes. Frontiers in Integrative Neuroscience, 19, 1523334. https://doi.org/10.3389/fnint.2025.1523334