Journals / Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi / 2026 / Cilt: 19 Sayı: 1

The Effect of Argumentation-Based Teaching on Conceptual Understanding in Transformation Geometry

Argümantasyon Tabanlı Öğretimin Dönüşüm Geometrisinde Kavramsal Anlayış Üzerine Etkisi

Samet Korkmaz(KARABÜK ÜNİVERSİTESİ, EDEBİYAT FAKÜLTESİ, EĞİTİM BİLİMLERİ BÖLÜMÜ, EĞİTİMDE ÖLÇME VE DEĞERLENDİRME ANABİLİM DALI)0000-0002-1815-8872
Abdullah Çağrı Biber(KASTAMONU ÜNİVERSİTESİ, EĞİTİM FAKÜLTESİ)0000-0001-7635-3951
Pages
218–247
Publication Date
2025-06-27
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

As a result, it has been concluded that argumentation-based teaching positively affects pre-service teachers' academic achievements and conceptual understanding of transformation geometry.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study examines the effect of argumentation-based teaching on pre-service teachers' conceptual understanding of transformation geometry.
📊
Key Findings & Data:The study participants consisted of 43 secondary school pre-service math teachers who studied in the third grade at the education faculty of a state university in Turkey and took the Analytical Geometry course in the fall semester of the 2019-2020 academic year.
💡
Conclusion & Impact:As a result, it has been concluded that argumentation-based teaching positively affects pre-service teachers' academic achievements and conceptual understanding of transformation geometry.
🔬Design:Araştırma Makalesi
📍Scope:2019-2020 Verileri
⚙️Variables:Argümantasyon · dönüşüm geometrisi · öğretmen adayları

Abstract

This study examines the effect of argumentation-based teaching on pre-service teachers' conceptual understanding of transformation geometry. The mixed research design was used in this study. In the quantitative dimension of the study, a quasi-experimental design with pretest and post-test control groups was used, in which the existing classes were randomly assigned as experimental and control groups. The qualitative dimension of the research is a case study. The study participants consisted of 43 secondary school pre-service math teachers who studied in the third grade at the education faculty of a state university in Turkey and took the Analytical Geometry course in the fall semester of the 2019-2020 academic year. In line with the purpose of the study, the Transformation Geometry Achievement Test (TGAT) was used as a data collection tool, and interviews were conducted with pre-service teachers. As a result, it has been concluded that argumentation-based teaching positively affects pre-service teachers' academic achievements and conceptual understanding of transformation geometry. In line with this result, it can be said that examining the effects of this teaching practice on academic success and conceptual understanding in other areas of mathematics will contribute to the field.

Özet

Bu çalışmada, argümantasyon tabanlı öğretimin öğretmen adaylarının dönüşüm geometrisi konusundaki kavramsal anlayışlarına etkisi incelenmektedir. Çalışmada karma araştırma deseni kullanılmıştır. Çalışmanın nicel boyutunda, mevcut sınıfların deney ve kontrol grubu olarak rastgele atandığı, ön test ve son test kontrol gruplu yarı deneysel desen kullanılmıştır. Araştırmanın nitel boyutu ise bir durum çalışmasıdır. Çalışmanın katılımcılarını, Türkiye'deki bir devlet üniversitesinin eğitim fakültesinde üçüncü sınıfta öğrenim gören ve 2019-2020 eğitim öğretim yılı güz döneminde Analitik Geometri dersini alan 43 ortaokul öğretmen adayı oluşturmuştur. Çalışmanın amacı doğrultusunda, Dönüşüm Geometrisi Başarı Testi (DGBT) veri toplama aracı olarak kullanılmış ve öğretmen adaylarıyla görüşmeler yapılmıştır. Sonuç olarak, argümantasyon tabanlı öğretimin, öğretmen adaylarının akademik başarılarını ve dönüşüm geometrisi kavramsal anlamalarını olumlu yönde etkilediği sonucuna varılmıştır. Bu sonuç doğrultusunda, bu öğretim uygulamasının matematiğin diğer alanlarındaki akademik başarı ve kavramsal anlama üzerindeki etkilerinin incelenmesinin alana katkı sağlayacağı söylenebilir.

🔖

Cite This Article

Korkmaz, S., Biber, A. Ç. (2025). The Effect of Argumentation-Based Teaching on Conceptual Understanding in Transformation Geometry. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, Cilt: 19 Sayı: 1, 218–247. https://doi.org/10.17522/balikesirnef.1628926

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (83)

  1. Ada, T., & Kurtuluş, A. (2010). Students’ misconceptions and errors in transformation geometry. International Journal of Mathematical Education in Science and Technology, 41(7), 901-909. https://doi.org/10.1080/0020739X.2010.486451
  2. Altun, M. H. (2018). Lise matematik 12 ders kitabı. Tutku.
  3. Argün, Z., Arikan, A., Bulut, S., & Halicioglu, S. (2014). Temel matematik kavramların künyesi. Gazi.
  4. Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers’ pay attention to potential classroom situations of argumentation. The Journal of Mathematical Behavior, 49(1), 163-173. https://doi.org/10.1016/j.jmathb.2017.11.010
  5. Balcı, M. (2007). Analitik geometri (1st ed.). Balcı.
  6. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it unique?. Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
  7. Bansilal, S., & Naidoo, J. (2012). Learners are engaging with transformation geometry. South African Journal of Education, 32(1), 26–39. https://doi.org/10.15700/saje.v32n1a452
  8. Boero, P. (1999). Argumentation and mathematical proof: A complex, productive, unavoidable relationship in mathematics and mathematics education. International Newsletter on the Teaching and Learning of Mathematical Proof. http://www.lettredelapreuve.org/OldPreuve/Newsletter/990708Theme/990708ThemeUK.html
  9. Brown, R., & Redmond, T. (2007). Collective argumentation and modeling mathematics practices outside the classroom. In J. Watson, & K. Beswick (Eds.), Mathematics: Essential research, essential practice: Vol. 1. Proceedings of the 30th annual conference of the mathematics education research group of Australasia (pp. 163–171). MERGA Inc. https://core.ac.uk/download/pdf/143875561.pdf
  10. Brown, R., & Reeves, B. (2009). Students’ recollections of participating in collective argumentation when doing mathematics. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of Australasia's 32nd annual conference of the mathematics education research group: Vol. 1. (pp. 73–80). MERGA. http://hdl.handle.net/10072/31916
  11. Büyüköztürk, Ş. (2014). Sosyal bilimler için veri analizi el kitabı (20th ed.). Pegem Akademi.
  12. Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2016). Bilimsel araştırma yöntemleri (21st ed.). Pegem Akademi.
  13. Campbell, T. G., & Zelkowski, J. (2020). Technology as a support for proof and argumentation: A systematic literature review. The International Journal for Technology in Mathematics Education, 27(2), 113–124. https://doi.org/10.1564/tme_v27.2.04
  14. Can, Ö. S., İşleyen, T., & Küçük Demir, B. (2017). Argumentation-based science learning approach on probability teaching. Bayburt Faculty of Education Journal, 12(24), 559-572. https://dergipark.org.tr/en/pub/befdergi/issue/33599/344722
  15. Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Information Age.
  16. Civil, M., & Hunter, R. (2015). Participation of non-dominant students in argumentation in the mathematics classroom. Intercultural Education, 26(4), 296–312. https://doi.org/10.1080/14675986.2015.1071755
  17. Clements, D. H., & Burns, B. A. (2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41(1), 31–45. https://doi.org/10.1023/A:1003938415559
  18. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum. https://doi.org/10.4324/9780203771587
  19. Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. https://doi.org/10.1007/s10649-014-9532-8
  20. Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (5th ed.). Pearson Education.
  21. Creswell, W. J., & Plano Clark, V. L. (2007). Designing and conducting mixed methods research. Sage.
  22. Cross, D. I. (2009). Creating optimal mathematics learning environments: Combining argumentation and writing to enhance achievement. International Journal of Science and Mathematics Education, 7(5), 905–930. https://doi.org/10.1007/s10763-008-9144-9
  23. Çetin, İ., Erdoğan, A., & Yazlık, D. Ö. (2015). The effect of teaching on the success of the eighth grade students with Geogebra on the success of transformation geometry. International Journal of Turkish Educational Sciences, 2015(4), 84-92. https://dergipark.org.tr/en/pub/goputeb/issue/34518/381200
  24. Douek, N. (1999). Argumentative aspects of proving: analysis of some undergraduate mathematics students’ performances. In O. Zaslavsky (Eds.), Proceedings of the 23rd conference of the international group for the psychology of mathematics education: Vol. 2. (pp. 2–273). Technion Printing Center. https://files.eric.ed.gov/fulltext/ED436403.pdf#page=703
  25. Driver, R., Newton, P., & Osborne, J. (2000). Establishing the norms of scientific argumentation in classrooms. Science Education, 84(3), 287-312. https://doi.org/10.1002/(SICI)1098-237X(200005)84:3%3C287::AID SCE1%3E3.0.CO;2-A
  26. Eemeren Van, F. H., & Grootendorst, R. (2010). A systematic theory of argumentation: the pragma-dialectical approach. Cambridge University Press.
  27. Emin, A., Gerboğa, A., Güneş, G., & Kayacıer, M. (2018). Lise matematik 12 ders kitabı. MEB.
  28. Erduran, S., Simon, S., & Osborne, J. (2004). Tapping into argumentation: developments in applying Toulmin's argument pattern for studying science discourse. Science Education, 88(6), 915–933. https://doi.org/10.1002/sce.20012
  29. Fiallo, J., & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 96(2), 145-167. https://doi.org/10.1007/s10649-017-9755-6
  30. George, D., & Mallery, P. (2020). IBM SPSS statistics 26 for Windows step by step: A simple guide and reference (16th ed.). Routledge.
  31. Gürbüz, R., & Gülburnu, M. (2013). The effect of Cabri 3D used in the teaching of 8th grade geometry on conceptual learning. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 4(3), 224–241. https://dergipark.org.tr/en/pub/turkbilmat/issue/21571/231484
  32. Güven, B., & Kaleli Yılmaz, G. (2012). Effect of pre-service teachers’ academic achievement of dynamic geometry software used on the transformations. e-Journal of New World Sciences Academy, 7(1), 442-452. https://www.researchgate.net/publication/299412547_Effect_of_Pre- Service_Teachers'_Academic_Achievement_of_Dynamic_Geometry_Software_used_on_the_Transformation_Geometry
  33. Hollebrands, K. F. (2003). High school students' understanding of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22, 55–72. https://doi.org/10.1016/S0732-3123(03)00004-X
  34. Hollebrands, K., Conner, A., & Smith, R. C. (2010). The nature of arguments college geometry students provide with access to technology while solving problems. Journal for Research in Mathematics Education, 41(4), 324–350. https://doi.org/10.5951/jresematheduc.41.4.0324
  35. Inglis, M., Mejia-Ramos, J. P., & Simpson, A. (2007). Modeling mathematical argumentation: The importance of qualification. Educational Studies in Mathematics, 66(1), 3-21. https://doi.org/10.1007/s10649-006-9059-8
  36. Jackiw, N. (2003). Visualizing complex functions with the Geometer’s Sketchpad. In T. Triandafillidis, & K. Hatzikiriakou (Eds.), Proceedings of the 6th international conference on technology in mathematics teaching (pp. 291–299). University of Thessaly.
  37. Johnson, R. B., & Christensen, L. B. (2004). Educational research: Quantitative, qualitative, and mixed approaches. Allyn & Bacon.
  38. Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14-26. https://doi.org/10.3102/0013189X033007014
  39. Kandaga, T., Rosjanuardi, R., & Juandi, D. (2022). Epistemological obstacle in transformation geometry based on Van Hiele's level. Eurasia Journal of Mathematics, Science and Technology Education, 18(4), Article em2096. https://doi.org/10.29333/ejmste/11914
  40. Kemancı, B., Büyükokutan, A., Çelik, S., & Kemancı, Z. (2018). Fen lisesi matematik 12 ders kitabı. MEB.
  41. Knipping, C., & Reid, D. (2015). Reconstructing argumentation structures: A perspective on proving processes in secondary mathematics classroom interactions. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 75-101). Springer. https://doi.org/10.1007/978-94-017-9181-6_4
  42. Kosko, K. W., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26(3), 459-476. https://doi.org/10.1007/s13394-01301161
  43. LeCompte, M. D., & Goetz, J. P. (1982). Problems of reliability and validity in ethnographic research. Review of Educational Research, 52(1), 31-60. https://doi.org/10.3102/00346543052001031
  44. Lee, H. J., & Boyadzhiev, I. (2020). Underprepared college students’ understanding of and misconceptions about fractions. International Electronic Journal of Mathematics Education, 15(3), Article em0583. https://doi.org/10.29333/iejme/7835
  45. Leech, N. L., Barrett, K. C., & Morgan, G. A. (2008). SPSS for intermediate statistics: Use and interpretation (3rd ed.). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410616739
  46. Leikin, R., Berman, A., & Zaslavsky, O. (2000). Learning through teaching: The case of symmetry. Mathematics Education Research Journal, 12(1), 18–36. https://doi.org/10.1007/BF03217072
  47. Luneta, K. (2015). Understanding students’ misconceptions: An analysis of final grade 12 examination questions in geometry. Pythagoras, 36(1). http://dx.doi.org/10.4102/pythagoras.v36i1.261
  48. Marshman, M., & Brown, R. (2014). Coming to know and do mathematics with disengaged students. Mathematics Teacher Education & Development, 16(2), 71–88. https://research.usc.edu.au/esploro/outputs/journalArticle/Coming-to-Know-and-Do-Mathematics/99449264402621/filesAndLinks?index=0
  49. Martin, G. E. (2012). Transformation geometry: An introduction to symmetry. Springer Science & Business Media.
  50. Merriam, S. B. (2009). Qualitative research: A guide to design and implementation (Revised and expanded from qualitative research and case study application in education). Jossey-Bass.
  51. Metaxas, N., Potari, D., & Zachariades, T. (2016). Analysis of a teacher’s pedagogical arguments using Toulmin’s model and argumentation schemes. Educational Studies in Mathematics, 93(3), 383-397. https://doi.org/10.1007/s10649-016-9701-z
  52. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
  53. Ministry of National Educatin [MoNE]. (2017). Lise ileri düzey matematik 11. sınıf. MoNE.
  54. Mueller, M., & Yankelewitz, D. (2014). Fallacious argumentation in student reasoning: Are there benefits?. European Journal of Science and Mathematics Education, 2(1), 27-38. https://files.eric.ed.gov/fulltext/EJ1107646.pdf
  55. Myors, B., Murphy, K. R., & Wolach, A. (2010). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests. Routledge.
  56. Naylor, S., Keogh, B., & Downing, B. (2007). Argumentation and primary science. Research in Science Education, 37(1), 17–39. https://doi.org/10.1007/s11165-005-9002-5
  57. NCTM. (2000). Principles and standards for school mathematics. NCTM.
  58. Oldknow, A., & Tetlow, L. (2008). Using dynamic geometry software to encourage 3D visualization and modeling. The Electronic Journal of Mathematics and Technology, 2(1), 54-61. https://ejmt.mathandtech.org/Contents/eJMT_v2n1p4.pdf
  59. Olson, M., Zenigami, F. & Okazaki, C. (2008). Students’ geometric thinking about rotations and benchmark angles. Mathematics Teaching in The Middle School, 14(1), 24–26. https://doi.org/10.5951/MTMS.14.1.0024
  60. Pesen, M. (2018). An examination of the proof and argumentation skills of eighth-grade students (Publication No. 528226) [Master’s thesis, Boğaziçi University]. Council of Higher Education Thesis Center.
  61. Portnoy, N., Grundmeimer, T. A., & Graham, K. J. (2006). Students' understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs. Journal of Mathematical Behavior, 25(3), 196–207. https://doi.org/10.1016/j.jmathb.2006.09.002
  62. Reid, D. A., & Knipping, C. (2010). Proof in mathematics education: Research, learning, and teaching. Sense Publishers.
  63. Rollick, M. B. (2009). Toward a definition of reflection. Mathematics Teaching in The Middle School, 14(7), 396–398. https://doi.org/10.5951/MTMS.14.7.0396
  64. Rumsey, C., & Langrall, C. W. (2016). Promoting mathematical argumentation. Teaching Children Mathematics, 22(7), 412-419. http://dx.doi.org/10.5951/teacchilmath.22.7.0412
  65. Sanchez, M. G. C., & Uriza, R. C. (2008, July). Studying arguments in the mathematics classroom: A case study [Conference presentation]. The 11th International Congress on Mathematical Education, Monterrey, Mexico. https://www.academia.edu/1226104/STUDYING_ARGUMENTS_IN_MATHEMATICS_CLASSROOM_A_CASE_STUDY
  66. Santos-Trigo, M., & Cristóbal-Escalante, C. (2008). Emerging high school students' problem-solving trajectories based on the use of dynamic software. Journal of Computers in Mathematics and Science Teaching, 27(3), 325-340. https://www.academia.edu/download/68365819/Emerging_High_School_Students_Problem_S20210728-5715-16hsrc4.pdf
  67. Selig, J. M. (2013). Geometrical methods in robotics. Springer Science & Business Media.
  68. Semana, S., & Santos, L. (2010). Written report in learning geometry: Explanation and argumentation. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Sixth congress of the european society for research in mathematics education (pp. 766 775). INRP.
  69. Sevgi, S., & Erduran, A. (2020). Student Approaches Resulting from Integration of Cultural Context into Transformation Geometry Activities. Acta Didactica Napocensia, 13(2), 174-185. https://doi.org/10.24193/adn.13.2.12
  70. Shadaan, P., & Leong, K. E. (2013). Effectiveness of using GeoGebra on students' understanding in learning circles. The Malaysian Online Journal of Educational Technology, 1(4), 1-11. https://files.eric.ed.gov/fulltext/EJ1086434.pdf
  71. Sinclair, N., Bussi, B., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Owens, K. (2016). Recent research on geometry education: An ICME-13 survey team report. ZDM: International Journal on Mathematics Education, 48(5), 691–719. https://doi.org/10.1007/s11858-016-0796-6
  72. Solomon, B. (2014). Linear Algebra, geometry, and transformation. CRC Press.
  73. Streiner, D. L. (2003). Starting at the beginning: An introduction to coefficient alpha and internal consistency. Journal of Personality Assessment, 80(1), 99–103. https://doi.org/10.1207/S15327752JPA8001_18
  74. Şengül, S., & Tavşan, S. (2019). The examination of the argumentation processes of 8th grade students in the context of mathematical problems. Kastamonu Education Journal, 27(4), 1679-1693. https://doi.org/10.24106/kefdergi.3241
  75. Thaqi, X., Giménez, J., & Rosich, N. (2011, February). Geometrical transformations as viewed by pre-service teachers [Conference presentation]. 7th Conference of European Research in Mathematics Education, Rzeszów, Poland. https://www.researchgate.net/profile/Joaquin-Gimenez/publication/265810785_GEOMETRICAL_TRANSFORMATIONS_AS_VIEWED_BY_PROSPECTIVE_TEACHERS/links/5543b56b0cf24107d39634b0/GEOMETRICAL-TRANSFORMATIONS-AS-VIEWED-BY-PROSPECTIVE-TEACHERS.pdf
  76. Timans, R., Wouters, P., & Heilbron, J. (2019). Mixed methods research: what it is and what it could be. Theory and Society, 48, 193–216. https://doi.org/10.1007/s11186-019-09345-5
  77. Toulmin, S. E. (2003). The uses of argument (Updated ed.). Cambridge University Press.
  78. Ünlü, A. A., & Er, H. (2015). Lise ileri düzey matematik 11. Nova.
  79. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477. https://doi.org/10.5951/jresematheduc.27.4.0458
  80. Yanık, H. B. (2011). Pre-service middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78, 231–260. https://doi.org/10.1007/s10649-011-9324-3
  81. Yanık, H. B., & Flores, A. (2009). Understanding rigid geometric transformations: Jeff’ s learning path for translation. The Journal of Mathematical Behaviour, 28(1), 41–57. https://doi.org/10.1016/j.jmathb.2009.04.003
  82. Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri (10th ed.). Seçkin.
  83. Zembat, İ. Ö. (2013). Geometrik dönüşümlerden öteleme ve farklı anlamları. In İ. Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır, & A. Delice (Eds.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar (First ed., pp. 665-680). Pegem Akademi.