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The Relationship Between Elementary School Students’ Proportional Reasoning Skills And Problem Posing Skills

Year 2011, Volume: 30 Issue: 30, 1 - 11, 01.02.2011

Ahmet Çelik , Elif Yetkin Özdemir

Abstract

In this study, we examined the relationship between proportional reasoning skills and problem posing skills involving ratio and proportion. 392 seventh and eighth grade students participated in this study. Data were collected through the proportional reasoning test developed by Akkus & Duatepe (2006) and problem posing test developed by the researchers. In order to analyze data, descriptive statistics (frequency and percentages) and chi-square test were used. Results showed that there is a statistically significant relationship between proportional reasoning skills and problem posing skills. Most of the students with low levels of proportional reasoning skills were not able to pose problems that involve ratio and proportion. On the other hand, students with high levels of proportional reasoning were more successful in posing problems that required proportional reasoning.

Keywords

Ratio and proportion proportional reasoning skills problem posing skills

References

  • Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.) Proceedings Of The International Conference On Mathematical Education Into the 21st Century: Social Challenges, Issues And Approaches, Cairo, Egypt. 2, (pp. 1-8).
  • Akkuş, O. ve Duatepe A. (2002). İlköğretim matematik öğretmen adaylarının akıl yürütme becerileri üzerine bir çalışma. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23, 32-40.
  • Akkuş, O. ve Duatepe-Paksu, A. (2006). Orantısal akıl yürütme becerisi testi ve teste yönelik dereceli puanlama anahtarı geliştirilmesi, Eğitim Araştırmaları, 6, 25, 1-10.
  • Akar, G. K. (2009). Oran konusunun kavramsal öğreniminde karşılaşılan zorluklar ve çözüm önerileri. E. Bingölbali & M.F. Özmantar (Eds.) İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri,(sf. 263-285). Pegem Akademi.
  • Akkan, Y., Çakıroğlu, Ü. ve Güven, B. (2009). İlköğretim 6. ve 7. sınıf öğrencilerinin 10 denklem oluşturma ve problem kurma yeterlilikleri. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 17, Haziran 2009, 41-55.
  • Cai, (2003) Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34 (5), 719-737.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta- Pantazi, D. & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. The International Journal on Mathematics Education, Vol, 37, 3, 149-158.
  • Cramer, K., Post, T., Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In Research Ideas For The Classroom: Middle Grades Mathematics, D. Owens (Ed.), pp. 159–178. New York: Macmillan.
  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, Vol. 52, No. 3, 243-270.
  • English, L, D. (1997a). The development of fifth- grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, (pp. 183 -217).
  • English, L, D. (1997b). Development of seventh- grade students’ problem-posing. Proceedings of the Conference of the International Group for the Psychology of Mathematics Education, 2, (pp. 249- 256).
  • English, L, D. (1998). Children’s problem posing within formal and informal contexs. Journal for Research in Mathematics Education. 29 (1), (pp. 83- 106).
  • Fidan, S. (2008) İlköğretim 5. sınıf matematik dersinde öğrencilerin problem kurma çalışmalarının problem çözme başarısına etkisi. Yüksek lisans tezi, Gazi Üniversitesi, Ankara.
  • Kilpatrick, J. (1987). Problem formulating: where do good problems come from? In A.H.Schoenfeld (Ed). Cognitive Science and Mathematics Education, Hillsdale, NJ; Erlaum, (pp.123-147).
  • Korkmaz, E. ve Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. BAÜ Fen Bilimleri Enstitüsü Dergisi. 2006, 8 (1), 64-74.
  • Langrall, C. W. & Swafford, J. (2000). Three balloons for two dollars; Developing proportional reasoning. Mathematics Teaching in the Middle School, 6 (4), (pp. 254-261).
  • Lesh R., Behr, M., & Post, T. (1988). “Number concepts and operations in the middle grades” Proportional Reasoning. In J. Hiebert & M. Behr (Eds.), (pp. 93-118). Reston, VA: National Council of Teachers of Mathematics.
  • Lesh, R., Post, T. & Behr, M. (1989). Proportional Reasoning. In M. Behr & J. Hiebert (Eds.) Number Concepts and Operations in the Middle Grades. Reston, VA: National Council of Teachers of Mathematics.
  • Lowrie, T. (2002). Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal 2002, Vol. 14, No. 2, 87-98.
  • Millî Eğitim Bakanlığı (MEB) (2008). İlköğretim matematik dersi 6-8. Sınıflar öğretim program ve kılavuzu. M.E.B: Ankara.
  • Mamona-Downs, J. (1993). On analysing problem posing. In: I. Hirabayashi, N. Nohada, K. Shigematsu, F. L. Lin (Eds.), Proceedings of the 17th Conference of the International Group for the Psychology of Mathematics Education. Tsukuba, Japan, 3, (pp. 41-47).
  • National Council of Teachers of Mathematics (NCTM) (1989). Curriculum And Evaluation Standards For School Mathematics, National Council Teachers of Mathematics Pub, Reston: VA.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards For School Mathematics. Reston VA: NCTM.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14 (1), (pp. 19-28).
  • Silver, E., A., Cai, J. (1996). An analysis of arithmetic problem posing by middle school. Journal For Research in Mathematics Education, 27, (pp. 521- 539). 11

İlköğretim Öğrencilerinin Orantısal Akıl Yürütme Becerileri İle Problem Kurma Becerileri Arasındaki İlişki

Year 2011, Volume: 30 Issue: 30, 1 - 11, 01.02.2011

Ahmet Çelik , Elif Yetkin Özdemir

Abstract

Bu çalısmada ilkögretim yedinci ve sekizinci sınıf ögrencilerinin orantısal akıl yürütme becerileri ile oran-orantı problemi kurma becerileri arasındaki iliski incelenmistir. Çalısmaya toplam 392 tane 7. ve 8. sınıf ögrencisi katılmıstır. Veri toplama aracı olarak arastırmacılar tarafından gelistirilen oran-orantı problemlerini kurma testi ile Akkus ve Duatepe (2006) tarafından gelistirilen orantısal akıl yürütme testi kullanılmıstır. Veri analizi için betimsel istatistik yöntemleri (frekans, yüzde hesabı) ve kiâ€"kare testi kullanılmıstır. Sonuçlar orantısal akıl yürütme becerisi ile problem kurma becerisi arasında istatistiksel olarak anlamlı bir iliski oldugunu göstermistir. Orantısal akıl yürütme becerisi bakımından yetersiz düzeyde olan ögrencilerin çogunun oranorantı problemi kuramadıkları görülmüstür. Buna karsılık yüksek düzeyde orantısal akıl yürütme becerisine sahip ögrencilerin oran-orantı problemi kurmada daha basarılı oldukları tespit edilmistir.

Keywords

Oran ve orantı orantısal akıl yürütme becerisi problem kurma becerisi

References

  • Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.) Proceedings Of The International Conference On Mathematical Education Into the 21st Century: Social Challenges, Issues And Approaches, Cairo, Egypt. 2, (pp. 1-8).
  • Akkuş, O. ve Duatepe A. (2002). İlköğretim matematik öğretmen adaylarının akıl yürütme becerileri üzerine bir çalışma. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23, 32-40.
  • Akkuş, O. ve Duatepe-Paksu, A. (2006). Orantısal akıl yürütme becerisi testi ve teste yönelik dereceli puanlama anahtarı geliştirilmesi, Eğitim Araştırmaları, 6, 25, 1-10.
  • Akar, G. K. (2009). Oran konusunun kavramsal öğreniminde karşılaşılan zorluklar ve çözüm önerileri. E. Bingölbali & M.F. Özmantar (Eds.) İlköğretimde Karşılaşılan Matematiksel Zorluklar ve Çözüm Önerileri,(sf. 263-285). Pegem Akademi.
  • Akkan, Y., Çakıroğlu, Ü. ve Güven, B. (2009). İlköğretim 6. ve 7. sınıf öğrencilerinin 10 denklem oluşturma ve problem kurma yeterlilikleri. Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 17, Haziran 2009, 41-55.
  • Cai, (2003) Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34 (5), 719-737.
  • Christou, C., Mousoulides, N., Pittalis, M., Pitta- Pantazi, D. & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. The International Journal on Mathematics Education, Vol, 37, 3, 149-158.
  • Cramer, K., Post, T., Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In Research Ideas For The Classroom: Middle Grades Mathematics, D. Owens (Ed.), pp. 159–178. New York: Macmillan.
  • Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, Vol. 52, No. 3, 243-270.
  • English, L, D. (1997a). The development of fifth- grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, (pp. 183 -217).
  • English, L, D. (1997b). Development of seventh- grade students’ problem-posing. Proceedings of the Conference of the International Group for the Psychology of Mathematics Education, 2, (pp. 249- 256).
  • English, L, D. (1998). Children’s problem posing within formal and informal contexs. Journal for Research in Mathematics Education. 29 (1), (pp. 83- 106).
  • Fidan, S. (2008) İlköğretim 5. sınıf matematik dersinde öğrencilerin problem kurma çalışmalarının problem çözme başarısına etkisi. Yüksek lisans tezi, Gazi Üniversitesi, Ankara.
  • Kilpatrick, J. (1987). Problem formulating: where do good problems come from? In A.H.Schoenfeld (Ed). Cognitive Science and Mathematics Education, Hillsdale, NJ; Erlaum, (pp.123-147).
  • Korkmaz, E. ve Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. BAÜ Fen Bilimleri Enstitüsü Dergisi. 2006, 8 (1), 64-74.
  • Langrall, C. W. & Swafford, J. (2000). Three balloons for two dollars; Developing proportional reasoning. Mathematics Teaching in the Middle School, 6 (4), (pp. 254-261).
  • Lesh R., Behr, M., & Post, T. (1988). “Number concepts and operations in the middle grades” Proportional Reasoning. In J. Hiebert & M. Behr (Eds.), (pp. 93-118). Reston, VA: National Council of Teachers of Mathematics.
  • Lesh, R., Post, T. & Behr, M. (1989). Proportional Reasoning. In M. Behr & J. Hiebert (Eds.) Number Concepts and Operations in the Middle Grades. Reston, VA: National Council of Teachers of Mathematics.
  • Lowrie, T. (2002). Young children posing problems: The influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal 2002, Vol. 14, No. 2, 87-98.
  • Millî Eğitim Bakanlığı (MEB) (2008). İlköğretim matematik dersi 6-8. Sınıflar öğretim program ve kılavuzu. M.E.B: Ankara.
  • Mamona-Downs, J. (1993). On analysing problem posing. In: I. Hirabayashi, N. Nohada, K. Shigematsu, F. L. Lin (Eds.), Proceedings of the 17th Conference of the International Group for the Psychology of Mathematics Education. Tsukuba, Japan, 3, (pp. 41-47).
  • National Council of Teachers of Mathematics (NCTM) (1989). Curriculum And Evaluation Standards For School Mathematics, National Council Teachers of Mathematics Pub, Reston: VA.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards For School Mathematics. Reston VA: NCTM.
  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14 (1), (pp. 19-28).
  • Silver, E., A., Cai, J. (1996). An analysis of arithmetic problem posing by middle school. Journal For Research in Mathematics Education, 27, (pp. 521- 539). 11
There are 25 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Ahmet Çelik

Elif Yetkin Özdemir This is me

Publication Date February 1, 2011
Submission Date August 1, 2014
Published in Issue Year 2011 Volume: 30 Issue: 30

Cite

APA Çelik, A., & Özdemir, E. Y. (2011). İlköğretim Öğrencilerinin Orantısal Akıl Yürütme Becerileri İle Problem Kurma Becerileri Arasındaki İlişki. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(30), 1-11. https://doi.org/10.5455/tjfmpc.45290

27767 https://creativecommons.org/licenses/by-nc-nd/4.0/