Investigating The Effect Of Origami Use In Geometry Teaching On Pre-service Teachers' Concept Images

Öz

The paper folding method for teaching mathematics is used as a concrete material in primary and secondary schools to explore concepts, primarily geometry, and understand the relationship between these concepts. The overarching definitions expressing the relations of the quadrilaterals are ignored when teaching plane geometry. This research is differentiated from other studies in creating original content by approaching origami and quadrilaterals conceptually. In this study, pre-service teachers will be provided to rethink the conceptual relationship between quadrilaterals with origami. The primary purpose is to determine the effect of paper folding activities on pre-service teachers' concept images of quadrilaterals. A quantitative research method, a single group pre-test-post-test design, will be used to achieve this aim. The study data were collected with "Concept Image Questions" and "Geometry Attitude Scale." As a result of the data analysis, it was seen that while the pre-test was directed to the exclusionary definitions, the concept images of the inclusive definitions intensified in the post-test. In addition, no significant change was observed in the geometry attitudes of pre-service teachers. At the end of the study, it was concluded that the application of origami activities would enable pre-service teachers to express comprehensive definitions of quadrilaterals and to deal with the relations of quadrilaterals with each other in a conceptual dimension. Thus, students' awareness of plane geometry subjects taught in schools will increase indirectly.

Anahtar Kelimeler

• Origami
• geometry
• quadrilaterals
• concept image

Geometri Öğretiminde Origami Kullanımının Öğretmen Adaylarının Kavram İmajlarına Etkisinin İncelenmesi

Öz

Matematik öğretimi için kağıt katlama yöntemi ilkokul ve ortaokulda geometri öncelikli olmak üzere kavramların keşfedilmesi ve bu kavramlar arasındaki ilişkinin anlaşılması için somut bir materyal olarak kullanılmaktadır. Dörtgenlerin birbiriyle olan ilişkilerini ifade eden kapsayıcı tanımları ise düzlem geometrisi öğretilirken göz ardı edilmektedir. Bu araştırma origami ile dörtgenler konusuna kavramsal olarak yaklaşarak özgün içerikler oluşturulması açısından diğer çalışmalardan farklılaştırılmıştır. Bu çalışmada öğretmen adaylarının dörtgenler arasındaki kavramsal ilişkiyi origami ile yeniden düşünmeleri sağlanacaktır. Burada temel amaç kağıt katlama etkinliklerinin öğretmen adaylarının dörtgenlere ilişkin kavram imajlarına olan etkisini belirlemektir. Bu amaca ulaşmak için nicel araştırma yöntemi, tek grup ön test – son test deseni kullanılacaktır. Çalışmanın verileri ‘’Kavram İmajı Soruları’’ ve ‘’Geometri Tutum Ölçeği’’ ile toplanmıştır. Veri analizinin sonucunda ön testte daha çok hariç tutan tanımlara yönlenirken son testte kapsayıcı tanımlara ilişkin kavram imajlarının yoğunlaştığı görülmüştür. Bunun yanında öğretmen adaylarının geometri tutumlarında anlamlı bir değişme görülmemiştir. Çalışma sonunda origami etkinliklerinin uygulanmasının öğretmen adaylarının dörtgenlere ilişkin kapsayıcı tanımları ifade edebilme ve dörtgenlerin birbirleriyle olan ilişkilerini kavramsal boyutta ele alabilmelerini sağlayacağı sonucuna ulaşılmıştır. Böylece okullarda öğretilen düzlem geometri konularında öğrencilerde bu farkındalıkları dolaylı olarak artırılacaktır

Anahtar Kelimeler

• Origami
• geometri
• dörtgenler
• kavram imajı

Kaynakça

1. Aksu, H. H. (2020). The effect of teaching the triangular issue thorugh origami-based learning approach on the success of 9th grade students. Turkish Studies-Educational Sciences, 15(4), 2343-2354.
2. Baki, A. (2018). Matematiği öğretme bilgisi [Knowledge of teaching mathematics] (1st edition). Ankara: Pegem Akademi.
3. Bayraktar-Kurt, E. (2012). In elementary geometry education the passing of geometric shapes and objects by the help of origami. [Unpublished master’s thesis]. On Dokuz Mayıs University.
4. Bingölbali, E. & Monaghan, J. (2008). Concept image revisited. Educational Studies in Mathematics, 68(1), 19-35.
5. Boakes, N. J. (2009). Origami instruction in the middle school mathematics classroom: Its impact on spatial visualization and geometry knowledge of students. RMLE Online, 32(7), 1-12.
6. Boyacıoğlu, H., Köroğlu, H., & Alkan, H. (2003). İlköğretimin ilk beş sınıfında matematik etkinlikleri [Mathematics activities in the first five grades of primary education]. Matematikçiler Derneği Bilim Köşesi.
7. Boz-Yaman, B. (2015). A journey from two-dimensional papers to three-dimensional origamic cube. Journal of Inquiry Based Activities, 5(1), 20-33.
8. Boz-Yaman, B., & Duatepe-Paksu, A. (2019). Triggering geometrical habits of mind by origami activity: Folding a dodecahedron. Australian Mathematics Education Journal, 1(4), 4-10.

9. Duatepe-Paksu, A., & Boz-Yaman, B. (2021). Short activity: Examining a platonic octahedron through origami. Australian Mathematics Education Journal, 3(2), 4-7.
10. Bütüner, S. Ö. & Filiz, M. (2016). Examining prospective mathematics teachers' understanding of the classification of quadrilaterals. Journal of Subject Teaching Research, 2 (2), 43-56.
11. Cansız-Aktaş, M. & Aktaş, D. Y. (2013). The development of a current attitude scale towards geometry. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 7 (2), 225-247.
12. Creswell, J. W. (2012). Educational research: planning. Conducting, and Evaluating, 260, 375-382.
13. Çalık-Uzun, S. (2020). Dörtgen kavramı ve öğretimi [Quadrilateral concept and teaching]. Ertekin, E., Ünlü, M. (Ed.) Geometri ve ölçme öğretimi: tanımlar, kavramlar ve etkinlikler [Geometry and measurement teaching: definitions, concepts and activities]. Ankara: Pegem Akademi.
14. Dağdelen, M. G. (2012). Effect of origami in comprehending special quadrilaterals in primary 5th grade geometry education. [Unpublished master’s thesis.] On Dokuz Mayıs University.
15. De Villers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11-18.
16. Doğan, M., & Bayraktar-Kurt, E. (2021). Origami in mathematics education: the research trends of the postgraduate theses. Journal of International Social Research, 14(77).
17. Duatepe-Paksu, A. (2016). Van Hiele geometrik düşünme düzeyleri [Van Hiele geometric thinking levels] . Bingölbali, E., Arslan, S. ve Zemzat, İÖ. (Ed.), Matematik eğitiminde teoriler [Theories in mathematics education] (ss. 265-275). Ankara: Pegem Akademi.
18. Erşen, Z.&Karakuş, F. (2013). Evaluation of pre-service elementary teachers’ concept ımages for quadrilaterals. Turkish Journal of Computer and Mathematics Education, 4(2), 124-146.
19. Fischbein, E. (1993). The theory of figural concept. Educational Studies in Mathematics, 24(2), 139-162.
20. Fujita, T. (2008). Learners’ understanding of the hierarchical classification of quadrilaterals. Joubert. Proceedings of the British Society for Research into Learning Mathematics, 28(2).
21. Fujita, T. (2012). Learners‘ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31, 60–72.
22. 0Fujita, T., & Jones, K. (2006). Primary trainee teachers‘ understanding of basic geometrical figures in Scotland. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education (Vol.3, pp. 129–136). Prague: PME.
23. Fujita, T.&Jones, K., (2007). Learners’ understanding of the definitions and hierarchical classification of quadriılaterals: towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
24. Gülkılık, H. (2008). A phenomenographic study on the concept images and image development of prospective secondary mathematics teachers related with some geometric concepts. [Unpublished master’s thesis] Gazi University, Ankara.
25. Hacısalihoğlu-Karadeniz, M. (2020). Mathematics teaching via paper folding method, Elementary Education Online, 16(2): 663-692.
26. Hershkowitz, R. (1990). Psychological aspects of learning geometry, in P. Nesher and J. Kilpatrick (Ed.) Mathematics and cognition. Cambridge: Cambridge University Press.
27. Horzum, T. (2018). The investigation of pre-service mathematics teachers’ knowledge about quadrilaterals through concept maps. Turkish Journal of Computer and Mathematics Education, 9 (1), 1-30.
28. Howitt, D. & Cramer, D. (2011). Introduction to SPSS statistics in psychology: For version 19 and earlier (5th Ed.). Pearson Education Limited.
29. İnce, B., Mertol, H. & Kaya, N. (2021). Historical development and benefits of origami. XI. Umteb International Congress On Vocational & Technical Sciences, Ankara.
30. Kağıtçıbaşı, Ç. & Cemalcılar, Z. (2014). Dünden bugüne insan ve insanlar [People and people from yesterday to today]. İstanbul: Evrim Publishing.
31. Kazak, S., Duatepe-Paksu, A. (2019). The Impact of Exploring Quadrilaterals from Symmetry Perspective on Geometric Thinking: Cases of Definitions of Rectangle and Rhombus. Gazi University Journal of Gazi Education Faculty, 39(3), 1421 - 1451.
32. Koç, H., Aksoy, B., Sönmez, Ö.F., & Yeşiltaş, E. (2010). The activities making students active during teaching process and geography teaching depending on activities. The Journal of Social Sciences Research. Volume 5, Issue 2, 181 - 196
33. Küçük-Demir, B. (2020). Geometri ve geometrik düşünce [Geometry and geometric thinking]. T. Ağırman, B. Küçük-Demir (Ed.), Geometri ve öğretimi [Geometry and its teaching](pp. 1-10). Ankara: Pegem Akademi.
34. Masal, M., Ergene, Ö., Takunyacı, M., & Masal, E. (2018). Prospective teachers’ views about using origami in mathematics lessons. International Journal of Educational Studies in Mathematics, 5(2), 56-65.
35. Mertler, C. A. & Vannatta, R. A. (2005). Advanced and multivariate statistical methods: Practical application and interpretation (3rd Ed.). Pyrczak Publishing.
36. 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.
37. NCTM. (2000). Curriculum and Evaluation Standards for School Mathematics, Retrieved from http://standards.nctm.org/document/chapter7/geom.htm
38. Özdemir, A. & Çekirdekci, S. (2022). Geometric Habits of Mind: The Meaning of Quadrilaterals for Elementary School Student Teachers . International Journal of Educational Studies in Mathematics, 9 (1), 49-66.
39. Öztoprakçı, S. & Çakıroğlu, E. (2013). Dörtgenler [Quadrangles]. Zembat, İ. Ö., Özmantar, M. F., Bingölbali, E., Şandır, H. ve Delice, A. (Ed.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar [Mathematical concepts with their definitions and historical development] (2nd edition, pp. 249-272). Ankara: Pegem Akademi.
40. Polat, S. (2013). Teaching mathematic with origami. Mustafa Kemal University Journal of Social Sciences Institute, 10 (21), 15-27.
41. Senemoğlu, N., & Özçelik, D. A. (1989). Öğretmen adaylarına “öğretmenlik bilgisi” kazandırma bakımından fen-edebiyat ve eğitim fakültelerinin etkililiği [The effectiveness of science-literature and education faculties in terms of gaining "teaching knowledge" to teacher candidates]. Çağdaş Eğitim Dergisi, 142, 18-21.
42. Sönmez, V., & Alacapınar, F. G. (2016). Örneklendirilmiş araştırma yöntemleri [Illustrated Research Methods], Ankara: Anı Publishing.
43. Tabachnick, B. G. & Fidel, L. S. (2014). Using multivariate statistics (6th Ed.). Pearson Education Limited.
44. Tall, D., & 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.
45. Tarım, K.&Dinç-Artut, P. (2016). Attitude and math achievement. Bingölbali, E., Arslan, S. ve Zemzat, İÖ. (Ed.), Theories in mathematics education (pp. 767-784). Ankara: Pegem Academy.
46. Thode, H. C. (2002). Testing for normality. Marcel Dekker, Inc.
47. Toptas, V. (2008). Analysis of the teaching – learning process by the activities applied during geometry teaching. Elementary Education Online, Volume 7, Issue 1, 91.
48. Tuğrul, B. & Kavici, M. (2002). The art of paper folding origami and learning. Pamukkale University Journal of Education, 11(11), 1 – 17.
49. Türnüklü, E., Alaylı, F. G., & Akkaş, E. N. (2013). Investigation of prospective primary mathematics teachers’ perceptions and ımages for quadrilaterals. Educational Sciences: Theory & Practice. 3(2), 1213-1232.
50. Türnüklü, E. (2014). Construction of inclusion relations of quadrilaterals: Analysis of pre-service elementary mathematics teachers‘ lesson plans. Education and Science, 39(173), 198–208.
51. Ubuz, B. (2017). Relations among quadrilaterals: 7th grade students’ concept ımages. Education for Life. 31(1), 55-68.
52. Usiskin, Z., Griffin, J., Witonsky, D. & Willmore, E. (2008). The classification of quadrilaterals: a study in definition. Charlotte, NC: Information Age Publishing.
53. Van De Walle, J. A., Karp, K. S.&Bay-Williams, J. M. (2019). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim [Elementary and middle school mathematics: teaching developmentally]. (S. Durmuş, Translation edit.) Ankara: Nobel Academy.
54. Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14, 293– 305.
55. Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in developing some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the Fourth International Conference for the Psychology of Mathematics Education: Vol.1 (pp. 177–184). Berkeley: University of California, Lawrence Hall of Science.
56. Yaman, B. B., & Bulut, S. Stake holders experıences of usıng 5e learnıng cycle approach ın teachıng of Euler’s formula. Bolu Abant Izzet Baysal University Journal of Faculty of Education, 19(3), 836-852.
57. Yavuz, E. (2020). An investigation into concept image of primary school mathematics pre-service teacher is on the hyperbola. [Unpublished master's thesis] Dokuz Eylül University.
58. Zeybek-Şimşek, Z. (2019). Investigating pre-service teachers’ ability to recognize and classify geometric concepts hierarchically. Turkish Journal of Computer and Mathematics Education, 10 (3), 680-710.