Investigation of Gifted Students' Errors Related to Height and Diagonal Concepts in Geometry Teaching

Yıl 2024, Cilt: 12 Sayı: 24, 523 - 548, 21.10.2024

Gülşah Saltık Ayhanöz , Solmaz Damla Gedik Altun

https://doi.org/10.18009/jcer.1470685

Öz

The aim of this study was to examine the errors of gifted students regarding the concepts of height and diagonal in Geometry. Eighteen gifted students studying at a Science and Art Center in central Anatolia participated in the study. A knowledge test consisting of 5 questions was prepared to collect data. The knowledge test was applied to gifted students. Descriptive analysis method was used to analyze the data in the study. The data obtained in line with the responses of the students to the knowledge test used as a data collection tool were classified under categories in line with the purpose of the study by coding the errors in the solutions of the questions. According to the data obtained, it was concluded that the concept of diagonal and height, which constitute the basis of many subjects in geometry education of gifted individuals, should be emphasized more.

Anahtar Kelimeler

Gifted students, geometry, error, height, diagonal

Etik Beyan

Ethical Committee Permission Information Name of the board that carries out ethical assessment: Niğde Ömer Halisdemir University Social and Humanities Scientific Research and Publication Ethics Board The date and number of the ethical assessment decision: 31.01.2024 and 2024/01-16

Kaynakça

• Altıntaş, E. & İlgün Ş. (2017). Ortaokul matematik öğretmenlerinin geometride “yükseklik” ve “diklik merkezi” kavramına ilişkin kavram yanılgıları misconceptions of secondary school mathematics teachers regarding the concepts of "height" and "center of perpendicularity" in geometry. International Periodical for the Languages Literature and History of Turkish or Turkic, 12(29), 73-86.
• Arabacı, D., & Kanbolat, O. (2023). Pre-service elementary mathematics teachers’ evaluations of meetings with expert and peer participation based on Van Hiele geometric thinking levels. International e-Journal of Educational Studies, 7(15), 752-768. https://doi.org/10.31458/iejes.1345567
• Ataman, A. (2003). Üstün zekâlı ve üstün yetenekli çocuklar (Ed: A. Ataman). Özel gereksinimli çocuklar ve özel eğitime giriş gifted and gifted children (Ed: A. Ataman) Children with special needs and introduction to special education. (s. 173-195). Gündüz Eğitim ve Yayıncılık.
• Ayvaz, Ü., Gündüz, N. & Bozkuş, F. (2017). Understanding of prospective mathematics teachers of the concept of diagonal. Journal on Mathematics Education, 8(2), 165-184.
• Bütüner, S. Ö. (2017). Matematik öğretmen adaylarının geometri alan bilgilerinin belirlenmesi: Açı, köşegen, yükseklik, dörtgen [Determination of mathematics teacher candidates' geometry field knowledge: Angle, diagonal, height, quadrilateral]. Amasya Üniversitesi Eğitim Fakültesi Dergisi, 6(2), 501-530. Cunningham, R. F., & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. Erişim Tarihi: 7 Haziran 2023, www.k12prep. math.ttu.edu.tr
• Çoker, D. & Karaçay, T. (1983). Matematik terimleri sözlüğü [Dictionary of mathematical terms]. (1. Baskı). Türk Dil Kurumu Yayınları.
• Dağlı, H. (2010). İlköğretim beşinci sınıf öğrencilerinin çevre, alan ve hacim konularına ilişkin kavram yanılgıları [Misconceptions of primary school fifth grade students regarding perimeter, area and volume]. Yüksek Lisans Tezi, Afyon Kocatepe Üniversitesi.
• Fazlı, E., & Avcı, Ö. (2022). Matematik eğitiminde motivasyon ve öz-düzenleme: Tek bir durum çalışması [otivation and self-regulation in mathematics education: A single case study]. Harran Maarif Dergisi, 7(1), 1-45.
• Fıçıcı A., & Siegle D. (2008). International teachers’ judgment of gifted mathematics student characteristics. Journal of Gifted Talented International, 23(1), 22-37. https://doi.org/10.1080/15332276.2008.11673510
• Gutierrez, A. & Jaime, A. (1999). Pre-service primary teachers’ understanding of the concept of attitude of a triangle. Journal of Mathematics Teacher of Education, 2(3), 253-275.
• Gül, Ş., & Sözbilir, M. (2015). Fen ve matematik eğitimi alanında gerçekleştirilen ölçek geliştirme araştırmalarına yönelik tematik içerik analizi [Thematic content analysis of scale development research in the field of science and mathematics education]. Eğitim ve Bilim, 40, 85-102.
• Gürefe, N. & Gültekin, S.H. (2016). Yükseklik kavramına dair öğrenci bilgilerinin incelenmesi [Examination of student knowledge about the concept of height]. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 17(2), 429-450.
• Hızarcı, S., Ada, Ş. & Elmas, S. (2006). Geometride temel kavramların öğretilmesi ve öğrenilmesindeki hatalar [errors in teaching and learning basic concepts in geometry]. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 13, 337-342.
• Jones, S., & Tanner, H. (2000). Becoming a successful teacher of mathematics (pp. 86-104). Routledge Falmer.
• Koester, B. A. (2003). Prisms and pyramids: Constructing three-dimensional models to build understanding, Teaching Children Mathematics, 9(8), 436- 442.
• Konyalıoğlu, A.C., Özkaya, M. & Gedik, S. D. (2012). Matematik öğretmen adaylarının konu alan bilgilerinin hataya yaklaşımları açısından incelenmesi [Examining the subject knowledge of mathematics teacher candidates in terms of their approach to errors]. Iğdır University Journal of the Institute of Science and Technology, 2(2SpA), 27-32.
• Linchevsky, L., Vinner, S., & Karsenty, R. (1992). To be or not to be minimal? Student teachers views about definitions in geometry. In W. Geeslin & K. Graham (Eds.), Proceedings of the 16th international conference for the psychology of mathematics education (pp. 48–55). Durham USA.
• Ministry of National Education [MONE], (2018). Matematik dersi öğretim program [Mathematics course curriculum]. MoNE Publications.
• Ministry of National Education [MONE], (2023). Ortaokul 5. sınıf matematik ders kitabı [secondary school 5th grade mathematics textbook]. MoNE Publications.
• Ministry of National Education [MONE], (2023). Ortaokul 8. sınıf matematik ders kitabı [secondary school 8th grade mathematics textbook]. MoNE Publications.
• Ministry of National Education [MONE], 1991. Üstün yetenekli çocuklar ve eğitimleri raporu [gifted children and their education report]. MoNE Publications.
• Miles, M. B., & Huberman A. M. (1994). Qualitative data analysis: An expanded source book. (2nd Edition). Sage Publications.
• Mullis, I.V.S., Martin, M. O., Foy, P., Kelly, D.L., & Fishbein B. (2019). TIMSS 2019 Internatinal Results in Mathematis and Scıence, Boston College, TIMSS & PIRLS International Study Center. Erişim Tarihi: 9 Haziran 2023
• NCTM. (2000). Principles and standarts for school mathematics. NCTM.
• Owens, K. (2005). Substantıve communication of space mathematics in upper primary school. Proceedings of the 29 the Conference of the International Group for the Psychology of Mathematics Education, 4, 33-40.
• Öçal, M.F. (2017). Geometri sorularındaki kavramsal hataları belirlemede geogebra'nın rolü [the role of geogebra in identifying conceptual errors in geometry questions]. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 19(3), 204-224.
• Paksu, A. D., İymen, E. & Pakmak, G. S. (2013). Sınıf öğretmeni adaylarının dörtgenlerin köşegenleri konusundaki kavram görüntüleri [Concept images of classroom teacher candidates on the subject of diagonals of quadrilaterals]. Eğitim ve Bilim, 38(167), 162-178.
• Saltık-Ayhanöz, G. (2022). The place of intelligence games in mathematics education for gifted students. In Zahal O. (Eds.), Current research in edititon (pp. 152-168), Gece Publishing.
• Sak, U. (2011). Üstün zekâlılar: Özellikleri, tanılanmaları, eğitimleri [Gifted people: Characteristics, diagnosis, education]. Maya Akademi.
• Siegle, D. (2001). Overcoming bias in gifted and talented referrals. Gifted and Talented Communicator, 32(3), 22-25.
• Şahin, M., Güven, M. B., & Cemalettin, I. (2023). Yükseklik kavramında ortaokul öğrencilerinin yaşadıkları zorluklar ve matematik öğretmenlerinin bu konudaki görüşleri [The difficulties experienced by secondary school students in the concept of height and the opinions of mathematics teachers on this subject]. Nevşehir Hacı Bektaş Veli Üniversitesi SBE Dergisi, 13(3), 1479-1502.
• Şengün, K. Ç., & Yılmaz, S. (2021). Ortaokul 8. sınıf öğrencilerinin üçgende açıortay ve kenarortay belirleme durumlarının incelenmesi [Examining the situations of 8th grade secondary school students in determining the angle bisector and median of a triangle]. International Journal of Active Learning (IJAL), 6(1), 81-97.
• Taber, K. S. (2017). Neden üstün yetenekliler için fen eğitimi [why science education for the gifted]. Ed: Gökdere, Üstün Yetenekliler İçin Fen Eğitimi, 4-16.
• Türnüklü, E., Ergin, A.S., & Aydoğdu, M.Z. (2017). Examination of 8th grade students' problem posing studies on triangles. Bayburt Eğitim Fakültesi Dergisi, 12(24), 467-486.
• Van de Walle, J. A. (1998). Elementary and middle school mathematics: Teaching developmentally. Longman.
• Yanık, B. (2016). Kavramsal ve işlemsel anlama [conceptual and operational understanding]. E. Bingölbali, S. Arslan. & İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler [theories in mathematics education] (pp. 101-114). Ankara: Pegem Publishing.
• Yenilmez, K., & Yaşa, E. (2008). İlköğretim öğrencilerinin geometrideki kavram yanılgıları [Primary school students' misconceptions in geometry]. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 21 (2), 461-483.
• Yıldırım, A. & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences (10th ed.)]. Seçkin Publishing.
• Yin, R. (1984). Case study research: Design and methods (3th ed.). Sage publications.
• Yurtyapan, M. İ., & Karataş, İ. (2020). Examination of secondary school mathematics teachers' pedagogical content knowledge on the subject of triangles and quadrilaterals]. Turkish Journal of Computer and Mathematics Education, 11(1), 53-90.
• Zembat, İ. Ö. (2015). Kavram yanılgısı nedir? [What is a misconception?] M. F. Özmantar, E. Bingölbali ve H. Akkoç (Ed.), Matematiksel kavram yanılgıları ve çözüm önerileri (4. Baskı, s. 1-8). PegemA Yayıncılık.