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Üstün Yetenekli Öğrencilerin Matematiksel Akıl Yürütme Yaklaşımlarının İncelenmesi

Yıl 2025, Sayı: 66, 4490 - 4532, 29.12.2025
https://doi.org/10.53444/deubefd.1564667

Öz

Üstün yetenek, bireyde sürekli bulunan ve her zaman ortaya çıkabilen bir özellik değil, tam tersine ortaya çıkarılması ve geliştirilmesi özel bir çaba gerektiren hassas bir değerdir. Bu nedenle bu özel potansiyelin muazzam bir yeteneğe ve sonuca dönüşebilmesi için uygun eğitim desteğinin sağlanması kritik öneme sahiptir. Eğitim sürelerinin çoğunu akranlarıyla aynı ortamda, aynı eğitim içeriğine yönelik uygulamalarla geçiren, matematik alanında özel yetenekli öğrenciler, üst düzey düşünme ve muhakeme becerilerini değerlendirmede sınırlamalarla karşı karşıya kalmaktadır. Üstün yetenekli öğrencilerin matematikteki muhakeme süreçleri tam bir muamma olup, bu öğrencilerin bazı önemli ve ortak özelliklerinden literatürde araştırmacılar tarafından bahsedilmektedir. Bu bulgulara dayanarak çalışmanın amacı üstün yetenekli öğrencilerin matematiksel muhakeme yaklaşımlarını incelemektir. Araştırma eylem araştırması yöntemiyle tasarlanmıştır. Araştırmanın örneklemini Özel Yetenek Geliştirme Programında öğrenim gören 18 yedinci sınıf öğrencisi oluşturmaktadır. Uygulama süresi on haftadır. Veri toplama araçları; akıl yürütme etkinliklerinin çözüm sayfaları, klinik görüşmeler, araştırmacı günlüğü ve uygulamaya ilişkin ses kayıtlarıdır. Araştırma, bulguları ve önerileriyle daha sonraki araştırmalar için önemli bileşenler sunuyor.

Kaynakça

  • Akkaş, E., & Tortop, H. S. (2015). Üstün yetenekliler eğitiminde farklılaştırma: temel kavramlar, modellerin karşılaştırılması ve öneriler [Differentiation in gifted education: basic concepts, comparison of models and suggestions]. Journal of Gifted Education and Creativity, 2(2), 31-44.
  • Apaydın, Z., & Taş, E. (2010). Farklı etkinlik tiplerinin öğretmen adaylarının akıl yürütme becerileri üzerindeki etkileri [The effects of different activity types on prospective teachers' reasoning skills]. Türk Fen Eğitimi Dergisi, 7(4), 172-188.
  • Aydoğan Yenmez, A., & Gökçe, S. (2022). Matematiksel akıl yürütme [Mathematical reasoning]. Anı Yayıncılık. Baron, J. (1984). Personality and intelligence. In R. J. Sternberg (Ed.), Handbook of human intelligence (pp. 308–351). Cambridge University Press.
  • Başaran, S. (2011). Üniversite öğrencilerinin matematiksel düşünme ve akıl yürütme becerileriyle ilgili duyuşsal ve demografik etmenlerin araştırılması [Doktora tezi, Orta Doğu Teknik Üniversitesi]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
  • Baykul, Y. (2014). İlkokulda matematik öğretimi [Teaching Mathematics in Primary School] (12. baskı). Pegem Akademi.
  • Bingham, A. (1983). Çocuklarda problem çözme yeteneklerinin geliştirilmesi [Developing problem solving skills in children]. 4. Baskı, (F. Oğuzkan, Trans.). Milli Eğitim Basımevi.
  • Bishop, J. W., Otto, A. D., & Lubinski, C. A. (2001). Promoting algebraic reasoning using students' thinking. Mathematics Teaching in the Middle School, NCTM, 6(9), 508-514.
  • Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics. 75(1), 89-105. https://doi.org/10.1007/s10649-010-9242-9
  • Borovik, A., & Gardiner, T. (2006, July). Mathematical abilities and mathematical skills [Paper presentation]. World Federation of National Mathematics Com- petitions Conference, University of Manchester, Cambridge, England.
  • Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer Science and Business Media.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2016). Bilimsel araştırma yöntemleri [Scientific research methods]. Pegem Akademi Yayıncılık.
  • Copur-Gencturk, Y., Thacker, I., & Quinn, D. (2021). K-8 teachers’ overall and gender-specific beliefs about mathematical aptitude. International Journal of Science and Mathematics Education, 19, 1251-1269. https://doi.org/10.1007/s10763-020-10104-7
  • Creswell, J. W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39(3), 124-130. https://doi.org/10.1207/s15430421tip3903_2
  • Çiftci, Z., & Akgün, L. (2021). Matematiksel akıl yürütme becerisini sınıflandırmaya yönelik kavramsal bir çerçeve [A conceptual framework for classifying mathematical reasoning skills]. Atatürk Üniversitesi Kazım
  • Karabekir Eğitim Fakültesi Dergisi, (43), 556-575. https://doi.org/10.33418/ataunikkefd.891101 Diezmann, C. M., & Watters, J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal for the Education of the Gifted, 25, 7- 31. https://doi.org/10.1177/016235320102500102
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An Examination of Gifted Students’ Mathematical Reasoning Approaches

Yıl 2025, Sayı: 66, 4490 - 4532, 29.12.2025
https://doi.org/10.53444/deubefd.1564667

Öz

Special talent is not a feature that is constantly present in the individual and can always appear, on the contrary, it is a sensitive value that requires a special effort to reveal and develop. For this reason, it is critical to provide appropriate educational support for this special potential to evolve into a tremendous talent and outcome. Students with special abilities in mathematics, who spend most of their educational time in the same environment with their peers, with applications for the same educational content, face limitations in assessing their higher-order thinking and reasoning skills. The reasoning processes of gifted students in mathematics is a complete mystery, some important and common features of these students are mentioned by researchers in the literature. Based on these findings, the aim of the study is to examine the mathematical reasoning approaches of gifted students. The research was designed with the action research method. The sample of the study consists of 18 seventh grade students studying in the Special Talents Development Program. The duration of the implementation is ten weeks. Data collection tools are solution sheets of the reasoning activities, clinical interviews, researcher log and audio recording of the implementation. With its findings and suggestions, the research offers crucial components for subsequent investigations.

Kaynakça

  • Akkaş, E., & Tortop, H. S. (2015). Üstün yetenekliler eğitiminde farklılaştırma: temel kavramlar, modellerin karşılaştırılması ve öneriler [Differentiation in gifted education: basic concepts, comparison of models and suggestions]. Journal of Gifted Education and Creativity, 2(2), 31-44.
  • Apaydın, Z., & Taş, E. (2010). Farklı etkinlik tiplerinin öğretmen adaylarının akıl yürütme becerileri üzerindeki etkileri [The effects of different activity types on prospective teachers' reasoning skills]. Türk Fen Eğitimi Dergisi, 7(4), 172-188.
  • Aydoğan Yenmez, A., & Gökçe, S. (2022). Matematiksel akıl yürütme [Mathematical reasoning]. Anı Yayıncılık. Baron, J. (1984). Personality and intelligence. In R. J. Sternberg (Ed.), Handbook of human intelligence (pp. 308–351). Cambridge University Press.
  • Başaran, S. (2011). Üniversite öğrencilerinin matematiksel düşünme ve akıl yürütme becerileriyle ilgili duyuşsal ve demografik etmenlerin araştırılması [Doktora tezi, Orta Doğu Teknik Üniversitesi]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
  • Baykul, Y. (2014). İlkokulda matematik öğretimi [Teaching Mathematics in Primary School] (12. baskı). Pegem Akademi.
  • Bingham, A. (1983). Çocuklarda problem çözme yeteneklerinin geliştirilmesi [Developing problem solving skills in children]. 4. Baskı, (F. Oğuzkan, Trans.). Milli Eğitim Basımevi.
  • Bishop, J. W., Otto, A. D., & Lubinski, C. A. (2001). Promoting algebraic reasoning using students' thinking. Mathematics Teaching in the Middle School, NCTM, 6(9), 508-514.
  • Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics. 75(1), 89-105. https://doi.org/10.1007/s10649-010-9242-9
  • Borovik, A., & Gardiner, T. (2006, July). Mathematical abilities and mathematical skills [Paper presentation]. World Federation of National Mathematics Com- petitions Conference, University of Manchester, Cambridge, England.
  • Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer Science and Business Media.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2016). Bilimsel araştırma yöntemleri [Scientific research methods]. Pegem Akademi Yayıncılık.
  • Copur-Gencturk, Y., Thacker, I., & Quinn, D. (2021). K-8 teachers’ overall and gender-specific beliefs about mathematical aptitude. International Journal of Science and Mathematics Education, 19, 1251-1269. https://doi.org/10.1007/s10763-020-10104-7
  • Creswell, J. W., & Miller, D. L. (2000). Determining validity in qualitative inquiry. Theory into Practice, 39(3), 124-130. https://doi.org/10.1207/s15430421tip3903_2
  • Çiftci, Z., & Akgün, L. (2021). Matematiksel akıl yürütme becerisini sınıflandırmaya yönelik kavramsal bir çerçeve [A conceptual framework for classifying mathematical reasoning skills]. Atatürk Üniversitesi Kazım
  • Karabekir Eğitim Fakültesi Dergisi, (43), 556-575. https://doi.org/10.33418/ataunikkefd.891101 Diezmann, C. M., & Watters, J. (2001). The collaboration of mathematically gifted students on challenging tasks. Journal for the Education of the Gifted, 25, 7- 31. https://doi.org/10.1177/016235320102500102
  • Dowdall, C. B., & Colangelo, N. (1982). Underachieving gifted students: Review and implications. Gifted Child Quarterly, 26(4), 179-184.
  • Erdem, E. (2015). Zenginleştirilmiş öğrenme ortamının matematiksel muhakemeye ve tutuma etkisi [The effect of enriched learning environment on mathematical reasoning and attitude] [Doctoral dissertation, Atatürk University]. Yükseköğretim Kurulu Ulusal Tez Merkezi.
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  • Leikin, R. (2010). Teaching the mathematically gifted. Gifted Education International, 27(2), 161-175. https://doi.org/10.1177/026142941002700206
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  • Leikin, R. (2019). Giftedness and high ability in mathematics. Encyclopedia of MathematicsEducation, 315-325.https://doi.org/10.1007/978-3-030-15789-0_65
  • Lithner, J. (2000a). Mathematical reasoning and familiar procedures. International Journal of Mathematical Education in Science and Technology, 31(1), 83–95. https://doi.org/10.1080/002073900287417
  • Lithner, J. (2000b). Mathematical reasoning in school tasks. Educational Studies in Mathematics, 41(2), 165–190. https://doi.org/10.1023/A:1003956417456
  • Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52(1), 29–55. https://doi.org/10.1023/A:1023683716659
  • Lithner, J. (2004). Mathematical reasoning in calculus textbook exercise. Journal of Mathematical Behavior, 23(4), 371–496. https://doi.org/10.1016/j.jmathb.2004.09.003
  • Lithner, J. (2005). A framework for analysing qualities of mathematical reasoning: Version 3. Research Reports in Mathematics Education 3, Department of Mathematics, Umea University.
  • Lithner, J. (2006). A framework for analysing creative and imitative mathematical reasoning. Research Reports in Mathematics Education (In Press), Department of Mathematics, Ume˚a University.
  • Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67 (3), 255-276.
  • Lupkowski-Shoplik, A., Benbow, C. P., Assouline, S. G., & Brody, L. E. (2003). Ta- lent searches: Meeting the needs of academically talented youth. Handbook of Gifted Education, 3, 204-218.
  • Malloy, C. E. (1999). Developing mathematical reasoning in the middle grades recognizing diversity. In Lee V. Stiff, 1999 (Eds.) Developing mathematical reasoning in grades K12,1999 year book. Virginia; National Council of Teachers of Mathematics.
  • Martin, M. R., & Pickett, M. T. (2008). The effects of differentiated instruction on motivation and engagement in fifth-grade gifted math and music students (Unpublished master’s thesis). Saint Xavier University, United States.
  • McCoach, D. B., & Siegle, D. (2003). Factors that differentiate underachieving gifted students from high-achieving gifted students. Gifted Child Quarterly, 47(2), 144-154. https://doi.org/10.1177/001698620304700205
  • McKernan, J. (2007). Curriculum and imagination: Process theory, pedagogy and action research. Routledge.
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  • Miller R. C. (1990). Discovering mathematical talent: Model for creative productivity.Connection of Giftedness. Cambridge.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
  • Moshman, D. (1994). Reason, reasons, and reasoning: A constructivist account of human rationality. Theory & Psychology, 4, 245-260. https://doi.org/10.1177/0959354394042005
  • National Association for Gifted Children. (2005). State of the states 2004-2005. Washington, Author.
  • National Council of Teachers of Mathematics [NCTM], (1980). Agenda for Action. NCTM, Reston, Virginia.
  • National Council of Teachers of Mathematics [NCTM], (2013). Principles and standards for school mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
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  • Nickerson, R. S. (2004). Cognition and Chance: The Psychology of Probabilistic Reasoning. Lawrence Erlbaum Associates.
  • Ngiamsunthorn, P. S. (2020). Promoting creative thinking for gifted students in undergraduate mathematics. Journal of Research and Advances in Mathematics Education, 5(1), 13-25. https://doi.org/10.23917/jramathedu.v5i1.9675
  • Ozdemir, D., & Isiksal Bostan, M. (2021). A Design Based Study: Characteristics of Differentiated Tasks for Mathematically Gifted Students. European Journal of Science and Mathematics Education, 9(3), 125-144. https://doi.org/10.30935/scimath/10995
  • Parish, L. (2014). Defining mathematical giftedness. In J. Anderson, M. Cavanagh & A. Prescott (Ed). Curriculum in focus: Research guided practice (pp. 509-516). MERGA.
  • Pitta-Pantazi, D., Christou, C., Kontoyianni, K., & Kattou, M. (2011). A model ofmathematical 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
  • Perkins, D., Jay, E., & Tishman, S. (1993). Beyond abilities: A dispositional theory of thinking. The Merrill-Palmer Quarterly, 39(1), 1-2.
  • Rotigel, J. V., & Fello, S. (2004). Mathematically gifted students: How can we meet their needs? Gifted Child Today, 27(4), 46-51. https://doi.org/10.4219/gct-2004-150
  • Rule, A. C. (2007). Mystery boxes: Helping children improve their reasoning. Early Childhood Education Journal, 35(1), 13-18. https://doi.org/10.1007/s10643-007-0156-9
  • Saltık Ayhanöz, G. (2022). The place of intelligence games in mathematics education for gifted students. In Zahal O. (Ed.), Current Research In Edititon (pp. 152-168), Gece Publishing.
  • Sheffield, L. J. (2017). Dangerous myths about “gifted” mathematics students. ZDM, 49(1), 13-23. https://doi.org/10.1007/s11858-016-0814-8
  • Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. Springer Nature.
  • 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
  • Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? Journal of Secondary Gifted Education, 17(1), 20-36. https://doi.org/10.4219/jsge-2005-389
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  • Stiff, L. V., & Curcio, F. R. (1999). Developing Mathematical Reasoning in GradesK-12. 1999 Yearbook. National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA 20191-1593.
  • Storey, S. O. (2004). Teacher questioning to improve early childhood reasoning (Publication No. 3132260). [Doctoral Thesis, The University of Arizona]. ProQuest Dissertations and Theses database.
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  • Trna, J. (2014). IBSE and gifted students. Science Education International, 25(1), 19- 28. Umay, A., & Kaf, Y. (2005). Matematikte kusurlu akıl yürütme üzerine bir çalışma[A study on flawed reasoning in mathematics]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28(1), 188-195.
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  • Van de Walle, J., Karp, K., Bay-Williams, J. M., Brass, A., Bentley, B., Ferguson, S.,... & Wilkie, K. (2019). Primary and middle years mathematics: teaching developmentally. Pearson Australia.
  • Westberg, K. L., Archambault Jr, F. X., Dobyns, S. M., & Salvin, T. J. (1993). The classroom practices observation study. Journal for the Education of the Gifted, 16(2), 120-146. https://doi.org/10.1177/016235329301600204
  • Whittaker, J. V. (2014). Good thinking! Fostering young children’s reasoning and problem solving. Young Children, 69, 80-89.
  • Wilkins, M. M., Wilkins, J. L., & Oliver, T. (2006). Differentiating the curriculum for elementary gifted mathematics students. Teaching Children Mathematics, 13(1), 6-13. https://doi.org/10.5951/TCM.13.1.0006
  • Winner, E. (2000). The origins and ends of giftedness. American Psychologist, 55(1), 159. https://doi.org/10.1037/0003-066X.55.1.159
  • Winteridge, D. (1989). A handbook for primary mathematics co-ordinators. Paul Chapman Publishing, Lond. Yankelewitz, D. (2009). The development of mathematical reasoning in elementary school students’ exploration of fraction ideas [Doctoral dissertation, New Brunswick, Rutgers, The State University of New Jersey].
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri[Qualitative research methods in the social sciences]. Seçkin Yayıncılık.
  • Zembat, I. O. (2008). Pre-service teachers’ use of different types of mathematical reasoning in paper-and-pencil versus technology-supported environments. International Journal of Mathematical Education in Science and Technology, 39(2), 143–160. https://doi.org/10.1080/00207390701828705
Toplam 95 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik Eğitimi, Özel Yetenekli Eğitimi
Bölüm Araştırma Makalesi
Yazarlar

Gülşah Saltık Ayhanöz 0000-0003-0174-9999

Arzu Aydoğan Yenmez 0000-0001-8595-3262

Gönderilme Tarihi 11 Ekim 2024
Kabul Tarihi 11 Kasım 2025
Yayımlanma Tarihi 29 Aralık 2025
Yayımlandığı Sayı Yıl 2025 Sayı: 66

Kaynak Göster

APA Saltık Ayhanöz, G., & Aydoğan Yenmez, A. (2025). An Examination of Gifted Students’ Mathematical Reasoning Approaches. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi(66), 4490-4532. https://doi.org/10.53444/deubefd.1564667