Book Review
BibTex RIS Cite

Matematiksel Modellemenin Öğretim Araçlarına Yansımaları: Ders Kitabı Analizi

Year 2017, Volume: 7 Issue: 1, 61 - 86, 30.06.2017
https://doi.org/10.17984/adyuebd.309793

Abstract

Bu çalışmada son yıllarda birçok
ülkenin öğretim programına girmiş olan matematiksel modellemeye ders
kitaplarında ne derece kadar yer verildiği ve kitaplarda yer alan modelleme
kavramının matematiksel modellemeyi ne ölçüde yansıttığı incelenmiştir. Doküman
incelemesi yönteminden yararlanılan çalışmada, 2016-2017 eğitim-öğretim yılında
uygulamada olan tüm ortaokul (5, 6, 7, 8) matematik ders kitaplarında yer alan
model ve modelleme kavramları tespit edilerek öğrenme alanı, sınıf seviyesi,
modelin kullanıldığı bölüm ve kullanılan model türü açısından içerik analizi
yöntemiyle değerlendirilmiştir. Yapılan değerlendirmeler neticesinde, ders
kitaplarında modelleme kavramının matematiksel
modellemeden ziyade “matematiği modelleme” şeklinde ele alındığı ve modellerin
bazı konularda yoğun bir şekilde kullanılırken bazı konularda model kavramına
değinilmediği ve modellerin ise sadece somut ve görsel yapılarla sınırlı
kaldığı söylenebilir. Ders kitaplarındaki modelleme anlayışı
somutlaştırma ve görselleştirme şeklindedir. Programda matematiksel modellemeye
yapılan vurgu da dikkate alındığında, söz konusu sınırlı algının değiştirilmesi
için ders kitaplarında modelleme anlayışının revize edilmesi gerektiği
önerilebilir.

References

  • Alacacı, C. (2015). Matematik Ders Kitabı Tasarımında Temel Unsurlar ve Matematiksel Modelleme. Türk Bilgisayar ve Matematik Eğitimi Sempozyumu-2 (s. 124). Adıyaman: Adıyaman Üniversitesi. http://www.bilmat.org/ adresinden alınmıştır.
  • Altun, M., Arslan, Ç., & Yazgan, Y. (2004). Lise matematik ders kitaplarının kullanım şekli ve sıklığı üzerine bir çalışma. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 131-147.
  • Berry, J. (2002). Developing mathematical modelling skills: The role of CAS. The International Journal on Mathematics Education, 34(5), 212-220.
  • Berry, J., & Houston, K. (1995). Mathematical modelling. Butterworth-Heinemann.
  • Blomhøj, M. Jensen T.H. (2006). What’s all the fuss about competencies? Experiences with using a competence perspective on mathematics education to develop the teaching of mathematical modelling. In W. Blum, P.L. Galbraith and M. Niss: Modelling and applications in mathematics education
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling - Proceedings of ICTMA14. (pp. 15-30). New York: Springer.
  • Blum, W. (1993). Mathematical modelling in mathematics education and instruction. Teaching and learning mathematics in context, 3-14.
  • Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
  • Blum, W., & Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects-state, trends and issues in mathematics instruction. Roskilde universitetscenter.
  • Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37-68.
  • Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative research journal, 9(2), 27-40.
  • Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
  • Common Core State Standards Initiative. (2011). Common core state standards for mathematics.
  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory.
  • Doerr, H. M. (1997). Experiment, Simulation And Analysis: An Integrated Instructional Approach To The Concept Of Force. International Journal Of Science Education. 19, 265-282.
  • English, L. D., & Watters, J. J. (2004). Mathematical modelling with young children. In Proceedings of the 28th International PME Conference (pp. 335-342).
  • Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143-162.
  • Güç, F.A. (2015). Matematiksel Modelleme Yeterliklerinin Geliştirilmesine Yönelik Tasarlanan Öğrenme Ortamlarında Öğretmen Adaylarının Matematiksel Modelleme Yeterliklerinin Değerlendirilmesi (Doktora tezi). Karadeniz Teknik Üniversitesi, Eğitim Bilimleri Enstitüsü, Trabzon.
  • Güzel, E. B., Dede, A. T., Hıdıroğlu, Ç. N., Ünver, S. K., & Çelik, A. Ö. (2016). Matematik eğitiminde matematiksel modelleme: araştırmacılar, eğitimciler ve öğrenciler için. Pegem Atıf İndeksi, 001-146.
  • Harel, G., &Lesh, R. (2003). Local conceptual development of proof schemes in a cooperative learning setting. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching, and learning (pp.359-382). New York: Routledge.
  • Haines, C., & Crouch, R. (2001). Recognizing constructs within mathematical modelling. Teaching Mathematics and its Applications, 20(3), 129-138.
  • Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıklama (Doctoral dissertation, DEÜ Eğitim Bilimleri Enstitüsü).
  • Hıdıroğlu, Ç. N. (2015). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analizi: Bilişsel ve üst bilişsel yapılar üzerine bir açıklama. Doktora Tezi. Dokuz Eylül Üniversitesi, İzmir.
  • Hitt, F., & González-Martín, A. S. (2015). Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method. Educational studies in mathematics, 88(2), 201-219.
  • Kaiser, G. (2007). Modelling and modelling competencies in school. Mathematical modelling (ICTMA 12): Education, engineering and economics, 110-119.
  • Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom-problems and opportunities. NEW ICMI STUDIES SERIES, 10, 99.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
  • Kapur, J. N. (1982). The art of teaching the art of mathematical modelling. International Journal of Mathematical Education in Science and Technology, 13(2), 185-192.
  • Labuschagne, A. (2003). Qualitative research-airy fairy or fundamental?. The qualitative report, 8(1), 100-103.
  • Lesh,R., &Carmona, G. (2003). Piagetian conceptual systems and models for mathematizing everyday experiences. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching, and learning (pp.71-96). New York: Routledge.
  • Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Model development sequences.
  • Lesh, R., Doerr, H. (2003). Foundation of a models and modeling perspective on mathematics teaching and learning. Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving, 9-34.
  • Lesh, R., &Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2&3), 157-189. http://dx.doi.org/10.1080/10986065.2003.9679998
  • Lesh, R., Landau, M., & Hamilton, E. (1983). Conceptual models and applied mathematical problem-solving research. Acquisition of mathematics concepts and processes, 263-343.
  • MaaB, K. (2006). Modelling in classrooms: What do we want the students to learn. Mathematical Modelling (ICTMA 12): Engineering and Economy. Chichester: Ellis Horwood.
  • MEB. (2017). İlköğretim ve Ortaöğretim Öğretim Programlarının Güncellenmesi. Erişim adresi: https://ttkb.meb.gov.tr/www/ilkogretim-ve-ortaogretim-ogretim-programlarinin güncellenmesi/icerik/289#
  • Milli Eğitim Bakanlığı, (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. Ankara: MEB.
  • Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293-304.
  • National Council of Teachers of Mathematics (Ed.). (2000). Principles and standards for school mathematics (Vol. 1). National Council of Teachers of.
  • Ng, K.E.D. (2011). Mathematical knowledge application and student difficulties in a design-based interdisciplinary project. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. (pp.107-116). New York: Springer. http://dx.doi.org/10.1007/978-94-007-0910-2_12
  • Niss, M., Blum, W., and Galbraith, P. L. (2007). Introduction. In M. Niss, W. Blum, H. Henn, and P. L. Galbraith (Eds.), Modelling and Applications in Mathematics Education (pp. 3-32). New York: Springer.
  • Park, J., Park, M.S., Park, M., Cho, J., & Lee, K.H. (2013). Mathematical modelling as a facilitator to conceptualization of the derivative and the integral in a spreadsheet environment.Teaching Mathematics and Its Applications, 32, 123-139.http://dx.doi.org/10.1093/teamat/hrt012
  • Pollak, H. O. (1969). How can we teach applications of mathematics?. Educational studies in mathematics, 2(2), 393-404.
  • Pollak, H. O. (1997). Solving problems in the real world (pp. 91-105). Why Nymbers Count: Quantitative Literacy for Tomorrow's America, New York: The College Board.
  • Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at year 9. In Modeling students' mathematical modeling competencies (pp. 385-398). Springer US.
  • Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges.
  • Şen-Zeytun, A. (2013). An ınvestigation of prospective teachers’ mathematical modeling processes and their views about factors affecting these processes. Unpublished Doctoral Dissertation. Middle East Tecnical University, Ankara.
  • Thompson, D. R. (2014). Reasoning-and-proving in the written curriculum: Lessons and implications for teachers, curriculum designers, and researchers. International Journal of Educational Research, 64, 141-148.

The Reflections of Mathematical Modeling in Teaching Tools: Textbook Analysis

Year 2017, Volume: 7 Issue: 1, 61 - 86, 30.06.2017
https://doi.org/10.17984/adyuebd.309793

Abstract

In this study, we investigate to what extent
mathematical modelling, which has been included extensively in many countries'
curriculum in recent years, is included in middle school textbooks in Turkey
and how the concept  of modeling in
textbooks reflects mathematical modeling. By conducting the document review,
model and modeling concepts in all middle school (5, 6, 7, 8) mathematics
textbooks in the 2016-2017 academic year were determined and evaluated, by
means of content analysis method, in terms of the learning area, the class
level, the section that model used, and the type of model used. The results
show that the concept of modeling in middle school mathematics textbooks is
used as a “modeling mathematics" rather than as means of mathematical
modelling. Also, the concept of modelling is used intensively in some topics,
but not mentioned in some topics and class levels at all. The concept of
modelling used in the textbooks was limited only to concrete and visual
structures.  Thus, the purpose of modelling
in the textbooks was to model mathematical concepts into the concrete and
visual forms rather than mathematizing the problem. Considering the emphasis on
mathematical modeling in the current mathematics standards, we suggest that
this limited and problematic understanding of modeling should be revised to
reflect purpose of mathematical modelling in order to have better learning
opportunities for both teachers and students. 

References

  • Alacacı, C. (2015). Matematik Ders Kitabı Tasarımında Temel Unsurlar ve Matematiksel Modelleme. Türk Bilgisayar ve Matematik Eğitimi Sempozyumu-2 (s. 124). Adıyaman: Adıyaman Üniversitesi. http://www.bilmat.org/ adresinden alınmıştır.
  • Altun, M., Arslan, Ç., & Yazgan, Y. (2004). Lise matematik ders kitaplarının kullanım şekli ve sıklığı üzerine bir çalışma. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 131-147.
  • Berry, J. (2002). Developing mathematical modelling skills: The role of CAS. The International Journal on Mathematics Education, 34(5), 212-220.
  • Berry, J., & Houston, K. (1995). Mathematical modelling. Butterworth-Heinemann.
  • Blomhøj, M. Jensen T.H. (2006). What’s all the fuss about competencies? Experiences with using a competence perspective on mathematics education to develop the teaching of mathematical modelling. In W. Blum, P.L. Galbraith and M. Niss: Modelling and applications in mathematics education
  • Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling - Proceedings of ICTMA14. (pp. 15-30). New York: Springer.
  • Blum, W. (1993). Mathematical modelling in mathematics education and instruction. Teaching and learning mathematics in context, 3-14.
  • Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58.
  • Blum, W., & Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects-state, trends and issues in mathematics instruction. Roskilde universitetscenter.
  • Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37-68.
  • Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative research journal, 9(2), 27-40.
  • Cirillo, M., Pelesko, J. A., Felton-Koestler, M. D., & Rubel, L. (2016). Perspectives on modeling in school mathematics. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
  • Common Core State Standards Initiative. (2011). Common core state standards for mathematics.
  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory.
  • Doerr, H. M. (1997). Experiment, Simulation And Analysis: An Integrated Instructional Approach To The Concept Of Force. International Journal Of Science Education. 19, 265-282.
  • English, L. D., & Watters, J. J. (2004). Mathematical modelling with young children. In Proceedings of the 28th International PME Conference (pp. 335-342).
  • Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38(2), 143-162.
  • Güç, F.A. (2015). Matematiksel Modelleme Yeterliklerinin Geliştirilmesine Yönelik Tasarlanan Öğrenme Ortamlarında Öğretmen Adaylarının Matematiksel Modelleme Yeterliklerinin Değerlendirilmesi (Doktora tezi). Karadeniz Teknik Üniversitesi, Eğitim Bilimleri Enstitüsü, Trabzon.
  • Güzel, E. B., Dede, A. T., Hıdıroğlu, Ç. N., Ünver, S. K., & Çelik, A. Ö. (2016). Matematik eğitiminde matematiksel modelleme: araştırmacılar, eğitimciler ve öğrenciler için. Pegem Atıf İndeksi, 001-146.
  • Harel, G., &Lesh, R. (2003). Local conceptual development of proof schemes in a cooperative learning setting. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching, and learning (pp.359-382). New York: Routledge.
  • Haines, C., & Crouch, R. (2001). Recognizing constructs within mathematical modelling. Teaching Mathematics and its Applications, 20(3), 129-138.
  • Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıklama (Doctoral dissertation, DEÜ Eğitim Bilimleri Enstitüsü).
  • Hıdıroğlu, Ç. N. (2015). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analizi: Bilişsel ve üst bilişsel yapılar üzerine bir açıklama. Doktora Tezi. Dokuz Eylül Üniversitesi, İzmir.
  • Hitt, F., & González-Martín, A. S. (2015). Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method. Educational studies in mathematics, 88(2), 201-219.
  • Kaiser, G. (2007). Modelling and modelling competencies in school. Mathematical modelling (ICTMA 12): Education, engineering and economics, 110-119.
  • Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom-problems and opportunities. NEW ICMI STUDIES SERIES, 10, 99.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
  • Kapur, J. N. (1982). The art of teaching the art of mathematical modelling. International Journal of Mathematical Education in Science and Technology, 13(2), 185-192.
  • Labuschagne, A. (2003). Qualitative research-airy fairy or fundamental?. The qualitative report, 8(1), 100-103.
  • Lesh,R., &Carmona, G. (2003). Piagetian conceptual systems and models for mathematizing everyday experiences. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, teaching, and learning (pp.71-96). New York: Routledge.
  • Lesh, R., Cramer, K., Doerr, H., Post, T., & Zawojewski, J. (2003). Model development sequences.
  • Lesh, R., Doerr, H. (2003). Foundation of a models and modeling perspective on mathematics teaching and learning. Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving, 9-34.
  • Lesh, R., &Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2&3), 157-189. http://dx.doi.org/10.1080/10986065.2003.9679998
  • Lesh, R., Landau, M., & Hamilton, E. (1983). Conceptual models and applied mathematical problem-solving research. Acquisition of mathematics concepts and processes, 263-343.
  • MaaB, K. (2006). Modelling in classrooms: What do we want the students to learn. Mathematical Modelling (ICTMA 12): Engineering and Economy. Chichester: Ellis Horwood.
  • MEB. (2017). İlköğretim ve Ortaöğretim Öğretim Programlarının Güncellenmesi. Erişim adresi: https://ttkb.meb.gov.tr/www/ilkogretim-ve-ortaogretim-ogretim-programlarinin güncellenmesi/icerik/289#
  • Milli Eğitim Bakanlığı, (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı. Ankara: MEB.
  • Mousoulides, N. G., Christou, C., & Sriraman, B. (2008). A modeling perspective on the teaching and learning of mathematical problem solving. Mathematical Thinking and Learning, 10(3), 293-304.
  • National Council of Teachers of Mathematics (Ed.). (2000). Principles and standards for school mathematics (Vol. 1). National Council of Teachers of.
  • Ng, K.E.D. (2011). Mathematical knowledge application and student difficulties in a design-based interdisciplinary project. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. (pp.107-116). New York: Springer. http://dx.doi.org/10.1007/978-94-007-0910-2_12
  • Niss, M., Blum, W., and Galbraith, P. L. (2007). Introduction. In M. Niss, W. Blum, H. Henn, and P. L. Galbraith (Eds.), Modelling and Applications in Mathematics Education (pp. 3-32). New York: Springer.
  • Park, J., Park, M.S., Park, M., Cho, J., & Lee, K.H. (2013). Mathematical modelling as a facilitator to conceptualization of the derivative and the integral in a spreadsheet environment.Teaching Mathematics and Its Applications, 32, 123-139.http://dx.doi.org/10.1093/teamat/hrt012
  • Pollak, H. O. (1969). How can we teach applications of mathematics?. Educational studies in mathematics, 2(2), 393-404.
  • Pollak, H. O. (1997). Solving problems in the real world (pp. 91-105). Why Nymbers Count: Quantitative Literacy for Tomorrow's America, New York: The College Board.
  • Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at year 9. In Modeling students' mathematical modeling competencies (pp. 385-398). Springer US.
  • Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges.
  • Şen-Zeytun, A. (2013). An ınvestigation of prospective teachers’ mathematical modeling processes and their views about factors affecting these processes. Unpublished Doctoral Dissertation. Middle East Tecnical University, Ankara.
  • Thompson, D. R. (2014). Reasoning-and-proving in the written curriculum: Lessons and implications for teachers, curriculum designers, and researchers. International Journal of Educational Research, 64, 141-148.
There are 48 citations in total.

Details

Journal Section Research Articles
Authors

Zeynep Çavuş Erdem

Muhammed Fatih Doğan

Ramazan Gürbüz

Seda Şahin

Publication Date June 30, 2017
Acceptance Date June 29, 2017
Published in Issue Year 2017 Volume: 7 Issue: 1

Cite

APA Çavuş Erdem, Z., Doğan, M. F., Gürbüz, R., Şahin, S. (2017). The Reflections of Mathematical Modeling in Teaching Tools: Textbook Analysis. Adıyaman University Journal of Educational Sciences, 7(1), 61-86. https://doi.org/10.17984/adyuebd.309793

Cited By









Investigation of Learning Environment Based on Mathematical Modeling Activities
Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi
Zeynep ÇAVUŞ ERDEM
https://doi.org/10.17522/balikesirnef.896038



Analysis of Internet Resources’ Use by Pre-service Mathematics Teachers
Uludağ Üniversitesi Eğitim Fakültesi Dergisi
Menekşe Seden TAPAN-BROUTIN
https://doi.org/10.19171/uefad.369246

                                                                                                                                                                                                                                                      
by-nc-nd.png?resize=300%2C105&ssl=1 This work is licensed under CC BY-NC-ND 4.0