{"id":10621,"date":"2026-06-16T08:13:51","date_gmt":"2026-06-16T05:13:51","guid":{"rendered":"https:\/\/range.haifa.ac.il\/%d7%91%d7%a1%d7%99%d7%a1-%d7%9e%d7%93%d7%a2%d7%99-%d7%95%d7%aa%d7%a9%d7%aa%d7%99%d7%aa-%d7%9e%d7%97%d7%a7%d7%a8%d7%99%d7%aa\/"},"modified":"2026-07-23T11:10:24","modified_gmt":"2026-07-23T08:10:24","slug":"scientific-basis-and-research-infrastructure","status":"publish","type":"post","link":"https:\/\/range.haifa.ac.il\/en\/scientific-basis-and-research-infrastructure\/","title":{"rendered":"Scientific Basis and Research Infrastructure"},"content":{"rendered":"\t\t
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Home<\/span><\/a> \\(\\blacktriangleright\\) Studies and Publications<\/span><\/a> \\(\\blacktriangleright\\) Scientific Basis and Research Infrastructure<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Scientific Basis and Research Infrastructure<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tTheoretical Basis<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tApplied Research<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tPedagogical Content<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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Theoretical Basis and Research Infrastructure<\/h2>

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).<\/p>

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).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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In-depth Conceptual Distinction<\/h3>

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).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Creativity and Problem Solving<\/h3>

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).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Applied Research<\/h2>

Neurocognitive Research in Mathematics<\/h3>

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).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Models of Teacher Knowledge<\/h3>

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).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Transition from Applied Research to Pedagogical Practice<\/h2>

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.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Result-Oriented Research:\u00a0\u00a0<\/strong> Using Multiple solution Outcome and Strategy Tasks (MOTs, MSTs) to assess flexibility.<\/p>

Supportive Environment:\u00a0\u00a0<\/strong> Implementing classroom norms that encourage mathematical daring.<\/p>

Evidence-Based Feedback:\u00a0\u00a0<\/strong> Adjusting cognitive load according to neuroeducational research findings.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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Theory and Cognitive Research<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Applied Pedagogical Model<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Classroom Practice and Thinking Development<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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The Learning Environment and the Mathematical Challenge<\/h3>

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.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t

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\n\t\t\t\t\t\t\t\tTeacher Guidance\t\t\t\t\t\t\t<\/h3>\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tLesson Management, Openness, and Constraints\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t
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\n\t\t\t\t\t\t\tManaging Teacher Challenges\t\t\t\t\t\t<\/h3>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\tThe center offers problem-based models for multi-level teaching adapted to different student levels, using open, structured tasks (Leikin, 2018; 2019; 2023).\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\tSocio-Mathematical Norms\t\t\t\t\t\t\t<\/h3>\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tClassroom Culture and Shared Perceptions\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t
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\n\t\t\t\t\t\t\tSocio-Mathematical Norms\t\t\t\t\t\t<\/h3>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\tChallenge relies on classroom social interaction. Cultural and social perceptions decisively define how challenge and creativity are shaped in lessons (Leikin & Elgrably, 2022).\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\tCuriosity and Learner Abilities\t\t\t\t\t\t\t<\/h3>\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\t\tDriving Factor, Creativity, and Learning\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t
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\n\t\t\t\t\t\t\tThe Role of Curiosity and the Learner\t\t\t\t\t\t<\/h3>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t
\n\t\t\t\t\t\t\tCuriosity powers the learning process. Combining curiosity and creativity enables students to successfully cope with mathematical challenges set by the teacher (Leikin et al., 2025).\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t
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\ud83d\udcda References <\/h1><\/span>\n\t\t\t\t\t\t\t\n\t\t\t<\/i><\/span>\n\t\t\t<\/i><\/span>\n\t\t<\/span>\n\n\t\t\t\t\t\t<\/summary>\n\t\t\t\t
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Cai, J., Leikin, R., & Robison, V. (2026). New Advances and Directions of Mathematical Problem-Posing Research.\u00a0Research in Mathematical Problem Posing: New Advances and Directions, 1-15. https:\/\/doi.org\/10.1007\/978-3-032-05493-7_1<\/p>\n

Guberman, R., & Leikin, R. (2013). Interesting and difficult mathematical problems: changing teachers\u2019 views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56. https:\/\/doi.org\/10.1007\/s10857-012-9210-7<\/p>\n

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<\/p>\n

Leikin, R., & Elgrably, H. (2022). Strategy creativity and outcome creativity when solving open tasks: focusing on problem posing through investigations. ZDM\u2013Mathematics Education, 54(1), 35-49. https:\/\/doi.org\/10.1007\/s11858-021-01319-1<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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<\/p>\n

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\u2013Mathematics Education, 54(1), 1-17. https:\/\/doi.org\/10.1007\/s11858-022-01340-y<\/p>\n

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<\/p>\n

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<\/p>\n

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\u2013113). Springer. https:\/\/doi.org\/10.1007\/978-3-031-18868-8_6<\/p>\n

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 \u2013 Mathematics Education, 57, 583\u2013602. https:\/\/doi.org\/10.1007\/s11858-025-01705-z<\/p>\n

Leikin, R., Pitta-Pantazi, D., Cai, J., Hsu, H.-Y., Felmer, P., G\u00f6deke, 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. G\u00f3mez, 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<\/p>\n

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<\/p>\n

Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. CERME 5, 2330-2339<\/p>\n

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\u2013411). Sense Publishers<\/p>\n

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<\/p>\n

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\u2013391). Research in Mathematics Education. https:\/\/doi.org\/10.1007\/978-1-4614-6258-3_18<\/p>\n

Leikin, R. (2018). Part IV: Commentary\u2013characteristics 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<\/p>\n

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\u2013396). Springer. https:\/\/doi.org\/10.1007\/978-3-319-99861-9_17<\/p>\n

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\u2013186). Springer Nature Switzerland AG. https:\/\/doi.org\/10.1007\/978-3-030-29215-7_9<\/p>\n

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<\/p>\n

Leikin, R. (2021). Characterisation of mathematics teacher educators\u2019 knowledge in terms of teachers\u2019 professional potential and challenging content for mathematics teachers. In M. Goos & K. Beswick (Eds.), The learning and development of mathematics teacher educators (pp. 109\u2013121). Springer. https:\/\/doi.org\/10.1007\/978-3-030-62408-8_6<\/p>\n

Leikin, R. (2021). When practice needs more research: the nature and nurture of mathematical giftedness. ZDM-Mathematics Education, 53, 1579\u20131589. https:\/\/doi.org\/10.1007\/s11858-021-01276-9<\/p>\n

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<\/p>\n

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<\/p>\n

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\u201332. https:\/\/doi.org\/10.1080\/14794802.2011.550715<\/p>\n

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<\/p>\n

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<\/p>\n

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\u2013264). Springer. https:\/\/doi.org\/10.1007\/978-3-319-38840-3_16<\/p>\n

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\u2013696. https:\/\/doi.org\/10.1007\/s10763-014-9516-0<\/p>\n

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<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/details>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

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