### Transitions Among The Representations in The Middle School Mathematics Textbooks

#### Abstract

The purpose of this study is to identify the types of representation used in the middle school mathematics textbooks and to establish associations among representation types. This research is a qualitative research and document analysis method is used to analyze the representation types in secondary school mathematics textbooks. In this study, mathematics textbooks were examined by considering verbal, algebraic, model, table, graphic and real life representations. In the study, the activities in the textbooks, prepared by the MoNE commission and used in the academic year of 2015-2016, the solutions given in the book and the questions to be solved were analyzed. During the coding process of the data, two researchers working independently were involved. According to research findings, the transition between representations in textbooks was mostly realized among algebraic, verbal, model and open representations. It is striking that the other pairings remain at very low rates.

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Adadan, E. (2006). Promoting high school students’ conceptual understandings of the particu-late nature of matter through multiple representations. Unpublished Doctoral Dissertation, Ohio State University, Ohio.

Adadan, E. (2013). Using multiple representations to promote grade 11 students’scientific understanding of the particle theory of matter. Research in Science Education, 43, 1079–1105.

Ainsworth, S. (1999). The functions of multiple representations. Computers and Education, 33,131-152.

Ainsworth, S., & Van Labeke, N. (2004). Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241-255.

Akkuş, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representation preferen¬ce. Yayımlanmamış Doktora Tezi. Middle East Technical University, Ankara.

Amit, M., & Fried, M. (2002). Research, reform and times of change. In L. D. English (Ed.), Handbook of international research in mathematics Education (pp. 355-382). New Jersey: LEA Publishers.

Choike, J. R. (2000). Teaching strategies for “Algebra for all”. Mathematics Teacher, 93(7), 556-560.

Çıkla, O. A. (2004). The effects of multiple representations-based instruction on seventh grade students’algebra performance, attitude toward mathematics, and representation preference. Unpublished doctoral dissertation, Middle East Technical University, Ankara.

Even, R. (1998). Factors Involved in Linking Representations of Functions. Journal of Mathe-matical Behavior, 17(1), 105-121.

Floden, R. E. (2002). The measurement of opportunity to learn. In A. C. Porter & A. Gamoran (Eds.), Methodological advances in cross-national surveys of educational achievements (pp. 231-266). Washington: National Academy Press.

Fujita, T., & Jones, K. (2003). The place of experimental tasks in geometry teaching: Learning from the textbooks design of the early 20th Century. Research in Mathematics Education, 5, 47-62.

Ginsburg, A., & Leinwand, S. (2005). Singapore math: Can it help close the U.S mathematics learning gap? Presented at CSMC’s First International Conference on Mathematics Curricu-lum, November 11-13.

Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French, and German classrooms: who gets an opportunity to learn what? British Ed-ucational Research Journal, 28(4), 567-590.

Herman, J. L., Klein, D. C. D., & Abedi, J. (2000). Assessing student’s opportunity to learn: Teacher and student perspectives. Educational Measurement: Issues and Practice, 19 (4), 16-24.

Hines, E. (2002). Developing the concept of linear function: One student’s experiences with dynamic physical models. Journal of Mathematical Behavior, 20, 337-361.

Incikabi, L. (2011). The coherence of the curriculum, textbooks and placement examinations in geometry education: How reform in Turkey brings balance to the classroom. Education as Change, 15(2), 239-255.

Janvier, C. (1987). Conceptions and representations: The circle as an example. In C. Janvier (Ed.), Problems of Representations in the Learning and Teaching of Mathematics (pp. 147-159). New Jersey: Lawrence Erlbaum Associates.

Johansson, M. (2003). Textbooks in mathematics education: a study of textbooks as the poten-tially implemented curriculum (Yayımlanmamış Yüksek Lisans Yezi). Lulea: Department of Mathematics, Lulea University of Technology.

Johansson, M. (2005). Mathematics textbooks - the link between the intended and the imple-mented curriculum. Paper presented to ―the Mathematics Education into the 21st Century Project‖ Universiti Teknologi, Malaysia. Ekim 20, 2015 tarihinde http://math.unipa.it/~grim/21_project/21_malasya_Johansson119-123_05.pdf adresinden alınmıştır.

Kaput, J. J. (1999). Linking representations in the symbol systems of algebra. In S. Wagner & C. Kieran (Eds). Research issues in the learning and teaching of algebra (pp. 167-194). Hillsdale, NJ: LEA.

Keller, B. A. & Hirsch, C. R. (1998). Student preferences for representations of functions. International Journal in Mathematics Education Science Technology, 29(1), 1-17.

Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 33-40). New Jersey: Lawrence Erlbaum Associates.

Li, Y. (2000). A comparison of problems that follow selected content presentation in American and Chinese mathematics textbooks. Journal for Research in Mathematical Education, 31, 234-241.

Milli Eğitim Bakanlığı (MEB) (2005). İlköğretim matematik dersi (6, 7., ve 8. Sınıflar) ma-tematik dersi öğretim programı. Ankara.

Milli Eğitim Bakanlığı (MEB) (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) ma-tematik dersi öğretim programı. Ankara.

National Council of Teachers of Mathematics (NCTM) (2000). Standarts for School Mathemat-ics. Reston, VA: NCTM

Pape, S. J., Bell, J. & Yetkin, I. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Stud-ies in Mathematics, 53, 179-202.

Prain, V. & Tytler, R. (2012). Learning through constructing representations in science: A framework of representational construction affordances, International Journal of Science Edu-cation, 34(17), 2751-2773.

Sankey, M., Birch, D., & Gardiner, M. (2010). Engaging students through multimodal learning environments: The journey continues. In C.H. Steel, M.J. Keppell, P. Gerbic & S. Housego (Eds.), Curriculum, technology & transformation for an unknown future. Proceedings ascilite Sydney 2010 (pp.852-863).

Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many visions, many aims: a cross-national investigation of curricular intentions in school mathematics (Vol. 1). Dordrecht: Kluwer.

Schultz, J., & Waters, M. (2000). Why represenatations? Mathematics teacher, 93(6), 448-453.

Sert, Ö. (2007). Eighth grade students’ skills ın translating among different representations of algebraic concepts. Yüksek Lisans Tezi. Middle East Technical University, Ankara.

Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation. 31(4), 315-327.

Ünal, H. (2006). Preservice secondary mathematics teachers’ comparative analyses of Turkish and American high school geometry textbooks. Kastamonu Eğitim Dergisi, 14(2), 509-516.

Van der Meij, J., & De Jong, T. (2006). Supporting students’ learning with multiple representa-tions in a dynamic simulation-based learning environment. Learning and Instruction, 16(3), 199–212.

Wu, H-K, & Puntambekar, S. (2012). Pedagogical affordances of multiple external representa-tions in scientific processes. Journal of Science and Educational Technology, 21, 754–767.

Zhu, Y., & Fan, L. (2004). An analysis of the representation of problem types in Chinese and US mathematics textbooks. Paper accepted for ICME-10 Discussion Group 14, 4-11 July: Copenhagen, Denmark.

DOI: https://doi.org/10.24106/kefdergi.415690

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