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Analysis of Middle School Mathematics Applications Textbook Activities Based on Model-Eliciting Principles

Yıl 2024, Cilt: 13 Sayı: 1, 84 - 99, 17.01.2024
https://doi.org/10.14686/buefad.1299706

Öz

Model-eliciting activities (MEA) represent a distinct form of problem-solving exercises that deviate from conventional problem-solving approaches. They encompass complex real-life scenarios characterized by multiple feasible solutions, demanding non-routine thinking with open-ended possibilities. Lesh and Doerr (2003) posit that MEA conform to specific principles, encompassing model construction, reality, self-evaluation, model externalization (construct certification), model generalization, and effective prototype principles. This study examines the compatibility of tasks in Turkey's middle school mathematics applications textbooks (grades 5-8) with the principles of model-eliciting activities (MEA). The analysis focuses on five principles: reality, model construction, self-evaluation, model documentation, and model generalization. The findings reveal varying degrees of compatibility across different grades. The reality and model generalization principles show more robust compatibility, while the model construction and model documentation principles have mixed levels of compatibility. The self-evaluation principle demonstrates varied compatibility. The study highlights strengths and areas for improvement in the tasks' alignment with MEA principles and emphasizes the importance of real-life relevance and model application. Suggestions are made to enhance explicit guidance in model construction and documentation. The study provides implications for curriculum design, teacher professional development, instructional strategies, student engagement, assessment practices, and future research in mathematics education. However, limitations, such as the absence of student perspectives and contextual factors, should be considered when interpreting the findings.

Destekleyen Kurum

N/A

Proje Numarası

N/A

Teşekkür

N/A

Kaynakça

  • Alacacı, C. (2015). Matematik Ders Kitabı Tasarımında Temel Unsurlar ve Matematiksel Modelleme. Türk Bilgisayar ve Matematik Eğitimi Sempozyumu, 124.
  • 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.
  • Blum, W., & Borromeo Ferri, R. (2009) Mathematical modelling: Can it be taught and learnt?, Journal of Mathematical Modelling and Application, 1(1), 45-58.
  • Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics - ICTMA 12, 222-231. Chichester: Horwood Publishing.
  • Borromeo Ferri, R. (2017). Learning how to teach mathematical modeling in school and teacher education. Springer.
  • Bracke, M. & Geiger, A. (2011). Real-world modelling in regular lessons: a long[1]term experiment. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp.529– 549). Springer.
  • Bukova-Güzel, E. (Ed.). (2016). Matematik eğitiminde matematiksel modelleme. Ankara: Pegem Akademi.
  • Bukova-Güzel, E., 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.
  • Chamberlin, S. A. & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians, The journal of secondary gifted education, 17(1), 37–47.
  • Doerr, H. M. & O'Neill, A. H. (2011). A Modelling Approach to Developing an Understanding of Average Rate of Change, Proceedings of CERME 7, Eds: Marta Pytlak, Tim Rowland, Ewa Swoboda, Poland: University of Rzesvow. 2113–2122.
  • Dominguez, A. (2010). Single Solution, Multiple Perspectives, Modeling Students’ Mathematical Modeling Competencies, Eds: Richard Lesh, Peter L Galbraith, Cristopher R Haines, Andrew Hurford, New York: Springer. 223–233.
  • Dost, Ş. (2019). Matematik eğitiminde modelleme etkinlikleri. Ankara: Pegem Akademi Yayınları.
  • English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303–323.
  • Eric, C. M. (2008). Using model-eliciting activities for primary mathematics classroom. The Mathematics Educator, 11(1/2), 47–66.
  • Frejd, P. (2012). Teachers’ conceptions of mathematical modelling at Swedish upper secondary school. Journal of Mathematical Modelling and Application, 1(5), 17–40.
  • Galbraith, P. (2007) Authenticity and goals—overview. In Modelling and applications in mathematics education, Springer, Boston, MA, 181–184.
  • Gould, H. (2013). Teacher’s conceptions of mathematical modeling. Published Doctoral Dissertation. Columbia University, New York, US.
  • 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.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
  • Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri. (Doktora Tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi'nden edinilmiştir. (Tez No. 275237)
  • Lesh, R., Doerr, H. M., Carmona, G., & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking and Learning, 5(2–3), 211–233. doi:10.1080/10986065.2003.9680000
  • Lesh, R. & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah: Lawrence Erlbaum.
  • Lesh, R. & Caylor, B. (2007). Introduction To Special Issue: Modeling As Application Versus Modeling As A Way To Create Mathematics, International Journal of Computers for Mathematical Learning. 12 (3), 173–194.
  • 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. & Zawojewski, J. S. (2007). Problem solving and modeling, The Second Handbook of Research on Mathematics Teaching and Learning, Ed: Frank K. Lester, Charlotte, NC: Information Age Publishing. 763–804.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., Post, T., (2000) Principles for Developing Thought-Revealing Activities for Students and Teachers. In A. Kelly, R. Lesh (Eds.). Research Design in Mathematics and Science Education. (pp. 591-646). Lawrence Erlbaum Associates, Mahwah, New Jersey.
  • Lu, X., & Kaiser, G. (2022). Can mathematical modelling work as a creativity-demanding activity? An empirical study in China. ZDM–Mathematics Education, 1-15.
  • Meerwaldt, D., Ferri, R. B., & Nevers, P. (2023). Philosophizing with children in the course of solving modeling problems in a sixth grade mathematics classroom. Dialogical Inquiry in Mathematics Teaching and Learning: A Philosophical Approach, 103.
  • MoNE (Ministry of National Education) (2018a). İlköğretim matematik dersi (1–8 sınıflar) öğretim programı [Elementary and middle math class (1–8 classes) teaching program.]. Ankara, Turkey.
  • MoNE (Ministry of National Education) (2018b). Matematik uygulamaları dersi (5–8 sınıflar) öğretim programı [Math applications course (5–8 classes) teaching program.]. Ankara, Turkey.
  • 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 Mathematics.
  • Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge.
  • 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.
  • Stillman G.A. (2019). State of the art on modelling in mathematics education—Lines of inquiry. In G. Stillman, & J. Brown (Eds.), Lines of inquiry in mathematical modelling research in education. ICME-13 Monographs. Springer.
  • Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research, 64, 63–70.
  • Suh, J. M., Matson, K., & Seshaiyer, P. (2017) Engaging elementary students in the creative process of mathematizing their world through mathematical modeling. Education Sciences, 7(2), 62.
  • 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.
  • Urhan, S., & Dost, Ş. (2018). Analysis of ninth-grade mathematics course book activities based on model-eliciting principles. International Journal of Science and Mathematics Education, 16, 985–1002.
  • Yoon, C., Dreyfus, T., & Thomas, M. O. (2010). How High Is the Tramping Track? Mathematising and Applying in a Calculus Model-Eliciting Activity. Mathematics Education Research Journal, 22(2), 141–157.
Yıl 2024, Cilt: 13 Sayı: 1, 84 - 99, 17.01.2024
https://doi.org/10.14686/buefad.1299706

Öz

Proje Numarası

N/A

Kaynakça

  • Alacacı, C. (2015). Matematik Ders Kitabı Tasarımında Temel Unsurlar ve Matematiksel Modelleme. Türk Bilgisayar ve Matematik Eğitimi Sempozyumu, 124.
  • 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.
  • Blum, W., & Borromeo Ferri, R. (2009) Mathematical modelling: Can it be taught and learnt?, Journal of Mathematical Modelling and Application, 1(1), 45-58.
  • Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics - ICTMA 12, 222-231. Chichester: Horwood Publishing.
  • Borromeo Ferri, R. (2017). Learning how to teach mathematical modeling in school and teacher education. Springer.
  • Bracke, M. & Geiger, A. (2011). Real-world modelling in regular lessons: a long[1]term experiment. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp.529– 549). Springer.
  • Bukova-Güzel, E. (Ed.). (2016). Matematik eğitiminde matematiksel modelleme. Ankara: Pegem Akademi.
  • Bukova-Güzel, E., 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.
  • Chamberlin, S. A. & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians, The journal of secondary gifted education, 17(1), 37–47.
  • Doerr, H. M. & O'Neill, A. H. (2011). A Modelling Approach to Developing an Understanding of Average Rate of Change, Proceedings of CERME 7, Eds: Marta Pytlak, Tim Rowland, Ewa Swoboda, Poland: University of Rzesvow. 2113–2122.
  • Dominguez, A. (2010). Single Solution, Multiple Perspectives, Modeling Students’ Mathematical Modeling Competencies, Eds: Richard Lesh, Peter L Galbraith, Cristopher R Haines, Andrew Hurford, New York: Springer. 223–233.
  • Dost, Ş. (2019). Matematik eğitiminde modelleme etkinlikleri. Ankara: Pegem Akademi Yayınları.
  • English, L. D. (2006). Mathematical modeling in the primary school: Children’s construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303–323.
  • Eric, C. M. (2008). Using model-eliciting activities for primary mathematics classroom. The Mathematics Educator, 11(1/2), 47–66.
  • Frejd, P. (2012). Teachers’ conceptions of mathematical modelling at Swedish upper secondary school. Journal of Mathematical Modelling and Application, 1(5), 17–40.
  • Galbraith, P. (2007) Authenticity and goals—overview. In Modelling and applications in mathematics education, Springer, Boston, MA, 181–184.
  • Gould, H. (2013). Teacher’s conceptions of mathematical modeling. Published Doctoral Dissertation. Columbia University, New York, US.
  • 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.
  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
  • Korkmaz, E. (2010). İlköğretim matematik ve sınıf öğretmeni adaylarının matematiksel modellemeye yönelik görüşleri ve matematiksel modelleme yeterlikleri. (Doktora Tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi'nden edinilmiştir. (Tez No. 275237)
  • Lesh, R., Doerr, H. M., Carmona, G., & Hjalmarson, M. (2003). Beyond constructivism. Mathematical Thinking and Learning, 5(2–3), 211–233. doi:10.1080/10986065.2003.9680000
  • Lesh, R. & Doerr, H. M. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah: Lawrence Erlbaum.
  • Lesh, R. & Caylor, B. (2007). Introduction To Special Issue: Modeling As Application Versus Modeling As A Way To Create Mathematics, International Journal of Computers for Mathematical Learning. 12 (3), 173–194.
  • 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. & Zawojewski, J. S. (2007). Problem solving and modeling, The Second Handbook of Research on Mathematics Teaching and Learning, Ed: Frank K. Lester, Charlotte, NC: Information Age Publishing. 763–804.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., Post, T., (2000) Principles for Developing Thought-Revealing Activities for Students and Teachers. In A. Kelly, R. Lesh (Eds.). Research Design in Mathematics and Science Education. (pp. 591-646). Lawrence Erlbaum Associates, Mahwah, New Jersey.
  • Lu, X., & Kaiser, G. (2022). Can mathematical modelling work as a creativity-demanding activity? An empirical study in China. ZDM–Mathematics Education, 1-15.
  • Meerwaldt, D., Ferri, R. B., & Nevers, P. (2023). Philosophizing with children in the course of solving modeling problems in a sixth grade mathematics classroom. Dialogical Inquiry in Mathematics Teaching and Learning: A Philosophical Approach, 103.
  • MoNE (Ministry of National Education) (2018a). İlköğretim matematik dersi (1–8 sınıflar) öğretim programı [Elementary and middle math class (1–8 classes) teaching program.]. Ankara, Turkey.
  • MoNE (Ministry of National Education) (2018b). Matematik uygulamaları dersi (5–8 sınıflar) öğretim programı [Math applications course (5–8 classes) teaching program.]. Ankara, Turkey.
  • 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 Mathematics.
  • Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge.
  • 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.
  • Stillman G.A. (2019). State of the art on modelling in mathematics education—Lines of inquiry. In G. Stillman, & J. Brown (Eds.), Lines of inquiry in mathematical modelling research in education. ICME-13 Monographs. Springer.
  • Stylianides, G. J. (2014). Textbook analyses on reasoning-and-proving: Significance and methodological challenges. International Journal of Educational Research, 64, 63–70.
  • Suh, J. M., Matson, K., & Seshaiyer, P. (2017) Engaging elementary students in the creative process of mathematizing their world through mathematical modeling. Education Sciences, 7(2), 62.
  • 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.
  • Urhan, S., & Dost, Ş. (2018). Analysis of ninth-grade mathematics course book activities based on model-eliciting principles. International Journal of Science and Mathematics Education, 16, 985–1002.
  • Yoon, C., Dreyfus, T., & Thomas, M. O. (2010). How High Is the Tramping Track? Mathematising and Applying in a Calculus Model-Eliciting Activity. Mathematics Education Research Journal, 22(2), 141–157.
Toplam 40 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Alan Eğitimleri
Bölüm Makaleler
Yazarlar

Rüveyda Karaman Dündar 0000-0002-8903-9627

Rabia Betül Bora Bu kişi benim 0009-0005-2258-8989

Proje Numarası N/A
Erken Görünüm Tarihi 17 Aralık 2023
Yayımlanma Tarihi 17 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 13 Sayı: 1

Kaynak Göster

APA Karaman Dündar, R., & Bora, R. B. (2024). Analysis of Middle School Mathematics Applications Textbook Activities Based on Model-Eliciting Principles. Bartın University Journal of Faculty of Education, 13(1), 84-99. https://doi.org/10.14686/buefad.1299706
All the articles published in the journal are open access and distributed under the conditions of CommonsAttribution-NonCommercial 4.0 International License
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