7.Sınıf Öğrencilerinin Dörtgenler Konusundaki İspat Seviyelerinin İncelenmesi

Yıl 2019, , 196 - 216, 30.06.2019

Zülfiye Zeybek-şimşek , Aslıhan Üstün

https://doi.org/10.17522/balikesirnef.541576

Cited By: 1

Öz

Güncel eğitim reformları ve matematik eğitimcileri
matematiksel ispatların ana okuldan lise son sınıfa kadar matematik eğitiminin
önemli bir parçası olması gerektiğini savunurlar. Milli Eğitim Bakanlığı
tarafından yayınlanan yeni öğretim programı ile de matematiksel ispatların
önemi vurgulanmış ve matematiksel ispatlara tüm matematik sınıflarında yer
verilmesi önerilmiştir. Bu araştırmada 7.sınıf öğrencilerinin dörtgenler
konusundaki ispat seviyelerinin incelenmesi amaçlanmıştır. Çalışmanın
bulgularına göre öğrencilerin verilen matematiksel ifadeleri ispatlarken argüman
oluşturmada zorlandıkları tespit edilmiştir. Sunulan matematiksel ifadeler için
argüman geliştirebilen öğrencilerin ise, argümanları incelendiğinde bu
argümanların deneysel düzeyde argümanlar olduğu görülmüştür. Doğru matematiksel
ifadeler için araştırmacılar tarafından çeşitli düzeylerde hazırlanmış
argümanların incelenmesi aşamasında ise, öğrencilerin çoğunlukla deneysel
düzeydeki argümanları en ikna edici buldukları görülmüştür.  Yanlış olan matematiksel ifadenin ispatında
ise öğrencilerin çoğunun karşıt örnek oluşturabildiği gözlemlenmiştir. 

Anahtar Kelimeler

geometri, matematik eğitimi, ispat, ispat şeması, karşıt örnek verme

Investigating 7th Grade Students’ Proof Levels About Quadrilaterals

Öz

Proof is considered to be an essential aspect of mathematics education
from kindergarten through high school as highlighted by current educational
reforms. The importance of proof has also been recognized by current curriculum
in Turkey. This study aims to investigate 7th grade students proof schemes on
the topic of quadrilaterals. According to the findings of the study, it is
evident that the participants struggle to construct arguments to prove
mathematical statements. The students, who are able to construct an argument to
justify the correctness of the presented statements, construct arguments that
are coded as empirical arguments. When asked to evaluate presented arguments,
the majority of the participants find empirical arguments as the most
convincing. Even though the students struggle to construct arguments to prove
the correct mathematical statements, the majority of them are able to provide a
valid counterexample to refute the incorrect mathematical statement. 

Anahtar Kelimeler

counterexample, geometry, mathematics education, proof, proof schemes

Kaynakça

• Aylar, E. (2014). 7. sınıf öğrencilerinin ispata yönelik algı ve ispat yapabilme becerilerinin irdelenmesi. (Yayınlanmamış doktora tezi). Hacettepe Üniversitesi, Ankara.Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. In D. Pimm (Ed.), Mathematics, teachers, and children (pp.216-238). London: Hodder & Stoughton. Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In G. Martin (Ed.), Research companion for the principles and standards for school mathematics (pp. 27–44). Reston, VA: National Council of Teachers of Mathematics.Bieda, K. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351- 382.Blum, W., & Kirsch, A. (1991). Preformal proving: Examples and reflections. Educational Studies in Mathematics, 22(2), 183-203.Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö.E., Karadeniz, Ş., & Demirel, F. (2010). Bilimsel araştırma yöntemleri . Anakara: Pegem Yayıncılık. Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359-387.Coe, R., & Ruthven, K. (1994). Proof practices and constructs of advanced mathematics students. British Educational Research Journal, 20(1), 41-53.Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for mathematics. Retrieved from http://corestandards.org/asserts/CCSSI_Math%20Standards.pdfCooper, J. L., Walkington, C. A., Williams, C. C., Akinsiku, O. A., Kalish, C. W., Ellis, A. B. & Knuth, E. J. (2011). Adolescent reasoning in mathematics: Exploring middle school students‟ strategic approaches in empirical justifications, In Proceedings of the 33rd Annual Conference of the Cognitive Science Society. Boston, MA..Çalışkan, Ç. (2012), 8. sınıf öğrencilerinin matematik başarılarıyla ispat yapabilme seviyelerinin ilişkilendirilmesi. (Yayınlanmamış Yüksek lisans Tezi). Uludağ Üniversitesi Eğitim Bilimleri Enstitüsü, Bursa.Gökkurt, B., Deniz, D., Akgün, L., & Soylu, Y.(2014). Matematik alanında ispat yapma süreci üzerine yapılmış bazı araştırmalardan bir derleme. Baskent University Journal of Education, 1(1), 55-63. Harel, G. (2001). The development of mathematical induction as a proof scheme: A model for DNR-based instruction. In S. Campbell &R. Zaskis (Eds.), Learning and teaching number theory (pp. 185-212). New Jersey, Ablex Publishing.Harel, G., & Sowder, L (2007). Toward a comprehensive perspective on proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp.805-842). Reston, VA: National Council of Teachers of Mathematics. Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubiensky (Eds.), Research in collegiate mathematics education III (ss. 234-283). Providence, R.I.: American Mathematical Society. Healy , L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning, (pp. 707-762). Charlotte, NC: Information Age PublishingKnuth, E. J. (2002). Secondary school mathematics teachers' conceptions of proof. Journal for Research in Mathematics Education, 33, (5) , 379-405.Knuth, E. J., & Sutherland, J. (2004, October). Student understanding of generality. In Proceedings of the 26th Annual Meeting - of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 561-567). Toronto: University of TorontoLannin, J. K. (2003). Algebraic reasoning through generalization. Mathematics Teaching in the Middle School, 8(7), 342–348.Maher, C. A., & Martino, A. M. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal for Research in Mathematics Education, 27(2), 194–214. McMillan, H. J. (2000). Educational research: fundamentals for the consumer (3rd ed.). New York: Longman.MEB (2013). Ortaokul matematik dersi ( 5,6,7 ve 8. Sınıflar) öğretim programı. Ankara: MEB.MEB (2018). Matematik dersi (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB.Movshovitz-Hadar, N. (1998). Stimulating presentations of theorems followed by responsive proofs. Forthe Learning of Mathematics, 8(2), 12–19, 30. National Council for Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Özer, Ö. & Arıkan, A. (2002). Lise matematik derslerinde öğrencilerin ispat yapabilme düzeyleri. V.Ulusal Fen Bilimleri Ve Matematik Eğitimi Kongresinde Sunulmuş Bildiri, Ortadoğu Teknik Üniversitesi, Ankara.Quinn, A. L. (2009). Count on number theory to inspire proof. Mathematics Teachers, 103 (4), 298-304.Rowland, T. (2002). Generic proofs in number theory. In S.R. Campbell & R. Zazkis (Eds.), Learning and teaching number theory: Research in cognition and instruction (pp.157-183). Westport, CT: Ablex Publishing. Schoenfeld, A. H. (2009). Series editor’s foreword: The soul of mathematics. In D. Stylianou, M. Blanton, & E. Knuth (Eds.), Teaching and learning proof across the grades: A K-16 perspective (pp. xii-xvi). New York, NY: Routledge.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.Stylianides A. J. (2007). Proof and proving in school mathematics, Journal of Research in Mathematics Education, 38, 289-321.Stylianides, A.J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11, 307-332.Stylianides, G. J., & Stylianides, A. J. (2008). Proof in school mathematics: Insights from psychological research into students’ ability for deductive reasoning. Mathematical Thinking and Learning, 10(2), 103–133.Thompson, D. R. , Senk, S. L. & Johnson, G. J. ( 2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education,43 (3), 253- 295. Uğurel, I.; & Moralı, S. (2010). Bir ortaöğretim matematik dersindeki ispat yapma etkinliğine yönelik sınıf içi tartışma sürecine öğrenci söylemleri çerçevesinde yakından bakış. Buca Eğitim Fakültesi Dergisi, 28, 135 – 154.Van Dormolen, J. (1977). Learning to understand what giving a proof really means. Educational Studies in Mathematics, 8 (1), 27-34. Weber, K. (2012). Mathematicians’ pedagogical practice with respect to proof. International Journal of Mathematics Education in Science and Technology, 43, 463–482.Yin, , R. K. (2003). Case study research design and methods (Third Edition). Thousand Oaks, CA: Sage Publications, Inc. Zeybek, Z. (2017). Pre-service elementary teachers’ conceptions of counterexamples. International Journal of Education in Mathematics, Science and Technology (IJEMST), 5(4), 295-316. Zeybek, Z., Üstün, A., & Birol, A. (2018).Matematiksel ispatların ortaokul matematik ders kitaplarındaki yeri. İlköğretim Online, 17(3), 1317-1335.