Ortaokul Altıncı Sınıf Öğrencilerinin Kesir Bilgilerinin Yapılandırılmasına İlişkin Tahmini Öğrenme Yol Haritası: Bir Öğretim Tasarımı

Kesirler hem öğretme hem de öğrenme açısından özellikle ilkokul matematiğinin en sorunlu ve en karmaşık konularından biridir. Öğrencilerin kesirler konusundaki başarısızlıklarının yanı sıra öğretmenlerin kesir öğretimine yönelik özensiz yaklaşımlarının ön plana çıktığı araştırmalar, kesir öğretimine yönelik araştırmalara gereksinim oluşturmaktadır. Bu gereksinimden hareketle, bu araştırmada ortaokul altıncı sınıf öğrencilerinin kesirlerde toplama ve çıkarma işlemlerini anlamalarını destekleyen bir tahmini öğrenme yol haritası geliştirmek ve aynı zamanda bu konulara yönelik bir öğretim tasarımı önermek amaçlanmıştır. Araştırmaya İç Anadolu bölgesindeki bir ilde bulunan devlet okulunda öğrenim görmekte olan gönüllü 16 altıncı sınıf öğrencisi katılmıştır. Araştırma matematik eğitiminde sıklıkla kullanılan öğretim deneyi kullanılarak tasarlanmıştır. Öğretim deneyinde beş hafta boyunca ve her hafta iki ders saati süresince veri toplanmıştır. Araştırmanın sonucunda kesir kavramı ile kesirlerle toplama ve çıkarma işlemlerine yönelik bir TÖYH geliştirilmiş ve bu konuya yönelik bir öğretim tasarımı önerilmiştir. Ayrıca önerilen öğretim tasarımında kullanılan kesirlerde toplama ve çıkarma konusu için belirlenen öğretim sırası ile kullanılan çoklu temsillerin, öğrencilerin konuları kavramsal olarak öğrenmelerine yardımcı olduğu görülmüştür.

Anahtar Kelimeler:

tahmini öğrenme yol haritası, öğretim deneyi, kesirlerde toplama ve çıkarma

Hypothetical Learning Trajectory to the Development of Sixth Grade Students’ Knowledge about Fractions and Addition-Subtraction in Fractions

Fractions are one of the most difficult and complex topics in elementary school mathematics, both in terms of teaching and learning. Indicated research results on students’ failure in fractions and teachers’ inadequate approaches to teaching fractions reveal the necessity of research for teaching fractions. From this point of view, the purpose of this study is to develop a hypothetical learning trajectory that supports understanding of sixth grade elementary students’ addition and subtraction in fractions and to suggest a teaching design on these topics. 16 sixth grade students attended the study in a public school located on the Central Anatolia Region. This research is designed as a teaching experiment which is often used in mathematics education research. Data collection proceeded throughout mathematics classes, two class hours per week for five weeks. At the end of the teaching experiment, a hypothetical learning trajectory and a teaching design for fraction addition and subtraction was proposed. Furthermore, it was revealed that students have learned fraction operations conceptually through the teaching sequence and the multiple representations used in the proposed instructional design for teaching fraction addition and subtraction.

Keywords:

addition and subtraction in fractions, hypothetical learning trajectory, teaching experiment,

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Bailey, D. H., Hoard, M. K., Nugent, L., & Geary, D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of experimental child psychology, 113(3), 447-455.
Ball, D. L. (1993). Halves, pieces, and twoths: Constructing and using representational contexts in teaching fractions. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Studies in mathematical thinking and learning. Rational numbers: An integration of research (pp. 157-195). Hillsdale, NJ, US: Lawrence Erlbaum Associates, Inc.
Behr, M., Lesh, R., Post, T., & Silver E. (1983). Rational Number Concepts. In R. Lesh & M. Landau (Eds.), Acquisition of Mathematics Concepts and Processes, (pp. 91-125). New York: Academic Press.
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). NY: Macmillan Publishing.
Behr, M., Wachsmuth, I., Post, T., & Lesh, R. (1984). Order and equivalence relations: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341.
Biber, A. Ç., Tuna, A., ve Aktaş, O. (2013). Öğrencilerin kesirler konusundaki kavram yanılgıları ve bu yanılgıların kesir problemleri çözümlerine etkisi. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 3(2), 152-162.
Bottge, B. A., Ma, X., Gassaway, L., Butler, M., & Toland, M. D. (2014). Detecting and correcting fractions computation error patterns. Exceptional Children, 80(2), 237-255.
Charalambous, C. Y., Delaney, S., Hsu, H., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning: An International Journal, 12(2), 117-151.
Clarke, D. M., Roche, A., & Mitchell, A. (2008). Ten Practical Tips for Making Fractions Come Alive and Make Sense. Mathematics Teaching in the Middle School, 13(7), 372-380.
Common Core State Standards Initiative. (2011). About the standards. Retrieved from http://www.corestandards.org/about-the-standards. Erişim tarihi:
Cramer, K. A., Post, T. R., & Delmas, R. C. (2002). Initial fraction learning by fourth-and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144.
Cramer, K., Wyberg, T., & Leavitt, S. (2008). The role of representations in fraction addition and subtraction. Mathematics teaching in the middle school, 13(8), 490-496.
DeWolf, M., & Vosniadou, S. (2015). The representation of fraction magnitudes and the whole number bias reconsidered. Learning and Instruction, 37, 39-49.
Fennell, F., & Karp, K. (2017). Fraction Sense: Foundational Understandings. Journal of learning disabilities, 50(6), 648-650.
Greeno, J. G. (1997). On claims that answer the wrong questions. Educational Researcher, 26, 5–17.
Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for research in mathematics education, 30(1), 3-19.
Kieren, T. E. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In P. T. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (49-84). Newyork: Routledge.
Lamon, S. (2001). Presenting and representing: From fractions to rational numbers. In A. Cuoco & F. Curcio (Eds.), The roles of representations in school mathematics-2001 yearbook (pp. 146-165). Reston: NCTM.
Lesh, R. (1979). Mathematical learning disabilities: Considerations for identification, diagnosis, and remediation. In R. Lesh, D. Mierkiewicz, & M. G. Kantowski (Eds.), Applied mathematical problem solving (pp. 111-180). Columbus, OH: ERIC/SM.
Mack, N. K. (2004). Connecting to Develop Computational Fluency with Fractions. Teaching Children Mathematics, 11(4), 226-233.
Milli Eğitim Bakanlığı [MEB] (2017). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1,2,3,4,5,6, 7. ve 8. sınıflar). Ankara: Talim Terbiye Kurulu Başkanlığı.
Moss, J., & Case, R. (1999). Developing children's understanding of the rational numbers: A new model and an experimental curriculum. Journal for research in mathematics education, 30(2), 122-147.
National Council of Teachers of Mathematics. (2000). Principles and standards for school rnnthematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics.
Ocak, G., & Ateş, F. Ç. (2015). Matematik dersinde yapılandırmacı yaklaşımın uygulanabilirliğinin öğretmen görüşleri açısından değerlendirilmesi. Uluslararası Alan Eğitimi Dergisi, 1(2), 1-23.
Pesen, C. (2007). Students' misconceptions about fractions. Eğitim ve Bilim, 32(143), 79-88.
Rangkuti, A. N. (2015). Developing a learning trajectory on fraction topics by using realistic mathematics education approach in primary school. IOSR Journal of Research & Method in Education Ver. III, 5(5), 2320-7388.
Rational Number Project. (2001). [On-line]. Available: http://www.cehd.umn.edu/ci/rationalnumberproject/ Erişim tarihi: 8.05.2018.
Reys, B. J., Kim, O. K., & Bay, J. M. (1999). Establishing fraction benchmarks. Mathematics teaching in the middle school, 4(8), 530.
Saxe, G. B. (1988). The mathematics of child street vendors. Child Development, 59(5), 1415-1425.
Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical thinking and learning, 6(2), 91-104.
Simon, M. (2014). Hypothetical learning trajectories in mathematics education. In Encyclopedia of Mathematics Education (pp. 272-275). Springer Netherlands.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for research in mathematics education, 26(2), 114-145.
Simon, M. A. (2000). Research on the development of mathematics teachers: The teacher development experiment. A. E. Kelly & R. A. Lesh (Eds.) in Handbook of research design in mathematics and science education (335-360), London: Lawrence Erlbaum Associates Publishers.
Simon, M. A., Tzur, R., Heinz, K., & Kinzel, M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for research in mathematics education, 35(5), 305-329.
Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh & A. E. Kelly (Eds.), Research design in mathematics and science education (pp. 267- 307). Hillsdale, NJ: Erlbaum.
Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In Radical constructivism in mathematics education (pp. 177-194). Springer, Dordrecht.
Suydam, M. N. (1978). Review of recent research related to the concept of fractions and ratio'. In Proceedings of the Second International Conference for the Psychology of Mathematics Eduction.
Torbeyns, J., Schneider, M., Xin, Z., & Siegler, R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13.
Tunc-Pekkan, Z. (2015). An analysis of elementary school children’s fractional knowledge depicted with circle, rectangle, and number line representations. Educational Studies in Mathematics, 89, 419–441.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2004). Elementary and middle school mathematics. Boston: Allyn and Bacon.
Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103-121.
Wilson, P. H., Sztajn, P., Edgington, C., & Confrey, J. (2014). Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory. Journal of Mathematics Teacher Education, 17(2), 149-175.
Wood, T., Cobb, P., & Yackel, E. (1990). The contextual nature of teaching: Mathematics and reading instruction in one second-grade classroom. The Elementary School Journal, 90(5), 497-513.
Şimşek, H., & Yıldırım, A. (2011). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
Zembat, İ. Ö. (2016). Matematik Öğretim Döngüsü ve ‘Tahmini Öğrenme Yol Haritaları’. E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Ed.), Matematik Eğitiminde Teoriler (s.509-518) içinde. Ankara: PegemAkademi.