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Enhancing Gifted Students’ Mathematical Thinking Skills (An Example of the Waldorf Approach)

Yıl 2026, Cilt: 34 Sayı: 2 , 207 - 237 , 30.04.2026
https://doi.org/10.24106/kefdergi.1939228
https://izlik.org/JA65CT59EG

Öz

This study investigates the potential of activities structured around the Waldorf educational approach’s emphasis on play, art, nature, and practical implementation to enhance the mathematical thinking skills of gifted students. It was conducted within a qualitative action research design over a twelve-week period with four gifted fourth-grade students enrolled in a formal educational institution, the Science and Art Center. The process began with initial activities and interviews, followed by the development and implementation of four action plans based on play, art, nature, and practical implementation, designed by the researchers with expert guidance. Data were collected through a mathematical thinking test, semi-structured interviews, and field notes recorded by one of the researchers, and were analyzed through content analysis. The findings revealed significant progress in students’ specializing, generalizing, and conjecturing skills. However, compared with other dimensions of mathematical thinking, improvement in justifying and convincing skills remained relatively limited. The study is significant in addressing the limited body of research on the role of the Waldorf approach in fostering the mathematical thinking of gifted students. The findings indicate that art, nature-, and play-based pedagogy can make a meaningful contribution to the development of several dimensions of mathematical thinking, while also revealing the need for more explicit instructional support in the areas of justification and convincing. In this respect, the study offers both theoretical and practical implications for teachers and researchers concerning the use of alternative pedagogical approaches in mathematics education.

Kaynakça

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Özel Yetenekli Öğrencilerin Matematiksel Düşünme Becerilerinin Geliştirilmesi (Waldorf Yaklaşımı Örneği)

Yıl 2026, Cilt: 34 Sayı: 2 , 207 - 237 , 30.04.2026
https://doi.org/10.24106/kefdergi.1939228
https://izlik.org/JA65CT59EG

Öz

Bu çalışma, Waldorf eğitim yaklaşımının öğrenme süreçlerinde öne çıkardığı oyun, sanat, doğa ve pratik uygulama temelli etkinliklerin üstün yetenekli öğrencilerin matematiksel düşünme becerilerini geliştirme potansiyelini incelemeyi amaçlamaktadır. Araştırma, nitel araştırma yaklaşımı çerçevesinde eylem araştırması deseninde yürütülmüştür. Çalışma grubu, dördüncü sınıf düzeyinde öğrenim gören ve aynı zamanda formel bir eğitim kurumu olan Bilim ve Sanat Merkezinde de eğitim gören dört üstün yetenekli öğrenciden oluşmaktadır. Araştırma süreci on iki hafta sürmüş; başlangıç etkinlikleri ve görüşmelerin ardından, uzman görüşü doğrultusunda araştırmacılar tarafından oyun, sanat, doğa ve pratik uygulama kavramlarına dayalı dört eylem planı geliştirilmiş ve uygulanmıştır. Veriler, matematiksel düşünme testi, yarı yapılandırılmış görüşmeler ve araştırmacılardan birine ait saha notları aracılığıyla toplanmış; elde edilen veriler içerik analiziyle çözümlenmiştir. Bulgular, öğrencilerin özelleştirme, genelleme yapma ve varsayım oluşturma becerilerinde belirgin bir gelişim gösterdiğini ortaya koymuştur. Buna karşılık, gerekçelendirme ve ikna etme becerilerindeki gelişimin diğer matematiksel düşünme becerilerine kıyasla daha sınırlı kaldığı belirlenmiştir. Sonuç olarak çalışma, Waldorf yaklaşımına dayalı sanat, doğa, oyun ve deneyim odaklı pedagojik uygulamaların üstün yetenekli öğrencilerin belirli matematiksel düşünme becerilerini desteklemede işlevsel bir potansiyel taşıdığını göstermektedir. Ayrıca bulgular, gerekçelendirme ve ikna etme becerilerinin geliştirilmesi için daha açık yapılandırılmış öğretimsel desteklere ihtiyaç duyulduğunu ortaya koyarak matematik eğitiminde alternatif pedagojik yaklaşımların uygulanabilirliğine ilişkin kuramsal ve pratik çıkarımlar sunmaktadır.

Kaynakça

  • Aljabreen, H. (2020). Montessori, Waldorf, and Reggio Emilia: A comparative analysis of alternative models of early childhood education. International Journal of Early Childhood, 52(3), 337–353. https://doi.org/10.1007/s13158-020-00277-1
  • Amador, J. M. (2022). Mathematics teacher educator noticing: Examining interpretations and evidence of students’ thinking. Journal of Mathematics Teacher Education, 25(2), 163–189. https://doi.org/10.1007/s10857-020-09483-z
  • Assmus, D. (2018). Characteristics of mathematical giftedness in early primary school age. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students (pp. 145–167). Springer. https://doi.org/10.1007/978-3-319-73156-8_6
  • Assmus, D., & Fritzlar, T. (2022). Mathematical creativity and mathematical giftedness in the primary school age range: An interview study on creating figural patterns. ZDM–Mathematics Education, 54(1), 113–131. https://doi.org/10.1007/s11858-022-01328-8
  • Attfield, K. (2024). The humane education of Waldorf. Frontiers in Education, 9, Article 1332597. https://doi.org/10.3389/feduc.2024.1332597
  • Bak, T. (2023). Stepping into the mainstream: Exploring Steiner streams in publicly funded schools in Australia, 1990–2011. Educational Review, 75(5), 833–850. https://doi.org/10.1080/00131911.2021.1942792
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  • Evans, T., Mejía-Ramos, J. P., & Inglis, M. (2022). Do mathematicians and undergraduates agree about explanation quality? Educational Studies in Mathematics, 111(3), 445–467. https://doi.org/10.1007/s10649-022-10164-2
  • Eysink, T. H., Gersen, L., & Gijlers, H. (2015). Inquiry learning for gifted children. High Ability Studies, 26(1), 63–74. https://doi.org/10.1080/13598139.2015.1038379
  • Faizah, S., Nusantara, T., Sudirman, S., & Rahardi, R. (2020). Exploring students’ thinking process in mathematical proof of abstract algebra based on Mason’s framework. Journal for the Education of Gifted Young Scientists, 8(2), 871–884. http://dx.doi.org/10.17478/jegys.689809
  • Goldshmidt, G. (2017). On the unique place of art in Waldorf education. European Journal of Education Studies, 3(8), 36–50. https://doi.org/10.5281/zenodo.818084
  • Goos, M., & Kaya, S. (2020). Understanding and promoting students’ mathematical thinking: A review of research published in ESM. Educational Studies in Mathematics, 103, 7–25. https://doi.org/10.1007/s10649-019-09921-7
  • Gunadi, F., Sudirman, S., Runisah, R., Senjaya, A., & Mustari, S. (2023, February). Impact of STEM learning (Science, Technology, Engineering, and Mathematics) on students’ mathematics thinking ability: Systematic literature review. In Proceedings of the 2nd Multidisciplinary International Conference, MIC 2022, Semarang, Central Java, Indonesia.
  • Hallam, J., Egan, S., & Kirkham, J. (2016). An investigation into the ways in which art is taught in an English Waldorf Steiner school. Thinking Skills and Creativity, 19, 136–145. https://doi.org/10.1016/j.tsc.2015.07.003
  • Hallgren, K. A. (2012). Computing inter-rater reliability for observational data: An overview and tutorial. Tutorials in Quantitative Methods for Psychology, 8(1), 23–34. https://doi.org/10.20982/tqmp.08.1.p023
  • Huchingson, R. (1990). A comparative study between the behaviors of students in a public school program for the gifted and those in Waldorf schools in terms of Renzulli's “gifted behaviors” [Doctoral dissertation, University of Michigan]. ProQuest Dissertations and Theses Global.
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  • Kodsi, S. H. (2022). Constructive play in Waldorf and normative preschools in Israel: Technological thinking and design process during free play. International Journal of Technology and Design Education, 32(2), 735–748. https://doi.org/10.1007/s10798-020-09623-9
  • Komatsu, K., Stylianides, G. J., & Stylianides, A. J. (2019). Task design for developing students’ recognition of the roles of assumptions in mathematical activity. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the eleventh congress of the European Society for Research in Mathematics Education (pp. 233–240). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
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  • Lambert, R., Tan, P., Hunt, J., & Candela, A. G. (2018). Rehumanizing the mathematics education of students with disabilities; Critical perspectives on research and practice. Investigations in Mathematics Learning, 10(3), 129–132. https://doi.org/10.1080/19477503.2018.1463006
  • Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231–258. https://doi.org/10.1207/s15327833mtl0703_3
  • 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
  • Lev, M., & Leikin, R. (2017). The interplay between excellence in school mathematics and general giftedness: Focusing on mathematical creativity. In R. Leikin & B. Sriraman (Eds.), Creativity and giftedness: Interdisciplinary perspectives from mathematics and beyond (pp. 225–238). Springer. https://doi.org/10.1007/978-3-319-38840-3_14
  • Liamputtong, P. (2019). Qualitative inquiry. In P. Liamputtong (Ed.), Handbook of research methods in health social sciences. Springer. https://doi.org/10.1007/978-981-10-5251-4_53
  • Lim, S. A., Jung, J. Y., & Kalyuga, S. (2023). Effectiveness of invention tasks and explicit instruction in preparing intellectually gifted adolescents for learning. Instructional Science, 51(6), 921–952. https://doi.org/10.1007/s11251-023-09616-w
  • Lorenza, N., Sudirman, S., & Susiswo, S. (2024). Students' specializing thinking in solving arithmetic sequence and series problems. PRISMA, 13(1), 70–80. https://doi.org/10.35194/jp.v13i1.3930
  • Lutzker, P. (2024). Artistic practice in Waldorf teacher education: A sensory-aesthetic concept for a digital age. Frontiers in Education, 9, 1363254. https://doi.org/10.3389/feduc.2024.1363254
  • Maker, C. J. (1982). Curriculum development for the gifted. Aspen System Corporation.
  • Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically. Pearson.
  • Masters, B. (2009). Distinctive features of Waldorf education and their relevance for or bearing on assessment. El Guiniguada, 18, 81–100.
  • McNiff, J., & Whitehead, J. (2010). You and your action research project (3rd ed.). Routledge.
  • MoNE. (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics course curriculum primary and secondary school 1, 2, 3, 4, 5, 6, 7, and 8th grades]. https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMATİK%20ÖĞRETİM%20PROGRAMI%202018v.pdf
  • MoNE. (2024). İlkokul matematik dersi öğretim programı (1, 2, 3 ve 4. Sınıflar) [Mathematics curriculum primary school 1, 2, 3, and 4th grades]. https://tymm.meb.gov.tr/ogretim-programlari/ders/ilkokul-matematik-dersi
  • MoNE. (2025). 2025-2026 yılı bilim ve sanat merkezleri öğrenci tanılama ve yerleştirme kılavuzu. [2025-2026 science and art centers student identification and placement guide]. https://www.meb.gov.tr/meb_iys_dosyalar/2025_11/13094632_2025-2026_Bilim_Sanat_Merkezleri_Ogrenci_Tanilama_ve_Yerlestirme_Klavuzu.pdf
  • Mora, M., Jaime, A., & Gutiérrez, A. (2022). Descriptors of generalization in primary school mathematically gifted students. In S. A. Chamberlin (Ed.), Proceedings of the 12th InternationalConference on Mathematical Creativity andGiftedness (MCG 12) (pp. 203–209). WTM-Verlag für wissenschaftliche Texte und Medien Münster.
  • Neumann, R. (2024). Media education in Waldorf/Steiner schools. Frontiers in Education, 9, 1365149. https://doi.org/10.3389/feduc.2024.1365149
  • Nicholson, D. W. (2000). Layers of experience: Forms of representation in a Waldorf school classroom. Journal of Curriculum Studies, 32(4), 575–587. https://doi.org/10.1080/00220270050033637
  • Nordlund, C. N. (2013). Waldorf education: Breathing creativity. Art Education, 66(2), 13–19. https://doi.org/10.1080/00043125.2013.11519211
  • Oberski, I., Pugh, A., MacLean, A., & Cope, P. (2007). Validating a Steiner–Waldorf teacher education programme. Teaching in Higher Education, 12(1), 135–139. https://doi.org/10.1080/13562510601102388
  • O'Connor, D., & Angus, J. (2014). Give them time—An analysis of school readiness in Ireland's early education system: A Steiner Waldorf perspective. Education 3–13, 42(5), 488–497. https://doi.org/10.1080/03004279.2012.723726
  • Paschen, H. (2014). Waldorf education and Rudolf Steiner schools as a topic of educational science. Croatian Journal of Education, 16(1), 191–215. https://hrcak.srce.hr/120162
  • Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage.
  • Pedersen, M. K. (2023). The use of DGE and CAS to support mathematical thinking competency: A literature review. NOMAD: Nordic Studies in Mathematics Education, 28(3-4), 177–197. https://doi.org/10.7146/nomad.v28i3-4.149267
  • Piske, F. H. R., & Stoltz, T. (2021). Creativity in socio-interactional pedagogy and Waldorf Pedagogy: implications for working with the gifted students. Educar em Revista, 37, e81545. https://doi.org/10.1590/0104-4060.81545
  • Pitta-Pantazi, D., Constantinos, C., Kontoyianni, K., & Kattou, M. (2011). A model of mathematical giftedness: Integrating natural, creative, and mathematical abilities. Canadian Journal of Science, Mathematics and Technology Education, 11(1), 39–54. https://doi.org/10.1080/14926156.2011.548900
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  • Robson, C. (2024). Real world research (5th ed.). Wiley.
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  • Stacey, K. (2006). What is mathematical thinking and why is it important? Proceedings of the APEC- Tsukuba International Conference 2007: Innovative Teaching Mathematics through Lesson Study, Tokyo, Japan. https://www.criced.tsukuba.ac.jp/math/apec/apec2007/kaye_stacey.pdf
  • Steiner, R. (1996). The education of the child. Steiner Books.
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  • Van Schie, T. J., & Vedder, P. (2023). Different pedagogies, equivalent results: A comparison of language skills and school attitude between Waldorf school students and public school students in the Philippines. Globalisation, Societies and Education, 24 (29), 490-503. https://doi.org/10.1080/14767724.2023.2248902
  • VanTassel-Baska, J. (2013). The world of cross-cultural research: Insights for gifted education. Journal for the Education of the Gifted, 36(1), 6–18. https://doi.org/10.1177/0162353212471451
  • Veiga, M. D. (2015). Revisiting humanism as a guiding principle for education: An excursion into Waldorf pedagogy. Educar em Revista, 56, 19–31. http://dx.doi.org/10.1590/0104-4060.41417
  • Villa-Ochoa, J. A., & Suárez-Téllez, L. (2021). Computer algebra systems and dynamic geometry for mathematical thinking. In M. Danesi (Ed.), Handbook of cognitive mathematics (pp. 1–27). Springer.
  • Waldorf World List. (2024). Directory of Steiner-Waldorf schools, kindergartens and teacher education centers worldwide. https://www.freunde-waldorf.de/freunde/fileadmin/user_upload/images/Waldorf_World_List/Waldorf_World_List.pdf
  • Wright, P. (2013). Theory of knowledge or knowledge of the child? Challenging the epistemological assumptions of the curriculum debate on geography from an alternative viewpoint. Oxford Review of Education, 39(2), 193–210. http://www.jstor.org/stable/42001820
  • Wu, W. R., & Yang, K. L. (2022). The relationships between computational and mathematical thinking: A review study on tasks. Cogent Education, 9(1). https://doi.org/10.1080/2331186X.2022.2098929
  • Yıldırım, A., & Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences (11th ed.). Seçkin.
Toplam 89 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik Eğitimi
Bölüm Araştırma Makalesi
Yazarlar

Niymet Demirci 0000-0002-2763-1879

Ebru Ergül Bu kişi benim

Gönderilme Tarihi 4 Nisan 2025
Kabul Tarihi 10 Şubat 2026
Yayımlanma Tarihi 30 Nisan 2026
DOI https://doi.org/10.24106/kefdergi.1939228
IZ https://izlik.org/JA65CT59EG
Yayımlandığı Sayı Yıl 2026 Cilt: 34 Sayı: 2

Kaynak Göster

APA Demirci, N., & Ergül, E. (2026). Enhancing Gifted Students’ Mathematical Thinking Skills (An Example of the Waldorf Approach). Kastamonu Education Journal, 34(2), 207-237. https://doi.org/10.24106/kefdergi.1939228

Kastamonu Eğitim Dergisi, Creative Commons Atıf 4.0 Uluslararası Lisansı (CC BY) ile lisanslanmıştır.

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