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Ortaokul Öğrencilerinin Üslü İfadeler Konusunda Modelleme Yeterliklerinin İncelenmesi: Sarmal Kitaplık Problemi

Yıl 2022, Cilt: 2 Sayı: 2, 39 - 56, 31.12.2022

Öz

Bu çalışmanın amacı, eğitimsel modelleme perspektifi benimsenerek üslü ifadeler konusunda bir matematiksel modelleme etkinliğinin tasarlanması ve bu etkinlik aracılığı ile ortaokul öğrencilerinin matematiksel modelleme yeterliklerinin belirlenmesidir. Bu kapsamda araştırmacılar tarafından üslü ifadeler kazanımlarını içeren bir matematiksel modelleme etkinliği tasarlanmıştır. Bu etkinlik, ortaokulda öğrenim öğren 35 öğrenciye uygulanmış ve süreçteki çözümlerini nedenleri ile birlikte ifade etmeleri istenmiştir. Betimsel analiz yöntemi ile analiz edilen veriler bilişsel perpektif çerçevesinde oluşturulmuş “Modelleme Yeterlikleri Değerlendirme Rubriği” aracılığı ile değerlendirilerek öğrencilerin matematiksel modelleme yeterliklerindeki seviyeleri belirlenmiştir. Çalışmanın sonucunda öğrencilerin genellikle zorluk yaşadıkları üslü ifadeler konusunda matematiksel modelleme etkinliğinde görüntülenen süreçler Blum ve Leiss'in (2007) döngüsel modellemesiyle tutarlı olarak gözlemlenmiştir. Genellikle modelleme basamaklarında başarılı olan öğrencilerin yorumlama ve doğrulama basamaklarında düşük performans gösterdikleri belirlenmiştir. Bu süreç bağlamında öğretim programındaki kazanımları içeren matematiksel modelleme etkinliklerinin kullanımı ve uygulama çeşitliliğinin arttırılmasına ihtiyaç duyulduğu tespit edilmiştir.

Kaynakça

  • Aztekin, S. ve Taşpınar Şener, Z. (2015). Türkiye’de matematik eğitimi alanındaki matematiksel modelleme araştırmalarının içerik analizi: Bir meta-sentez çalışması. Eğitim ve Bilim, 40(178), 139-161. http://dx.doi.org/10.15390/EB.2015.4125
  • BlomhØj, M. ve Kjeldsen, T. (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 (Eds.), Modelling and Applications in Mathematics Education (s. 45–56). New York: Springer.
  • 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 Teaching and Learning of Mathematical Modelling (pp. 15-30). New York: Springer.
  • Blum, W. ve Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example “Sugarloaf”. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling (ICTMA 12): Education, Engineering and Economics (s. 222–231). Chiester: Horwood Publishing. https://doi.org/10.1533/9780857099419.5.221
  • Blum, W. ve Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. In M. Niss, W. Blum and I. Huntley (Eds.), Modelling Applications and Applied Problem Solving (s. 1–19). England: Halsted Press.
  • Borromeo-Ferri, R. (2006). Theoretical and empirical differentations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38 (2), 86-95. https://doi.org/10.1007/BF02655883
  • Bukova-Güzel, E. (Ed.) (2018). Matematik eğitiminde matematiksel modelleme (2. baskı). Pegem Akademi.
  • Crouch, R. ve Haines, C. (2004). Mathematical modelling: transitions between the real world and the mathematical model. International Journal of Mathematical Education in Science and Technology, 35(2), 197-206. https://doi.org/10.1080/00207390310001638322
  • Doerr, H. ve English, L. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.
  • Duatepe-Paksu, A. (2015). Üslü ve köklü sayılar konularındaki öğrenme güçlükleri. M. F. Özmantar, E. Bingölbali ve H. Akkoç (Ed.), Matematiksel Kavram Yanılgıları ve Çözüm Önerileri (4. Baskı, s. 9–39). Pegem Akademi.
  • 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.
  • English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling, Zentralblatt für Didaktik der Mathematik-ZDM, 41(1), 161–181.
  • English, L. D. ve Watters, J. J. (2004). Mathematical modelling with young children. In M. Johnsen Hoines and A. Berit Fuglestad (Eds.), Proceedings of the 28th International PME Conference (s. 335–342). Bergen: Bergen University College.
  • Eric, C. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47–66.
  • Gall, M. D., Borg, W. R. ve Gall, J. P. (1996). Educational research an introduction (6th ed.). Longman Publisher.
  • Haines, C., Crouch, R. ve Davies, J (2001). Understanding students’ modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and mathematics Education, ICTMA 9: Applications in science and technology (s. 366–380).
  • Ikeda, T. ve Stephens, M. (2001). The effects of students’ discussion in mathematical modelling. In: J. F. Matos, W. Blum, S. K. Houston and S. P. Carreira, (Eds.), Modelling and mathematics education: Applications in science and technology (381-390).
  • Ji, X. (2012, July 8 -15). A quasi-experimental study of high school students’ mathematics modelling competence. 12th International Congress on Mathematical Education, COEX, Seoul, Korea.
  • Kaiser, G. ve Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302–310. https://doi.org/10.1007/BF02652813
  • Klymchuk, S. ve Zverkova, T. (2001). Role of mathematical modelling and applications in university mathematics service courses: An across countries study. In: J. F. Matos, W. Blum, S. K. Houston and S. P. Carreira (Eds.), Modelling and mathematics education: Applications in science and technology, (227-235).
  • Lingefjärd, T. (2006). Faces of mathematical modeling. Zentralblatt für Didaktik der Mathematik ZDM, 38(2), 96–112.
  • Maaß, K. (2006). What are modelling competencies?. Zentralblatt für Didaktik der Mathematik-ZDM, 38 (2), 113-142.
  • Maaß, K. (2007). Modelling in class: What do we want the students to learn In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical modelling education, engineering and economics (s. 65-78). Horwood Publishing.
  • McMillan, J. H. (2000). Educational research: Fundamentals fort he consumer (3th ed.). Longman.
  • Milli Eğitim Bakanlığı (MEB) (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar).
  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. Galbraith, C. R. Haines, and A. Hurford (Eds.), Modelling students’ mathematical competencies (s. 43-59). New York: Springer.
  • OECD. (2010). Draft PISA 2012 mathematics framework. 18 Ekim 2022 tarihinde http://www. oecd.org adresinden edinilmiştir.
  • Schaap, S., Vos, P. ve Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling (s. 137–146). New York: Springer.
  • Sekerak, J. (2010). Phases of mathematical modelling and competence of high school students. The Teaching of Mathematics, 13 (2), 105-112.
  • Shahbari, J.A. ve Peled, I. (2017) Modelling in primary school: Constructing conceptual models and making sense of fractions. International Journal of Science and Mathematics Education, 15, 371–391 (2017). https://doi.org/10.1007/s10763-015-9702-x
  • Stillman, G. ve Brown, J. (2014). Evidence of “implemented anticipation” in mathematising by beginning modellers. Mathematics Education Research Journal, 26(4), 763–789. https://doi.org/10.1007/s13394-014-0119-6
  • Stillman, G., Brown, J. ve Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at Year 9. In R. Lesh, P. Galbraith, C. R. Haines, and A. Hurford (Eds.), Modelling students’ mathematical competencies (s. 385–398). Springer.
  • Sol, M., Giménez, J. ve Rosich, N. (2011). Project modelling routes in 12–16-year-old pupils. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling (s. 231–240). Springer.
  • Şenay, Ş. C. (2002). Üslü ve köklü sayıların öğretiminde öğrencilerin yaptıkları hatalar ve yanılgıları üzerine bir araştırma [Yayınlanmamış yüksek lisans tezi]. Selçuk Üniversitesi.
  • Tekin-Dede, A. ve Bukova-Güzel, E. (2014, 11-14 Eylül). Matematiksel modelleme yeterliklerini değerlendirmeye yönelik bir rubrik geliştirme çalışması. XI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Adana, Türkiye.
  • Tekin-Dede, A. ve Yılmaz, S. (2013). İlköğretim Matematik Öğretmeni Adaylarının Modelleme Yeterliliklerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education. 4(3), 185-206.
  • Ural, A. (2018). Matematiksel modelleme eğitimi (1.baskı). Anı Yayıncılık.
  • Zbiek, R.M. ve Conner, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students' understandings of curricular mathematics. Educational Studies in Mathematics, 63(1), 89–112. https://doi.org/10.1007/s10649-005-9002-4
  • Zihar, M. (2018). Matematiksel modelleme yöntemiyle 8. Sınıf üslü ifadeler konusunun öğretimine yönelik bir eylem araştırması [Yayınlanmamış yüksek lisans tezi]. Atatürk Üniversitesi.
  • Zawojewski, J. ve Lesh, R. (2003). A models and modeling perspective on productive problem solving strategies. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: a models and modeling perspective on problem solving, learning and instruction in mathematics and science education (pp. 317–336). Mahwah, NJ: Erlbaum.

Examination of Secondary School Students' Modelling Competencies on Exponential Expressions: The Spiral Bookshelf

Yıl 2022, Cilt: 2 Sayı: 2, 39 - 56, 31.12.2022

Öz

The aim of this study is to design a mathematical modelling activity on exponential expressions by adopting an educational modelling perspective and to determine the mathematical modelling competencies of secondary school students through this activity. In this context, a mathematical modelling activity including exponential expression gains was designed by the researchers. This activity was applied to 35 secondary school students and they were asked to express their solutions in the process with their reasons. The data analyzed with the descriptive analysis method were evaluated through the “Modelling Competencies Evaluation Rubric” created within the framework of cognitive perspective, and the students' levels of mathematical modeling competencies were determined. As a result of the study, the processes displayed in the mathematical modelling activity for exponential expressions, which students generally have difficulty with, were observed to be consistent with the cyclic modelling of Blum and Leiss (2007). It was determined that the students who were successful in the modeling steps generally showed poor performance in the interpretation and validation steps. In the context of this process, it has been determined that there is a need to increase the use and application diversity of mathematical modelling activities that include the gains in the curriculum.

Kaynakça

  • Aztekin, S. ve Taşpınar Şener, Z. (2015). Türkiye’de matematik eğitimi alanındaki matematiksel modelleme araştırmalarının içerik analizi: Bir meta-sentez çalışması. Eğitim ve Bilim, 40(178), 139-161. http://dx.doi.org/10.15390/EB.2015.4125
  • BlomhØj, M. ve Kjeldsen, T. (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 (Eds.), Modelling and Applications in Mathematics Education (s. 45–56). New York: Springer.
  • 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 Teaching and Learning of Mathematical Modelling (pp. 15-30). New York: Springer.
  • Blum, W. ve Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example “Sugarloaf”. In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical Modelling (ICTMA 12): Education, Engineering and Economics (s. 222–231). Chiester: Horwood Publishing. https://doi.org/10.1533/9780857099419.5.221
  • Blum, W. ve Niss, M. (1989). Mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. In M. Niss, W. Blum and I. Huntley (Eds.), Modelling Applications and Applied Problem Solving (s. 1–19). England: Halsted Press.
  • Borromeo-Ferri, R. (2006). Theoretical and empirical differentations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik-ZDM, 38 (2), 86-95. https://doi.org/10.1007/BF02655883
  • Bukova-Güzel, E. (Ed.) (2018). Matematik eğitiminde matematiksel modelleme (2. baskı). Pegem Akademi.
  • Crouch, R. ve Haines, C. (2004). Mathematical modelling: transitions between the real world and the mathematical model. International Journal of Mathematical Education in Science and Technology, 35(2), 197-206. https://doi.org/10.1080/00207390310001638322
  • Doerr, H. ve English, L. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.
  • Duatepe-Paksu, A. (2015). Üslü ve köklü sayılar konularındaki öğrenme güçlükleri. M. F. Özmantar, E. Bingölbali ve H. Akkoç (Ed.), Matematiksel Kavram Yanılgıları ve Çözüm Önerileri (4. Baskı, s. 9–39). Pegem Akademi.
  • 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.
  • English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling, Zentralblatt für Didaktik der Mathematik-ZDM, 41(1), 161–181.
  • English, L. D. ve Watters, J. J. (2004). Mathematical modelling with young children. In M. Johnsen Hoines and A. Berit Fuglestad (Eds.), Proceedings of the 28th International PME Conference (s. 335–342). Bergen: Bergen University College.
  • Eric, C. C. M. (2008). Using model-eliciting activities for primary mathematics classrooms. The Mathematics Educator, 11(1), 47–66.
  • Gall, M. D., Borg, W. R. ve Gall, J. P. (1996). Educational research an introduction (6th ed.). Longman Publisher.
  • Haines, C., Crouch, R. ve Davies, J (2001). Understanding students’ modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and mathematics Education, ICTMA 9: Applications in science and technology (s. 366–380).
  • Ikeda, T. ve Stephens, M. (2001). The effects of students’ discussion in mathematical modelling. In: J. F. Matos, W. Blum, S. K. Houston and S. P. Carreira, (Eds.), Modelling and mathematics education: Applications in science and technology (381-390).
  • Ji, X. (2012, July 8 -15). A quasi-experimental study of high school students’ mathematics modelling competence. 12th International Congress on Mathematical Education, COEX, Seoul, Korea.
  • Kaiser, G. ve Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302–310. https://doi.org/10.1007/BF02652813
  • Klymchuk, S. ve Zverkova, T. (2001). Role of mathematical modelling and applications in university mathematics service courses: An across countries study. In: J. F. Matos, W. Blum, S. K. Houston and S. P. Carreira (Eds.), Modelling and mathematics education: Applications in science and technology, (227-235).
  • Lingefjärd, T. (2006). Faces of mathematical modeling. Zentralblatt für Didaktik der Mathematik ZDM, 38(2), 96–112.
  • Maaß, K. (2006). What are modelling competencies?. Zentralblatt für Didaktik der Mathematik-ZDM, 38 (2), 113-142.
  • Maaß, K. (2007). Modelling in class: What do we want the students to learn In C. Haines, P. Galbraith, W. Blum, and S. Khan (Eds.), Mathematical modelling education, engineering and economics (s. 65-78). Horwood Publishing.
  • McMillan, J. H. (2000). Educational research: Fundamentals fort he consumer (3th ed.). Longman.
  • Milli Eğitim Bakanlığı (MEB) (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar).
  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. Galbraith, C. R. Haines, and A. Hurford (Eds.), Modelling students’ mathematical competencies (s. 43-59). New York: Springer.
  • OECD. (2010). Draft PISA 2012 mathematics framework. 18 Ekim 2022 tarihinde http://www. oecd.org adresinden edinilmiştir.
  • Schaap, S., Vos, P. ve Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling (s. 137–146). New York: Springer.
  • Sekerak, J. (2010). Phases of mathematical modelling and competence of high school students. The Teaching of Mathematics, 13 (2), 105-112.
  • Shahbari, J.A. ve Peled, I. (2017) Modelling in primary school: Constructing conceptual models and making sense of fractions. International Journal of Science and Mathematics Education, 15, 371–391 (2017). https://doi.org/10.1007/s10763-015-9702-x
  • Stillman, G. ve Brown, J. (2014). Evidence of “implemented anticipation” in mathematising by beginning modellers. Mathematics Education Research Journal, 26(4), 763–789. https://doi.org/10.1007/s13394-014-0119-6
  • Stillman, G., Brown, J. ve Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at Year 9. In R. Lesh, P. Galbraith, C. R. Haines, and A. Hurford (Eds.), Modelling students’ mathematical competencies (s. 385–398). Springer.
  • Sol, M., Giménez, J. ve Rosich, N. (2011). Project modelling routes in 12–16-year-old pupils. In G. Kaiser, W. Blum, R. Borromeo Ferri and G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling (s. 231–240). Springer.
  • Şenay, Ş. C. (2002). Üslü ve köklü sayıların öğretiminde öğrencilerin yaptıkları hatalar ve yanılgıları üzerine bir araştırma [Yayınlanmamış yüksek lisans tezi]. Selçuk Üniversitesi.
  • Tekin-Dede, A. ve Bukova-Güzel, E. (2014, 11-14 Eylül). Matematiksel modelleme yeterliklerini değerlendirmeye yönelik bir rubrik geliştirme çalışması. XI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Adana, Türkiye.
  • Tekin-Dede, A. ve Yılmaz, S. (2013). İlköğretim Matematik Öğretmeni Adaylarının Modelleme Yeterliliklerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education. 4(3), 185-206.
  • Ural, A. (2018). Matematiksel modelleme eğitimi (1.baskı). Anı Yayıncılık.
  • Zbiek, R.M. ve Conner, A. (2006). Beyond motivation: Exploring mathematical modeling as a context for deepening students' understandings of curricular mathematics. Educational Studies in Mathematics, 63(1), 89–112. https://doi.org/10.1007/s10649-005-9002-4
  • Zihar, M. (2018). Matematiksel modelleme yöntemiyle 8. Sınıf üslü ifadeler konusunun öğretimine yönelik bir eylem araştırması [Yayınlanmamış yüksek lisans tezi]. Atatürk Üniversitesi.
  • Zawojewski, J. ve Lesh, R. (2003). A models and modeling perspective on productive problem solving strategies. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: a models and modeling perspective on problem solving, learning and instruction in mathematics and science education (pp. 317–336). Mahwah, NJ: Erlbaum.
Toplam 40 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Alan Eğitimleri
Bölüm Araştırma Makaleleri
Yazarlar

Demet Baran Bulut Bu kişi benim 0000-0003-1085-7342

Musa Türker Bu kişi benim 0000-0003-0205-1007

Yayımlanma Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 2 Sayı: 2

Kaynak Göster

APA Baran Bulut, D., & Türker, M. (2022). Ortaokul Öğrencilerinin Üslü İfadeler Konusunda Modelleme Yeterliklerinin İncelenmesi: Sarmal Kitaplık Problemi. Recep Tayyip Erdoğan Üniversitesi Eğitim Fakültesi Dergisi, 2(2), 39-56.