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Using GeoGebra in Mathematical Modeling: The Height-Foot Length Problem

Year 2014, Volume: 36 Issue: 36, 29 - 44, 01.07.2014

Abstract

The integration of mathematical modeling with technology and the advantages of technology to

modeling process have become more important in today's fast-growing society. The studies about how the

technology affects the mathematical modeling process and how to use the technology more effectively are

of importance. The purpose of this study is to illustrate how to use GeoGebra in the process of mathematical

modeling. In this study, GeoGebra was used in solution process of a problem designed in accordance with

mathematical modeling and the intended uses of GeoGebra were described in the mathematical modeling

process. The solution of the Height-Foot Length Problem designed by the researchers was carried out taking

into account the seven step modeling process. With this study, it was exemplified how the mathematics

teachers will be able to use the mathematical modeling and the GeoGebra in their lessons. It is thought that

GeoGebra will contribute to the uncovering and the development of modeling skills and will be provided

more conceptual and mathematical thinking by preventing losing in procedures.

References

  • Baki, A. (2002). Öğrenen ve Öğretenler İçin Bilgisayar Destekli Matematik. BİTAV-Ceren Yayın Dağıtım, İstanbul.
  • Barbosa, J. C. (2008). What do students discuss when developing Mathematical Modelling activities?. Electronically published, State University of Feira de Santana. Can be downloaded from <http://site.educ.indiana.edu/Portals/161/Public/Barbosa.pdf> erişim tarihi 20.03.2012.
  • Berry, J. ve Houston K. (1995). Mathematical Modelling. Bristol: J. W. Arrowsmith Ltd.
  • Berry, J. (2002). Developing Mathematical Modelling Skills: The Role of CAS. Zentralblatt für Didaktik der Mathematik-ZDM. 34(5), 212-220.
  • Blum, W. ve Niss, M. (1989). Mathematical Problem Solving, Modelling, Applications, and Links to Other Subjects – State, Trends and Issues in Mathematics Instruction. M. Niss, W. Blum ve I. Huntley (Ed.). Modelling Applications and Applied Problem Solving. (s.1-19). England: Halsted Pres.
  • Blum, W. (2002). ICMI Study 14: Applications and Modelling in Mathematics Education- Discussion Document. Zentralblatt für Didaktik der Mathematik. 34(5), 229-239.
  • Borromeo-Ferri, R. B. (2007). Personal Experiences and Extra-Mathematical Knowledge as an Influence Factor on Modelling Routes of Pupils. CERME 5 (2007) Working Group 1. 2080-2089.
  • Cheng, A. K. (2010). Teaching and Learning Mathematical Modelling with Technology, Nanyang Technological University. <http://atcm.mathandtech.org/ep2010/invited/3052010_18134.pdf> erişim tarihi 20.03.2012.
  • English, L. D. ve Watters, J. J. (2004). Mathematical Modeling in the Early School Years. Mathematics Education Research Journal, 16(3), 59-80.
  • Galbraith, P., Stillman, G., Brown, J. ve Ian, Edwards (2007). Facilitating Middle Secondary Modelling Competencies. C. Haines, P. Galbraith, W. Blum, S. Khan (Ed.), Mathematical Modelling: ICTMA 12: Education, Engineering an Economics. 130-140.
  • Greer, B. (1997). Modelling Reality in Mathematics Classroom: The Case of Word Problems. Learning and Instruction, 7, 293- 307.
  • Hıdıroğlu, Ç. N. (2012). Teknoloji Destekli Ortamda Matematiksel Modelleme Problemlerinin Çözüm Süreçlerinin Analiz Edilmesi: Yaklaşım ve Düşünme Süreçleri Üzerine Bir Açıklama. Yüksek Lisans Tezi. Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
  • Kabaca, T. ve Aktümen, M. (2010) Using GeoGebra as an Expressive Modeling Tool: Discovering the Anatomy of the Cycloid’s Parametric Equation. GeoGebra The New Language For The Third Millennium. 1(1), 63-82.
  • Kabaca, T., Aktümen, M., Aksoy, Y. ve Bulut, M., (2010), GeoGebra ve GeoGebra ile Matematik Öğretimi. Gülseçen, S., Ayvaz Reis, Z. ve Kabaca, T. (Eds), First Eurasia Meeting Of GeoGebra (EMG): Proceedings, 79-115. İstanbul Kültür Üniversitesi Yayınları.
  • Lingefjärd, T. (2000). Mathematical Modeling by Prospective Teachers Using Technology. Electronically published doctoral dissertation, University of Georgia. <http://ma-serv.did.gu.se/matematik/thomas.htm> erişim tarihi 28.11.2010.
  • Maaß, K. (2006) What are Modelling Competencies? Zentralblatt für Didaktik der Mathematik. 38 (2),113-142.
  • MEB, (2006). Ortaöğretim Matematik Dersi Öğretim Programı. Ankara: MEB Basımevi.
  • Mousoulides, N., Christou, C., ve Sriraman, B., (2006). From Problem Solving to Modelling- a Meta Analysis. <http://www.umt.edu/math/reports/sriraman/mousoulideschristousriraman.pdf> erişim tarihi 26.11.2010
  • National Council of Teachers of Mathematics (1979). Applications In School Mathematics: 1979 Yearbook. Reston, VA: National Council of Teachers of Mathematics.
  • National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • National Council of Teachers of Mathematics (1998). Principles and standards for school mathematics: Discussion draft. Reston, VA: Author.
  • National Council of Teachers of Mathematics (2000). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM Publications.
  • Peter-Koop, A. (2004). Fermi Problems in Primary Mathematics Classrooms: Pupils’ Interactive Modelling Processes. In I. Putt, R. Farragher, & M. McLean (Eds.), Mathematics education for the Third Millenium: Towards 2010 (Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 454-461). Townsville, Queensland: MERGA.
  • Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. D. A. Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning (s. 334– 370). Macmillan: New York.
  • Skolverket (1997). Kommentar till grundskolans kursplan och betygskriterier i matematik [Commentary on the Comprehensive School Curriculum and Marking Criteria in Mathematics]. Stockholm: Liber Utbildningsförlaget.
  • Sriraman, B. (2005). Conceptualizing the Notion of Model Eliciting. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guíxols, Spain.
  • Stillman, G., Galbraith, P., Brown, J. ve Edwards, I.(2007). A Framework for Success in Implementing Mathematical Modelling in the Secondary Classroom. Mathematics: Essential Research, Essential Practice. 2, 688- 697.
  • Swedish Ministry of Education. (1994). Kursplaner för grundskolan. [Syllabus for Subjects in the Comprehensive School Curriculum]. Stockholm, Fritzes.
  • Thomas, G. B., Weir, M. D., Hass, J. ve Giordano, F. R. (2010). Thomas Calculus 1 (2. Baskı, Çeviri: Recep Korkmaz). Beta Basım A.Ş. İstanbul.
  • Verschaffel, L., De Corte, E. ve Borghart, I. (1997). Pre-service Teachers’ Conceptions and Beliefs about the role of Real-World Knowledge in Mathematical Modeling of School Word Problems. Learning and Instruction. 7(4), 339-359.
  • Zawojewski, J. S., Lesh, R., ve English, L. D. (2003). A Models and Modelling Perspective on the Role of Small Group Learning. In R. A. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning and Teaching, (pp. 337-358). Mahwah, NJ: Lawrence Erlbaum.

Matematiksel Modellemede GeoGebra Kullanımı: Boy-Ayak Uzunluğu Problemi

Year 2014, Volume: 36 Issue: 36, 29 - 44, 01.07.2014

Abstract

Matematiksel modelleme ile teknolojinin entegrasyonu ve modelleme sürecine teknolojinin sağladığı
avantajlar günümüzün hızlı gelişen toplumunda daha önemli hale gelmektedir. Teknolojinin
matematiksel modelleme sürecini nasıl etkilediği ve daha etkili nasıl kullanılabileceğine ilişkin çalışmalar
önem taşımaktadır. Bu çalışmanın amacı, matematiksel modelleme sürecinde GeoGebra’nın nasıl
kullanılabileceğini örneklemektir. Çalışmada, matematiksel modellemeye uygun olarak tasarlanan bir
problemin çözüm sürecinde GeoGebra’dan yararlanılmış ve GeoGebra’nın süreçteki kullanım amaçları
açıklanmıştır. Araştırmacılar tarafından tasarlanmış Boy-Ayak Uzunluğu probleminin çözümü, yedi
basamaklı matematiksel modelleme süreci dikkate alınarak gerçekleştirilmiştir. Çalışma ile öğretmenlerin
matematiksel modelleme ile GeoGebra’yı derslerinde nasıl kullanabilecekleri örneklenmeye çalışılmıştır.
GeoGebra’nın modelleme becerilerinin ortaya çıkarılmasında ve geliştirilmesinde katkı sağlayacağı ve
işlemler içinde kaybolmayı önleyerek daha fazla kavramsal ve matematiksel düşüncenin ortaya çıkarılmasını
sağlayacağı düşünülmektedir.

References

  • Baki, A. (2002). Öğrenen ve Öğretenler İçin Bilgisayar Destekli Matematik. BİTAV-Ceren Yayın Dağıtım, İstanbul.
  • Barbosa, J. C. (2008). What do students discuss when developing Mathematical Modelling activities?. Electronically published, State University of Feira de Santana. Can be downloaded from <http://site.educ.indiana.edu/Portals/161/Public/Barbosa.pdf> erişim tarihi 20.03.2012.
  • Berry, J. ve Houston K. (1995). Mathematical Modelling. Bristol: J. W. Arrowsmith Ltd.
  • Berry, J. (2002). Developing Mathematical Modelling Skills: The Role of CAS. Zentralblatt für Didaktik der Mathematik-ZDM. 34(5), 212-220.
  • Blum, W. ve Niss, M. (1989). Mathematical Problem Solving, Modelling, Applications, and Links to Other Subjects – State, Trends and Issues in Mathematics Instruction. M. Niss, W. Blum ve I. Huntley (Ed.). Modelling Applications and Applied Problem Solving. (s.1-19). England: Halsted Pres.
  • Blum, W. (2002). ICMI Study 14: Applications and Modelling in Mathematics Education- Discussion Document. Zentralblatt für Didaktik der Mathematik. 34(5), 229-239.
  • Borromeo-Ferri, R. B. (2007). Personal Experiences and Extra-Mathematical Knowledge as an Influence Factor on Modelling Routes of Pupils. CERME 5 (2007) Working Group 1. 2080-2089.
  • Cheng, A. K. (2010). Teaching and Learning Mathematical Modelling with Technology, Nanyang Technological University. <http://atcm.mathandtech.org/ep2010/invited/3052010_18134.pdf> erişim tarihi 20.03.2012.
  • English, L. D. ve Watters, J. J. (2004). Mathematical Modeling in the Early School Years. Mathematics Education Research Journal, 16(3), 59-80.
  • Galbraith, P., Stillman, G., Brown, J. ve Ian, Edwards (2007). Facilitating Middle Secondary Modelling Competencies. C. Haines, P. Galbraith, W. Blum, S. Khan (Ed.), Mathematical Modelling: ICTMA 12: Education, Engineering an Economics. 130-140.
  • Greer, B. (1997). Modelling Reality in Mathematics Classroom: The Case of Word Problems. Learning and Instruction, 7, 293- 307.
  • Hıdıroğlu, Ç. N. (2012). Teknoloji Destekli Ortamda Matematiksel Modelleme Problemlerinin Çözüm Süreçlerinin Analiz Edilmesi: Yaklaşım ve Düşünme Süreçleri Üzerine Bir Açıklama. Yüksek Lisans Tezi. Dokuz Eylül Üniversitesi, Eğitim Bilimleri Enstitüsü, İzmir.
  • Kabaca, T. ve Aktümen, M. (2010) Using GeoGebra as an Expressive Modeling Tool: Discovering the Anatomy of the Cycloid’s Parametric Equation. GeoGebra The New Language For The Third Millennium. 1(1), 63-82.
  • Kabaca, T., Aktümen, M., Aksoy, Y. ve Bulut, M., (2010), GeoGebra ve GeoGebra ile Matematik Öğretimi. Gülseçen, S., Ayvaz Reis, Z. ve Kabaca, T. (Eds), First Eurasia Meeting Of GeoGebra (EMG): Proceedings, 79-115. İstanbul Kültür Üniversitesi Yayınları.
  • Lingefjärd, T. (2000). Mathematical Modeling by Prospective Teachers Using Technology. Electronically published doctoral dissertation, University of Georgia. <http://ma-serv.did.gu.se/matematik/thomas.htm> erişim tarihi 28.11.2010.
  • Maaß, K. (2006) What are Modelling Competencies? Zentralblatt für Didaktik der Mathematik. 38 (2),113-142.
  • MEB, (2006). Ortaöğretim Matematik Dersi Öğretim Programı. Ankara: MEB Basımevi.
  • Mousoulides, N., Christou, C., ve Sriraman, B., (2006). From Problem Solving to Modelling- a Meta Analysis. <http://www.umt.edu/math/reports/sriraman/mousoulideschristousriraman.pdf> erişim tarihi 26.11.2010
  • National Council of Teachers of Mathematics (1979). Applications In School Mathematics: 1979 Yearbook. Reston, VA: National Council of Teachers of Mathematics.
  • National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • National Council of Teachers of Mathematics (1998). Principles and standards for school mathematics: Discussion draft. Reston, VA: Author.
  • National Council of Teachers of Mathematics (2000). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM Publications.
  • Peter-Koop, A. (2004). Fermi Problems in Primary Mathematics Classrooms: Pupils’ Interactive Modelling Processes. In I. Putt, R. Farragher, & M. McLean (Eds.), Mathematics education for the Third Millenium: Towards 2010 (Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australasia, pp. 454-461). Townsville, Queensland: MERGA.
  • Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics. D. A. Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning (s. 334– 370). Macmillan: New York.
  • Skolverket (1997). Kommentar till grundskolans kursplan och betygskriterier i matematik [Commentary on the Comprehensive School Curriculum and Marking Criteria in Mathematics]. Stockholm: Liber Utbildningsförlaget.
  • Sriraman, B. (2005). Conceptualizing the Notion of Model Eliciting. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education. Sant Feliu de Guíxols, Spain.
  • Stillman, G., Galbraith, P., Brown, J. ve Edwards, I.(2007). A Framework for Success in Implementing Mathematical Modelling in the Secondary Classroom. Mathematics: Essential Research, Essential Practice. 2, 688- 697.
  • Swedish Ministry of Education. (1994). Kursplaner för grundskolan. [Syllabus for Subjects in the Comprehensive School Curriculum]. Stockholm, Fritzes.
  • Thomas, G. B., Weir, M. D., Hass, J. ve Giordano, F. R. (2010). Thomas Calculus 1 (2. Baskı, Çeviri: Recep Korkmaz). Beta Basım A.Ş. İstanbul.
  • Verschaffel, L., De Corte, E. ve Borghart, I. (1997). Pre-service Teachers’ Conceptions and Beliefs about the role of Real-World Knowledge in Mathematical Modeling of School Word Problems. Learning and Instruction. 7(4), 339-359.
  • Zawojewski, J. S., Lesh, R., ve English, L. D. (2003). A Models and Modelling Perspective on the Role of Small Group Learning. In R. A. Lesh & H. Doerr (Eds.), Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning and Teaching, (pp. 337-358). Mahwah, NJ: Lawrence Erlbaum.
There are 31 citations in total.

Details

Journal Section Articles
Authors

Çağlar Naci Hıdıroğlu

Esra Bukova-güzel

Publication Date July 1, 2014
Submission Date March 15, 2014
Acceptance Date June 20, 2014
Published in Issue Year 2014 Volume: 36 Issue: 36

Cite

APA Hıdıroğlu, Ç. N., & Bukova-güzel, E. (2014). Matematiksel Modellemede GeoGebra Kullanımı: Boy-Ayak Uzunluğu Problemi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 36(36), 29-44.