Matematiksel İspat Kavramına Pedagojik Bir Bakış: Kuramsal Bir Çalışma

Yıl 2014, , 47 - 71, 04.03.2015

Yüksel Dede , Fatih Karakuş

https://doi.org/10.17984/adyuebd.52880

Cited By: 7

Öz

Bu çalışma, matematik öğretiminde matematiksel ispat kavramının rolü ve önemi üzerine odaklanmıştır. Bu amaç için, matematiksel ispatın tanımı, yapılış amacı, fonksiyonları, ispat şemaları ve matematiksel ispatın matematik öğrenme ve öğretme sürecindeki işlevi ile matematik öğretim programlarındaki rolüne ilişkin açıklamalara ve tartışmalara yer verilmiştir.

Anahtar Kelimeler

İspat, matematiksel ispat, matematik öğretimi

A Pedagogical Perspective Concerning the Concept of Mathematical Proof: A Theoretical Study

Öz

The purpose of the study is to determine the thoughts of pre-school teachers in making use of computers in maths teaching. The study has been conducted with 14 pre-school teachers with 1-13 years of experience, and employed in Ministry of National Education schools-kindergartens and primary schools- in Giresun, Keşap and Bulancak in 2012-13 academic years. The data of the study gained from a structured form developed by the researcher. It is found out that teachers have positive tendencies towards technology, yet they cannot use it adequately in maths practices, they do not have enough information about technology, they do not allocate time for technology, and they postpone using technology in planning their activities. Therefore, it is necessary that teachers need to be informed via in-service trainings at intervals and they need to see the right models in using technology, and get enough training and level of information to make use of technology.

Anahtar Kelimeler

Proof, mathematical proof, mathematics teaching

Kaynakça

• Albert, D. & Thomas, M. (1991). Research on mathematical proof. In: Tall D. (ed.) Advanced Mathematical Thinking (pp. 215-230). Mathematics Education Library, Kluwer Academic Publishers, Dordrecht.
• Alsina, C. & Nelsen, R. B. (2010). An invitation to proofs without words. European Journal of Pure and Applied Mathematics, 3(1), 118-127.
• Arsac, G. (2007). Origin of mathematical proof: History and epistemology. In P. Boero (Ed.), (pp. 27-42). Theorems in schools: From history, epistemology and cognition to classroom practice. Sense Publishers. Rotterdam, The Netherlands.
• Barendregt, H., & Wiedijk, F. (2005). The challenge of computer mathematics. Philosophical Transactions of the Royal Society A, 363, 2351-2375.
• Bell, A. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics 7, 23–40.
• Benson, D. C.(2000). The Moment of Proof: Mathematical Epiphanies. Oxford University Press. New York.
• CadwalladerOlsker, T. (2011). What Do We Mean By Mathematical Proof? Journal of Humanistic Mathematics, 1(1), 33- 60.
• de Villiers, M. (1999). Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press.
• Dede, Y. (2013). Matematikte İspat: Önemi, Çeşitleri ve Tarihsel Gelişimi (ss.15-34). İ.Ö. Zembat, M.F. Özmantar, E. Bingölbali, H. Şandır ve A. Delice (Eds.) Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar. Ankara: Pegem Akademi.
• Detlefsen, M. (2008). Proof: Its nature and significance. In Gold, B. And Simons, R. A., editors, Proof and Other Dillemas:Mathematics and Philosophy, (pp. 61-77). Mathematical Association of America, Washington,
• Hanna, G. & Jahnke, H.N. (1996) Proof and proving. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde (eds.), International Handbook of Mathematics Education. Kluwer Academic Publishers, Dordrecht, pp. 877–908.
• Hanna, G. (2000a). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5- 23.
• Hanna, G. (2000b). Proof and its classroom role: A survey. In M.J. Saraiva et al (Eds.), Proceedings of Conference en el IX Encontro de Investigaçao en Educaçao Matematica (pp. 75 -104). Funado.
• Hanna, G. (2002). Mathematical proof. In: Tall D. (ed.) Advanced Mathematical Thinking. Mathematics Education Library, Kluwer, Dordrecht.
• Hanna, G. (2007). The Ongoing Value of Proof. In Boero, P. (Ed.), Theorems in schools: From History, Epistemology and Cognition to Classroom Practice to Classroom Practice (pp. 3-18). Rotterdam: Sense Publishers.
• Hanna, G.,&Barbeau, E. (2002). What is proof? In Baigrie, B. (Ed.), History of Modern Science and Mathematics. (pp.36- 48.), vol. 1, New York: Charles Scribner's Sons.
• Hanna, G.& Sidoli, N. (2007).Visualization and proof: A brief survey of philosophical perspectives. ZDM. The International Journal on Mathematics Education, 39, 73-78
• Hanna, G., de Villiers, M., Arzarello, F., Dreyfus, T., Durand-Guerrier, V., Jahnke, H.N., Lin, F.L., Selden, A., Tall, D.& Yevdokimov, O. (2009). Discussion Document. In F. Lin, F. Hsieh, G. Hanna, & M. de Villiers (Eds.), Proceedings of the 19th International Commission on Mathematical Instruction: Proof and Proving in Mathematics Education (vol. 1). National Taiwan Normal University, Taipei, Taiwan: ICMI Study Series 19, Springer.
• Harel, G., & Sowder, L. (1998). Students' proof schemes. Research on Collegiate Mathematics Education, Vol. III. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), AMS, 234-283.
• Harel, G., & Sowder, L (2007). Toward comprehensive perspectives on learning and teaching proof, In F. Lester (Ed.), Handbook of Research on Teaching and Learning Mathematics (2nd Ed.). Greenwich, CT: Information Age Publishing.
• Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389-399.
• Hersh, R. (1997). What is mathematics, really? London: Jonathan Cape.
• İskenderoğlu, T. (2010). İlköğretim matematik öğretmeni adaylarının kanıtlamayla ilgili görüşleri ve kullandıkları kanıt şemaları. Yayınlanmamış doktora Tezi. Trabzon: Karadeniz Teknik Üniversitesi.
• İskenderoğlu Aydoğdu, T. & Baki, A. (2011). İlköğretim matematik öğretmeni adaylarının matematiksel kanıt yapmaya yönelik görüşlerinin nicel analizi. Kuram ve Uygulamada Eğitim Bilimleri, 11(4), 2275-2290.
• Jones, K.(2000).The student experience of mathematical proof at university level. International Journal of Mathematical Education in Science and Technology, 31(1), 53- 60.
• Milli Eğitim Bakanlığı [MEB]. (2005). Matematik Dersi 9–12. Sınıflar, Öğretim Programı ve Kılavuzu, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• Milli Eğitim Bakanlığı [MEB]. (2009). İlköğretim Matematik Dersi 6–8. Sınıflar, Öğretim Programı ve Kılavuzu, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• Milli Eğitim Bakanlığı [MEB]. (2013). Ortaokul Matematik Dersi (5,6,7 ve 8.Sınıflar) Öğretim Programı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• Milli Eğitim Bakanlığı [MEB]. (2013). Ortaöğretim Matematik Dersi (9,10,11ve 12.Sınıflar) Öğretim Programı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston VA.
• Nelsen, R. B. (2000). Proofs without Words II:More Exercises in Visual Thinking. Mathematical Association of America.
• Polster, B. (2004).Q.E.D. Beauty in mathematical proof. Walker Publishing Company, New York.
• Reid, D. & Knipping, C. (2010). Proof in mathematics education: Research, learning and teaching. Rotterdam: Sense
• Reis, K.& Renkl, A. (2002). Learning to prove: The idea of heuristic examples, Zentralblatt für Didaktik der Mathematik (ZDM), 34 (1), 29- 35.
• Sangalli, A. (1991). The burden of proof is on the computer. New Scientist, 129(1757), 38-40.
• Sarı, M., Altun, A. & Aşkar, P. (2007). Üniversite öğrencilerinin analiz dersi kapsamında matematiksel kanıtlama süreçleri: örnek olay çalışması. Ankara University, Journal of Faculty of Educational Sciences, 40(2), 295-319.
• Tall, D. (2002). The Psychology of Advanced Mathematical Thinking. In: Tall D. (ed.) Advanced Mathematical Thinking. Mathematics Education Library, Kluwer, Dordrecht.
• Türk Dil Kurumu [TDK].(2005). Türkçe Sözlük. Türk Dil Kurumu Yayınları: 549, Türk Dil Kurumu, 4. Akşam Sanat Okulu Matbaası, Ankara.
• Uygan, C., Tanışlı, D. & Köse, N.Y. (2014). İlköğretim matematik öğretmeni adaylarının kanıt bağlamındaki inançlarının, kanıtlama süreçlerinin ve örnek kanıtlardaki değerlendirme süreçlerinin incelenmesi. Turkish Journal of Computer and Mathematics Education, 5(2), 137- 157.