Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat

Sare ŞENGÜL, (Marmara Üniversitesi, Atatürk Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü, İstanbul, Türkiye,)
Büşra KIRAL (İstanbul Aydın Üniversitesi, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü, İstanbul, Türkiye)
Yaşadıkça Eğitim Dergisi
19 10
Yıl: 2023 Cilt: 37 Sayı: 2 Sayfa Aralığı: 508 - 530 Metin Dili: Türkçe DOI: 10.33308/26674874.2023372589 İndeks Tarihi: 31-05-2023

Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat

Öz:
Matematik öğretme ve öğrenme sürecinde öğretmenlere kılavuz, öğrencilere yardımcı kaynak olan ders kitaplarındaki akıl yürütme ve ispatlama durumlarını analiz etmek, öğrencilerin akıl yürütme ve ispatlamayı öğrenme fırsatlarını anlamak için atılacak önemli adımlardan biridir. Bu araştırmada, Millî Eğitim Bakanlığının Eğitim Bilişim Ağından tüm öğrencilere sunduğu bir beşinci ve bir altıncı sınıf matematik ders kitabı incelenmiştir. Verilerin analizinde literatürdeki çalışmaların değerlendirme kriterleri esas alınarak araştırmacılar tarafından analitik çerçeve geliştirilmiştir. Bu kapsamda akıl yürütme ve ispat etkinlikleri, beşinci ve altıncı sınıf matematik öğrenme alanlarına, etkinliklerin amaçlarına ve olası argüman türlerine göre değerlendirilmiştir. Araştırmanın bulgularına göre, akıl yürütme ve ispata yönelik etkinlikler, beşinci ve altıncı sınıf ders kitaplarındaki tüm etkinliklerin sırasıyla %21 ve %13’ünü oluşturmaktadır. Sonuçta, matematik ders kitabı etkinliklerinde, akıl yürütme ve ispatın ağırlıklı yer almadığı görülmüştür.
Anahtar Kelime:

Mathematical Reasoning and Proof in Mathematics Textbooks

Öz:
Analyzing reasoning and proving contexts in textbooks, which guide teachers and students in the process of teaching and learning mathematics, is an important step in comprehending the opportunities for students to learn to reason and prove. This study examined two mathematics textbooks for grades five and six, which were distributed to all students by the Ministry of National Education’s Education Information Network. The researchers created an analytical framework for the data analysis based on the standards used to evaluate studies in the literature. In this context, reasoning and proof activities were evaluated separately based on the fifth- and sixth-grade mathematics learning areas, the purposes of the activities in the books, and possible argument types. Findings show that reasoning and proof activities account for 21% and 13%, respectively, of all activities in fifth- and sixth-grade textbooks. As a result, reasoning and proof were found to be absent from mathematics textbook activities.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Akkan, Y. (2016). Cebirsel düşünme. E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler (ss. 43-64) içinde. Pegem Akademi.
  • Alibert, D. (1988). Towards new customs in the classroom. For the Learning of Mathematics, 8(2), 31–35.
  • Amit, M., & Neria, D. (2008). Rising to the challenge: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM, 40(1), 111-129. https://doi.org/10.1007/s11858-007-0069-5
  • Askew, M., Hodgen, J., Hossain, S. & Bretscher, N. (2010). Values and variables: Mathematics education in high-performing countries. Nuffield foundation.
  • Aydoğdu-İskenderoğlu, T. (2016). Kanıt ve kanıt şemaları. E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler (ss. 65-84) içinde. Pegem Akademi.
  • Balacheff, N. (1991). The benefits and limits of social interaction: The case of mathematical proof. In Mathematical knowledge: Its growth through teaching (pp. 173-192). Springer. https://doi.org/10.1007/978-94-017-2195-0_9
  • Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373-397. https://doi.org/10.1086/461730
  • Barak, M., & Levenberg, A. (2016). A model of flexible thinking in contemporary education. Thinking Skills and Creativity, 22, 74-85. https://doi.org/10.1016/j.tsc.2016.09.003
  • Baroody, A. J., & Costlick, R. T. (1998). Fostering children’s mathematical power. An investigative approach to K-8 mathematics instruction. Erlbaum. https://doi.org/10.4324/9781410602084
  • Begle, E. (1973). Some lessons learned by SMSG. Mathematics Teacher, 66, 207-214. https://doi.org/10.5951/MT.66.3.0207
  • 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. https://doi.org/10.1016/j.ijer.2013.06.005
  • CadwalladerOlsker, T. (2011). What do we mean by mathematical proof?. Journal of Humanistic Mathematics, 1(1), 33-60. https://doi.org/10.5642/jhummath.201101.04
  • Doğan, M. F. (2019). Opportunities to learn reasoning and proof in eighth-grade mathematics textbook. Inonu University Journal of the Faculty of Education, 20(2), 601-618. https://doi.org/10.17679/inuefd.527243
  • Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM, 45(5), 765-777. https://doi.org/10.1007/s11858-013-0530-6
  • Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status and directions. ZDM, 45(5), 633-646. https://doi.org/10.1007/s11858-013-0539-x
  • Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38(1-3), 11-50. https://doi.org/10.1023/A:1003488222875
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education. McGraw-hill.
  • Fujita, T., & Jones, K. (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81-91. https://doi.org/10.1016/j.ijer.2013.09.014
  • Hanna, G. (1989). More than formal proof. For the Learning of Mathematics, 9(1), 20-23.
  • Hanna, G. (1990). Some pedagogical aspects of proof. Interchange, 21, 6-13. https://doi.org/10.1007/BF01809605
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44, 5-23. https://doi.org/10.1023/A:1012737223465
  • Hanna, G. (2020). Mathematical proof, argumentation, and reasoning. Encyclopedia of Mathematics Education, 561-566. https://doi.org/10.1007/978-3-030-15789-0_102
  • Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Ed.), Research in collegiate mathematics education III, (pp. 234-283). American Mathematical Society.
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning, (pp. 805-842). National Council of Teachers of Mathematics.
  • Hersh, R. (1993). Proving is convincing and explaining, Educational Studies in Mathematics, 24, 389-399. https://doi.org/10.1007/BF01273372
  • Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Eds.), Conceptual and procedural knowledge: The case of mathematics, (pp. 1-27). Erlbaum.
  • Hong, D. S., & Choi, K. M. (2018). Reasoning and Proving Opportunities in Textbooks: A Comparative Analysis. International Journal of Research in Education and Science, 4(1), 82-97. https://doi.org/10.21890/ijres.382937
  • Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1-16. https://doi.org/10.1007/s10649-017-9761-8
  • Johansson, M. (2003). Textbooks in mathematics education: A study of textbooks as the potentially implemented curriculum [Unpublished doctoral dissertation]. Luleå Tekniska Universitet.
  • Karakuş, F., & Korkutan, E. (2021). Ortaokul matematik ders kitaplarında geometri ve ölçme konularına yönelik yapılan ispatların muhakeme ve ispat analitik çerçevesi kapsamında incelenmesi. Manisa Celal Bayar Üniversitesi Eğitim Fakültesi Dergisi, 9(1), 1-16. https://doi.org/10.52826/mcbuefd.840090
  • Kilpatrick, J. (1996). Introduction to Section 1. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick & C. Laborde (Ed.), International handbook of mathematics education, (pp. 7-10), (Vol. 4). Kluwer.
  • Knuth, E. J. (2002). Secondary school mathematics teachers’ conceptions of proof. Journal for Research in Mathematics Education, 33(5), 379-405. https://doi.org/10.2307/4149959
  • Komatsu, K. (2016). A framework for proofs and refutations in school mathematics: Increasing content by deductive guessing, Educational Studies in Mathematics, 92(2), 147-162. https://doi.org/10.1007/s10649-015-9677-0
  • Küchemann, D., & Hoyles, C. (2006). Influences on students' mathematical reasoning and patterns in its development: insights from a longitudinal study with particular reference to geometry. International Journal of Science and Mathematics Education, 4(4), 581-608. https://doi.org/10.1007/s10763-006-9039-6
  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29-63. https://doi.org/10.3102/00028312027001029
  • Lithner, J. (2000). Mathematical reasoning in task solving. Educational Studies in Mathematics, 41(2), 165-190. https://doi.org/10.1023/A:1003956417456
  • Manin, Y. (1977). A course in mathematical logic, Springer-Verlag.
  • Manin, Y. (1992, August, 17-23). Contribution in panel discussion on “The theory and practice of proof”. In C. Gaulin, B. R. Hodgson, D. H. Wheeler, J. C. Egsgard (Ed.), Proceedings of the seventh International Congress on Mathematical Education, Québec.
  • Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutiérrez & P. Boero (Ed.), Handbook of research on the psychology of mathematics education (pp. 173-204). Brill.
  • Mason, J. (2001). Questions about mathematical reasoning and proof in schools. http://xtec.cat/centres/a8005072/articles/proof_and_reasoning.pdf
  • Merzbach, U. C., & Boyer, C. B. (2011). A history of mathematics (3. Ed.). Wiley.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis, Sage Publications.
  • Millî Eğitim Bakanlığı [MEB] (2018a). Matematik Dersi 1-8. Sınıflar Öğretim Programı. MEB Talim ve Terbiye Kurulu Başkanlığı.
  • Millî Eğitim Bakanlığı [MEB] (2018b). Ortaokul ve İmam Hatip Ortaokulu Matematik Ders Kitabı-5. MEB Talim ve Terbiye Kurulu Başkanlığı.
  • Millî Eğitim Bakanlığı [MEB] (2018c). Ortaokul ve İmam Hatip Ortaokulu Matematik Ders Kitabı-6. MEB Talim ve Terbiye Kurulu Başkanlığı.
  • National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. Reston.
  • Newton, D. P., & Newton, L. D. (2006). Could elementary mathematics textbooks help give attention to reasons in the classroom?. Educational Studies in Mathematics, 64(1), 69-84. https://doi.org/10.1007/s10649-005-9015-z
  • Nordström, K., & Löfwall, C. (2005, February, 17-21). Proof in Swedish upper secondary school mathematics textbooks: The issue of transparency. In M. Bosch (Ed.), CERME 4-Fourth Congress of the European Society for Research in Mathematics Education (pp. 448-457).
  • Rav, Y. (1999). Why do we prove theorems?. Philosophia Mathematica, 7(3), 5-41. https://doi.org/10.1093/philmat/7.1.5
  • Remillard, J. T., & Heck, D. J. (2014). Conceptualizing the curriculum enactment process in mathematics education. ZDM, 46(5), 705-718. https://doi.org/10.1007/s11858-014-0600-4
  • Rezat, S. & Sträßer, R. (2015). Methodological issues and challenges in research on mathematics textbooks. Nordic Studies in Mathematics Education, 20(3-4), 247-266.
  • Ross, K. A. (1998). Doing and proving: The place of algorithms and proofs in school mathematics. The American Mathematical Monthly, 105(3), 252-255. https://doi.org/10.1080/00029890.1998.12004875
  • Schoenfeld, A. H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behavior, 13(1), 55-80. https://doi.org/10.1016/0732-3123(94)90035-3
  • Silverman, B., & Even, R. (2015, February, 4-8). Textbook explanations: Modes of reasoning in 7 th grade Israeli mathematics textbooks. In K. Krainer & N. Vondrová (Ed.), CERME 9-Ninth Congress of the European Society for Research in Mathematics Education (pp. 205-212).
  • Stacey, K., & Vincent, J. (2009). Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks. Educational Studies in Mathematics, 72(3), 271-288. https://doi.org/10.1007/s10649-009-9193-1
  • Stacey, K., Burton, L., & Mason, J. (1985). Thinking mathematically. Addison-Wesley Publishers.
  • Stefanowicz, A., Kyle, J., & Grove, M. (2014). Proofs and mathematical reasoning. University of Birmingham.
  • Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-370). National Council of Teachers of Mathematics, Information Age Publishing.
  • Stylianides, G. J. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9-16.
  • Stylianides, G. J. (2009). Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11(4), 258-288. https://doi.org/10.1080/10986060903253954
  • Tall, D. (2014). Making sense of mathematical reasoning and proof. In M. Fried & T. Dreyfus (Ed.), Mathematics & mathematics education: Searching for common ground (pp. 223-235). Springer.
  • Tarr, J. E., Chávez, Ó., Reys, R. E., & Reys, B. J. (2006). From the written to the enacted curricula: The intermediary role of middle school mathematics teachers in shaping students' opportunity to learn. School Science and Mathematics, 106(4), 191-201. https://doi.org/10.1111/j.1949-8594.2006.tb18075.x
  • 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. https://doi.org/10.5951/jresematheduc.43.3.0253
  • Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim (Çev. S. Durmuş). Nobel.
  • Weber, K. & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56, 209-234. https://doi.org/10.1023/B:EDUC.0000040410.57253.a1
  • Weiss, I. R., Pasley, J. D., Smith, P. S., Banilower, E. R., & Heck, D. J. (2003). Looking inside the classroom. Horizon Research Inc.
  • Wood, T., & Turner-Vorbeck, T. (2001). Extending the conception of mathematics Teaching. In T. Wood, B. S. Nelson, & J. Warfield (Ed.), Beyond classical pedagogy: Teaching elementary school mathematics (pp. 185-208). Erlbaum.
  • Yackel, E., & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, W. G. Martin, & D. Schifter (Ed.), A research companion to principles and standards for school mathematics (pp. 22-44). National Council of Teachers of Mathematics.
  • Yanık, H. B. (2016). Kavramsal ve işlemsel anlama. E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler (ss. 101-116) içinde. Pegem Akademi.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri (6. Basım). Seçkin.
  • Zhang, D., & Qi, C. (2019). Reasoning and proof in eighth-grade mathematics textbooks in China. International Journal of Educational Research, 98, 77-90. https://doi.org/10.1016/j.ijer.2019.08.015
APA Şengül S, Kıral B (2023). Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. , 508 - 530. 10.33308/26674874.2023372589
Chicago Şengül Sare,Kıral Büşra Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. (2023): 508 - 530. 10.33308/26674874.2023372589
MLA Şengül Sare,Kıral Büşra Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. , 2023, ss.508 - 530. 10.33308/26674874.2023372589
AMA Şengül S,Kıral B Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. . 2023; 508 - 530. 10.33308/26674874.2023372589
Vancouver Şengül S,Kıral B Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. . 2023; 508 - 530. 10.33308/26674874.2023372589
IEEE Şengül S,Kıral B "Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat." , ss.508 - 530, 2023. 10.33308/26674874.2023372589
ISNAD Şengül, Sare - Kıral, Büşra. "Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat". (2023), 508-530. https://doi.org/10.33308/26674874.2023372589
APA Şengül S, Kıral B (2023). Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. Yaşadıkça Eğitim Dergisi, 37(2), 508 - 530. 10.33308/26674874.2023372589
Chicago Şengül Sare,Kıral Büşra Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. Yaşadıkça Eğitim Dergisi 37, no.2 (2023): 508 - 530. 10.33308/26674874.2023372589
MLA Şengül Sare,Kıral Büşra Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. Yaşadıkça Eğitim Dergisi, vol.37, no.2, 2023, ss.508 - 530. 10.33308/26674874.2023372589
AMA Şengül S,Kıral B Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. Yaşadıkça Eğitim Dergisi. 2023; 37(2): 508 - 530. 10.33308/26674874.2023372589
Vancouver Şengül S,Kıral B Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat. Yaşadıkça Eğitim Dergisi. 2023; 37(2): 508 - 530. 10.33308/26674874.2023372589
IEEE Şengül S,Kıral B "Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat." Yaşadıkça Eğitim Dergisi, 37, ss.508 - 530, 2023. 10.33308/26674874.2023372589
ISNAD Şengül, Sare - Kıral, Büşra. "Matematik Ders Kitaplarında Matematiksel Akıl Yürütme ve İspat". Yaşadıkça Eğitim Dergisi 37/2 (2023), 508-530. https://doi.org/10.33308/26674874.2023372589
Sayfa Oluşturulma Tarihi
24-04-2024 7:38

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