Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process

Işıkhan Uğurel; Hasibe Sevgi Moralı; Melike Yiğit-Koyunkaya; Özge Karahan

doi:10.12973/eurasia.2016.1523a

Full Text (PDF)

Işıkhan Uğurel ¹ ^* , Hasibe Sevgi Moralı ¹, Melike Yiğit-Koyunkaya ¹, Özge Karahan ¹

More Detail

¹ Dokuz Eylul University, Faculty of Buca Education^* Corresponding Author

Abstract

Background:
Pre-service secondary mathematics teachers’ (PSMTs) understanding and ability of constructing a proof is not only important for their own learning process, but also important to help their students to gain the ability to do proof in their future teaching. Therefore, this study is focused on and explained PSMTs’ behaviors that they revealed throughout the proving process of a proposition.

Materials and methods:
In this qualitative case study, the participants were fifteen volunteer PSMTs from a public university in Turkey. The participants were given a proposition which they were asked to think aloud and prove it on the blackboard.

Results:
In detail, PSMTs had difficulties in application of mathematical language and notations, understanding the meaning of the given proposition, knowing where to get started on a proof, using examples efficiently, using appropriate and efficient methods to construct the proof, and defining logical structures of the proposition to construct the proof.

Conclusions:
The findings of this study show that PSMTs’ behaviors and thoughts regarding the given proposition were limited.

Keywords

proof
proving
pre-service secondary mathematics teachers
teacher education

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 12, Issue 2, February 2016, 203-231

https://doi.org/10.12973/eurasia.2016.1523a

Publication date: 11 Nov 2015

Article Views: 2261

Article Downloads: 998

Open Access References How to cite this article

References

Alcock, L. (2008). Mathematicians’ perspectives on the teaching and learning of Proof. CBMS Issues in Mathematics Education, 16, 73-100.
Altiparmak, K. (2014). An examination of freshman student’s mathematical proof skills. Educational Research, 5(1), 1-7.
Baker, D. & Campbell, C. (2004). Fostering the development of mathematical thinking: Observations from a proofs course. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 14(4), 345-353.
Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L.I. Tatsien (Ed.). Proceedings of the International Congress of Mathematicians (Vol. III, pp. 907–920). Beijing: Higher Education Press.
Bell, A. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1), 23–40.
Blanton, M. L., Stylianou, D. A., & David, M. M. (2003). The nature of scaffolding in undergraduate students’ transition to mathematical proof. In Prooceedings of the 27th Annual Meeting for the International Group for Psychology of Mathematics Education (Vol 2., pp. 113-120). Honolulu, Hawaii: PME.
Ceylan, T. (2012). GeoGebra yazilim ortamında ilköğretim matematik öğretmen adaylarının geometrik ispat biçimlerinin incelenmesi. (Unpublished Master Thesis). Ankara University, Ankara, Turkey.
Chin E. & Lin, F. (2009). A comparative study on junior high school students’ proof conceptions in algebra between Taiwan and the UK. Journal of Mathematics Education, 2(2), 52-67.
Common Core State Standards Initiative (2010). Mission statement. Retrieved from http://www.corestandards.org/
Çiltaş, A., & Yilmaz, K. (2013). Ilköğretim matematik öğretmeni adaylarının teoremlerin ifadeleri için kurmuş oldukları matematiksel modeller. Journal of Research in Education and Teaching, 2(2), 108-114.
Demiray, E. (2013). Ortaokul matematik öğretmen adaylarının matematiksel ispat başarı düzeylerinin ve yanlış anlamlandırma nedenlerinin incelenmesi (Unpublished Master Thesis). Middle East Technical University, Ankara, Turkey.
De Villiers, M. (2002). Developing understanding for different roles of proof in dynamic geometry. The paper is presented at ProfMat2002, Visue, Portugal, 2-4 October 2002.
Doruk, M., & Kaplan, A. (2013). Ilköğretim matematik öğretmeni adaylarının dizilerin yakınsaklığı kavramı üzerine ispat değerlendirme becerileri. Journal of Research in Education and Teaching, 2(1), 231-240.
Ekiz, D. (2003). Eğitim araştırma yöntem ve metodlarına giriş. Ankara, Turkey: Anı Yayıncılık.
Finlow-Bates, K., Lerman, S., & Morgan, C. (1993). A survey of current concepts of proof held by first year mathematics students. Proceedings of the 17th Conference of the International Group for the Psychology of Mathematics Education (pp. 252-259). Tokyo, Japan: PME.
Güler, G., Kar, T., Öçal, M. F. ve Çiltaş, A. (2011). Prospective mathematics teachers’ difficulties in proof. Procedia Social and Behavioral Sciences, 15, 336-340.
Güler, G., Özdemir, E., & Dikici, R. (2012). Öğretmen adaylarının matematiksel tümevarım yoluyla ispat becerileri ve matematiksel ispat hakkındaki görüşleri. Kastamonu Egitim Dergisi, 20(1), 219-236.
Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13.
Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1-2), 5–23.
Hanna, G., & Barbeau, E. (2008). Proofs as bearers of mathematical knowledge. ZDM-The International Journal on Mathematics Education. 40(3), 345-353.
Haverhals, N. J. (2011). Students’ development in proof. (Unpublished PhD dissertation). University of Montana, Missoula, Montana.
Heinze, A. & Reiss, K. (2003). Reasoning and proof: Methodological knowledge as a component of proof competence. In M.A. Mariotti (Ed.), Proceedings of the Third Conference of the European Society for Research in Mathematics Education. Bellaria, Italy.
Hemmi, K. (2008). Students’ encounter with proof: The condition of transparency. ZDM Mathematics Education, 40, 413-426.
Hemmi, K. (2010). Three styles characteristing mathematicians’ pedagogical perspectives on proof. Educational Studies in Mathematics, 75(3), 271-291.
Hemmi, K., & Löfwall, C. (2009). Why do we need proof. In Sixth Conference of European Research in Mathematics Education (CERME-6). Lyon, France: CERME-6. Retrieved from http://www.cerme7.univ.rzeszow.pl/WG/1/CERME7_WG1_Lofwall.pdf
Hoyles, C. (1997). The curricular shaping of students’ approaches to proof. For The Learning of Mathematics, 17(1), 7-16.
Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry context. In C. Mammana and V. Villiani (Eds.), Perspectives on the Teaching of Geometry for the 21st Century (pp. 121- 128). Dordrecht: Kluwer.
Imamoglu, Y. (2010). Birinci ve son sınıf matematik ve matematik öğretmenliği öğrencilerinin ispatla ilgili kavramsallaştırma ve becerilerinin incelenmesi (Unpublished PhD dissertation). Boğaziçi University, Istanbul, Turkey.
İpek, S. (2010). İlköğretim matematik öğretmen adaylarının dinamik geometri yazılımları kullanarak gerçekleştirdikleri geometrik ve cebirsel ispat süreçlerinin incelenmesi. (Unpublished Master thesis), Hacettepe University, Ankara, Turkey.
İskenderoğlu, T. (2010). İlköğretim matematik öğretmeni adaylarının kanıtlamayla ilgili görüşleri ve kullandıkları kanıt şemaları. (Unpublished PhD dissertation). Karadeniz Technical University, Trabzon, Turkey.
Jones, K. (1997). Student teachers’ conceptions of mathematical proof. Mathematics Education Review, 9, 21-32.
Karahan, Ö. (2013). Matematik öğretmen adaylarının çift sütun ispat yöntemine yönelik görüşleri ve bu yönteme dayalı ispatlama süreçlerinin analizi. (Unpublished Master thesis), Dokuz Eylul University, Izmir, Turkey.
Knapp, J. (2005). Learning to prove in order to prove to learn. Retrieved from http://mathpost.asu.edu/~sjgm/issues/2005_spring/SJGM_knapp.pdf
Knuth, E. J. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5(1), 61-88.
Knuth, E. J. & Elliot, R. (1997). Preservice secondary mathematics teachers’ interpretations of mathematical proof. Proceedings of the 19th Conference of Psychology of Mathematics Education, North American Chapter (pp. 545-551). Bloomington, Indiana: PME-NA.
Köğce, D. (2013). Ilköğretim matematik öğretmen adaylarının ispatın matematik öğrenmeye katkısı ile ilgili gorüşleri ve ispat düzeyleri. International Periodical for the Languages, Literature and History of Turkish and Turkic, 8(12), 765-776.
Martin, G. & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20, 41–51.
Ministry of National Education (Milli Eğitim Bakanlığı) (2011). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı, Retrieved from http://ogm.meb.gov.tr/programlar.asp
Ministry of National Education (Milli Eğitim Bakanlığı) (2013). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı, Retrieved from http://ogm.meb.gov.tr/
Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3-18.
Moore, R. C. (1990). College students’ difficulties in learning to do mathematical proofs (Unpublished PhD dissertation). University of Georgia, Athens, USA.
Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249-266.
NCTM, (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
Özkaya, M., Işık, A., & Konyalıoğlu, A. (2014). İlköğretim matematik öğretmenliği öğrencilerinin sürekli fonksiyonlarla ilgili ispatlama ve ters örnek oluşturmaperformansları. Middle Eastern & African Journal of Educational Research, 11, 26-42.
Patton, M. Q. (2002). Qualitative research and evaluative methods (3 ed.). Thousand Oaks, California: Sage Publications.
Recio, A. M. & Godino, J. D. (2001). Institutional and personal meanings of proof, Educational Studies in Mathematics, 48(1), 83-99.
Remillard, K. S. (2010). Exploring the learning of mathematical proof by undergraduate mathematics majors through discourse analysis. In Prooceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education. Raleigh, NC: RUME.
Resnik, M. D. (1992). Proof as a source of truth. In M. Detlefsen (Ed.), Proof and knowledge in mathematics. London and New York: Routledge.
Sarı, M., Altun, A., & Aşkar, P. (2007). Undergraduate students’ mathematical proof processes in a calculus course: A case study. Ankara University, Journal of Faculty of Educational Sciences, 40(2), 295-319.
Sarı Uzun, M., & Bülbül, A. (2013). Matematik öğretmen adaylarının kanıtlama becerilerinigeliştirmeye yönelik bir öğretme deneyi. Education and Science, 38(169), 372-390.
Schoenfeld, A. H. (1994). What do we know about mathematics curricula. Journal of Mathematical Behavior, 13(1), 55-80.
Segal, J. (1999). Learning about mathematical proof: Conviction and validity. Journal of Mathematical Behavior, 18(2), 191-210.
Selden, J., & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29(2), 123-151.
Smith, J. C. (2006). A sense-making approach to proof: strategies of students in traditional and problem-based number theory course, Journal of Mathematical Behavior, 25, 73-90.
Stylianides, G. J., Stylianides, A. J., & Philippou, G. N. (2007). Preservice teachers knowledge of proof by mathematical induction. Journal of Mathematics Teachers Education, 10, 145– 166.
Stylianides, G. J., & Stylianides, A. J. (2009). Proof constructions and evaluations. Educational Studies in Mathematics, 72, 237-253.
Tall, D. (2002). Differing models of proof and belief in mathematics. In International Conference on Mathematics: Understanding Proving and Proving to Understand (pp. 91- 107). Tapei, Taiwan: National Taiwan Normal University.
Uğurel, I., & Moralı, H. S. (2010). Matematik öğretmen adaylarının ispat ve ispatlamayayönelik bazı temel kavramlar üzerine düşünceleri. 9. Matematik Sempozyumu, Sergi ve Şenlikleri, Karadeniz Technical University, Trabzon, Turkey.
Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48, 101-119.
Weber, K. (2006). Investigating and teaching the processes used to construct proofs. In F. Hitt, G. Harel & A. Selden (Eds.), Research in Collegiate Mathematics Education, VI (pp. 197-232). RUMEC.

How to cite this article

APA

Uğurel, I., Moralı, H. S., Yiğit-Koyunkaya, M., & Karahan, Ö. (2016). Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process. Eurasia Journal of Mathematics, Science and Technology Education, 12(2), 203-231. https://doi.org/10.12973/eurasia.2016.1523a

Vancouver

Uğurel I, Moralı HS, Yiğit-Koyunkaya M, Karahan Ö. Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process. EURASIA J Math Sci Tech Ed. 2016;12(2):203-31. https://doi.org/10.12973/eurasia.2016.1523a

AMA

Uğurel I, Moralı HS, Yiğit-Koyunkaya M, Karahan Ö. Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process. EURASIA J Math Sci Tech Ed. 2016;12(2), 203-231. https://doi.org/10.12973/eurasia.2016.1523a

Chicago

Uğurel, Işıkhan, Hasibe Sevgi Moralı, Melike Yiğit-Koyunkaya, and Özge Karahan. "Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 2 (2016): 203-231. https://doi.org/10.12973/eurasia.2016.1523a

Harvard

Uğurel, I., Moralı, H. S., Yiğit-Koyunkaya, M., and Karahan, Ö. (2016). Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process. Eurasia Journal of Mathematics, Science and Technology Education, 12(2), pp. 203-231. https://doi.org/10.12973/eurasia.2016.1523a

MLA

Uğurel, Işıkhan et al. "Pre-service Secondary Mathematics Teachers’ Behaviors in the Proving Process". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 2, 2016, pp. 203-231. https://doi.org/10.12973/eurasia.2016.1523a