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Ortaokul Matematik Öğretmen Adaylarının Üçgenlere İlişkin Bağıntıları Öğretmek İçin Matematik Bilgilerinin İncelenmesi

Yıl 2023, Cilt: 24 Sayı: 2, 818 - 879, 31.08.2023

Öz

Bu araştırma ile öğretmen adaylarının, ortaokul matematik müfredatında yer alan üçgenlerle ilgili bağıntılara ilişkin ispat yapma durumlarını ve bu bağıntıların öğretimine dair bilgileri ile ortaokul öğrencilerinin karşılaşabileceği zorluklara ilişkin bilgilerini belirlemek amaçlanmaktadır. Araştırma, nitel araştırma olup, bir devlet üniversitesinde öğretim görmekte olan 45 öğretmen adayı ile yürütülmüştür. Veriler, üçgenle ilgili 5 bağıntıya ilişkin dörder tane açık uçlu soru ile toplanmıştır. Elde edilen veriler, “Öğretmek için Matematiksel Bilgi” modeli temel alınarak incelenmiştir Verilerin analizinde içerik analizi kullanılmıştır. Bulgular öğretmen adaylarının üçgen bağıntıları ile ilgili alan bilgilerinin yeterli olmadığı ve pedagojik alan bilgilerinde de eksiklikler olduğunu ortaya koymuştur. Öğretmen adaylarının genellikle üçgenlerle ilgili bağıntılara ait matematiksel gösterimleri tam doğru bir şekilde ifade edemedikleri ve notasyonları eksik kullandıkları tespit edilmiştir. Çoğu öğretmen adayının geçerli ispat yapamadığı görülmüştür. Öğretmen adaylarının öğretim bilgisi değerlendirildiğinde ise bağıntıların her biri için öğrenci merkezli öğretim planlayabildikleri ve çeşitli etkinlikler oluşturabildikleri ancak, öğretim sürecindeki aşamaların yeterince açıklanmadığı belirlenmiştir. Öğrencilerin yaşayabilecekleri zorluklarla ilgili de çoğu öğretmen adayının genel bilgiler sundukları fakat bağıntılara özgü yaşanabilecek zorlukları ifade etmedikleri tespit edilmiştir.

Kaynakça

  • Alatorre, S., & Saiz, M. (2009). Teachers and triangles. In R. Sutherland (Ed.). Proceedings of Congress of Educational Research in Mathematics Education (pp. 1890-1900). 28 January- 1 February, Lyon; France.
  • Altıntaş, e., & İlgün, ş. (2017). Ortaokul matematik öğretmenlerinin geometride “yükseklik” ve “diklik merkezi” kavramına ilişkin kavram yanılgıları. Turkish Studies (Elektronik), 12(29), 73-86. http://dx.doi.org/10.7827/TurkishStudies.12532
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
  • Aslan-tutak, F., & Adams, T. L. (2015). A study of geometry content knowledge of elementary pre-service teachers. International Electronic Journal of Elementary Education, 7(3), 301–318.
  • Aslan-Tutak, F. & Köklü, O. (2016). Öğretmek için matematik bilgisi. In E. Bingölbali, A. Arslan, & İ. Ö. Zembat (Eds.). Matematik eğitiminde teoriler (pp. 701- 719). Ankara: Pegem Akademi.
  • Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51 (3), 241-247. https://doi.org/10.1177/0022487100051003013
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59 (5), 389- 407. https://doi.org/10.1177/0022487108324554
  • Bilik, A. (2016). Pre-service middle school mathematics teachers' pedagogical content knowledge regarding the area of triangles (Unpublished master thesis). Middle East Technical University, Turkey.
  • Blömeke, S., Delaney, S. (2014). Assessment of Teacher Knowledge Across Countries: A Review of the State of Research. In: Blömeke, S., Hsieh, FJ., Kaiser, G., Schmidt, W. (eds) International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6437-8_25
  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44, 263-272. https://doi.org/10.1177/0022487193044004004
  • Couta, A., & Vale, I. (2014). Pre-service teachers knowledge on elementary geometry concepts. In J. Portela, I. Vale, F. Huckaby & G. Bieger (Eds.). The Proceedings of the 23th Annual Conference of the European Teacher Education Network (pp. 37-51). Hasselt, Belgium.
  • Cunningham, R. F., & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. IUMPST: The Journal, 1, 1–17.
  • Even, R. & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1-20. https://doi.org/10.1007/BF01273897
  • Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
  • Fidan, Y. & Türnüklü, E. (2010). İlköğretim 5. sınıf öğrencilerinin geometrik düşünme düzeylerinin bazı değişkenler açısından incelenmesi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 27(27), 185-197.
  • Gökdal, N. (2004). Ilköğretim 8. sınıf ve ortaöğretim 11. sınıf öğrencilerinin alan ve hacim konularındakı kavram yanılgıları. Unpublished master thesis, Gazi University.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College.
  • Gutiérrez, A., & Jaime, A. (1999). Preservice primary teachers' understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253–275. https://doi.org/10.1023/A:1009900719800
  • Güner, P. & Topan, B. (2016). Prospective elementary mathematics teachers’ abilities of using geometric proofs in teaching of triangle. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (EFMED), 10(2), 210-242. doi: 10.17522/balikesirnef.277730
  • Hızarcı, S., Ada, Ş. & Elmas, S. (2006). Geometride temel kavramların öğretilmesi ve öğrenilmesindeki hatalar. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 13, 337-342.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
  • Huang, R., & Leung, F. K. (2002). How Pythagoras' theorem is taught in Czech Republic, Hong Kong and Shanghai: A case study. ZDM, 34(6), 268-277. https://doi.org/10.1007/BF02655725
  • Jin, H., & Wong, K. Y. (2021). Complementary measures of conceptual understanding: a case about triangle concepts. Mathematics Education Research Journal, 1-22. https://doi.org/10.1007/s13394-021-00381-y
  • Johnson, H. L., Blume, G. W., Shimizu, J. K., Graysay, D., & Konnova, S. (2014). A teacher’s conception of definition and use of examples when doing and teaching mathematics. Mathematical Thinking and Learning, 16(4), 285–311. https://doi.org/10.1080/10986065.2014.953018
  • Jones, K. (2000). Teacher knowledge and professional development in geometry. Proceedings of the British society for research into learning mathematics, 20(3), 109–114.
  • Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry: original research. Pythagoras, 36(1), 1-11.
  • Martin, W. G. & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51. https://doi.org/10.5951/jresematheduc.20.1.0041
  • Milli Eğitim Bakanlığı (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Erişim adresi: https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf 30.08.2020.
  • Moutsios-Rentzos, A., Spyrou, P., & Peteinara, A. (2014). The objectification of the right-angled triangle in the teaching of the Pythagorean Theorem: an empirical investigation. Educational Studies in Mathematics, 85(1), 29-51. https://doi.org/10.1007/s10649-013-9498-y
  • NCTM, (2000). Principles and standarts for school mathematics. Reston, VA: Author.
  • Orhan, N. (2013). An investigation of private middle school students’ common errors in the domain of area and perimeter and the relationship between their geometry self-efficacy beliefs and basic procedural and conceptual knowledge of area and perimeter. (Unpublished master thesis). Middle East Technical University, Turkey.
  • Patkin, D., & Levenberg, I. (2012). Geometry from the world around us. Learning and Teaching Mathematics, 13(1), 14–18. Rowland, T., Turner, F., Thwaites, & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the Knowledge Quartet. London: Sage.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Simon, M. & Blume, G. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3–31. https://doi.org/10.1016/S0732-3123(96)90036-X
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2014). Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDM Mathematics Education 47, 497–509 (2015). https://doi.org/10.1007/s11858-014-0641-8
  • Ubah, I. (2021). Pre-service mathematics teachers’ semiotic transformation of similar triangles: Euclidean geometry. International Journal of Mathematical Education in Science and Technology, 1-22. https://doi.org/10.1080/0020739X.2020.1857858
  • Ubuz, B. & Aydın, U. (2018). Geometry knowledge test about triangles: evidence on validity and reliability. ZDM Mathematics Education, 50, 659–673. https://doi.org/10.1007/s11858-018-0964-y
  • Ulusoy, F. (2021). Prospective early childhood and elementary school mathematics teachers’ concept images and concept definitions of triangles. International Journal of Science and Mathematics Education, 19(5), 1057-1078. https://doi.org/10.1007/s10763-020-10105-6
  • Uygun, T. (2016). Developing mathematical practices in a social context: A hypothetical learning trajectory to support preservice middle school mathematics teachers’ learning of triangles. Unpublished doctoral dissertation, Middle East Technical University, Turkey.
  • Van der Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers' and prospective teachers' content knowledge of geometry. South African Journal of Education, 23(3), 199–205.
  • Ward, R. A. (2004). An investigation of K-8 preservice teachers' concept images and mathematical definitions of polygons. Issues in Teacher Education, 13(2), 39–56.
  • Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. https://doi.org/10.1023/A:1015535614355
  • Yang, Y. (2009). How a Chinese teacher improved classroom teaching in Teaching Research Group: A case study on Pythagoras theorem teaching in Shanghai. ZDM Mathematics Education, 41, 279–296 (2009). https://doi.org/10.1007/s11858-009-0171-y
  • Yew, W.T., Zamri, S.N.A.S. & Lian, L.H. (2010). Examining preservice teachers’ knowledge of area formulae. Procedia Social and Behavioral Sciences, 8, 198-206. https://doi.org/10.1016/j.sbspro.2010.12.027
  • Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9.baskı). Ankara: Seçkin Yayıncılık. Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, California: Sage Publications.
  • Yurtyapan, M. İ., & Karataş, İ. (2020). Ortaokul Matematik Öğretmenlerinin Üçgenler ve Dörtgenler Konusuna İlişkin Pedagojik Alan Bilgilerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 53-90. doi:10.16949/turkbilmat.443825
  • Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: a case of a square. Educational Studies in Mathematics, 69(2), 131–148. https://doi.org/10.1007/s10649-008-9131-7
  • Zazkis, D., & Zazkis, R. (2016). Prospective teachers’ conceptions of proof comprehension: Revisiting a proof of the Pythagorean theorem. International Journal of Science and Mathematics Education, 14(4), 777-803. https://doi.org/10.1007/s10763-014-9595-0

Investigation of Middle School Pre-service Mathematics Teachers’ Mathematical Knowledge for Teaching Relations of Triangles

Yıl 2023, Cilt: 24 Sayı: 2, 818 - 879, 31.08.2023

Öz

The purpose of this study is to determine the pre-service teachers' proofs on the relations of triangles in the middle school mathematics curriculum, as well as their knowledge of the teaching of these relations and the difficulties that students may face. 45 pre-service teachers attending a state university participated in the qualitative investigation. Four open-ended questions were used to obtain data for each of the five relations. The gathered data were evaluated using the "Mathematical Knowledge for Teaching" model and content analysis. The findings demonstrated that pre-service teachers' content knowledge about triangle relations was not adequate and there were deficiencies in their pedagogical content knowledge. It was discovered that in general, pre-service teachers were unable to effectively explain the mathematical representations of triangle relations and employed the notations improperly. It has been noticed that the majority of pre-service teachers were unable to give proof. When evaluating the pre-service teachers' teaching knowledge, it was established that they were able to organize student-centered instruction and provide a variety of activities for each of the students, but the steps of the teaching process were not clearly articulated. It has been found out that majority of pre-service teachers offer generic information about the difficulties that students may encounter, but do not emphasize the content-specific difficulties that may be encountered.

Kaynakça

  • Alatorre, S., & Saiz, M. (2009). Teachers and triangles. In R. Sutherland (Ed.). Proceedings of Congress of Educational Research in Mathematics Education (pp. 1890-1900). 28 January- 1 February, Lyon; France.
  • Altıntaş, e., & İlgün, ş. (2017). Ortaokul matematik öğretmenlerinin geometride “yükseklik” ve “diklik merkezi” kavramına ilişkin kavram yanılgıları. Turkish Studies (Elektronik), 12(29), 73-86. http://dx.doi.org/10.7827/TurkishStudies.12532
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
  • Aslan-tutak, F., & Adams, T. L. (2015). A study of geometry content knowledge of elementary pre-service teachers. International Electronic Journal of Elementary Education, 7(3), 301–318.
  • Aslan-Tutak, F. & Köklü, O. (2016). Öğretmek için matematik bilgisi. In E. Bingölbali, A. Arslan, & İ. Ö. Zembat (Eds.). Matematik eğitiminde teoriler (pp. 701- 719). Ankara: Pegem Akademi.
  • Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51 (3), 241-247. https://doi.org/10.1177/0022487100051003013
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59 (5), 389- 407. https://doi.org/10.1177/0022487108324554
  • Bilik, A. (2016). Pre-service middle school mathematics teachers' pedagogical content knowledge regarding the area of triangles (Unpublished master thesis). Middle East Technical University, Turkey.
  • Blömeke, S., Delaney, S. (2014). Assessment of Teacher Knowledge Across Countries: A Review of the State of Research. In: Blömeke, S., Hsieh, FJ., Kaiser, G., Schmidt, W. (eds) International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6437-8_25
  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44, 263-272. https://doi.org/10.1177/0022487193044004004
  • Couta, A., & Vale, I. (2014). Pre-service teachers knowledge on elementary geometry concepts. In J. Portela, I. Vale, F. Huckaby & G. Bieger (Eds.). The Proceedings of the 23th Annual Conference of the European Teacher Education Network (pp. 37-51). Hasselt, Belgium.
  • Cunningham, R. F., & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. IUMPST: The Journal, 1, 1–17.
  • Even, R. & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1-20. https://doi.org/10.1007/BF01273897
  • Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillan.
  • Fidan, Y. & Türnüklü, E. (2010). İlköğretim 5. sınıf öğrencilerinin geometrik düşünme düzeylerinin bazı değişkenler açısından incelenmesi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 27(27), 185-197.
  • Gökdal, N. (2004). Ilköğretim 8. sınıf ve ortaöğretim 11. sınıf öğrencilerinin alan ve hacim konularındakı kavram yanılgıları. Unpublished master thesis, Gazi University.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York, NY: Teachers College.
  • Gutiérrez, A., & Jaime, A. (1999). Preservice primary teachers' understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher Education, 2(3), 253–275. https://doi.org/10.1023/A:1009900719800
  • Güner, P. & Topan, B. (2016). Prospective elementary mathematics teachers’ abilities of using geometric proofs in teaching of triangle. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi (EFMED), 10(2), 210-242. doi: 10.17522/balikesirnef.277730
  • Hızarcı, S., Ada, Ş. & Elmas, S. (2006). Geometride temel kavramların öğretilmesi ve öğrenilmesindeki hatalar. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 13, 337-342.
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
  • Huang, R., & Leung, F. K. (2002). How Pythagoras' theorem is taught in Czech Republic, Hong Kong and Shanghai: A case study. ZDM, 34(6), 268-277. https://doi.org/10.1007/BF02655725
  • Jin, H., & Wong, K. Y. (2021). Complementary measures of conceptual understanding: a case about triangle concepts. Mathematics Education Research Journal, 1-22. https://doi.org/10.1007/s13394-021-00381-y
  • Johnson, H. L., Blume, G. W., Shimizu, J. K., Graysay, D., & Konnova, S. (2014). A teacher’s conception of definition and use of examples when doing and teaching mathematics. Mathematical Thinking and Learning, 16(4), 285–311. https://doi.org/10.1080/10986065.2014.953018
  • Jones, K. (2000). Teacher knowledge and professional development in geometry. Proceedings of the British society for research into learning mathematics, 20(3), 109–114.
  • Luneta, K. (2015). Understanding students' misconceptions: an analysis of final Grade 12 examination questions in geometry: original research. Pythagoras, 36(1), 1-11.
  • Martin, W. G. & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41-51. https://doi.org/10.5951/jresematheduc.20.1.0041
  • Milli Eğitim Bakanlığı (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Erişim adresi: https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf 30.08.2020.
  • Moutsios-Rentzos, A., Spyrou, P., & Peteinara, A. (2014). The objectification of the right-angled triangle in the teaching of the Pythagorean Theorem: an empirical investigation. Educational Studies in Mathematics, 85(1), 29-51. https://doi.org/10.1007/s10649-013-9498-y
  • NCTM, (2000). Principles and standarts for school mathematics. Reston, VA: Author.
  • Orhan, N. (2013). An investigation of private middle school students’ common errors in the domain of area and perimeter and the relationship between their geometry self-efficacy beliefs and basic procedural and conceptual knowledge of area and perimeter. (Unpublished master thesis). Middle East Technical University, Turkey.
  • Patkin, D., & Levenberg, I. (2012). Geometry from the world around us. Learning and Teaching Mathematics, 13(1), 14–18. Rowland, T., Turner, F., Thwaites, & Huckstep, P. (2009). Developing primary mathematics teaching: Reflecting on practice with the Knowledge Quartet. London: Sage.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  • Simon, M. & Blume, G. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3–31. https://doi.org/10.1016/S0732-3123(96)90036-X
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2014). Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDM Mathematics Education 47, 497–509 (2015). https://doi.org/10.1007/s11858-014-0641-8
  • Ubah, I. (2021). Pre-service mathematics teachers’ semiotic transformation of similar triangles: Euclidean geometry. International Journal of Mathematical Education in Science and Technology, 1-22. https://doi.org/10.1080/0020739X.2020.1857858
  • Ubuz, B. & Aydın, U. (2018). Geometry knowledge test about triangles: evidence on validity and reliability. ZDM Mathematics Education, 50, 659–673. https://doi.org/10.1007/s11858-018-0964-y
  • Ulusoy, F. (2021). Prospective early childhood and elementary school mathematics teachers’ concept images and concept definitions of triangles. International Journal of Science and Mathematics Education, 19(5), 1057-1078. https://doi.org/10.1007/s10763-020-10105-6
  • Uygun, T. (2016). Developing mathematical practices in a social context: A hypothetical learning trajectory to support preservice middle school mathematics teachers’ learning of triangles. Unpublished doctoral dissertation, Middle East Technical University, Turkey.
  • Van der Sandt, S., & Nieuwoudt, H. D. (2003). Grade 7 teachers' and prospective teachers' content knowledge of geometry. South African Journal of Education, 23(3), 199–205.
  • Ward, R. A. (2004). An investigation of K-8 preservice teachers' concept images and mathematical definitions of polygons. Issues in Teacher Education, 13(2), 39–56.
  • Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. https://doi.org/10.1023/A:1015535614355
  • Yang, Y. (2009). How a Chinese teacher improved classroom teaching in Teaching Research Group: A case study on Pythagoras theorem teaching in Shanghai. ZDM Mathematics Education, 41, 279–296 (2009). https://doi.org/10.1007/s11858-009-0171-y
  • Yew, W.T., Zamri, S.N.A.S. & Lian, L.H. (2010). Examining preservice teachers’ knowledge of area formulae. Procedia Social and Behavioral Sciences, 8, 198-206. https://doi.org/10.1016/j.sbspro.2010.12.027
  • Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9.baskı). Ankara: Seçkin Yayıncılık. Yin, R. K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, California: Sage Publications.
  • Yurtyapan, M. İ., & Karataş, İ. (2020). Ortaokul Matematik Öğretmenlerinin Üçgenler ve Dörtgenler Konusuna İlişkin Pedagojik Alan Bilgilerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 53-90. doi:10.16949/turkbilmat.443825
  • Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: a case of a square. Educational Studies in Mathematics, 69(2), 131–148. https://doi.org/10.1007/s10649-008-9131-7
  • Zazkis, D., & Zazkis, R. (2016). Prospective teachers’ conceptions of proof comprehension: Revisiting a proof of the Pythagorean theorem. International Journal of Science and Mathematics Education, 14(4), 777-803. https://doi.org/10.1007/s10763-014-9595-0
Toplam 48 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Alan Eğitimleri
Bölüm Araştırma Makaleleri
Yazarlar

Funda Gündoğdu Alaylı 0000-0002-0382-9610

Dilek Girit Yıldız 0000-0003-3406-075X

Yayımlanma Tarihi 31 Ağustos 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 24 Sayı: 2

Kaynak Göster

APA Gündoğdu Alaylı, F., & Girit Yıldız, D. (2023). Ortaokul Matematik Öğretmen Adaylarının Üçgenlere İlişkin Bağıntıları Öğretmek İçin Matematik Bilgilerinin İncelenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 24(2), 818-879. https://doi.org/10.29299/kefad.1123922

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