Research Article

Pedagogical intervention with a mathematically gifted student–Expanding problem-solving strategies and developing metacognition: A case study

Jitka Panáčová 1 , Jana Veseláková 1 *
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1 Faculty of Education, Masaryk University, Brno, CZECH REPUBLIC* Corresponding Author
European Journal of Science and Mathematics Education, 14(3), July 2026, 427-448, https://doi.org/10.30935/scimath/18785
Published: 20 June 2026
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ABSTRACT

The topic of gifted students has been significantly reflected in a number of scientific publications in recent years, many of which point to the fact that the giftedness of these students is not always apparent in the school environment, and therefore not always identified (Siegle et al., 2025). This article presents a theory corresponding to this topic and related research that deals with a case study using qualitative research methods. The selected case study focuses on a student who, before entering primary education and during it, appeared to be mathematically gifted at the home environment, but his giftedness was not identified in the school environment, let alone further developed. The insufficient fulfilment of the student’s development needs in mathematics within the school environment led to the search for individual support outside the school environment. Based on this request, the student was involved in a one-year pedagogical intervention in mathematics. The article presents typical manifestations of the student’s mathematical giftedness and describes the process of this individual intervention with the student, which aimed to expand his strategies for solving mathematical problems and develop his metacognition. Metacognition is crucial not only for academic performance but also for the autonomy, self-confidence and socio-emotional well-being of gifted students. The study therefore highlights the importance of supporting metacognitive thinking as a key tool that will enable gifted learners to face challenges more effectively, adapt to new situations and fully realize their potentials.

CITATION (APA)

Panáčová, J., & Veseláková, J. (2026). Pedagogical intervention with a mathematically gifted student–Expanding problem-solving strategies and developing metacognition: A case study. European Journal of Science and Mathematics Education, 14(3), 427-448. https://doi.org/10.30935/scimath/18785

REFERENCES

  1. Baxter, P., & Jack, S. (2008). Qualitative case study methodology: Study design and implementation for novice researchers. The Qualitative Report, 13(4), 544–559. https://doi.org/10.46743/2160-3715/2008.1573
  2. Budínová, I. (2018). Přístupy nadaných žáků 1. a 2. stupně základní školy k řešení některých typů úloh v matematice [Approaches of gifted students in the 1st and 2nd grades of primary school to solving certain types of problems in mathematics]. Masarykova Univerzita. https://doi.org/10.5817/CZ.MUNI.M210-9216-2018
  3. Budínová, I. (2021). Matematicky nadaný žák ve školním prostředí: Případová studie [The mathematically gifted student in the school environment: A case study]. Svět Nadání: Časopis o Nadání a Nadaných, 10(2), 22-45. https://mathelp.cz/wp-content/uploads/2023/01/Matematicky-nadany-zak-ve-skolnim-prostredi.pdf
  4. Budínová, I., & Panáčová, J. (2022). Identifikace žáka nadaného na matematiku ve školním prostředí [Identification of a mathematically gifted pupil in the school environment]. Učitel Matematiky, 30(3), 129–148. https://dml.cz/bitstream/handle/10338.dmlcz/151110/UcitelMat_030-2022-3_1.pdf
  5. Campbell, S., Greenwood, M., Prior, S., Shearer, T., Walkem, K., Young, S., Bywaters, D., & Walker, K. (2020). Purposive sampling: Complex or simple? Research case examples. Journal of Research in Nursing, 25(8), 652-661. https://doi.org/10.1177/1744987120927206
  6. Carr, M., Alexander, J. M., & Schwanenflugel, P. J. (1996). Where gifted children do and do not excel on metacognitive tasks. Roeper Review, 18(3), 212-217. https://doi.org/10.1080/02783199609553740
  7. Efklides, A. (2014). How does metacognition contribute to the regulation of learning? An integrative approach. Psihologijske Teme, 23(1), 1-30. https://hrcak.srce.hr/en/file/178351
  8. Eraky, A., Leikin, R., & Hadad, B. (2022). Relationships between general giftedness, expertise in mathematics, and mathematical creativity associated with pattern generalization tasks in different representations. Asian Journal for Mathematics Education, 1(1), 36-51. https://doi.org/10.1177/27527263221093427
  9. Erdoğan, F. (2025). Unlocking the power of metacognition in mathematically gifted minds. Journal of Gifted Education and Creativity, 12(1), 128-140. https://doi.org/10.5281/zenodo.15752954
  10. Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906-911. https://doi.org/10.1037/0003-066X.34.10.906
  11. Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. Basic Books. https://ia600709.us.archive.org/11/items/psicology/Frames%20of%20Mind%20_%20The%20Theory%20of%20Multiple%20Intelligences%20-%20Howard%20Gardner.pdf
  12. Hidayat, R., Mohd Saad, M. R., & Wewe, M. (2025). A meta-analysis of the effect of metacognitive instruction on mathematics achievement. Cogent Education, 12(1), Article 2517510. https://doi.org/10.1080/2331186X.2025.2517510
  13. Knox, H. (2017). Using writing strategies in math to increase metacognitive skills for the gifted learner. Gifted Child Today, 40(1), 43-47. https://doi.org/10.1177/1076217516675904
  14. Koshy, V., Ernest, P., & Casey, R. (2009). Mathematically gifted and talented learners: Theory and practice. International Journal of Mathematical Education in Science and Technology, 40(2), 213-228. https://doi.org/10.1080/00207390802566907
  15. Lai, Y., Zhu, X., Chen, Y., & Li, Y. (2015). Effects of mathematics anxiety and mathematical metacognition on word problem solving in children with and without mathematical learning difficulties. PLoS ONE, 10(6), Article e0130570. https://doi.org/10.1371/journal.pone.0130570
  16. 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. https://doi.org/10.1163/9789087909352_010
  17. Leikin, R. (2020). Giftedness and high ability in mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 315-325). Springer. https://doi.org/10.1007/978-3-030-15789-0_65
  18. 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
  19. Moustakas, D., & Gonida, E. (2023). Motivational profiles of high achievers in mathematics: Relations with metacognitive processes and achievement emotions. Education Sciences, 13(10), Article 970. https://doi.org/10.3390/educsci13100970
  20. Murairwa, S. (2015). Voluntary sampling design. International Journal of Advanced Research in Management and Social Sciences, 4(2), 185-200. https://garph.co.uk/IJARMSS/Feb2015/18.pdf
  21. National Research Council [NRC] (2000). How people learn: Brain, mind, experience, and school: Expanded edition. National Academies Press. https://doi.org/10.17226/9853
  22. Noor, B. (2022). Students’ metacognition skills and problem-solving strategies in math. International Journal of Academic Research in Progressive Education and Development, 11(1), 82-88. https://doi.org/10.31703/gssr.2022(VII-IV).09
  23. Omerović, M., Resic, S., Palića, A., & Baždalić, T. (2020). Role of additional activities and competition in the teaching of mathematics. Human Research in Rehabilitation, 10(1), 41-50. https://doi.org/10.21554/hrr.042005
  24. Oppong, E. S., Shore, B. M., & Muis, K. R. (2019). Clarifying the connections among giftedness, metacognition, self-regulation, and self-regulated learning: Implications for theory and practice. Gifted Child Quarterly, 63(2), 102-119. https://doi.org/10.1177/0016986218814008
  25. Pintrich, P. R. (2002). The role of metacognitive knowledge in learning, teaching and assessing. Theory Into Practice, 41(4), 219-225. https://doi.org/10.1207/s15430421tip4104_3
  26. Pólya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press. https://doi.org/10.1515/9781400828678
  27. Portešová, Š., & Veenman, M. (2021). Možnosti dlouhodobé pedagogické intervence pro rozvoj metakognice nadaných i běžných žáků [Possibilities of long-term pedagogical intervention for the development of metacognition in gifted and ordinary students]. Svět Nadání: Časopis o Nadání a Nadaných, 10(1), 14-33. https://zapojmevsechny.cz/storage/app/media/Nad%C3%A1n%C3%AD%20-%20migrace/Sv%C4%9Bt%20Nad%C3%A1n%C3%AD/%C4%8C%C3%ADslo%201.%20ro%C4%8Dn%C3%ADk%20X.%202021/Metakognice%20.pdf
  28. Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180-184. https://www.researchgate.net/publication/234665343_What_Makes_Giftedness_A_Reexamination_of_the_Definition
  29. Sastre-Riba, S. (2011). Metacognitive functioning in gifted children. Neurología, 26(2), S11-S18. https://www.researchgate.net/publication/221942027_Metacognitive_functioning_in_gifted_children#fullTextFileContent
  30. Schindler, M., & Rott, B. (2017). Networking theories on giftedness—What we can learn from synthesizing Renzulli’s domain-general and Krutetskii’s mathematics-specific theory. Education Sciences, 7(1), Article 6. https://doi.org/10.3390/educsci7010006
  31. Schraw, G., & Graham, T. (1997). Helping gifted students develop metacognitive awareness. Roeper Review, 20(1), 4-8. https://doi.org/10.1080/02783199709553842
  32. Sercenia, J. C., & Prudente, M. S. (2023). Effectiveness of the metacognitive-based pedagogical intervention on mathematics achievement: A meta-analysis. International Journal of Instruction, 16(4), 561-578. https://doi.org/10.29333/iji.2023.16432a
  33. Shin, J., & Oh, W. (2024). Relation between characteristics of the gifted students in science and their task performance stages. Journal of the Korean Society for the Gifted Science Education, 16(1), 1-7. https://doi.org/10.29306/jseg.2024.16.1.1
  34. Sriraman, B. (2003). Mathematical giftedness, problem solving, and the ability to formulate generalizations: The problem-solving experiences of four gifted students. Journal of Secondary Gifted Education, 14(3), 151–165. https://doi.org/10.4219/jsge-2003-425
  35. Siegle, D., McCoach, D. B., Boldt, G. T., Hamilton, R., Gubbins, E. J., & Callahan, C. M. (2025). What really happens in gifted and talented education? A portrait of three states. Gifted Child Quarterly. https://doi.org/10.1177/00169862251370673
  36. Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. In F. M. Singer, L. J. Sheffield, V. Freiman, & M. Brandl (2016). (Eds.), Research on and activities for mathematically gifted students (pp. 1-41). Springer. https://doi.org/10.1007/978-3-319-39450-3_1
  37. Sipahi, Y., & Bahar, A. K. (2024). Who are the mathematically gifted? A systematic review of the research on cognitive characteristics. Journal of Educational Studies in Science and Mathematics, 3(2), 45-76. https://doi.org/10.29329/jessm.2024.1110.1
  38. Straka, O. (2021). Jak měřit metakognici (nejen) u nadaných dětí [How to measure metacognition (and not only) in gifted children]. Masarykova Univerzita. https://doi.org/10.5817/CZ.MUNI.M210-9905-2021
  39. Subotnik, R. F., Olszewski-Kubilius, P., & Worrell, F. C. (2011). Rethinking giftedness and gifted education: A proposed direction forward based on psychological science. Psychological Science in the Public Interest, 12(1), 3-54. https://doi.org/10.1177/1529100611418056
  40. Tibken, C., Richter, T., von der Linden, N., Schmiedeler, S., & Schneider, W. (2022). The role of metacognitive competences in the development of school achievement among gifted adolescents. Child Development, 93(1), 117-133. https://doi.org/10.1111/cdev.13640
  41. Toikka, S., Eronen, L., Atjonen, P., & Havu-Nuutinen, S. (2024). Combined conceptualisations of metacognitive knowledge to understand students’ mathematical problem solving. Cogent Education, 11(1), Article 2357901. https://doi.org/10.1080/2331186X.2024.2357901
  42. Veenman, M. V., Van Hout-Wolters, B. H., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3-14. https://doi.org/10.1007/s11409-006-6893-0
  43. Xie, Y., Zeng, F., & Yang, Y. (2024). A meta-analysis of the relationship between metacognition and academic achievement in mathematics: From preschool to university. Acta Psychologica, 249, Article 104486. https://doi.org/10.1016/j.actpsy.2024.104486
  44. Yanık, Z. Y., & Afat, N. (2022). Metacognitive awareness as a predictor of social-emotional learning skills in gifted and talented students. Gifted and Talented International, 37(2), 109-118. https://doi.org/10.1080/15332276.2022.2053316
  45. Yin, R. K. (2018). Case study research and applications: Design and methods. Sage Publications. https://study.sagepub.com/yin6e
  46. Young, A. E., & Worrell, F. C. (2018). Comparing metacognition assessments of mathematics in academically talented students. Gifted Child Quarterly, 62(3), 259-275. https://doi.org/10.1177/0016986218755915
  47. Zepeda, C. D., & Nokes Malach, T. J. (2023). Assessing metacognitive regulation during problem solving: A comparison of three measures. Journal of Intelligence, 11(3), Article 16. https://doi.org/10.3390/jintelligence11010016