İspatın Gerekliliğine İnanan Öğretmen Adayları İspatla İlgili Neden Düşük Düzeyde Özyeterliğe Sahiptir?

Year 2022, Volume: 16 Issue: 1, 49 - 63, 30.06.2022

Bahar Dinçer

https://doi.org/10.17522/balikesirnef.1120694

Abstract

Bu araştırma matematik öğretmen adaylarının ispata yönelik görüşlerini incelemeyi amaçlamaktadır. Araştırmanın nicel boyutunda, öğretmen adayları ispat öz değerlendirmesine yönelik maddelerden düşük puan aldığı için daha kapsamlı bilgi elde etmek amacıyla nitel bir ölçek uygulanmıştır. Bu nedenle nicel ve nitel araştırmanın birlikte uygulandığı karma yöntem yaklaşımı kullanılmıştır. Öğretmen adaylarının tamamı ispatın gerekliliği doğrultusunda görüş bildirmesine rağmen ispatın zorluk derecesi ve matematiksel bilgi eksikliklerinden dolayı ispat sürecinde zorlandıklarını belirtmişlerdir. Ayrıca öğretmen adaylarının büyük çoğunluğu mesleki hayatlarında ispat yerine alternatif öğrenme yaklaşımlarını kullanmayı amaçladıklarını belirtmişlerdir. İspat gerekli bir süreç olarak görülse de öğretmen adaylarının ispat öz-yeterlik düzeylerinin düşük ve meslek hayatlarında ispatı kullanma düşüncelerinin yetersiz olduğu sonucuna ulaşılmıştır..Bu nedenle lisans öncesi eğitimde de ispata yer verilmesi ve öğrencilerin temel bilgi eksikliklerinin giderilmesi önerilebilir.

Keywords

ispat, matematik eğitimi, ispat özyeterliliği

Why Do Pre-Service Teachers Who Believe In The Necessity Of Proof Have Low-Level Self-Efficacy With The Proof?

Abstract

Abstract – This research aimed to examine the opinions of pre-service mathematics teachers towards proof. The students received low scores in the items containing the self-evaluation of the proof in the quantitative dimension, a qualitative form was applied to obtain more comprehensive information. Therefore, quantitative and qualitative research approaches were used together along with mixed methods. Although all students expressed their opinions on the necessity of proof, it was concluded that they had difficulties in the proof process due to the difficulty level of proof and their lack of mathematical knowledge in their self-evaluation. And also, a great majority of pre-service teachers stated that they intended to use alternative learning approaches instead of proof in their future careers. Although proof is seen as a necessary process, pre-service teachers' proof self-efficacy levels are low and their thoughts on using proof in their professional life are insufficient. Therefore, it can be recommended to include proof in pre-graduate education and to eliminate the students' lack of basic knowledge.

Keywords

proof, mathematics teaching, proof self- efficacy.

References

• Almeida, D. (2000). A Survey of Mathematics Undergraduates’ Interaction with Proof: Some Implications for Mathematics Education. International Journal of Mathematics Education in Science and Technology. 31(6). 869-890.
• Almeida, D. (2003). Engendering proof attitudes: Can the genesis of mathematical knowledge teach us anything? International Journal of Mathematical Education in Science and Technology, 34(4), 479-488.
• Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi (4. Baskı). Ankara: Harf Eğitim Yayıncılık.
• Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7, 23-40.
• Cusi, A., & Malara, N. (2007). Proofs problems in elementary number theory: Analysis of trainee teachers' productions. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 591-600). Cyprus, Larnaca.
• Doruk, M., & Kaplan, A. (2015). Prospective mathematics teachers’ difficulties in doing proofs and causes of their struggle with proofs. Bayburt Üniversitesi Eğitim Fakültesi Dergisi, 10(2), 315-328.
• Doruk, M., & Kaplan, A. (2013). İlköğretim matematik öğretmeni adaylarının matematiksel ispata yönelik görüşleri. Eğitim ve Öğretim Araştırmaları Dergisi, 2(1),241-252.
• Hanna, G., & Barbeau, E. (2010). Proofs as bearers of mathematical knowledge. In Explanation and proof in mathematics (pp. 85-100). Springer, Boston, MA.
• King, J.,P. (1992). Matematik Sanatı. (Çev. Nermin Arık). Ankara: TÜBİTAK.
• Ko, Y.Y., & Knuth, E. (2009). Undergraduate mathematics majors’ writing performance producing proofs and counterexamples about continuous functions. The Journal of Mathematical Behavior, 28(1), 68-77. Kotelawala, U., M. (2007). Exploring Teachers’ Attitudes and Beliefs about Proving in the Mathematics Classroom. Unpublished PhD Dissetation, Columbia University, USA.
• Lee, J. K. (2002). Philosophical perspectives on proof in mathematics education. Philosophy of Mathematics Education Journal, 16.
• Mingus, T., T., Y., Grassl, R., M. (1999). Preservice Teacher Beliefs about Proofs. School Science and Mathematics. 99. Moralı, S., Uğurel, I., Türnüklü, E. & Yeşildere, S. (2006). Matematik Öğretmen Adaylarının İspat Yapmaya Yönelik Görüşleri. Kastamonu Eğitim Dergisi, 14(1). 147-160.
• Nordström, K., (2002). Swedish University Entrants Experiences about and Attitudes towards Proofs and Proving. A Paper Presented at TG On Argumentation and Proof, CERME 3, Italy
• Regier, P., & Savic, M. (2020). How teaching to foster mathematical creativity may impact student self-efficacy for proving. The Journal of Mathematical Behavior, 57, 100720.
• Reiss, K., Heinze, A. & Klieme, E. (2002). Argumentation, proof, and the understanding of proof. In G.H. Weigand, N. Neill, A. Peter-Koop, K. Reiss, G. Törner & B. Wollring (Eds.), Developments in Mathematics Education in German-speaking Countries. Selected Papers from the Annual Conference on Didactics of Mathematics, Potsdam, 2000 (S. 109-120). Hildesheim: Franzbecker.
• Saeed, R., M. (1996). An Exploratory Study of College Student’s Understanding of Mathematical Proof and the Relationship of this Understanding to their Attitude toward Mathematics. Unpublished PhD Dissetation, Ohio University, USA.
• Selden, A., & Selden, J. (2014). The roles of behavioral schemas, persistence, and self-efficacy in proof construction. In Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 246-255). Ankara, Turkey: Middle East Technical University.
• Sarı, M., Altun, A. & Aşkar, P. (2007). Üniversite Öğrencilerinin Analiz Dersi Kapsamında Matematiksel Kanıtlama Süreçleri: Örnek Olay Çalışması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi 40(2). 295-319.
• Schabel, C. (2005). An Instructional Model for Teaching proof Writing in the Number Theory Classroom. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 15(1). 45-59.
• Shongwe, B., & Mudaly, V. (2021). Introducing a measure of perceived self-efficacy for proof (PSEP): Evidence of validity. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(3), 260-276.
• Üzel, D., & Özdemir, E. (2009). Elementary Mathematics Teacher Candidates’ Attitudes towards Proof and Proving. New World Sciences Academy, 4(4).
• Viholainen, A., Tossavainen, T., Viitala, H., & Johansson, M. (2019). University mathematics students’ self-efficacy beliefs about proof and proving. LUMAT: International Journal on Math, Science and Technology Education, 7(1), 148-164.
• Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-1 19.
• Weber, K. (2004). Traditional instruction in advanced mathematics courses: a case study of one professor’s lectures and proofs in an introductory real analysis course. Journal of Mathematical Behavior 23, 115–133
• Zaslovsky, O., & Peled, I. (1996). ‘Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation’, Journal for Research in Mathematics Education, 27, 1, 67.