Pre-Service Mathematics Teachers’ Concept Definitions and Examples Regarding Sets

Yıl 2020, Cilt: 7 Sayı: 2, 21 - 36, 01.09.2020

Muhammet Doruk Alper Çiltaş

https://doi.org/10.17220/ijpes.2020.02.003

Öz

The purpose of this study is to reveal the concept definitions and examples of pre-service elementary mathematics teachers regarding sets. In this context, students’ formal definitions, personal definitions and examples in sets were investigated. Concept of equal sets, subsets, union, intersection, compliment, and difference were considered as basic concepts of sets in this study. The participants of the study consisted of 79 freshmen studying in the department of elementary mathematics teacher training at a state university of Turkey. The study adopted qualitative research approach and is a sample of a case study. The data of the study was collected from DKFS form and unstructured interviews. The results of the study indicated that most of the pre-service teachers had difficulty in giving notational definitions and daily-life examples while they gave successfully verbal definitions of the basic concepts in sets. It was revealed that verbal definitions, notational, prototype examples with schema, symbols and operational properties were parts of some pre-service teachers’ concept images. Furthermore, some pre-service teachers confused equal sets with equivalent sets and difference with symmetric difference. They also did not consider the universal set in defining the compliment. It was found that most of the pre-service teachers had difficulty in expressing their thoughts using mathematical language throughout the study.

Anahtar Kelimeler

Sets, concept definition, concept image, mathematics education

Kaynakça

• Açıkyıldız, G. (2013). Matematik öğretmeni adaylarının türev kavramını anlamaları ve yaptıkları hatalar [Mathematics candidate teachers’ understanding of derivative concept and their mistakes]. (Unpublished master thesis). Karadeniz Teknik University, Trabzon.
• Aydeniz, F. (2011). Öğretmen adaylarının eğim kavramı ile ilgili sahip oldukları kavram imajlarının ve matematiksel anlayışlarının incelenmesi üzerine bir durum çalışması [A case study on the concept images and mathematical understanding of prospective secondary mathematics teachers’ related with concept of ‘slope’] (Unpublished master thesis). Gazi University, Ankara.
• Baki, A. (2014). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. (5. Baskı). Ankara: Harf Eğitim Yayıncılık.
• Baki, A., & Şahin, S. M. (2002). Assessment of preservice teachers’ mathematical learning trough computer aided concept mapping method. Turkish Online Journal of Educational Technology, 3(2), 91-104.
• Balcı, M. (2005). Genel matematik [General mathematics]. Ankara: Balcı Yayınları
• Baykul, Y. (2002). İlköğretimde matematik ögretimi [Mathematics teaching in primary education]. Ankara: PegemA Yayıncılık.
• Baykul, Y. (2014). Ortaokullarda matematik öğretimi [Mathematics teaching in middle schools]. (2 baskı). Ankara: Pegem Akademi.
• Çakıroğlu, E. (2013). Matematik kavramlarının tanımlanması [Defining the concepts of mathematics]. İ.Ö. Zembat, M.F. Özmantar, E. Bilgölbali, H. Şandır ve A. Delice (Ed.). Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar içinde (s. 1-14). Ankara: PegemA yayıncılık.
• Çallıalp, F. (2009). Soyut matematik [Abstract mathematics]. İstanbul: Birsen Yayınevi.
• Çelik, B. (2018). Soyut Matematik [Abstract mathematics]. Bursa: Dora Yayıncılık.
• Council of Higher Education [YOK]. (2018). İlköğretim matematik öğretmenliği lisans programı. Ankara: YOK.
• Demirel, Ö. (2015). Kuramdan uygulamaya: eğitimde program geliştirme [From theory to practice: curriculum development in education]. (24. Baskı). Ankara: Pegem Yayıncılık.
• Doruk, M., Duran, M., & Kaplan, A. (2018). Interpredations related to the definition of derivative and ascribed meanings to derivative of undergraduate students. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 18 (2), 834-856. doi: 10.17240/aibuefd.2018..-431455
• Dündar, S. (2015). Knowledge of mathematics teacher-candidates about the concept of slope. Eğitimde Kuram ve Uygulama, 11(2), 673-693.
• Erdoğan, G. (2017). Lise ve matematik öğretmenlerinin noktada türev ve türev fonksiyonu hakkındaki kavram imajları [Concept image about derrivation at point and derrivation function of high school mathematics teachers] (Unpublished master thesis). Necmettin Erbakan University, Konya.
• Fischbein, E., & Baltsan M. (1999). The mathematical concept of set and the collection model, Educational Studies in Mathematics, 37,1-22.
• Gülkılık, H. (2008). Öğretmen adaylarının bazı geometrik kavramlarla ilgili sahip oldukları kavram imajlarının ve imaj gelişiminin incelenmesi üzerine fenomenografik bir çalışma [A phenomenographic study on the concept images and image development of prospective secondary mathematics teachers related with some geometric concepts] (Unpublished master thesis). Gazi University, Ankara.
• Kabael, T., Barak, B., & Özdaş, A. (2015). Students’ concept definitions and concept images about limit concept. Anadolu Journal of Educational Sciences International, 5(1), 88-114.
• Karakuş, F. (2018). Investigation of primary pre-service teachers’ concept ımages on cylinder and cone. Elementary Education Online, 17(2), 1033-1050. doi:10.17051/ilkonline.2018.419352
• Küçükkeleş, A., & Aktaş, Ş. (2018). Ortaokul ve imam hatip ortaokulu 6. Sınıf matematik ders kitabı. Ankara: Berkay Yayıncılık.
• Macit, E., & Nacar, S. (2019). Concept images for rational number and fraction of the students at the elementary mathematics education department. Inonu University Journal of the Graduate School of Education, 6(11), 50-62. doi: 10.29129/inujgse.547277
• Merriam, S.B. (2013). Nitel araştırma desen ve uygulama için bir rehber [A guide to qualitative research pattern and practice.]. (Çev. Ed. S. Turan). Ankara: Nobel Akademik Yayıncılık.
• Ministry of National Education [MEB] (2018a). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Ankara: Talim Terbiye Kurulu Başkanlığı.
• Ministry of National Education [MEB] (2018b). Ortaöğretim matematik dersi öğretim programı (9., 10., 11. ve 12. Sınıflar). Ankara: Talim Terbiye Kurulu Başkanlığı.
• Nordlander, M. C., & Nordlander, E. (2012). On the concept image of complex numbers. International Journal of Mathematical Education in Science and Technology, 43(5), 627-641. doi:10.1080/0020739X.2011.633629
• Öner, A., & Ertekin, E . (2015). Preservice elementary mathematics teachers’ concept images related to the period concept. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 35 (2), 333-353.
• Schoenfeld, A. H. (1991). What’s all the fuss about problem solving. Zentrallblatt Für Didaktik der Mathematik, 91(1), 4-8.
• Simon, M. A. (2017). Explicating mathematical concept and mathematical conception as theoretical constructs for mathematics education research. Educational Studies in Mathematics, 94(2), 117-137. doi:10.1007/s10649-016-9728-1
• 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. doi:10.1007/BF00305619
• Tekin Sitrava, R. (2017). Prospective mathematics teachers’ concept images of algebraic expressions and equations. Cumhuriyet International Journal of Education, 6(2), 249–268.
• Turkish Language Society [TDK] (2015). Türkçe sözlük. Ankara: Türk Dil Kurumu Yayınları
• Uçak, A., Emir, E., Uçkun, F., Kutlu, G., & Kahraman, S. (2018). Ortaöğretim fen lisesi matematik 9 ders kitabı. Ankara: Milli Eğitim Bakanlığı Yayınları.
• Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293-305. doi:10.1080/0020739830140305
• Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356-366. doi:10.2307/749441
• Yazıcı, N. (2017). Mathematıcal knowledge for teachıng of the math teachers: analysıs of the basıc concepts ın the sets (Unpublished doctoral dissertation). Ataturk University, Erzurum.
• Yılmaz, E. (2015). İlköğretim matematik öğretmen adaylarının katı cisimler ile ilgili kavram tanımı ve kavram imajlarının fenomenografik yaklaşımla incelenmesi [Examination of elemantary mathematics teacher candidates concept definitions and concept images related to solid objects through the phenomenological approach] (Unpublished master thesis). Erciyes Üniversitesi, Kayseri.
• Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education 36(4), 317–346. doi: 10.2307/30035043
• Zehir, H., Işık, A., & Zehir, K. (2008). The level of conceptual knowledge of pre-service elementary mathematics teachers about set. Bayburt Üniversitesi Eğitim Fakültesi Dergisi, 3(1-2), 61-75. Appendix