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Ortaokul Matematik Ders Kitaplarında Yer Verilen Temsiller Arası İlişkilendirmeler

Year 2018, Volume: 26 Issue: 3, 729 - 740, 15.05.2018
https://doi.org/10.24106/kefdergi.415690

Abstract

Bu çalışmanın amacı, ortaokul matematik ders kitaplarındaki
kullanılan temsil türlerini belirlemek ve temsil türleri arasında yer verilen
ilişkilendirmeleri ortaya koymaktır.  Bu
araştırma nitel bir araştırma olup, ortaokul matematik ders kitaplarında yer
alan temsil türlerini analiz etmek için doküman analizi yöntemi kullanılarak
matematik ders kitapları, matematikte kullanılan sözel, cebirsel, model, tablo,
grafik ve gerçek yaşam temsilleri dikkate alınarak incelenmiştir.  Çalışmada MEB komisyonu tarafından
hazırlanmış ve 2015-2016 akademik yılında kullanımda olan ders kitaplarında yer
alan etkinlikler, çözümü kitapta verilen sorular ve çözülecek sorular analiz
edilmiştir. Verilerin kodlama sürecinde birbirinden bağımsız çalışan iki
araştırmacı yer almıştır. Araştırma bulgularına göre ders kitaplarında yer
verilen temsiller arası geçiş en fazla cebirsel, sözel ve model temsiller ile
cebirsel, sözel, model ve açık temsiller arasında gerçekleşmiştir. Diğer ikili
eşleşmelerin oldukça düşük oranlarda kalması dikkat çekicidir.

References

  • Adadan, E. (2006). Promoting high school students’ conceptual understandings of the par-ticulate nature of matter through multiple representations. Unpublished Doctoral Disserta-tion, Ohio State University, Ohio.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 Educa-tion, 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.
  • Baştürk, S. (2006). Üniversiteye giriş sınavı sorularında fonksiyon kavramı. Eğe Eğitim Dergisi, 7(1), 61-83.
  • Baştürk, S. (2007). Fonksiyon kavramının öğretiminin 9. sınıf ders kitapları bağlamında incelenmesi. Sakarya Üniversitesi Fen Edebiyat Dergisi, 9, Ek sayı, 270-283.
  • Baştürk, S. (2010). Öğrencilerinin fonksiyon kavramının farklı temsillerindeki matematik dersi performansları. Gazi Eğitim Fakültesi Dergisi, 30(2), 465-482.
  • Çelik, D., & Sağlam-Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
  • 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.
  • Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide For Teachers Grades 6-10. Portsmouth, NH: Heinemann.
  • Duval, R. (1993). Registres de Représentation Sémiotique et Fonctionnement Cognitif de la Pensée. Annales de Didactiques des Sciences Cognitives, 5, 37-65.
  • Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathe-matical 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.
  • 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 mathemat-ics 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.
  • 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. (2011). The coherence of the curriculum, textbooks and placement examina-tions 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. Janvi-er (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: De-partment 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. 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. Wag-ner & 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 representa-tions in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Rep-resentation in the Teaching and Learning of Mathematics (pp. 33-40). New Jersey: Law-rence 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) matematik dersi öğretim programı. Ankara.
  • 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) (2000). Standarts for School Math-ematics. 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 Studies 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 Education, 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. Pro-ceedings 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 representa-tions of algebraic concepts. Yüksek Lisans Tezi. Middle East Technical University, An-kara.
  • Tall, D., McGowen, M., & DeMarois, P. (2000). The Function Machine as a Cognitive Root for the Function Concept. In Proceedings of the Conference of the InternationalG-roup for the Psychology of Mathematics Education (pp. 247-254).
  • Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achieve-ment. Studies in Educational Evaluation. 31(4), 315-327.
  • Uçar, Z. T. (2015). Ortaokul matematik öğretmen adaylarının reel sayıları kavrayışlarına temsillerin etkisi. Kastamonu Eğitim Dergisi, 24(3), 1149-1164.
  • 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 repre-sentations in a dynamic simulation-based learning environment. Learning and Instruc-tion, 16(3), 199–212.
  • Wu, H-K, & Puntambekar, S. (2012). Pedagogical affordances of multiple external repre-sentations in scientific processes. Journal of Science and Educational Technology, 21, 754–767.
  • Yavuz, İ., & Baştürk, S. (2011). Ders kitaplarında fonksiyon kavramı: Türkiye ve Fransa örneği. Kastamonu Eğitim Dergisi, 19(1), 199-220.
  • Yeşildere-İmre, S., Akkoç, H., & Baştürk-Şahin, B. N. (2017). Ortaokul Öğrencilerinin Farklı Temsil Biçimlerini Kullanarak Matematiksel Genelleme Yapma Becer-ileri1. Turkish Journal of Computer and Mathematics Education Vol, 8(1), 103-129.
  • 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.

Transitions Among The Representations in The Middle School Mathematics Textbooks

Year 2018, Volume: 26 Issue: 3, 729 - 740, 15.05.2018
https://doi.org/10.24106/kefdergi.415690

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.

References

  • Adadan, E. (2006). Promoting high school students’ conceptual understandings of the par-ticulate nature of matter through multiple representations. Unpublished Doctoral Disserta-tion, 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 Educa-tion, 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.
  • Baştürk, S. (2006). Üniversiteye giriş sınavı sorularında fonksiyon kavramı. Eğe Eğitim Dergisi, 7(1), 61-83.
  • Baştürk, S. (2007). Fonksiyon kavramının öğretiminin 9. sınıf ders kitapları bağlamında incelenmesi. Sakarya Üniversitesi Fen Edebiyat Dergisi, 9, Ek sayı, 270-283.
  • Baştürk, S. (2010). Öğrencilerinin fonksiyon kavramının farklı temsillerindeki matematik dersi performansları. Gazi Eğitim Fakültesi Dergisi, 30(2), 465-482.
  • Çelik, D., & Sağlam-Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
  • 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.
  • Driscoll, M. (1999). Fostering Algebraic Thinking: A Guide For Teachers Grades 6-10. Portsmouth, NH: Heinemann.
  • Duval, R. (1993). Registres de Représentation Sémiotique et Fonctionnement Cognitif de la Pensée. Annales de Didactiques des Sciences Cognitives, 5, 37-65.
  • Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathe-matical 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.
  • 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 mathemat-ics 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.
  • 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. (2011). The coherence of the curriculum, textbooks and placement examina-tions 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. Janvi-er (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: De-partment 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. 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. Wag-ner & 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 representa-tions in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of Rep-resentation in the Teaching and Learning of Mathematics (pp. 33-40). New Jersey: Law-rence 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) matematik dersi öğretim programı. Ankara.
  • 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) (2000). Standarts for School Math-ematics. 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 Studies 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 Education, 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. Pro-ceedings 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 representa-tions of algebraic concepts. Yüksek Lisans Tezi. Middle East Technical University, An-kara.
  • Tall, D., McGowen, M., & DeMarois, P. (2000). The Function Machine as a Cognitive Root for the Function Concept. In Proceedings of the Conference of the InternationalG-roup for the Psychology of Mathematics Education (pp. 247-254).
  • Törnroos, J. (2005). Mathematics textbooks, opportunity to learn and student achieve-ment. Studies in Educational Evaluation. 31(4), 315-327.
  • Uçar, Z. T. (2015). Ortaokul matematik öğretmen adaylarının reel sayıları kavrayışlarına temsillerin etkisi. Kastamonu Eğitim Dergisi, 24(3), 1149-1164.
  • 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 repre-sentations in a dynamic simulation-based learning environment. Learning and Instruc-tion, 16(3), 199–212.
  • Wu, H-K, & Puntambekar, S. (2012). Pedagogical affordances of multiple external repre-sentations in scientific processes. Journal of Science and Educational Technology, 21, 754–767.
  • Yavuz, İ., & Baştürk, S. (2011). Ders kitaplarında fonksiyon kavramı: Türkiye ve Fransa örneği. Kastamonu Eğitim Dergisi, 19(1), 199-220.
  • Yeşildere-İmre, S., Akkoç, H., & Baştürk-Şahin, B. N. (2017). Ortaokul Öğrencilerinin Farklı Temsil Biçimlerini Kullanarak Matematiksel Genelleme Yapma Becer-ileri1. Turkish Journal of Computer and Mathematics Education Vol, 8(1), 103-129.
  • 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.
There are 49 citations in total.

Details

Primary Language Turkish
Subjects Studies on Education
Journal Section Review Article
Authors

Semahat İncikabı This is me

Abdullah Çağrı Biber

Publication Date May 15, 2018
Acceptance Date July 5, 2017
Published in Issue Year 2018 Volume: 26 Issue: 3

Cite

APA İncikabı, S., & Biber, A. Ç. (2018). Ortaokul Matematik Ders Kitaplarında Yer Verilen Temsiller Arası İlişkilendirmeler. Kastamonu Education Journal, 26(3), 729-740. https://doi.org/10.24106/kefdergi.415690

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