THE OPINIONS OF THE STUDENTS OF SECONDARY EDUCATION MATHEMATICS TEACHING ON MATHEMATICAL PROOF METHODS

Abstract

In this study, the opinions of the students of mathematics teaching on mathematical proof methods were examined using the case study design among qualitative research methods. The data were obtained with the help of the Opinion Form on Mathematical Proof Methods. The study group consists of 10 secondary school mathematics teaching students, who are determined according to the criterion sampling method and volunteer for participating in the research. A clinical interview was held with each student, and descriptive and content analysis were used together in the analysis of the data. Based on the findings, it was seen that students have positive thoughts about the necessity of proving by determining mathematical proof methods.

Keywords

• Mathematical proof methods, secondary school mathematics students, opinion on proof methods

ORTAÖĞRETİM MATEMATİK ÖĞRETMENLİĞİ ÖĞRENCİLERİNİN MATEMATİKSEL İSPAT YÖNTEMLERİ HAKKINDAKİ GÖRÜŞLERİ

Öz

Bu çalışmada, matematik öğretmenliği öğrencilerinin matematiksel ispat yöntemleri hakkındaki görüşleri nitel araştırma yöntemlerinden durum çalışması deseni kullanılarak incelenmiştir. Veriler Matematiksel İspat Yöntemlerine İlişkin Görüş Formu yardımıyla elde edilmiştir. Çalışma grubunu ölçüt örnekleme yöntemine göre belirlenen ve araştırmaya katılmaya gönüllü 10 ortaöğretim matematik öğretmenliği öğrencisi oluşturmaktadır. Her bir öğrenci ile klinik mülakat yapılmış ve verilerin analizinde betimsel ve içerik analizi birlikte kullanılmıştır. Bulgulardan, öğrencilerin matematiksel ispat yöntemlerini belirleyerek ispat yapmanın gerekliliği hakkında genellikle olumlu düşünceye sahip oldukları görülmüştür.

Anahtar Kelimeler

• Matematiksel İspat Yöntemleri, Ortaöğretim Matematik Öğrencileri, İspat Yöntemlerine Yönelik Görüş

Kaynakça

1. 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), 869–890.
2. Altıparmak, K. & Öziş, T. (2005). An Investigation Upon Mathematical Proof and Development of Mathematical Reasoning. Ege Journal of Education, 6 (1), 25-37.
3. Baker, J.D. (1996). Students’ difficulties with proof by mathematical induction. The Annual Meeting of the American Educational Research Association, New York.
4. Baştürk, S. (2010). First-year secondary school mathematics students' conceptions mathematical proofs and proving. Educational Studies, 36(3), 283-298.
5. Coe, R. & Ruthven, K. ( 1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20(1), 41–53.
6. Corbin, J. & Strauss, A. (2007). Basics of qualitative research: techniques and procedures for developing grounded theory (3rd ed.). Thousand Oaks, CA: Sage.
7. Çallıalp, F. (1999). Abstract mathematics with examples. İstanbul: Marmara University, Ataturk Education Faculty Publications, 3. Print.
8. Doruk, M., Özdemir, F., & Kaplan, A. (2015). The Relationship Between Prospective Mathematics Teachers’ Conceptions On Constructing Mathematical Proof And Their Self-Efficacy Beliefs Towards Mathematics. Kastamonu Education Journal, 23(2), 861- 874.

9. Dubinsky, E. & Lewin, P. (1986). Reflective abstraction and mathematics education: The genetic decomposition of induction and compactness. Journal of Mathematical Behavior, 5(1), 55–92.
10. Gibson, D. (1998). Students’ use of diagrams to develop proofs in an introductory analysis course. Students’ proof schemes. In Schoenfeld, A.H., Kaput, J., and Dubinsky, E., editors. CBMS Issues Mathematics Education, 7, 284-307. AMS.
11. Gökkurt, B. & Soylu, Y. (2012). The Ideas Related to Mathematical Proof of University Students. Journal of Research in Education and Teaching, 1( 4), 56-64.
12. Güler, G. (2013). Investigation of pre-service mathematics teachers’ proof processes in the learning domain of algebra [Ph. D. thesis]. Erzurum: Atatürk University, Institute of Education Sciences.
13. Güler, G. & Dikici, R. (2012). Secondary pre-service mathematics teachers’ views about mathematical proof. Kastamonu Education Journal, 20(2), 571-590.
14. Güler, G., Özdemir, E., & Dikici R. (2012). Pre-service teachers’ proving skills using mathematical induction and their views on mathematical proving. Kastamonu Education Journal, 20(1), 219–236.
15. Hanna, G. ( 2000). Proof, explanation, and exploration: an overview. Educational Studies in Mathematics, 44, 5–23.
16. Harel, G. (2002). The development of mathematical induction as a proof scheme: A model for DNR-based instruction. In Campbell, S.R., and Zazkis, R., editors. Learning and Teaching Number Theory: Research in Cognition and Instruction. 185-212. New Jersey: Ablex Publishing Corporation.
17. İmamoğlu, Y. (2010). An Investigation of Freshmen and Senior Mathematics and teaching Mathematics Students’ Conceptions and Practices Regarding Proof [Ph. D. thesis]. İstanbul: Boğaziçi University, Institute of Science.
18. İskenderoğlu, T. (2010). Proof Schemes Used by Prerservice Mathematics Teachers and Their Ideas About Proof [Ph. D. thesis]. Trabzon: Karadeniz Technical University, Institute of Science.
19. İskenderoğlu, T. A., Baki, A. & Palancı, M. (2011). Questionnaire for Constructing Proof at Mathematics Course: Study of the Reliability and Validity. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 181-203.
20. Kaplan, A., Doruk, M., Öztürk, M., & Duran, M. (2016). Is there any difference between mathematics and mathematics education students’ views about mathematical proof? Journal of Human Sciences, 13(3), 6020-6037.
21. Kayagil, S. (2012). The Views of Prospective Mathematics Teachers in Elementary Program on Proving and Examinig of These Views According to Some Variables. International Journal of New Trends in Arts, Sports & Science Education, 1(2), 134-141.
22. Knuth, E.J. (2002a). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teacher Education, 5, 61–88.
23. Knuth, E.J. (2002b). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379–405.
24. Leung, Y.G. (2005). An evaluation of a teaching approach to improve students' understanding of mathematical induction. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.
25. Martin, W.G. & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41–51.
26. Mingus, T. T. Y. & Grassl, R. M. ( 1999). Preservice teacher beliefs about proofs. School Science and Mathematics, 99(8), 438–444.
27. Ministry of Education [ME] (2005). Secondary (9–12). Classes programs promotion handbook (in Turkish). Chairman of the board of education ministry of education. Ankara: Department of State Printing House Books.
28. Ministry of Education [ME] (2013). Curriculum of 9-12 secondary mathematic (in Turkish). Chairman of the board of education ministry of education. Ankara: Department of State Printing House Books.
29. Moralı, S., Uğurel, I., Türnüklü, E., & Yeşildere, S. (2006). The views of the mathematics teachers on proving. Kastamonu Education Journal, 14(1), 147–160.
30. Movshovitz-Hadar, N. (1993). The false coin problem, mathematical induction and knowledge fragility. Journal of Mathematical Behavior. 12, 253–268.
31. National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
32. Öçal, M. F. & Güler, G. (2010). Pre-service mathematics teachers’ views about proof by using concept maps. Procedia Social and Behavioral Sciences, 9, 318–323.
33. Özer, Ö. & Arıkan, A. (16-18 September 2002). Lise matematik derslerinde öğrencilerin ispat yapabilme düzeyleri. Paper presented at the Congress of V. National Science and Mathematics Education. Ankara, Turkey.
34. Özer, Ö. & Arıkan, A. (2001). Lise matematik derslerinde öğrencilerin ispat yapabilme düzeyleri. Taken from http://infobank.fedu.odtu.edu.tr/ufbmek-5/netscape/b_kitabi/ PDF/ Matematik/Bildiri/t245d.pdf. on 8 July 2013.
35. Peşken Sağır, P. (2013). Analysing the process of prospective math teachers’ doing mathematical proof. [M. Sc. thesis]. İstanbul: Marmara University,Institute of Education Sciences.
36. Sarı Uzun, M. & Bülbül, A. (2013). A teaching experiment on development of pre-service mathematics teachers’ proving skills. Education and Science, 38(169), 372-390.
37. Schoenfeld, A.H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55–80.
38. Tall, D. (1998, August). The cognitive development of proof: Is mathematical proof for all or for some? This paper was presented at the Conference of the University of Chicago School Mathematics Project, USA.
39. Varghese, T. (2009). Secondary-level student teachers’ conceptions of mathematical proof. IUMPST: The Journal. Vol 1 (Content Knowledge), [www.k- 12prep.math.ttu.edu].
40. Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48, 101–119.
41. Weber, K. (2006). Investigating and teaching the processes used to construct proofs. In Hitt, F., Harel, G., and Selden, A., editors. Research in Collegiate Mathematics Education. IV . 197 -232).
42. Yıldırım, A. & Şimşek, H. (2011). Qualitative research methods in social sciences. Ankara: Seçkin Publications.