Sefa Dundar, Nazan Gunduz


This study aims to examine prospective elementary mathematics teachers' conceptual knowledge level for congruence and similarity in triangles subject and to examine their ability to represent the knowledge, to associate the knowledge with daily life, and to justify and solve the geometry problems about this subject. The study is designed in a characteristic pattern. Total of 46 prospective elementary mathematics teachers were selected using purposive sampling method. The instruments used to collect data in this study are: GJP (Geometry Justification Problems), GCKQ (Geometry Conceptual Knowledge Questions) and GQDLE (Geometry Questions of Daily Life Examples). The data were analyzed using descriptive statistics method. The results of the study show that 1) the prospective teachers are successful in geometry conceptual knowledge questions but had difficulty in the justification problems; 2) there is a relationship between the theoretical knowledge levels and the argument standards of the prospective teachers; 3) the prospective teachers had difficulty in the daily life examples of congruence and similarity in triangles subject.

Keywords: Congruence and Similarity, Justification, Conceptual Knowledge, Daily Life Association

Full Text:



Alamolhodaei, H. (1996). A study in higher education calculus and students' learning styles. Doctoral dissertation, University of Glasgow.

Balacheff, N. (1988). Aspect of Proof in Pupils’ Practice of School Mathematics. (Eds. D. Pimm). Mathematics Teachers and Children. London: Hodder & Stougtoni pp. 216-235.

Ball, D.L., Hill, H.C. & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator (Fall), 14–46

Bell, A.W. (1976). A study of pupils’ proff-explanations in mathematical situations. Educational Studies in Mathematics, 7, 23-40.

CadwalladerOlsker, T. (2011). What do we mean by mathematical proof? Journal of Humanistic Mathematics, 1(1), 33–60.

Ceylan, T. (2012). Investigating preservice elementary mathematics teachers' types of proofs in GeoGebra environment. Master Thesis, Ankara University.

de Villiers, M. (1999). Rethinking proof with the Geometer’s Sketchpad. Emeryville, CA: Key Curriculum Press.

de Villiers, M. (2002). Developing understanding for different roles of proof in dynamic geometry. Paper presented at ProfMat, Visue.

Elia I, GagatsisA, Deliyianni E. (2005). A reviewof the effects of different modes of representations in mathematical problem solving. In: Gagatsis A, Spagnolo F,Makrides Gr., Farmaki V, editors, Proceedings of the 4th Mediterranean Conference on Mathematics Education. Palermo, Italy: University of Palermo, Cyprus Mathematical Society; Vol. 1, p. 271–286.

Esty, W.W. (1992). Language Concepts of Mathematics. Focus on Learning Problems in Mathematics, 14(4), 31-54.

Fidan, Y. & Türnüklü, E. (2010). Examination of 5th Grade Students’ Levels of Geometric Thinking in Terms of Some Variables. Pamukkale University Journal of Education, 27, 185- 197.

Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81-91.

Gagatsis, A., Elia, I., & Mougi A. (2002). The nature of multiple representations in developing mathematical relations. Scientia Paedagogica Experimentalis, 39(1):9–24.

Goldin, G., & Shteingold, N. (2001). System of mathematical representations and development of mathematical concepts. In: Curcio FR, editor, The roles of representation in school mathematics: 2001 yearbook. Reston: National Council of teachers ofMathematics.

Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5–23.

Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning, 2, 805-842.

Harel, G. & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. American MathematicalSociety, 7, 234–283.

İlgar, L., & Gülten, D. Ç. (2013). Matematik Konularının Günlük Yaşamda Kullanımının Öğrencilere Öğretilmesinin Gerekliliği ve Önemi. İstanbul Zaim Üniversitesi Sosyal Bilimler Dergisi, Güz.

Jaffe, A. (1997). Proof and the evolution of mathematics. Synthese, 111(2), 133–146. JONES, K. (2000). “The student experience of mathematical proof at university levelâ€, International Journal of Mathematical Education in Science and Technology, vol. 31, no.1, p. 53-60.

Johnson, R.B., & Christensen, L.B. (2000). Educational research: Quantitative and qualitative approaches. Boston: Allyn and Bacon

Knuth, E.J. (2002a). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379–405.

Knuth, E.J. (2002b). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61–88.

Komatsu, K., Tsujiyama, Y., & Sakamaki, A. (2014). Rethinking the discovery function of proof within the context of proofs and refutations. International Journal of Mathematical Education in Science and Technology, 45(7), 1053-1067.

Milli Eğitim Bakanlığı [MoNE] (2013). Ortaokul matematik dersi (5,6, 7 ve 8 sınıflar) öğretim programı. Ankara: Talim Terbiye Kurulu Başkanlığı.

Moralı, S., Uğurel, I., Türnüklü, E., & Yeşildere, S. (2006). Matematik öğretmen adaylarının ispat yapmaya yönelik görüşleri. Kastamonu Eğitim Dergisi, 14(1), 147-160.

Olkun, S. & Toluk, Z. (2007). İlköğretimde Etkinlik Temelli Matematik Öğretimi. (3.Baskı). Ankara: Maya Akademi Yayın Dağıtım.

Otten, S., Gilbertson, N. J., Males, L. M., & Clark, D. L. (2014). The Mathematical Nature of Reasoning-and-Proving Opportunities in Geometry Textbooks. Mathematical Thinking and Learning, 16(1), 51-79.

Özer, Ö. & Arıkan, A. (2002). Lise matematik derslerinde öğrencilerin ispat yapabilme düzeyleri, V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, 16-18 Eylül, Ankara, Bildiriler Kitabı Cilt II, s.1083-1089.

Panaoura, A. (2013). Using representations in geometry: a model of students’ cognitive and affective performance. International Journal of Mathematical Education in Science and Technology, 45(4): 498-511.

Rossouw, L., & Smith, E. (1997). Teachers Knowledge of Geometry Teaching-Two Years on after an Inset Course. African Journal of Research in Mathematics, Science and Technology Education, 1(1), 88-98.

Seago, N.M., Jacobs, J.K., Heck, D.J., Nelson, C.L., & Malzahn, K.A. (2013). Impacting teachers’ understanding of geometric similarity: results from field testing of the Learning and Teaching Geometry professional development materials. Professional Development in Education, 40(4), 627-653. doi: 10.1080/19415257.2013.830144

Sears, R. (2012). The impact of subject-specific curriculum materials on the teaching of proof and proof schemes in high school geometry classrooms. Short Research Report Presentation at the 12th International Congress on Mathematical Education (ICME-12), Seoul, Korea.

Shulman, L. (1986). Paradigms and research programs in the study of teaching: a contemporary perspective. In M, Wittrock (Ed.), Handbook of Research on Teaching. NY: Macmillian Publishing Company.

Simon, M.A., & Blume, G.W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. Journal of Mathematical Behavior, 15, 3–31.

Staples, M., & Bartlo, J. (2010). Justification as a learning practice: Its purposes in middle grades mathematics classrooms. CRME Publications. Paper 3.

Staples, M., & Truxaw, M. (2009). A journey with justification: Issues arising from the implementation and evaluation of the Math ACCESS Project. In Proceedings of the thirty-first annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 827-835).

Staples, M.E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms. The Journal of Mathematical Behavior, 31(4), 447-462. doi: 10.1016/j.jmathb.2012.07.001

Stylianides, A.J., Stylianides, G.J., & Philippou, G.N. (2004). Undergraduate students’ understanding of the contraposition equivalence rule in symbolic and verbal contexts. Educational Studies in Mathematics, 55, 133–162.

Stylianou, D., Chae, N., & Blanton, M. (2006). Students' proof schemes: A closer look at what characterizes students' proof conceptions. In Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Mérida, México: Universidad Pedagógica Nacional.

Turgut, U.M., & Yılmaz, S. (2007). Geometri Derslerine Nasıl Giriş Yapardık? İlköğretim Matematik Öğretmen Adaylarının Görüşleri. Bilim Eğitim ve Düşünce Dergisi, 7(4).

Uppal, S., John, M., Gill, J., & Chawla, A. (2006). Triangles. Yackel, E. & Hanna, G. (2003). Reasoning and proof. J. Kilpatrick, W.G. Martin ve D. Schifter (Ed.), A research Companion to Principles and Standarts to School Mathematics, 227-236. Reston, VA: National Council of Teachers of Mathematics

DOI: https://doi.org/10.22342/jme.8.1.3256.35-54


  • There are currently no refbacks.

Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Creative Commons License
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.

View My Stats