A Cross-National Comparison of Turkish and American Mathematics Textbooks in Terms of Fraction Division Contexts
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Year-Number: 2018-Volume 10, Issue 4
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Abstract
Bu çalışmada Türk ve Amerikan matematik ders kitaplarında yer alan kesirlerle bölme görevlerinin içerdiği bağlamların analiz edilmesi ve karşılaştırılması amaçlanmıştır. Araştırmanın sonuçları kesirlerle bölme görevlerinin sayısının ve bağlamlarının, seçilen iki eğitim sistemi içinde ve genelinde dikkate değer ölçüde değiştiğini göstermiştir. Türk ders kitabı görevlerinin yarısından fazlası ve Amerikan ders kitabı görevlerinin sadece dörtte biri bağlamsaldır. ABD ders kitapları, Türk ders kitaplarına kıyasla daha çeşitli görev bağlamları içermektedir. Daha özel olarak, tüm ders kitaplarında yiyecek ve içecek bağlamını içeren görevler mevcuttur. ABD ders kitaplarında alış-veriş bağlamıyla ilgili görevler yer almazken öğrenci bağımlı bağlamlar, spor, tarla, resim, hayvanlar, coğrafya, serbest zaman aktiviteleri, geri dönüşüm, oto aksesuarları ve oda bağlamları da Türkçe ders kitaplarında yer almamıştır. Bu bulgulardan hareketle ders kitabı yazarlarının öğrencilere kesirlerle bölme görevlerinin içerdiği bağlamlar açısından daha kaliteli öğrenme fırsatları sunmalarına yönelik doğurgular tartışılmıştır.
Keywords
Abstract
The purpose of this study was to analyze and compare Turkish and the US mathematics textbooks with respect to contexts involved in fraction division tasks. The findings showed that the number and context of fraction division tasks varied to a considerable extent both within and across the selected two education systems. More than half of the Turkish textbook tasks and only a quarter of US textbook tasks were contextual. The US textbooks included more varied task contexts compared to Turkish textbooks. More specifically, food and beverages context was existent in all textbooks. Shopping context was non-existent in the US textbooks, while student dependent contexts, sports, land, painting, animals, geography, free time activities, recycling, auto accessories, and room contexts were absent from Turkish textbooks. The implications for textbooks developers in providing students more quality learning opportunities in terms of fraction division contexts were then discussed.
Keywords
- Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), 239-261.
- An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, 145-172.
- Aydoğdu İskenderoğlu, T., & Baki, A. (2011). Classification of the questions in an 8th grade mathematics textbook with respect to the competency levels of PISA. Education and Science, 36(161), 287-301.
- Barcelos Amaral, R., & Hollebrands, K. (2017). An analysis of context-based similarity tasks in textbooks from Brazil and the United States. International Journal of Mathematical Education in Science and Technology, 48(8), 1166-1184.
- Ben-Chaim, D., Keret, Y., & Ilany, B. S. (2012). Proportional reasoning–A psychological-didactical view. In D. Ben-Chaim, Y. Keret, & B. S. Ilany (Eds.), Ratio and proportion: Research and teaching in mathematics teachers’ education (pre- and in-service mathematics teachers of elementary and middle school classes) (pp. 4960). Rotterdam: Sense Publishers.
- Boaler, J. (1993). Encouraging the transfer of ‘school’ mathematics to the ‘real world’ through the integration of process and content, context and culture. Educational Studies in Mathematics, 25(4), 341-373.
- Cady, J. A., Collins, R. L., & Hodges, T. E. (2015). A comparison of textbooks’ presentation of fractions. School Science and Mathematics, 115 (3), 105-116.
- Cady, J. A., Meier, S. L., & Lubinski, C. A. (2006). Developing mathematics teachers: Transition from preservice to experienced teacher. Journal of Educational Research, 99 (5), 295-305.
- Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem posing research in mathematics: Some answered and unanswered questions. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3-34). New York, NY: Springer.
- Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62, 211-230.
- Clarke, D. M., & Roche, A. (2009). Students’ fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127-138.
- Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
- Cooper, B., & Harries, T. (2002). Children’s responses to contrasting ‘realistic’ mathematics problems: Just how realistic are children ready to be? Educational Studies in Mathematics, 49(1), 1–23.
- Dossey, J. A., McCrone, S. S., & Halvorsen, K. T. (2016). Mathematics education in the United States 2016: A capsule summary fact book. Reston, VA: National Council of Teachers of Mathematics.
- Elsaleh, I. (2010). Teachers’ interactions with curriculum materials in mathematics. School Science and Mathematics, 110 (4), 177-179.
- Fulkerson, W. O. (2013). 2012 National survey of science and mathematics education: Status of middle school mathematics. Chapel Hill, NC: Horizon Research, Inc.
- Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11 (3), 199-219.
- Graumann, G. (2011). Mathematics for problems in the everyday world. In J. Maasz & J. O'Donoghue (Eds.), Real-world problems for secondary school mathematics students: Case studies (pp. 113–122). Rotterdam: Sense Publishers.
- Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 309-347). Singapore: World Scientific.
- Howson, G. (1995). Mathematics textbooks: A comparative study of grade 8 texts. Vancouver: Pacific Educational Press.
- Huang, R.,Yetkiner Özel, Z. E., Li, Y., & Osborne, R. V. (2014). Does classroom instruction stick to textbooks? A case study of fraction division. In Y. Li & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 443-464). Berlin: Springer.
- İncikabı, L., & Tjoe, H. (2013). A comparative analysis of ratio and proportion problems in Turkish and the US middle school mathematics textbooks. Journal of Kırşehir Education Faculty, 14(1), 1-15.
- Izsak, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26, 95- 143.
- Jones, D. L. (2004). Probability in middle grades mathematics textbooks: An examination of historical trends, 1957-2004 (Unpublished doctoral dissertation). University of Missouri, Columbia.
- Kar, T., Güler, G., Şen, C., & Özdemir, E. (2018). Comparing the development of the multiplication of fractions in Turkish and American textbooks. International Journal of Mathematical Education in Science and Technology, 49(2), 200-226.
- Kazemi, F., & Rafiepour, A. (2018). Developing a scale to measure content knowledge and pedagogy content knowledge of in-service elementary teachers on fractions. International Journal of Science and Mathematics Education, 16(4), 737-757.
- Kulm, G., & Capraro, R. M. (2008). Textbook use and student learning of number and algebra ideas in middle grades. In G. Kulm (Ed.), Teacher knowledge and practice in middle grades mathematics (pp. 255-272). Rotterdam, the Netherlands: Sense Publishers.
- Lamon, S. (2007). Rational numbers and proportional reasoning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–666). Charlotte, NC: Information Age Publishing.
- Li, Y. (2000). A comparison of problems that follow selected content presentations in American and Chinese mathematics textbooks. Journal for Research in Mathematics Education, 31(2), 234-241.
- Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13, 546-552.
- Li, Y., & Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM, 40(5), 833-843.
- Li, Y., Chen, X., & An, S. (2009). Conceptualizing and organizing content for teaching and learning in selected Chinese, Japanese and US mathematics textbooks: The case of fraction division. ZDM, 41, 809-826.
- Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
- Ministry of National Education. (2013). Ortaokul matematik dersi 5-8.sınıflar öğretim programı [Middle school mathematics curriculum: Grades 5-8]. Ankara: Directorate of State Books.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM Publications.
- Ni, Y. J. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26, 400-417.
- OECD. (2003). The PISA 2003 assessment framework–Mathematics, reading, science, and problem solving knowledge and skills. Paris: OECD.
- OECD. (2016). PISA 2015 results (volume I): Excellence and equity in education. Paris: PISA, OECD Publishing.
- Özer, E., & Sezer, R. (2014). A comparative analysis of questions in American, Singaporean, and Turkish mathematics textbooks based on the topics covered in 8th grade in Turkey. Educational Sciences: Theory and Practice, 14(1), 411-421.
- Post, T. R., Harel, G., Behr, M., & Lesh, R. (1991). Intermediate teachers’ knowledge of rational number concepts. In E. Fennema, T. P. Carpenter, & J. S. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 177–198). Ithaca, NY: SUNY Press.
- Sam, L. C., Lourdusamy, A., & Ghazali, M. (2001). Factors affecting students’ abilities to solve operational and word problems in mathematics. Journal of Science and Mathematics Education in Southeast Asia, 24(1), 84
- Schmidt, W. H., McKnight, C. C., & Raizen, S. (Eds.). (2007). A splintered vision: An investigation of US science and mathematics education. New York: Kluwer Academic Publishers.
- Schwarzkopf, R. (2007). Elementary modeling in mathematics lessons: The interplay between “real-world” knowledge and “mathematics structures”. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 209–216). New York: Springer.
- Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1-7.
- Son, J. W. (2012). A cross-national comparison of reform curricula in Korea and the US in terms of cognitive complexity: The case of fraction addition and subtraction. ZDM, 44, 161-174.
- Son, J. W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261.
- Son, J. W., & Senk, S. L. (2010). How reform curricula in the USA and Korea present multiplication and division of fractions. Educational Studies in Mathematics, 74(2), 117-142.
- Stigler, J. W., Fuson, K. C., Ham, M., & Kim, M. S. (1986). An analysis of addition and subtraction word problems in American and Soviet elementary mathematics textbooks. Cognition and Instruction, 3(3), 153
- Tinsley, H. E. A., & Weiss, D. J. (2000). Interrater reliability and agreement. In H. E. A. Tinsley & S. D. Brown, (Eds.), Handbook of applied multivariate statistics and mathematical modeling (pp. 95-124). San Diego, CA: Academic Press.
- Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.
- Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students’ understanding about rational numbers and their notation. Cognition and Instruction, 28(2), 181-209.
- Van den Heuvel-Panhuizen, M. (2005). The role of context in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–9 and 23.
- Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Exton: Swets & Zeitlinger
- Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015a). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41-65.
- Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015b). Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks. Mathematics Education Research Journal, 27(4), 637-662.
- Wijaya, A., van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: An analysis of students' errors. The Mathematics Enthusiast, 11(3),
- Yang, D. C., Tseng, Y. K., & Wang, T. L. (2017). A comparison of geometry problems in middle-grade mathematics textbooks from Taiwan, Singapore, Finland, and the United States. Eurasia Journal of Mathematics Science and Technology Education, 13(7), 2841-2857.
- Aydın, E., & Gündoğdu, L. (2016). Middle school mathematics: Grade 6. Ankara: Sevgi Press.
- Bağcı, O. (2015). Middle school mathematics: Grade 6. Ankara: Dikey Press.
- Bell, M., Jean, B., Bretzlauf, J., Dillard, A., Flanders, J., Hartfield, R., Isaacs, A., Kelso, K. R., McBride, J. Pitvorec, K., & Saecker, P. (2015). Everyday Mathematics Student Reference Book: Grade 6 (4th ed.). Chicago, IL: McGraw-Hill Education.
- Berry, R. Q., Champagne, Z., Milou, E., Schielack, J. F., Wray, J. A., Charles, R. I., & Fennel, F. S. (2016). Envisionmath 2.0, Volume 1. Glenview, IL: Pearson Scott Foresman.
- Birgin, O., Bütün, M., Duru, A., İpek, A. S., Peker, M., Ayhan, S., Bulut, Y., Dayan, Ş., Doktoroğlu Işıldak, R., & Mıhçı, M. (2016). Middle school mathematics: Grade 6. Ankara: Ministry of National Education.
- Carter, J. A., Cuevas, G. J., Day, R., Malloy, C., Kersaint, G., Reynosa, M. E., Silbey, R., & Vielhaber., K. (2014). Glencoe Math Course 1, Volume 1. Bothell, WA: McGraw-Hill Education.
