Research Article
Year 2018,
Volume: 17 Issue: 3, 0 - 0, 31.07.2019
Abstract
İspat kavramının matematik eğitimindeki yeri ve önemi son yıllarda
yapılan eğitim reformlarının açıkça belirttiği “matematiksel ispatların ana
okuldan lise son sınıfa kadar matematik derslerinin önemli bir parçası olmalıdır”
yönündeki önerisi ile vurgulanmaktadır. Ders kitap inceleme çalışmaları ise ders
kitapları ile güncel reform önerilerinin aynı doğrultuda olmadığını kanıtlar
niteliktedir. Bu çalışmanın amacı matematiksel ispat etkinliklerinin ortaokul
5, 6, 7 ve 8. sınıf matematik ders kitaplarında hangi sıklıkla yer bulduğunu
araştırmaktır. Bu amaçla, Milli Eğitim Bakanlığı tarafından yayınlanan Tokat
ili bölgesinde 5, 6, 7 ve 8. sınıf matematik derslerinde kullanılan kitaplarda
yer alan ispat etkinlikleri incelenmiştir. Seçilen ders kitapları en az iki kodlayıcı
tarafından iki aşamada kodlanmıştır. Birinci aşamada ders kitaplarında yer alan
örnek, problem, etkinlik, uygulama ve değerlendirme soru sayları belirlenirken;
ikinci aşamada ise muhakeme-ve-ispat etkinlikleri tespit edilmiştir. Bu
çalışmanın bulgularına göre ortaokul ders materyallerinde yer alan toplamda incelenen
2831 matematiksel aktiviteden sadece 177 (%6) aktivitenin muhakeme-ve-ispat
etkinliği olma özelliği taşıdığı görülmüştür. Ders materyallerinde yer alan muhakeme-ve-ispat
etkinliklerinden 80 (%45) aktivitenin ispat olmayan argüman özelliği taşırken
sadece 18 (%10) aktivitenin ispat olma özelliği taşıdığı bulunmuştur. Bu
bulgular ışığında ders kitaplarında yer alan muhakeme-ve-ispat etkinliklerinin sayısı
güncel eğitim reformlarının ve matematik eğitimcilerinin önerileri ile
uyuşmadığı görülmüştür.
Keywords
References
- Altıparmak, K. , & Öziş, T. ( 2005). Matematiksel ispat ve matematiksel muhakemeni gelişimi üzerine bir inceleme. Ege Eğitim Dergisi, 6(1), 25–37 Aydın, E. (2016). Ortaokul 8. sınıf matematik ders kitabı (Sevgi Yayınları). Koza Yayın Dağıtım A.Ş: Ankara. Aydın, E., & Gündoğdu, L. (2016). Ortaokul matematik 6. sınıf ders kitabı (Sevgi Yayınları). Ankara: Koza Yayın Dağıtım A. Ş. 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., & Cohen, D. K. (1996). Reform by the book: What is – or might be – the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8, 14. Bieda, K.N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382. Bieda, K. N., Ji, X., Drwencke, J, & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80. Cai, J., & Howson, A. G. (2013). Toward an international mathematics curriculum. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & K. S. F. Leung (Eds.), Third international handbook of mathematics education research (pp. 949–978). Springer. Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011). Longitudinal investigation of the curriculum effect: An analysis of student learning outcomes from the LieCal Project. International Journal of Educational Research, 50(2), 117–136. 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. Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for mathematics. Retrieved from http://corestandards.org/asserts/ CCSSI_Math%20Standards.pdf Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375–402. 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. Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13. 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 (pp. 234-283). Providence, R.I.: American Mathematical Society. Hoyles, C. (1997). The curricular shaping of students’ approaches to proof. For the Learning of Mathematics, 17(1), 7-16. Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge: Cambridge University Press. İmamoğlu, Y. (2010). Birinci ve son sınıf matematik ve matematik öğretmenliği öğrencilerinin ispatla ilgili kavramsallaştırma ve becerilerinin incelenmesi. Yayımlanmamış doktora tezi. Boğaziçi Üniversitesi Fen Bilimleri Enstitüsü, İstanbul. Keskin, C. (2016). Ortaokul matematik 7. sınıf ders kitabi (Ada Yayınları). Ankara: Ada Matbaacılık. Kilpatrick, J., Swafford, J., Findell, B., & U.S. National Research Council Mathematics Learning Study Committee. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press. Knuth, E. J. (2002). Proof as a tool for learning mathematics. Mathematics Teacher, 95(7), 486-490. Knuth, E., Choppin, J., & Bieda, K. (2009). Proof: Examples and beyond. Mathematics Teaching in the Middle School, 15, 206–211. Komatsu, K. (2013). Principles of task design to foster proofs and refutations in mathematical learning: Proof problem with. In Margolinas, C. (Ed.).Task Design in Mathematics Education. Proceedings of ICMI Study 22 : Oxford. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge University Press. 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. Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277-89. MEB (2017). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar. Ankara: MEB. MEB (2013). Ortaokul matematik dersi öğretim programı(5,6, 7 ve 8. sınıflar). Ankara: MEB. MEB (2016). Ortaokul matematik 6.sınıf. Ankara: MEB Yayınları. Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics Education, 94, 223-239. Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27,249-266. National Council for Teachers of Mathematics [NCTM].(2000). Principles and standards for school mathematics. Reston, VA: Author. Newton, D. P., & Newton, L. D. (2007). Could elementary mathematics textbooks help give attention to reasons in the classroom? Educational Studies in Mathematics, 64, 69–84. Polya, G. (1954). Induction and analogy in mathematics. Princeton, NJ, Princeton University Press. Reid, D. A. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33, 5-29. Rowland, T. (1998). Conviction, explanation and generic examples. In Olivier, A. and Newstead, K. (Eds.), Proceedings of the 22nd International Conference for the Psychology of Mathematics Education (pp. 65-72). Stellenbosch, S. Africa, University of Stellenbosch. Senk, S. L., & Thompson, D. R. (2003). Standards-based school mathematics curricula: What are they? What do students learn? Mahwah, NJ: Lawrence Erlbaum Associates. Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H., Wiley, D. E., Cogan, L. S., & Wolfe, R. G. (2002). Why schools matter: A cross-national comparison of curriculum and learning. San Francisco, CA: Jossey-Bass. 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. Smith, M.S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350. Stein, M.K., Smith, M.S., & Remillard, J. (2007). How curriculum influences student learning. In Lester, F.K. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-370). Greenwich, CT: Information Age Publishing, Stylianides, G . (2010). Engaging secondary students in reasoning and proving. Mathematics Teaching, 129, 39-44. Stylianides, G. J. (2009). Reasoning and proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288. Stylianides, G. (2008). Analytic framework of reasoning-and-proving, For the Learning of Mathematics, 28, 9-16. Stylianides, A. J. (2007a). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289–321. Stylianides, A. J. (2007b). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65(1), 1–20. Tall, D. (1989). The nature of mathematical proof. Mathematics Teaching, 127, 28-32. Waring, S. (2000). Can you prove it? Developing concepts of proof in primary and secondary schools. Leicester, UK: The Mathematical Association. 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. Yaman, H., Akkaya, R., & Yeşilyurt, Ü. (2016). Ortaokul matematik 5. Sınıf ders kitabı (Özgün Yayınları). Ankara: Özgün A.Ş. Yıldırım, A., & Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (6. Baskı). Ankara: Seçkin Yayıncılık. Zack, V. (1997). You have to prove us wrong: Proof at the elementary school level. In E. Pehkonen (Ed.), Proceedings of the 21st international Conference of the Psychology of Mathematics Education, Vol. 4 (pp. 291–298). Lahti: Finland.
Year 2018,
Volume: 17 Issue: 3, 0 - 0, 31.07.2019
Abstract
References
- Altıparmak, K. , & Öziş, T. ( 2005). Matematiksel ispat ve matematiksel muhakemeni gelişimi üzerine bir inceleme. Ege Eğitim Dergisi, 6(1), 25–37 Aydın, E. (2016). Ortaokul 8. sınıf matematik ders kitabı (Sevgi Yayınları). Koza Yayın Dağıtım A.Ş: Ankara. Aydın, E., & Gündoğdu, L. (2016). Ortaokul matematik 6. sınıf ders kitabı (Sevgi Yayınları). Ankara: Koza Yayın Dağıtım A. Ş. 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., & Cohen, D. K. (1996). Reform by the book: What is – or might be – the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8, 14. Bieda, K.N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382. Bieda, K. N., Ji, X., Drwencke, J, & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71-80. Cai, J., & Howson, A. G. (2013). Toward an international mathematics curriculum. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & K. S. F. Leung (Eds.), Third international handbook of mathematics education research (pp. 949–978). Springer. Cai, J., Wang, N., Moyer, J. C., Wang, C., & Nie, B. (2011). Longitudinal investigation of the curriculum effect: An analysis of student learning outcomes from the LieCal Project. International Journal of Educational Research, 50(2), 117–136. 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. Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for mathematics. Retrieved from http://corestandards.org/asserts/ CCSSI_Math%20Standards.pdf Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15(4), 375–402. 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. Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21(1), 6-13. 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 (pp. 234-283). Providence, R.I.: American Mathematical Society. Hoyles, C. (1997). The curricular shaping of students’ approaches to proof. For the Learning of Mathematics, 17(1), 7-16. Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge: Cambridge University Press. İmamoğlu, Y. (2010). Birinci ve son sınıf matematik ve matematik öğretmenliği öğrencilerinin ispatla ilgili kavramsallaştırma ve becerilerinin incelenmesi. Yayımlanmamış doktora tezi. Boğaziçi Üniversitesi Fen Bilimleri Enstitüsü, İstanbul. Keskin, C. (2016). Ortaokul matematik 7. sınıf ders kitabi (Ada Yayınları). Ankara: Ada Matbaacılık. Kilpatrick, J., Swafford, J., Findell, B., & U.S. National Research Council Mathematics Learning Study Committee. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press. Knuth, E. J. (2002). Proof as a tool for learning mathematics. Mathematics Teacher, 95(7), 486-490. Knuth, E., Choppin, J., & Bieda, K. (2009). Proof: Examples and beyond. Mathematics Teaching in the Middle School, 15, 206–211. Komatsu, K. (2013). Principles of task design to foster proofs and refutations in mathematical learning: Proof problem with. In Margolinas, C. (Ed.).Task Design in Mathematics Education. Proceedings of ICMI Study 22 : Oxford. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge University Press. 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. Mason, J., & Pimm, D. (1984). Generic examples: Seeing the general in the particular. Educational Studies in Mathematics, 15, 277-89. MEB (2017). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar. Ankara: MEB. MEB (2013). Ortaokul matematik dersi öğretim programı(5,6, 7 ve 8. sınıflar). Ankara: MEB. MEB (2016). Ortaokul matematik 6.sınıf. Ankara: MEB Yayınları. Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics Education, 94, 223-239. Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27,249-266. National Council for Teachers of Mathematics [NCTM].(2000). Principles and standards for school mathematics. Reston, VA: Author. Newton, D. P., & Newton, L. D. (2007). Could elementary mathematics textbooks help give attention to reasons in the classroom? Educational Studies in Mathematics, 64, 69–84. Polya, G. (1954). Induction and analogy in mathematics. Princeton, NJ, Princeton University Press. Reid, D. A. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33, 5-29. Rowland, T. (1998). Conviction, explanation and generic examples. In Olivier, A. and Newstead, K. (Eds.), Proceedings of the 22nd International Conference for the Psychology of Mathematics Education (pp. 65-72). Stellenbosch, S. Africa, University of Stellenbosch. Senk, S. L., & Thompson, D. R. (2003). Standards-based school mathematics curricula: What are they? What do students learn? Mahwah, NJ: Lawrence Erlbaum Associates. Schmidt, W. H., McKnight, C. C., Houang, R. T., Wang, H., Wiley, D. E., Cogan, L. S., & Wolfe, R. G. (2002). Why schools matter: A cross-national comparison of curriculum and learning. San Francisco, CA: Jossey-Bass. 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. Smith, M.S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344-350. Stein, M.K., Smith, M.S., & Remillard, J. (2007). How curriculum influences student learning. In Lester, F.K. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-370). Greenwich, CT: Information Age Publishing, Stylianides, G . (2010). Engaging secondary students in reasoning and proving. Mathematics Teaching, 129, 39-44. Stylianides, G. J. (2009). Reasoning and proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–288. Stylianides, G. (2008). Analytic framework of reasoning-and-proving, For the Learning of Mathematics, 28, 9-16. Stylianides, A. J. (2007a). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289–321. Stylianides, A. J. (2007b). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65(1), 1–20. Tall, D. (1989). The nature of mathematical proof. Mathematics Teaching, 127, 28-32. Waring, S. (2000). Can you prove it? Developing concepts of proof in primary and secondary schools. Leicester, UK: The Mathematical Association. 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. Yaman, H., Akkaya, R., & Yeşilyurt, Ü. (2016). Ortaokul matematik 5. Sınıf ders kitabı (Özgün Yayınları). Ankara: Özgün A.Ş. Yıldırım, A., & Şimşek, H. (2008). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (6. Baskı). Ankara: Seçkin Yayıncılık. Zack, V. (1997). You have to prove us wrong: Proof at the elementary school level. In E. Pehkonen (Ed.), Proceedings of the 21st international Conference of the Psychology of Mathematics Education, Vol. 4 (pp. 291–298). Lahti: Finland.
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Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Araştırma Articlesi |
| Authors | |
| Publication Date | July 31, 2019 |
| Published in Issue | Year 2018 Volume: 17 Issue: 3 |