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ÖZEL DÖRTGENLERİN HİYERARŞİK İLİŞKİSİNİN KURULMASI SÜRECİNDE SORGULAMANIN ROLÜ

Year 2022, Volume: 12 Issue: 2, 1006 - 1035, 30.05.2022
https://doi.org/10.24315/tred.950449

Abstract

Bu çalışmanın temel amacı 10.sınıf öğrencilerinin özel dörtgenlerin hiyerarşik ilişkisini kurarken oluşturulan sorgulama topluluğundaki sürecin incelenmesidir. Yedi alt bileşene sahip olan matematiksel sorgulama topluluğu yaklaşımı çalışmanın kavramsal altyapısı olarak ele alınmıştır. Nitel araştırma paradigması benimsenen bu çalışma, durum çalışması ile desenlenmiştir. Bu bağlamda 10. sınıf öğrencilerinin özel dörtgenlerin tanım ve özellikleri hakkındaki var olan bilgileri ve özel dörtgenlerin hiyerarşik ilişkisini kurmada hangi sorgulama eylemlerinin kullanıldığı araştırılmıştır. Bununla birlikte öğrencilerin özel dörtgenler konusundaki ön bilgilerinin özel dörtgenlerin hiyerarşik ilişki kurmadaki sorgulama sürecine etkisinin nasıl olduğu belirlenmiştir. Çalışmanın katılımcıları, bir Anadolu lisesinde öğrenim gören dört 10. Sınıf öğrencisidir. Çalışmada dörtgenler konusu kapsamında sorgulama temelli sorular geliştirilmiş ve bu sorular yardımıyla görüşmeler yapılarak öğrencilerin sorgulama süreçleri incelenmiştir. 10.sınıf öğrencilerinin 6 haftalık uygulama sürecinde alınan video kayıtları ve öğrencilere ait cevap kağıtları çalışmanın veri grubunu oluşturmaktadır. Çalışmada uygulama sürecinde kaydedilen videolar, video metodolojisi kullanılarak analiz edilirken, öğrencilerin cevap kağıtları ise doküman analizi yöntemiyle analiz edilmiştir. Bu çalışmada, sorgulama sürecinde öğrencilerin en fazla diyalog yoluyla matematik anlayışı geliştirme eylemini kullandıkları görülürken bu eylemden sonra sırasıyla risk alma, iş birliği yapma, hataları gözden geçirip kendi kendini düzeltme, matematikçiler gibi matematik yapma, alternatif fikirler önerme eylemleri ortaya çıkmıştır. Bu araştırmanın sonuçları dörtgenlerin hiyerarşik ilişkisinin kurulması sürecinde matematiksel sorgulama topluluğunun öğrencilerin dörtgenlerin hiyerarşik ilişkisine dair var olan bilgilerini geliştirmede etkili olduğunu göstermiştir.

References

  • Artigue, M. ve Blomhøj, M. (2013). Conceptualising inquiry based education in mathematics. ZDM, 45(6). 797-810.
  • Bowen, Glenn A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40.
  • Clarke, D. (1997). The changing role of the mathematics teacher. Journal of Research in Mathematics Education, 28(3), 278-305.
  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatly, G., Trigatti, B. ve Perlwitz, M. (1991). Assessment of a problem-centered second grade mathematical project. Journal for Research in Mathematics Eduaction, 22, 3-29.
  • Clements, D. H. (2003). Learning and Teaching Measurement (2003 Yearbook). National Council of Teachers of Mathematics. Reston, VA: NCTM.
  • Davison, I. ve Pratt, D., (2003). Interactive Whiteboards and the Construction of Definitions for the Kite. International Group for the Psychology of Mathematics Education, 4, 31-38.
  • De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11-18.
  • De Villiers, M. (1998). To teach definitions in geometry or teach to define? In A.Oliver & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, (Volume 2, s. 248-255). University of Stellenbosch: Stellenbosch.
  • Engeln, K., Mikelskis-Seifert, S., ve Euler, M. (2014). Inquiry-based mathematics and science education across Europe: A synopsis of various approaches and their potentials. In Topics and trends in current science education (pp. 229-242). Springer, Dordrecht.
  • Fibonacci (2012a). Learning through inquiry, https://projectfibonacci.org/wp/ Erişim Tarihi ( 10/06/2021).
  • Fujita, T. ve Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
  • Fujita, T. ve Okazaki, M. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 41-48).
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60-72.
  • Gregory, M. (2002). Constructivism, standards, and the classroom community of inquiry. Educational Theory, 52(4), 397 - 408.
  • Harlen, W. (2012). Inquiry in science education. Resources for implementing inquiry in science and mathematics at school. https://projectfibonacci.org/wp/ adresinden alınmıştır. Erişim Tarihi (10/06/2021).
  • Horzum, T. (2018). Matematik öğretmeni adaylarının dörtgenler hakkındaki anlamalarının kavram haritası aracılığıyla incelenmesi. Turkish Journal of Computer and Mathematics Education, 9(1), 1- 30.
  • Hershkowitz, R., Ben-Chaim, D., Hoyles, C., Lappan, G., Mitchelmore, M., ve Vinner, S. (1990). Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 70-95).
  • Kahn, P., ve O’Rourke, K. (2005). Understanding enquiry-based learning. Handbook of Enquiry & Problem Based Learning, 1-12.
  • Kennedy, N., ve Kennedy, D. (2011). Community of philosophical inquiry as a discursive structure, and its role in school curriculum design. Journal of Philosophy of Education, 45(2), 265-283.
  • Kondratieva, M. F. ve Radu, O. G. (2009). Fostering connections between the verbal, algebraic, and geometric representations of basic planar curves for student’s success in the study of mathematics. The Mathematics Enthusiast, 6(1&2), 213-238.
  • Lin, F-L. ve Cooney, T. J. (2001). Making sense of mathematics teacher education. The Netherlands: Kluwer.
  • Leikin, R. ve Winicki-Landman, G. (2000). On equivalent and non-equivalent definitions: Part 1. For the learning of Mathematics, 20(1), 17-21.
  • Leikin, R. ve Zazkis, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131-148.
  • MEB (2018). Matematik dersi öğretim programı (Lise 9. 10. 11. Ve 12. sınıflar). Ankara: Milli Eğitim Bakanlığı.
  • Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass.
  • Monaghan, F. (2000). What difference does it make? Children's views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2), 179-196.
  • National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, Va: The Council.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Öztoprakçı, S. ve Çakıroğlu, E. (2013). Dörtgenler. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır ve A. Delice (Ed.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar (s. 249-272). Ankara: Pegem Akademi.
  • PRIMAS. (2012). Promoting inquiry in mathematics and science across Europe. Erişim adresi: http://www.primas-project.eu. Erişim Tarihi (10/06/2021).
  • Powell, A. B. (2003). “So let’s prove it!”: Emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task. (Unpublished doctoral dissertation) The State University of New Jersey, Rutgers.
  • Patton, W., Milton, Berne, L. A., J., Hunt, L. Y., Wright, S., Peppard, J., ve Dodd, J. (2000). A qualitative assessment of Australian parents' perceptions of sexuality education and communication. Journal of Sex Education and Therapy, 25(2-3), 161-168.
  • Rocard, M., Csermely, P., Jorde, D., Lenzen, D., Walberg-Henriksson, H. ve Hemmo, V. (2007). Science education now: A renewed pedagogy for the future of Europe (EU 22845). Brussels: Office for Official Publications of the European Communities.
  • Siegrist, R. (2005). A community of mathematical inquiry in a high school setting (Unpubliched Doctoral Dissertation). Montclair State University, Upper Montclair, NJ.
  • Schwarz, B. B. ve Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30(4), 362-389.
  • Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (s. 189-215). Hillsdale, NJ: Lawrence Earlbaum Associates.
  • Stake, R. E. (1994). Case study: Composition and performance. Bulletin of the Council for Research in Music Education, 31-44.
  • Toptaş, V. (2015). Matematiksel dile genel bir bakış. International Journal of New Trends in Arts, Sports &Science Education, 4(1), 18-22.
  • T.C. Millî Eğitim Bakanlığı Talim Terbiye Kurulu Başkanlığı, (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB.
  • Tall, D., ve Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.
  • Türnüklü, E., Akkaş, E. N., ve Gündoğdu-Alaylı, F. (2012). İlköğretim matematik öğretmen adaylarının dörtgen algılarına yönelik bir çalışma. X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi Bildiri Kitapçığı, (s.27-30). Niğde, TÜRKİYE.
  • Usiskin, Z., Griffin, J., Witonsky, D. ve Willmore, E. (2008). The classification of quadrilaterals: A study in definition. Charlotte, NC: Information Age Publishing.
  • Van De Walle, J. A., Karp, K. S., ve Bay-Williams, J. M. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim (Çev. S. Durmuş). Ankara: Nobel Yayıncılık.
  • Vighi, P. (2003). The triangle as a mathematical object. European Research in Mathematics Education III Congress Proceedings, Bellaria, Italy, 28 Februrary-3 March, 1-10.
  • Van Hiele, P. M. (1999). Begin with play. Teaching children mathematics, 6, 310-316.
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65–79). Kluwer Academic Publicions.
  • Vygotsky, L. (1986). Thought and Language. A. Kozulin (Çev. ve Ed.) Chambridge, MA: MIT Press.
  • Yıldırım, A. ve Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri (6. Baskı). Ankara: Seçkin Yayıncılık.
  • Yin, R. K. (2018). Case study research and applications. Design and methods, (6. Baskı). Sage, Thousand Oaks, CA.
  • Willis, J. (2010). Learning to love math: Teaching strategies that change student attitudes and get results. Alexandria, Virginia: ASCD.
Year 2022, Volume: 12 Issue: 2, 1006 - 1035, 30.05.2022
https://doi.org/10.24315/tred.950449

Abstract

References

  • Artigue, M. ve Blomhøj, M. (2013). Conceptualising inquiry based education in mathematics. ZDM, 45(6). 797-810.
  • Bowen, Glenn A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27-40.
  • Clarke, D. (1997). The changing role of the mathematics teacher. Journal of Research in Mathematics Education, 28(3), 278-305.
  • Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatly, G., Trigatti, B. ve Perlwitz, M. (1991). Assessment of a problem-centered second grade mathematical project. Journal for Research in Mathematics Eduaction, 22, 3-29.
  • Clements, D. H. (2003). Learning and Teaching Measurement (2003 Yearbook). National Council of Teachers of Mathematics. Reston, VA: NCTM.
  • Davison, I. ve Pratt, D., (2003). Interactive Whiteboards and the Construction of Definitions for the Kite. International Group for the Psychology of Mathematics Education, 4, 31-38.
  • De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11-18.
  • De Villiers, M. (1998). To teach definitions in geometry or teach to define? In A.Oliver & K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, (Volume 2, s. 248-255). University of Stellenbosch: Stellenbosch.
  • Engeln, K., Mikelskis-Seifert, S., ve Euler, M. (2014). Inquiry-based mathematics and science education across Europe: A synopsis of various approaches and their potentials. In Topics and trends in current science education (pp. 229-242). Springer, Dordrecht.
  • Fibonacci (2012a). Learning through inquiry, https://projectfibonacci.org/wp/ Erişim Tarihi ( 10/06/2021).
  • Fujita, T. ve Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
  • Fujita, T. ve Okazaki, M. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 41-48).
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60-72.
  • Gregory, M. (2002). Constructivism, standards, and the classroom community of inquiry. Educational Theory, 52(4), 397 - 408.
  • Harlen, W. (2012). Inquiry in science education. Resources for implementing inquiry in science and mathematics at school. https://projectfibonacci.org/wp/ adresinden alınmıştır. Erişim Tarihi (10/06/2021).
  • Horzum, T. (2018). Matematik öğretmeni adaylarının dörtgenler hakkındaki anlamalarının kavram haritası aracılığıyla incelenmesi. Turkish Journal of Computer and Mathematics Education, 9(1), 1- 30.
  • Hershkowitz, R., Ben-Chaim, D., Hoyles, C., Lappan, G., Mitchelmore, M., ve Vinner, S. (1990). Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 70-95).
  • Kahn, P., ve O’Rourke, K. (2005). Understanding enquiry-based learning. Handbook of Enquiry & Problem Based Learning, 1-12.
  • Kennedy, N., ve Kennedy, D. (2011). Community of philosophical inquiry as a discursive structure, and its role in school curriculum design. Journal of Philosophy of Education, 45(2), 265-283.
  • Kondratieva, M. F. ve Radu, O. G. (2009). Fostering connections between the verbal, algebraic, and geometric representations of basic planar curves for student’s success in the study of mathematics. The Mathematics Enthusiast, 6(1&2), 213-238.
  • Lin, F-L. ve Cooney, T. J. (2001). Making sense of mathematics teacher education. The Netherlands: Kluwer.
  • Leikin, R. ve Winicki-Landman, G. (2000). On equivalent and non-equivalent definitions: Part 1. For the learning of Mathematics, 20(1), 17-21.
  • Leikin, R. ve Zazkis, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131-148.
  • MEB (2018). Matematik dersi öğretim programı (Lise 9. 10. 11. Ve 12. sınıflar). Ankara: Milli Eğitim Bakanlığı.
  • Merriam, S. B. (1988). Case study research in education: A qualitative approach. San Francisco: Jossey-Bass.
  • Monaghan, F. (2000). What difference does it make? Children's views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2), 179-196.
  • National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, Va: The Council.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Öztoprakçı, S. ve Çakıroğlu, E. (2013). Dörtgenler. İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır ve A. Delice (Ed.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar (s. 249-272). Ankara: Pegem Akademi.
  • PRIMAS. (2012). Promoting inquiry in mathematics and science across Europe. Erişim adresi: http://www.primas-project.eu. Erişim Tarihi (10/06/2021).
  • Powell, A. B. (2003). “So let’s prove it!”: Emergent and elaborated mathematical ideas and reasoning in the discourse and inscriptions of learners engaged in a combinatorial task. (Unpublished doctoral dissertation) The State University of New Jersey, Rutgers.
  • Patton, W., Milton, Berne, L. A., J., Hunt, L. Y., Wright, S., Peppard, J., ve Dodd, J. (2000). A qualitative assessment of Australian parents' perceptions of sexuality education and communication. Journal of Sex Education and Therapy, 25(2-3), 161-168.
  • Rocard, M., Csermely, P., Jorde, D., Lenzen, D., Walberg-Henriksson, H. ve Hemmo, V. (2007). Science education now: A renewed pedagogy for the future of Europe (EU 22845). Brussels: Office for Official Publications of the European Communities.
  • Siegrist, R. (2005). A community of mathematical inquiry in a high school setting (Unpubliched Doctoral Dissertation). Montclair State University, Upper Montclair, NJ.
  • Schwarz, B. B. ve Hershkowitz, R. (1999). Prototypes: Brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30(4), 362-389.
  • Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (s. 189-215). Hillsdale, NJ: Lawrence Earlbaum Associates.
  • Stake, R. E. (1994). Case study: Composition and performance. Bulletin of the Council for Research in Music Education, 31-44.
  • Toptaş, V. (2015). Matematiksel dile genel bir bakış. International Journal of New Trends in Arts, Sports &Science Education, 4(1), 18-22.
  • T.C. Millî Eğitim Bakanlığı Talim Terbiye Kurulu Başkanlığı, (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB.
  • Tall, D., ve Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.
  • Türnüklü, E., Akkaş, E. N., ve Gündoğdu-Alaylı, F. (2012). İlköğretim matematik öğretmen adaylarının dörtgen algılarına yönelik bir çalışma. X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi Bildiri Kitapçığı, (s.27-30). Niğde, TÜRKİYE.
  • Usiskin, Z., Griffin, J., Witonsky, D. ve Willmore, E. (2008). The classification of quadrilaterals: A study in definition. Charlotte, NC: Information Age Publishing.
  • Van De Walle, J. A., Karp, K. S., ve Bay-Williams, J. M. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim (Çev. S. Durmuş). Ankara: Nobel Yayıncılık.
  • Vighi, P. (2003). The triangle as a mathematical object. European Research in Mathematics Education III Congress Proceedings, Bellaria, Italy, 28 Februrary-3 March, 1-10.
  • Van Hiele, P. M. (1999). Begin with play. Teaching children mathematics, 6, 310-316.
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65–79). Kluwer Academic Publicions.
  • Vygotsky, L. (1986). Thought and Language. A. Kozulin (Çev. ve Ed.) Chambridge, MA: MIT Press.
  • Yıldırım, A. ve Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri (6. Baskı). Ankara: Seçkin Yayıncılık.
  • Yin, R. K. (2018). Case study research and applications. Design and methods, (6. Baskı). Sage, Thousand Oaks, CA.
  • Willis, J. (2010). Learning to love math: Teaching strategies that change student attitudes and get results. Alexandria, Virginia: ASCD.
There are 50 citations in total.

Details

Primary Language Turkish
Subjects Studies on Education
Journal Section Articles
Authors

Özge Çoban 0000-0002-0653-9491

Melike Yiğit Koyunkaya 0000-0002-7872-3917

Early Pub Date May 30, 2022
Publication Date May 30, 2022
Published in Issue Year 2022 Volume: 12 Issue: 2

Cite

APA Çoban, Ö., & Yiğit Koyunkaya, M. (2022). ÖZEL DÖRTGENLERİN HİYERARŞİK İLİŞKİSİNİN KURULMASI SÜRECİNDE SORGULAMANIN ROLÜ. Trakya Eğitim Dergisi, 12(2), 1006-1035. https://doi.org/10.24315/tred.950449