### UNDERSTANDING OF PROSPECTIVE MATHEMATICS TEACHERS OF THE CONCEPT OF DIAGONAL

#### Abstract

This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the participants and the criterion was determined as taking the course of geometry in the graduate program. Data was collected in two steps: a diagnostic test form about the definition and features of diagonal was applied to participants firstly and according to the answers of the participants to the diagnostic test form, semi-structured interviews were carried out. Data collected form the diagnostic test form and the semi-structured interviews were analyzed with descriptive analysis. According to the results of the study, it is understood that the prospective teachers had difficulties with the diagonals of parallelogram, rhombus and deltoid. Moreover, it is also seen that the prospective teachers were inadequate to support their ideas with further explanations although they could answer correctly. Ä°t is thought that the inadequacy of the prospective teachers stems from the inadequacy related to proof.

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Abazao?lu, ?. (2012). TIMSS-2011 8. S?n?f Türkiye Raporu. 25 May?s 2013 tarihinde http://www.academia.edu/2479519/TIMSS_2011_8._Sinif_Turkiye_Raporu-Ilkay_Abazaoglu adresinden eri?ilmi?tir.

Akta?, D.Y., & Cans?z Akta?, M. (2012). Eighth grade students’ understanding and hierarchical classification of quadrilaterals. Elementary Education Online, 11(3), 714-728.

Alkan, H., & Bukova Güzel, E. (2005). Ö?retmen adaylar?nda matematiksel dü?ünmenin geli?imi. Gazi Üniversitesi Gazi E?itim Fakültesi Dergisi, 25(3).

Almeida, D. (2000). A survey of mathematics undergraduates interaction with proof: some implications for mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6),53-60.

Altun, M. (2004). Matematik ö?retimi. ?stanbul: Alfa Yay?nc?l?k.

Baki, A. (2008). Kuramdan uygulamaya matematik e?itimi (Geni?letilmi? 4. Bas?m). Ankara: Harf E?itim Yay?nc?l???.

Cans?z-Akta?, M., & ve Akta?, D.Y. (2011). 8. s?n?f ö?rencilerinin dörtgenleri kö?egen özelliklerinden yararlanarak tan?ma sürecinin incelenmesi. 10. Matematik Sempozyumu, 21-23 Eylül, ?stanbul.

Cunningham, F., & ve Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. IUMPS The Journal.,1, 1-17.

Çetin, Ö.F., & ve Dane, A. (2004). S?n?f Ö?retmenli?i III. S?n?f Ö?rencilerinin Geometrik Bilgilere Eri?i Düzeyleri Üzerine. Kastamonu E?itim Dergisi, 12(2), 427-436.

Çoker, D., & ve Karaçay, T. (1983). Matematik Terimleri Sözlü?ü. (1. Bask?). Türk Dil Kurumu Yay?nlar? no: 508. Ankara:Türk Dil Kurumu, 2016.

Dane, A. (2008). ?lkö?retim matematik ö?retmenli?i program? ö?rencilerinin nokta, do?ru ve düzlem kavramlar? alg?lar?. Erzincan E?itim Fakültesi Dergisi, 10(2), 41-58.

Duatepe, A. (2000). An investigation of the relationship between van hiele geometric level of thinking and demographic variable for pre-service elementary school teacher (Yay?mlanmam?? yüksek lisans tezi). Orta Do?u Teknik Üniversitesi, Ankara.

Duatepe-Paksu, A., ?ymen, E., & ve Pakmak, G.S. (2012). How well elementary teachers identify parallelogram? Educational Studies, 38(4), 415-418.

Duatepe Paksu, A., ?ymen, E., & ve Pakmak, G.S. (2013). S?n?f Ö?retmeni Adaylar?n?n Dörtgenlerin Kö?egenleri Konusundaki Kavram Görüntüleri. E?itim ve Bilim, 38(167), 162-178.

Ergün, S. (2010). ?lkö?retim 7. s?n?f ö?rencilerinin çokgenleri alg?lama, tan?mlama ve s?n?flama biçimleri (Yay?nlanmam?? yüksek lisans tezi). Dokuz Eylül Üniversitesi, ?zmir.

Er?en, Z.B., & Karaku?, F. (2013). S?n?f ö?retmeni adaylar?n?n dörtgenlere yönelik kavram imajlar?n?n de?erlendirilmesi. Turkish Journal of Computer and Mathematics Education, 4(2), 124-146.

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototy pephenomenon. The Journal of Mathematical Behavior, 31, 60-72.

Gall, M.D., Borg, W.R., & Gall, J.P. (1996). Educational research: An introduction. Longman Publishing.

Harel, G., & Sowder, L. (1998). Students’ proof schemes: results from an exploratory study. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research In College Mathematics Education III (pp. 234-283). Providence, RI: AMS.

Jones, K. (2000). The student experience of mathematical proof at university level. International Journal of Mathematical Education in Science and Technology, 31(1), 53-60.

Knapp, J. (2005). Learning to prove in order to prove to learn. [Online], URL:http://mathpost.asu.edu/~sjgm/issues/2005_spring/SJGM_knapp.pdf. 23.04.2012 tarihinde eri?ildi.

Köse, N.Y., Tan??l?, D., Erdo?an, E.Ö., & Ada, T.Y. (2012). ?lkö?retim Matematik Ö?retmen Adaylar?n?n Teknoloji Destekli Geometri Dersindeki Geometrik Olu?um Edinimleri. Mersin Üniversitesi E?itim Fakültesi Dergisi, 8(3).

Kuzniak, A., & ve Rauscher, J.C. (2007). On the geometrical thinking of pre-service school teachers. Proceedings Cerme4, SantFeliu de Guixols Spain.

Moore, R.C. (1990). College Students’ Difficulties In Learning To Do Mathematical Proofs. Unpublished Doctoral Dissertation. University of Georgia, Georgia.

Pickreign, J. (2007). Rectangles and rhombi: How well do pre-service teachers know them? IUMPST: The Journal, 1.[www.k-12prep.math.ttu.edu]

Prahmana, R.C.I., & Suwasti, P. (2014). Local instruction theory on division in mathematics GASING. Journal on Mathematics Education, 5(1), 17-26.

Putra, M., & Novita, R. (2015). Profile of secondary school students with high mathematics ability in solving shape and space problem. Journal on Mathematics Education, 6(1), 20-30.

Roberts, S.K. (1995). A study of the relationship between demographi cvariables and van Hielelevel of thinking for pre-service elementary school teachers. Doctoral Dissertation, Wayne State University. Dissertation Abstracts International, 57, 01A:0176.

Rusken, B., & Rolka, K. (2007). Integrating intuition: The role of concept image and concept definition for students’ learning of integral calculus. The Montana Mathematics Enthusiast, 3, 181-204.

Sandt, S., & ve Nieuwoudt, H.D. (2003). Grade 7 teachers’ and prospective teachers’ content knowledge of geometry. South African Journal of Education, 23(3), 199-205.

Tall, D., & ve Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151-169.

Toluk, Z., Olkun, S., & Durmu?, S. (2002). Problem merkezli ve görsel modellerle destekli geometri ö?retiminin s?n?f ö?retmenli?i ö?rencilerinin geometrik dü?ünme düzeylerinin geli?imine etkisi, Be?inci Ulusal Fen Bilimleri ve Matematik E?itimi Kongresinde sunulan bildiri, ODTÜ, Ankara.

Kurumu, T.D. (2016). Büyük Türkçe Sözlük. Ankara: Türk Dil Kurumu.

Türnüklü, E., Gündo?du-Alayl?, F., & Akka?, E.N. (2013). ?lkö?retim matematik ö?retmen adaylar?n?n dörtgenlere ili?kin alg?lar? ve imgelerinin incelenmesi. Kuram ve Uygulamada E?itim Bilimleri, 13(2), 1213-1232.

Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. (Final report of the Cognitive Development and Achievement in Secondary School Geometry Project.) Chicago: University of Chicago.

Usiskin, Z., Griffin, J., Witonsky, D., & Willmore, E. (2008). The classification of quadrilaterals: A study in definition. Charlotte, NC: Information Age Publishing.

Uzun, S., Bütüner, S.Ö., & ve Yi?it, N. (2010). 1999-2007 TIMSS fen bilimleri ve matematik sonuçlar?n?n kar??la?t?r?lmas?: s?navda en ba?ar?l? ilk be? ülke-Türkiye örne?i. ?lkö?retim Online, 9(3), 1174-1188.

Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. The concept of function: Aspects of epistemology and pedagogy, 25, 195-213.

DOI: https://doi.org/10.22342/jme.8.2.4102.165-184

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