ORTAOKUL MATEMATİK ÖĞRETMENLERİNİN ORAN VE ORANTI KONUSUNDA ALAN VE ÖĞRETME BİLGİSİ

Year 2022, Volume: 12 Issue: 1, 309 - 328, 31.03.2022

Ceylan Şen

https://doi.org/10.30783/nevsosbilen.946955

Cited By: 2

Abstract

Bu çalışmada ortaokul matematik öğretmenlerinin alan ve öğretme bilgilerinin ortaya konulması amaçlanmıştır. Bu amaçla araştırmada nitel araştırma desenlerinden çoklu durum çalışması benimsenmiştir. Araştırma, devlet ortaokulunda görev yapmakta olan 36 ortaokul matematik öğretmeni ile yürütülmüştür. Araştırmada veri toplama aracı olarak araştırmacı tarafından hazırlanan 9 yarı yapılandırılmış sorunun yer aldığı görüşme formu kullanılmıştır. Çalışmanın verileri betimsel analiz yolu ile analiz edilmiştir. Verilerin analizi sonucunda öğretmenlerin konuya giriş stratejileri, öğretimde ilişkilendirme bilgileri, temsil kullanma ve problem çözme stratejileri, öğrencilerin öğrenme stilleri ve öğretimi planlama bilgileri incelenmiştir. Çalışmadan elde edilen sonuçlar doğrultusunda, öğretmenlerin oran-orantı öğretimine girişte günlük hayatla ilişkili örnek durumlar vermeyi tercih ettikleri fakat öğrencilerin ön bilgilerini ortaya çıkarmada yetersiz kaldıkları görülmüştür. Öğretimde ilişkilendirme konusunda ise öğretmenlerin orantı-orantı konusunun günlük hayat ve diğer disiplinlerle ilişkisinin farkında oldukları fakat öğretimlerinde ilişkilendirmeye dayalı uygulamalar gerçekleştirmedikleri görülmüştür. Öğretmenlerin oran-orantı öğretiminde öğretimini zenginleştirme ve anlamlandırma amacıyla kullanılan çoklu temsillere yönelik bilgi sahibi oldukları bunun yanı sıra öğretim sürecinde en çok kullanıldıkları temsilin ise sözel problem olduğu görülmüştür. Öğretmenlerin sözel problemlerde kullanılabilecek problem çözme stratejilerine ait bilgilerinin kısıtlı olduğu görülmüştür. Öğretimi planlamada ise öğrencilerin bireysel özelliklerine yönelik öğretmenlerin yetersiz bilgiye sahip oldukları sonucuna ulaşılmıştır.

Keywords

Alan ve Öğretme Bilgisi, Ortaokul Matematik Öğretmeni, Matematik Öğretme Bilgisi

References

• An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education, 7(2), 145-172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
• Ball, D. L. & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical futures. Paper presented at the 43rd Janrestagung der Gesellschaft für Didaktik der Mathematik, Oldenburg, Germany.
• Ball, D. L. (2003). Mathematics in the 21st century: What mathematical knowledge is needed for teaching mathematics? Paper presented at the Secretary’s Summit on Mathematics, U.S. Department of Education, Washington, DC.
• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special. Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
• Behr, M. J., Harel, G., Post, T. R., & Lesh, R. (1993). Rational numbers: Toward a semantic analysis-emphasis on the operator construct. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 13-47). Lawrence Erlbaum Associates, Inc.
• Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296-333). Macmillan.
• Ben-Chaim, D., Fey, J.T., Fitzgerald, W.M., Benedetto, C., & Miller, J. (1998). Proportional reasoning among 7th grade students with different curricular experiences. Educational Studies in Mathematics, 36, 247-273. https://doi.org/ 10.1023/A:1003235712092
• Ben-Chaim, D., Keret, Y., & Ilany, B. S. (2012). Ratio and proportion. Rotterdam: Sense Publishers. https://doi.org/10.1007/978-94-6091-784-4
• Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Mathematical Behavior, 21(4), 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
• Cai, J., & Wang, T. (2006). U.S. and Chinese teachers' conceptions and constructions of representations: A case of teaching ratio concept. International Journal of Science and Mathematics Education, 4, 145-186. https://doi.org/10.1007/s10763-005-9006-7
• Common Core State Standards Initiative. (2010). Common Core State Standards for mathematics. http://www.corestandards.org/wpcontent/uploads/Math_Standards1.pdf adresinden 04.03.2021 tarihinde alınmıştır.
• Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportions: Research implications. In D. T. Owens (Ed), Research ideas for the classroom, middle grades mathematics (pp. 159-178). MacMillan Publishing Company.
• Dreyfus, T., & Eisenberg, T. (1996). On different facets of mathematical thinking. In R. J. Stermberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 253-284). Lawrence Erlbaum.
• Ekawati, R., Lin, F. L., & Yang, K. L. (2015). Developing an instrument for measuring teachers’ mathematics content knowledge on ratio and proportion: A case of Indonesian primary teachers. International Journal of Science and Mathematics Education, 13(1), 1-24. https://doi.org/10.1007/s10763-014-9532-2
• Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teachers: A model. Journal of Education for Teaching, 15(1), 13-34. https://doi.org/10.1080/0260747890150102
• Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). Macmillan.
• Harel, G., & Confrey, J. (1994). The development of multiplicative reasoning in the learning of mathematics. State University of New York Press.
• Heinz, K. R. (2000). Conceptions of ratio in a class of preservice and practicing teachers. [Unpublished doctoral dissertation], The Pennsylvania State University.
• Heller, K. A., Reimann, R., & Senfter, A. (2005). Hochbegabung im Grundschulalter: Erkennen und Fordern [Giftedness in primary-school-age children]. LIT.
• Heyder, A., Bergold, S., & Steinmayr, R. (2018). Teachers’ knowledge about intellectual giftedness: A first look at levels and correlates. Psychology Learning & Teaching, 17(1), 27-44. https://doi.org/10.1177/1475725717725493
• Hill, H. C., & Ball, D.L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35, 330-351. https://doi.org/10.2307/30034819
• Jacobson, E., Lobato, J., & Orrill, C. H. (2018). Middle school teachers’ use of mathematics to make sense of student solutions to proportional reasoning problems. International Journal of Science and Mathematics Education, 16(8), 1541-1559. https://doi.org/10.1007/s10763-017-9845-z
• Janvier, C. (Ed.). (1897). Problems of representation in the teaching and learning of mathematics. Lawrence Erlbaum.
• Kuzu, O. (2017). Matematik ve fen bilgisi öğretmen adaylarının integral konusundaki kazanımlarının incelenmesi. Kırşehir Eğitim Fakültesi Dergisi, 18(3), 948-970.
• Krutetskii, V. A. (1976). The psychology of mathematical abilities in school children. University of Chicago Press.
• Lamon, S. J. (2007). Rational numbers and proportional reasoning: Towards a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Information Age Publishing.
• Lamon, S. J. (2012). Teaching fractions and ratios for understanding essential content knowledge and instructional strategies for teachers. Routledge/Taylor & Francis Group.
• Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). National Council of Teachers of Mathematics.
• Ma, L. (1999). Knowing and teaching elementary mathematics: teacher's understanding of fundamental mathematics in China and the United States. Erlbaum.
• Maloney, E. A., & Beilock, S. L. (2012). Math anxiety: Who has it, why it develops, and how to guard against it. Trends in Cognitive Sciences, 16(8), 404-406. https://doi.org/10.1016/j.tics.2012.06.008
• Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Talim Terbiye Kurul Başkanlığı.
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
• Niss, M. (2018). Learning difficulties in mathematics. What are their nature and origin, and what can we do to counteract them? Cuadernos de Investigación y Formación en Educación Matemática, 13(17), 127-140. Post, T. R., Behr, M. J., & Lesh, R. (1988). Proportionality and the development of prealgebra understanding. In A. Coxford & A. Schute (Eds), The ideas of algebra, K-12 (pp. 78-90). Yearbook of the National Council of Teachers of Mathematics.
• Presmeg, N, C. (1997). A semiotic framework for linking cultural practice and classroom mathematics. In J. Dossey, J. Swafford, M. Parmantie, & A. Dossey (Eds.), Proceedings of the Nineteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education Vol. 1 (pp. 151-156). Columbus, Ohio: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
• Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281. https://doi.org/10.1007/s10857-005-0853-5
• Sen, C., & Güler, G. (2018). Effect of strategy teaching for the solution of ratio problems on students' proportional reasoning skills. MOJES: Malaysian Online Journal of Educational Sciences, 5(2), 1-15.
• Shield, M., & Dole, S. (2008). Proportion in middle-school mathematics: It is everywhere. Australian Mathematics Teacher, 64(3), 10-15. https://files.eric.ed.gov/fulltext/EJ818727.pdf adresinden 04.03.2021 tarihinde alınmıştır.
• Shulman, L. S. (1986). Paradigms and research programs in the study of teaching: A contemporary perspective. In M. C. Wittrock (Ed.), Handbook of research on teaching (pp. 3-36). Macmillan.
• Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25, 472-494. https://doi.org/10.2307/749486
• Singh, P. (2000). Understanding the concepts of proportion and ratio among grade nine students in Malaysia. International Journal of Mathematical Education in Science and Technology, 31(4), 579-599. https://doi.org/10.1080/002073900412688
• Smith, M. S., Silver, E. A., Leinhardt, G., & Hillen, A. F. (2003). Tracing the development of teachers' understanding of proportionality in a practice-based course. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.
• Son, J. W. (2013). How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84, 49-70. https://doi.org/ 10.1007/s10649-013-9475-5
• Sowder, J., Armstrong, B., Lamon, S., Simon, M., Sowder, L., & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1(2), 127-155. https://doi.org/10.1023/A:1009980419975
• Stake, R. E. (1995). The art of case study research. Sage.
• Şahin, Ö. (2018). Matematik öğretme bilgisi ve uygulamaları. Ş. Uluçınar Sağır (Ed.), Teoriden uygulamaya pedagojik alan bilgisi içinde (ss. 177-224). Pegem Akademi Yayıncılık.
• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. W. (2014). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim (7. Baskı). (S. Durmuş, Çev.). Nobel Yayınları.
• Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127-174). Academic Press.
• Yetkiner, Z. E., & Capraro, M. M. (2009). Research summary: Teaching fractions in middle grades mathematics. http://www.amle.org/TabId/270/ArtMID/888/ArticleID/326/Research-Summary-Teaching-Fractions-in-Middle-Grades-Mathematics.aspx adresinden 04.03.2021 tarihinde alınmıştır.