Pre-Service Science Teachers' Understanding of Infinity Concept: The Case of Image on Convex Lens

Öz

In this study, pre-service science teachers’ definitions of the concept of infinity were tried to be revealed and their understanding of the concept was tried to be examined through the image formation experiment in a convex lens. The study was conducted with 31 pre-service science teachers studying in the 3rd year of science teaching at a state university. Two separate scales were used as data collection tools in the research. The scales consist of open-ended questions designed to reveal pre-service teachers' definitions of the concept of infinity and to evaluate their knowledge about image formation and image properties in convex lenses in this context. One of the scales (Scale-1) was applied before the image formation demonstration experiment in the convex lens, and the other (Scale-2) was applied after the application. The data obtained from the scales were analyzed using the descriptive analysis technique. Pre-service science teachers’ definitions of infinity were grouped under three themes: general, mathematical and physical. Pre-service teachers mostly define and understand infinity with codes such as "unknown, undetectable, unmeasurable, undetectable, inexplicable, incomprehensible "under the "general" theme which includes the sub-themes of "unknown" and "having no end". This understanding of the prospective teachers leads them to the misunderstanding that the image of the object at infinity in the focal point of the convex lens is virtual and cannot be seen.

Anahtar Kelimeler

• Science education
• infinity
• image in optics

Kaynakça

1. Arabacıoğlu, S., Oğuz-Unver, A., & Unver, G. (2014). Three basic concepts in teaching the atom: Infinity, void and arche. International Journal of New Trends in Arts, Sport, & Science Education, 3(3), 72-78.
2. Başaran, M. T. (2016). Sonsuzluk kavramının mantıksal ve felsefi analizi. Kindî merkezli bir inceleme [Yayınlanmamış yüksek lisans tezi]. Hitit Üniversitesi.
3. Brieger, J. (2022). “You are thinking too much about reality. “Just think about unreality”-Implementing philosophical debates about infinity in mathematics lessons in primary school. Philosophy of Mathematics Education Journal, 39, 1-10.
4. Christensen, L. B., Johnson, BR, & Turner, L. A. (2015). Research methods, design and analysis. (Trans. Ed. A. Aypay). Anı Publishing.
5. Çelik, D., & Akşan, E. (2013). Preservice mathematics teachers' perceptions of infinity, indeterminate and undefined. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 7(1), 166-190.
6. Date, E., Huxtable, E., Cavanagh, M., Coady, C., & Easey, M. (2018) . Conceptualisations of infinity by primary pre-service teachers. Mathematics Education Research Journal, 30, 545–567.
7. Dede, Y., & Soybaş, D. (2011). Preservice mathematics teachers' concept images of polynomials. Quality & Quantity, 45(2), 391-402.
8. Demircan, B. (2012). On the outlines of the conceptual process of being itself of the infinite in Hegel. Archives of Philosophy, 37(2), 1-26.

9. Demirci, N., & Ahçı, M. (2016). Işık ve optik konuları ile ilgili üniversite öğrencilerinin kavramsal anlama düzeyleri. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 10(1).
10. Dong, Joong, K. (2010). The histories of the mathematical concepts of infinity and limit in a three-fold role. Journal of Educational Research in Mathematics,20 (3), 293-303.
11. Fernández-Plaza, J., & Simpson, A. (2016). Three concepts or one? Students' understanding of basic limit concepts. Educational Studies in Mathematics, 93(3), 315–332.

12. Fischbein, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 10(1), 3-40.
13. Goldberg F., & McDermott, L. C. (1987). An investigation of student understanding of the real image formed by a converging lens or concave mirror. American Journal of Physics, 55(2), 108-119.
14. Howes, E. V., & Rosenthal, B. (2001). A feminist revision of infinity: Small speculations on a large subject. Counterpoints, (Post) Modern Science (Education) Propositions and Alternative Paths. 137, 177-192.
15. İşleyen, T. (2013). Ortaöğretim öğrencilerinin sonsuzluk algıları. Kastamonu Eğitim Dergisi, 21(3), 1235-1252.
16. Kocakülah, A., & Şardağ, M. (2013). Fen bilgisi öğretmen adaylarının görüntü oluşumu hakkındaki kavramsal anlamaları. Eğitim ve Öğretim Araştırmaları Dergisi Journal of Research in Education and Teaching, 2(4), 1-14.
17. Kolar, V. M., & Cadez, T. H. (2012). Analysis of factors influencing the understanding of the concept of infinity. Educational Studies in Mathematics, 80(3), 389-412.
18. Krátká, M., Eisenmann, P., & Cihlář, J. (2021). Four conceptions of infinity. International Journal of Mathematical Education in Science and Technology, 53(1), 1-25.
19. MacMillan, J. H. (2004). Educational Research: Fundamentals for the Consumer (4th ed.). Pearson Education Inc.
20. MEB, (2018a). Ortaöğretim fen bilimleri dersi öğretim programları. T.C. Milli Eğitim Bakanlığı.
21. MEB, (2018b). Ortaöğretim fizik dersi öğretim programları. T.C. Milli Eğitim Bakanlığı.
22. Merand, D. N. (2014). A study of grade 11 learners' understanding of concepts related to infinity [Unpublished master of science thesis], University of the Witwatersrand.
23. Monaghan, J. (2001). Young people's ideas of infinity. Educational Studies in Mathematics, 48, 239–257.
24. Montes, M., Carrillo, J., & Ribeiro, C. M. ( 2014). Teachers knowledge of infinity, and its role in classroom practice. In Liljedahl, P., Oesterle, S., Nicol, C., & Allan, D. (Eds.) Proceedings of the Joint Meeting 4 - 233 of PME 38 and PME-NA 36, 4, 233-240. Vancouver, PME.
25. Oflaz, G., & Polat, K. (2022). Determining the epistemological obstacles regarding the concepts of infinity, undefined and uncertainty. Cumhuriyet International Journal of Education, 11(2), 301-320.
26. Palamioti, N., & Zachariades, T. (2022). Secondary teachers' conceptions of infinity in different context. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12).
27. Patton, M. Q. (2014). Qualitative research and evaluation methods (Translated from 3rd Edition). (Translation Editors: Mesut Tüm, Selçuk Beşir Demir). Pegem Akademi.
28. Savuran, R., & Isiksal-Bostan, M. (2022). Revealing implicit knowledge of pre-service mathematics teachers in lesson planning: Knowledge of infinity. European Journal of Science and Mathematics Education, 10(3), 269-283.
29. Singer, F. M. & Voica, C. (2010). In search of structures: How does the mind explore infinity? International Mind, Brain, and Education Society and Blackwell Publishing, Inc. 4(2), 81-93
30. Singer, F. M., & Voica, C. (2008). Between perception and intuition: Thinking about infinity. Journal of Mathematical Behavior, 27, 188–205.
31. Smith, C. L., Solomon, G. E. A., & Carey, S. (2005). Never getting to zero: Elementary school students' understanding of the infinite divisibility of number and matter. Cognitive Psychology, 51 , 101–140.
32. Suárez, Á., Monteiro, M., Dutra, M., & Martí, A. C. (2021). How far is infinity? An electromagnetics exercise to develop intuition regarding models. Physics Education, 56(5).
33. Tirosh, D. (1999). Finite and infinite sets: Definitions and intuitions. International Journal of Mathematical Education in Science and Technology, 30(3), 341-349.
34. Tsamir, P. (2002). From primary to secondary intuitions: prospective teachers' transitory intuitions of infinity. Mediterranean Journal for Research in Mathematics Education, 1, 11–29.
35. Türkmen, S. (2014). Spinoza’da Sonsuzluk Sorunu ve Praksis. Kaygı Uludağ Üniversitesi Fen-Edebiyat Fakültesi Felsefe Dergisi, 23, 117-127.
36. Uzoğlu, M., Yıldız, A., Demir, Y., & Büyükkasap, E. (2013). Fen Bilgisi Öğretmen Adaylarının Işıkla İlgili Kavram Yanılgılarının Belirlenmesinde Kavram Karikatürlerinin ve Açık Uçlu Soruların Etkililiklerinin Karşılaştırılması. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi. 14 (1), 367-388.
37. Yağbasan, R., & Gülçiçek, Ç. (2003). Defining the Characteristics of Misconceptions in Science Teaching. Pamukkale University Faculty of Education Journal, 13, 110-128.
38. Yıldırım, A., & Şimşek, H. (2006). Qualitative research methods in social sciences. (6th edition) Seçkin Publishing.
39. Yıldız, S. G., & Körpeoğlu, S. G. (2018). Exploring pre-service mathematics teachers' understandings of countability and infinity in webquest based learning environment. European Journal of Educational Studies, 5(1), 94-121.