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Students: Excellence, Giftedness, and Neurocognition

Excellence and Giftedness
Neurocognition
Practice

Conceptual and Methodological Distinction

Research at Range Center distinguishes conceptually and methodologically between General Giftedness (G) and Mathematical Excellence (EM).

Multidimensional studies emphasize that these are essentially different cognitive traits, which differentially affect information processing and problem-solving (Leikin et al., 2013, 2017; Paz-Baruch et al., 2022).

🧘 General Giftedness (G)

  • High reasoning abilities
  • Developed phonological working memory
  • Intuitive insight problem-solving (“Aha!” moment)
  • Reduced mastery of standard school content

(Leikin et al., 2013, 2016; Waisman et al., 2025)

📐 Mathematical Excellence (EM)

  • Deep mastery of school content
  • High automation of arithmetic operations
  • Visual-spatial memory and processing
  • Pattern recognition
  • Predicts success in knowledge and automation tasks (solving institutional learning problems)

(Leikin et al., 2013, 2018; Paz-Baruch et al., 2022)

Comparison of Estimated Cognitive Profile

Inference ability Working memory Automation Visual-spatial processing Pattern recognition

Pedagogical Aspect

Pedagogically, mathematical creativity serves as a bridge between expertise and giftedness. It has been found that gifted students who excel in mathematics demonstrate higher levels of creativity in open-ended tasks, but the ability to realize this potential depends on the type of task—such as the use of Multiple Solution Strategy Tasks (MSTs)—and the structure of the learning environment (Leikin & Lev, 2013; Lev & Leikin, 2016; Miller Markovitz et al., 2025).

Neurocognitive Methodology: EEG and ERP

The center uses advanced electro-physiological tools—EEG (electroencephalography) and ERP (event-related potentials)—to map brain activity in real-time. EEG provides a comprehensive picture of the electrical activity in the brain, while ERP allows for isolating specific responses to defined stimuli. These findings challenge the classical “neural efficiency” theory, as described in the boxes below (Shaul et al., 2013; Leikin et al., 2014, 2016; Waisman et al., 2023).

⚡ Neural Efficiency

Outstanding students demonstrate high efficiency in automatic processing, but recruit broader cognitive resources when dealing with challenges (Leikin et al., 2013; Waisman et al., 2016).

👁 Memory and Visual Processing

Mathematical excellence relies on visual-spatial memory and pattern recognition, unlike general giftedness, which is related to phonological memory (Leikin et al., 2013; Paz-Baruch et al., 2015, 2016).

📐 Geometry vs. Algebra

Geometry requires a higher working memory load than algebra due to the need to transition between visual and symbolic representations (Leikin et al., 2014; Waisman et al., 2012).

Electrical Activity Dynamics (ERP)

Neural efficiency: Students with exceptional abilities (S-MG) demonstrate more efficient activity patterns reflected in lower conductivity and automation of processing, but recruit extensive cognitive resources when solving high-level challenging problems, contrary to classical theories of energy conservation (Leikin et al., 2013; Waisman et al., 2016, 2023).

Translating Data into Action: From Lab to Classroom

Our pedagogical practice does not stand alone, but is derived directly from neurocognitive findings:

🧩 Cognitive Load Management

Since geometry requires a high cognitive load (transitioning between representations), we develop learning environments that reduce attentional load and balance it through visualization. Adapting the learning environment to the student’s information processing ability, and properly structuring tasks, allows for the breakdown of complex tasks and the prevention of unnecessary cognitive load (Shaul et al., 2013).

🎯 Informed Differentiation

The understanding that EM and G are different mechanisms allows us to adapt MST (Multiple Strategy Tasks) to the student’s type of excellence. By tailoring pedagogical tasks based on individual neurocognitive profiles, we ensure an accurate response to the unique needs of every student in a heterogeneous classroom (Leikin & Lev, 2013; Miller Markovitz et al., 2025).

👨‍🎓 Teacher Mediation

Teachers as mediation agents who bridge theoretical knowledge and classroom practice perform adjustments of teaching to the learning culture and systemic constraints. As such, the teacher uses neurocognitive understanding to bridge between science and learning in the field, and to direct, support, and encourage the student’s development (Leikin, 2021; Leikin & Levav-Waynberg, 2007).

Synthesis: Vision of Integration

Fostering mathematical potential is not limited to technical instruction. The center’s vision is to create a synergy where neuroscience illuminates the path to more precise didactics, which recognizes the student’s uniqueness and allows for the expression of creativity, mental flexibility, and deep insight (Leikin, 2026; Sriraman & Leikin, 2016).

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., 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., Paz-Baruch, N., & Leikin, R. (2013). Memory abilities in generally gifted and excelling-in-mathematics adolescents. Intelligence, 41(5), 566–578. https://doi.org/10.1016/j.intell.2013.07.018

Leikin, M., Waisman, I., & Leikin, R. (2013). How brain research can contribute to the evaluation of mathematical giftedness. Psychological Test and Assessment Modeling, 55(4), 415-437.

Leikin, M., Waisman, I., Shaul, S., & Leikin, R. (2013, November). Single-digit multiplication in Generally Gifted and Excelling-in-mathematics adolescents: ERP study. In Journal Of Molecular Neuroscience (Vol. 51, pp. S67-S68).

Leikin, R., Paz-Baruch, N., & Leikin, M. (2014). Cognitive characteristics of students with superior performance in mathematics. Journal of Individual Differences, 35(3), 119–129. https://doi.org/10.1027/1614-0001/a000140

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., Leikin, M., & Waisman, I. (2016). What Is Special About the Brain Activity of Mathematically Gifted Adolescents?. In Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 165-181). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-38840-3_11

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., Leikin, M., Paz-Baruch, N., Waisman, I., & Lev, M. (2017). On the four types of characteristics of super mathematically gifted students. High Ability Studies, 28(1), 107-125. https://doi.org/10.1080/13598139.2017.1305330

Leikin, M., Leikin, R., & Waisman, I. (2018). Expertise, giftedness and insight in mathematics. International Journal of Psychophysiology, 131S, S37. https://doi.org/10.1016/j.ijpsycho.2018.07.114

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. (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, M., & Leikin, R. (2016). The interplay between excellence in school mathematics and general giftedness: Focusing on mathematical creativity. In Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 225-238). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-38840-3_14

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

Paz-Baruch, N., Leikin, M., & Leikin, R. (2016). Visual processing and attention abilities of general gifted and excelling in mathematics students. In Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 1046–1051). Charles University in Prague, Faculty of Education; ERME. https://hal.science/hal-01287310

Paz-Baruch, N., Leikin, R., & Leikin, M. (2016). Visual processing in generally gifted and mathematically excelling adolescents. Journal for the Education of the Gifted, 39(3), 237-258. https://doi.org/10.1177/0162353216657184

Paz-Baruch, N., Leikin, M., & Leikin, R. (2022). Not any gifted is an expert in mathematics and not any expert in mathematics is gifted. Gifted and Talented International, 37(1), 25-41. https://doi.org/10.1080/15332276.2021.2010244

Shaul, S., Waisman, I., Leikin, M., & Leikin, R. (2013). From a visual to a symbolic object in algebra and geometry: ERP study with mathematically excelling male adolescents. Journal of Molecular Neuroscience, 51(Suppl 1), S111–S112. https://doi.org/10.1007/s12031-013-0084-2

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., 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. (2016). Brain activity associated with logical inferences in geometry: Focusing on students with different levels of ability. ZDM Mathematics Education, 48(3), 321–335. https://doi.org/10.1007/s11858-016-0760-5

Waisman, I., Brunner, C., Grabner, R. H., Leikin, M., & Leikina, R. (2023). (Lack of) neural efficiency related to general giftedness and mathematical excellence: An EEG study. Neuropsychologia, 179, 108448. https://doi.org/10.1016/j.neuropsychologia.2022.108448

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