| | | |

## entrMultiple Representations and Teaching Mathematics: An Analysis of the Mathematics TextbooksÇoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme

#### Semahat İNCİKABI [1]

##### 179 2588

In this study, representation types placed in the secondary school mathematics textbooks were determined and the transitions between these representations were analyzed in the context of in-class and out-of-class activities. Being qualitative in nature, this study utilized document analysis method to analyze the transitions between representations in secondary school mathematics textbooks. According to research findings, while textbooks contain algebraic representations most, they have significant distributions in verbal and model representations. On the other hand, it is noteworthy that the table, graphic and real life representations are included in the textbooks in a very small proportion. Looking at the transitions between representations, it is seen that the relationship between the representations in the class activities is in significant proportions between algebraic, verbal and model representations. Similarly, in out-of-class activities, the relationship between the representations appears to be in significant proportions between algebraic, verbal and model representations. In addition, secondary school mathematics textbooks prefer tables, real life and graphic representations in the solution of the questions both in- and out-of-class activities.

Bu araştırmada ortaokul matematik ders kitaplarında yer verilen temsil türleri belirlenmiş ve bu temsiller arasındaki geçişler sınıf içi ve sınıf dışı etkinlikler bağlamında analiz edilmiştir. Bu araştırma nitel bir araştırma olup, ortaokul matematik ders kitaplarında yer alan temsiller arasındaki geçiş durumlarını analiz etmek için doküman analizi yöntemi kullanılmıştır. Araştırma bulgularına göre ders kitaplarında en çok cebirsel temsillere yer verilirken sözel ve model temsillerde önemli oranlarda dağılımlara sahiptir. Diğer taraftan tablo, grafik ve gerçek yaşam temsillerine ders kitaplarında çok az oranlarda yer verilmesi dikkat çekmektedir. Temsiller arasında yer alan geçişlere bakıldığında, sınıf içi etkinliklerde temsiller arasındaki ilişkinin önemli oranlarda cebirsel, sözel ve model temsiller arasında olduğu görülmektedir. Benzer olarak sınıf dışı etkinliklerde de temsiller arasındaki ilişkinin önemli oranlarda cebirsel, sözel ve model temsiller arasında olduğu görülmektedir. Ayrıca sınıf içi ve sınıf dışı etkinliklerde de soruların gerek ifadesinde gerekse çözümünde tablo, gerçek yaşam ve grafik temsilleri çok az oranlarda tercih edildiği belirlenmiştir.
Multiple representations, middle school mathematics textbooks, mathematics education
• Adadan, E. (2006). Promoting high school students’ conceptual understandings of the particulate nature of matter through multiple representations. Unpublished Doctoral Dissertation, The 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.
• Adu-Gyamfi, K. (2000). External Multiple Representations in Mathematics Teaching. Unpublished master’s thesis. North Carolina State University, USA.
• Ainsworth, S., & Van Labeke, N. (2004). Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241-255.
• Akkuş, O. & Çakıroğlu, E. (2006). Seventh grade students’ use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31, 13-24.
• Akkuş, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representation preference. 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.
• Behr, M., Lesh, R., Post, T., & Silver, E. (1983). Rational Number concepts. In R. A. Lesh, & M. Landau (Eds.), The acquisition of mathematical concepts and processes. New York: Academic Press.
• Çepni, S. (2010). Araştırma ve proje çalışmalarına giriş. Pegem Akademi.
• Chen, G., & Fu, X. (2003). Effects of multimodal information on learning performance and judgment of learning. Journal of Educational Computing Research, 29(3), 349-362.
• Çıkla-Oylum, 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.
• Delice, A., & Sevimli, E. (2010). Öğretmen adaylarının çoklu temsil kullanma becerilerinin problem çözme başarıları yönüyle incelenmesi: Belirli integral örneği. Kuram ve Uygulamada Eğitim Bilimleri/Educational Sciences: Theory & Practice. 10 (1), 111-149.
• Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide For Teachers Grades 6-10. Portsmouth, NH: Heinemann.
• Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the Twenty First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3-26). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
• Even, R. (1998). Factors Involved in Linking Representations of Functions. Journal of Mathematical 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.
• Freeman, D. J., & Porter, A. C. (1989). Do textbooks dictate the content of mathematics instruction in elementary schools? American Educational Research Journal, 26(3), 403-421.
• 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. Cumhuriyet International Journal of Education-CIJE e–ISSN: 2147-1606 Vol 6 (1), 2017, 66 – 81 - 78 -
• 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 Curriculum, 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 Educational 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.
• Herman, M. F. (2002). Relationship of college students' visual preference to use of representations: Conceptual understanding of functions in algebra. Unpublished PhD dissertation, Columbus: Ohio State University.
• Hiebert, J., & Carpenter, T. P. (1992). Learning and Teaching with Understanding. In D. Grouws (Editör), Handbook of Research on Mathematics Teaching and Learning (65-97). New York: Macmillan Publishing Company.
• 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. (2011a). Analysis of grades 6 through 8 geometry education in Turkey after the reform movement of 2004, Doctoral dissertation, Teachers College, Columbia University.
• Incikabi, L. (2011b). 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.
• Incikabi, L. (2012). After the reform in Turkey: A content analysis of SBS and TIMSS assessment in terms of mathematics content, cognitive domains, and item types. Education as Change, 16(2), 301-312.
• İncikabı, L., Pektaş, M., & Süle, C. (2016). Ortaöğretime Geçiş Sınavlarındaki Matematik ve Fen Sorularının PISA Problem Çözme Çerçevesine Göre İncelenmesi. Journal of Kirsehir Education Faculty, 17(2).
• 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 potentially 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 implemented curriculum. Paper presented to ―the Mathematics Education into the 21st Century Project‖ Universiti Teknologi, Malaysia.
• Kaput, J. J. (1989). 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. Cumhuriyet International Journal of Education-CIJE e–ISSN: 2147-1606 Vol 6 (1), 2017, 66 – 81 - 79 -
• Mayer, R.E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32, 443-460.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage. Milli Eğitim Bakanlığı (MEB) (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) matematik dersi öğretim programı. Ankara.
• National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
• National Council of Teachers of Mathematics (NCTM) (2000). Standarts for School Mathematics. Reston, VA: NCTM
• Owens, K. D., & Clements, M. A. (1997). Representations in spatial problem solving in the classroom. Journal of Mathematical Behavior, 17(2), 197- 218.
• Pektas, M., & Kurnaz, M. A. (2013). Difficulties of Science Teacher Candidates in the Articulation of Transitions between Table, Graphical and Pictorial Representations. The International Journal of Social Sciences. 18(1), 160-167.
• Pepin, B. (2001). Mathematics textbooks and their use in English, French and German classrooms: a way to understand teaching and learning cultures. Zentralblatt fuer Didaktik der Mathematik, 33(5), 158-175.
• Piez, C., M. & Voxman, M., H. (1997). Multiple representations-- using different perspectives to form a clearer picture. Mathematics Teacher, 90(2), 164-167.
• Prain, V. & Tytler, R. (2012). Learning through constructing representations in science: A framework of representational construction affordances, International Journal of Science Education, 34(17), 2751-2773.
• Prain, V. & Waldrip, B. (2010). Representing Science Literacies: An Introduction. Research in Science Education, 40, 1-3.
• Randel, B., Stevenson, H. W., & Witruk, E. (2000). Attitudes, beliefs, and mathematics achievement of German and Japanese high school students. International Journal of Behavioral Development, 24, 190–198.
• 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., Houang, R. T., Wang, H., Wiley, D. E., Cogan, L. S., et al. (2001). Why schools matter: a cross-national comparison of curriculum and learning. San Francisco: Jossey-Bass.
• 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.
• Smith, S. P. (2004). Representation in school mathematics: Childrens representations of problems. In J. Kilpatrick (Ed.), A Research Companion to Principles and Standards for School Mathematics (pp. 263-274), Reston, VA: NCTM, Inc.
• Sun, Y., Kulm, G., & Capraro, M., M. (2009). Middle grade teachers’ use of textbooks and their classroom instruction. Journal of Mathematics Education, 2-2, 20-37.
• Swafford, J. O. & Langrall, C. W. (2000). Grade 6 students’ preinstructional use of equations to describe and represent problem situations. Journal of Research in Mathematics Education, 31(1), 89-112.
• Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation. 31(4), 315-327.
• Tyson, H., & Woodward, A. (1989). Why students aren’t learning very much from textbooks. Educational Leadership, 47(3), 14-17. Cumhuriyet International Journal of Education-CIJE e–ISSN: 2147-1606 Vol 6 (1), 2017, 66 – 81 - 80 -
• Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbook. Dordrecht; Boston: Kluwer Academic Publishers.
• Van der Meij, J., & De Jong, T. (2006). Supporting students’ learning with multiple representations in a dynamic simulation-based learning environment. Learning and Instruction, 16(3), 199–212.
• Waldrip, B., Prain, V., & Carolan, J. (2010). Using multi-modal representations to improve learning in junior secondary science. Research in Science Education, 40(1), 65–80.
• Wu , H. K., & Puntambekar, S. (2012). Pedagogical affordances of multiple external representations 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.
Subjects Social JA65MZ85RV Articles Author: Semahat İNCİKABIInstitution: Kastamonu Üniversitesi, Doktora ÖğrencisiCountry: Turkey
 Bibtex @ { cije321438, journal = {Cumhuriyet Uluslararası Eğitim Dergisi}, issn = {}, eissn = {2147-1606}, address = {Cumhuriyet University}, year = {2017}, volume = {6}, pages = {66 - 81}, doi = {10.30703/cije.321438}, title = {Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme}, key = {cite}, author = {İNCİKABI, Semahat} }` APA İNCİKABI, S . (2017). Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme. Cumhuriyet Uluslararası Eğitim Dergisi, 6 (1), 66-81. DOI: 10.30703/cije.321438 MLA İNCİKABI, S . "Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme". Cumhuriyet Uluslararası Eğitim Dergisi 6 (2017): 66-81 Chicago İNCİKABI, S . "Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme". Cumhuriyet Uluslararası Eğitim Dergisi 6 (2017): 66-81 RIS TY - JOUR T1 - Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme AU - Semahat İNCİKABI Y1 - 2017 PY - 2017 N1 - doi: 10.30703/cije.321438 DO - 10.30703/cije.321438 T2 - Cumhuriyet Uluslararası Eğitim Dergisi JF - Journal JO - JOR SP - 66 EP - 81 VL - 6 IS - 1 SN - -2147-1606 M3 - doi: 10.30703/cije.321438 UR - https://doi.org/10.30703/cije.321438 Y2 - 2019 ER - EndNote %0 Cumhuriyet International Journal of Education Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme %A Semahat İNCİKABI %T Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme %D 2017 %J Cumhuriyet Uluslararası Eğitim Dergisi %P -2147-1606 %V 6 %N 1 %R doi: 10.30703/cije.321438 %U 10.30703/cije.321438 ISNAD İNCİKABI, Semahat . "Çoklu Temsiller ve Matematik Öğretimi: Ders Kitapları Üzerine Bir İnceleme". Cumhuriyet Uluslararası Eğitim Dergisi 6 / 1 (March 2017): 66-81. https://doi.org/10.30703/cije.321438