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Year 2013, Volume: 7 Issue: 1, 222 - 241, 01.06.2013

Hülya Kılıç

https://doi.org/10.12973/nefmed160

Abstract

–The aim of this paper is to present the findings of a pilot study which was designed to investigate the effects of using dynamic geometry software on the tenth grade students’ geometric thinking, problem solving and proof skills. It was a quasi-experimental study consisted of 49 students from six different high schools around Istanbul. In the treatment groups, the students engaged with five dynamic geometry activities in the geometry lessons throughout the semester. Although no significant differences between the groups were observed, in the treatment groups, the students’ mean scores for each type of test increased significantly. The students’ answers for each item in the tests were also analyzed. It is found that students’ mean scores for each item were quite low such that they did not know the definitions of basic geometric concepts and the relationships between them and also they were not able to solve geometry problems and prove given arguments

Keywords

dynamic geometry software geometric thinking problem solving proof secondary

References

  • Arslan, S., & Yıldız, C. (2010). 11. sınıf öğrencilerinin matematiksel düşünmenin aşamalarındaki yaşantılarından yansımalar, Eğitim ve Bilim, 35, 17-31.
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843- 908). North Carolina: Information Age Publishing.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: MacMillan.
  • Driscoll, M. (2007). Fostering geometric thinking: A guide for teachers grades 5-10. New Hampshire: Heinemann.
  • Güven, B. (2008). Using dynamic geometry software to gain insight into a proof, International Journal of Computers for Mathematical Learning, 13, 251-262.
  • Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. CBMS Issues in Mathematics Education, 7, 234-283.
  • Healy, L., & Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers. Mathematical Thinking and Learning, 1, 59-84.
  • Heinze, A., Cheng, Y. H., Ufer, S., Lin, F. L., & Reiss, K. (2008). Strategies to foster students’ competencies in constructing multi-steps geometric proofs: Teaching experiments in Taiwan and Germany. ZDM Mathematics Education, 40, 443-453.
  • Hershkowitz, R., Dreyfus, T., Ben-Zvi, D., Friedlander, A., Hadas, N., Resnick, T., et al. (2002). Mathematics curriculum development for computerized environments: A designer-research-teacher-learner activity. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (pp. 657-694). New Jersey: Erlbaum.
  • Jones, K. (2000). Proving a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44, 55-85.
  • Jones, K. (2002). Issues in the teaching and learning geometry. In L. Haggarty (Ed.) Aspects of Teaching Secondary Mathematics: Perspectives on Practice (pp.121-139). London: Routledge Falmer.
  • July, R. A. (2001). Thinking in three dimensions: exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad. Yayınlanmamış doktora tezi, Florida International University, ABD.
  • Leong, Y. H. (2002). Effects of Geometers’ Sketchpad on spatial ability and achievement in transformation geometry among secondary 2 students in Singapore. Yayınlanmamış yüksek lisans tezi, Nanyang Technological University, Singapur.
  • Liu, L., & Cummings, R., A (2001). Learning model that stimulates geometric thinking through use of PCLogo and Geometers’ Sketchpad, Computers in the Schools, 17, 85- 104.
  • Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, 87-125.
  • Milli Eğitim Bakanlığı (MEB). (2010). Ortaöğretim geometri dersi 9.-10. sınıflar öğretim programı. Ankara: Komisyon.
  • Milli Eğitim Bakanlığı Eğitimi Araştırma ve Geliştirme Dairesi Başkanlığı. ÖBBS 2009 Raporu. http://earged.meb.gov.tr/arasayfa.php?g=81 adresinden alınmıştır.
  • Miller, M. D., Linn, R. L., & Gronlund, N. E. (2009). Measurement and assessment in teaching. New Jersey: Pearson.
  • Mullis, I.V.S., Martin, M.O., & Foy, P. (with Olson, J.F., Preuschoff, C., Erberber, E., Arora, A., Galia, J.), (2008). TIMSS 2007 International mathematics report. Massachusetts: TIMSS & PIRLS International Study Center.
  • Olkun, S., & Altun, A. (2003). İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarıları arasındaki ilişki, The Turkish Online Journal of Educational Technology, 2, 86-91.
  • PISA 2009 Results: What students know and can co – Student performance in reading, mathematics and science (Volume I). http://dx.doi.org/10.1787/9789264091450-en adresinden alınmıştır.
  • Reiss, K., Klieme, E., & Heinze, A. (2001). Prerequisites for the understanding of proofs in the geometry classroom. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (pp. 97 - 104). Utrecht University: PME.
  • Scher, D. (2005). Square or not? Assessing constructions in an interactive geometry software environment. In W. J. Masalaski & P. C. Elliott (Eds.), Technology supported mathematics learning environments (pp. 113-124). Virginia: NCTM.
  • Senemoğlu, N. (2009). Gelişim, öğrenme ve öğretim: Kuramdan uygulamaya. Ankara: Pegem Akademi.
  • Stylianides, G. J. (2008). An analytical framework of reasoning and proving, For the Learning of Mathematics, 28, 9-16.
  • Ubuz, B., Üstün, I., & Erbaş, A. K. (2009). Effect of dynamic geometry environment on immediate and retention level achievements of seventh grade students, Eurasian Journal of Educational Research, 35, 147-164.
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry (Cognitive Development and Achievement in Secondary School Geometry Project). University of Chicago, ABD.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356-366.

Lise Öğrencilerinin Geometrik Düşünme, Problem Çözme ve İspat Becerileri

Year 2013, Volume: 7 Issue: 1, 222 - 241, 01.06.2013

Hülya Kılıç

https://doi.org/10.12973/nefmed160

Abstract

Bu çalışmanın amacı, dinamik geometri yazılımlarının 10. sınıf öğrencilerinin geometrik düşünme, geometri başarısı ve ispat yapma becerisi üzerindeki etkilerini incelemektir. Bu makalede, bu amaçla gerçekleştirilen yarı deneysel pilot çalışmadan elde edilen bulgular tartışılacaktır. Çalışmaya, İstanbul ilindeki altı liseden 227 öğrenci katılmış ancak 49 öğrencinin verileri analiz edilmiştir. Öğrencilere geometrik düşünme, problem çözme ve ispat becerilerini ölçmeye yönelik üç farklı test uygulanmış, çalışma boyunca deney grubundaki öğrencilerle dinamik geometri yazılımının kullandığı beş etkinlik yapılmıştır. Son testlerde gruplar arasında anlamlı bir fark bulunmamış ancak deney grubunda üç testin ortalamalarında anlamlı artışlar olduğu görülmüştür. Bununla beraber, öğrencilerin testler bazında ortalamalarının genel olarak düşük olduğu, temel geometrik kavramları tanımlayamadıkları, kavramlar arasındaki ilişkileri kuramadıkları, kavram bilgisini farklı durumlarda uygulayamadıkları ve ispat becerilerinin düşük olduğu tespit edilmiştir.

Keywords

dinamik geometri yazılımları geometrik düşünme problem çözme ispat lise.

References

  • Arslan, S., & Yıldız, C. (2010). 11. sınıf öğrencilerinin matematiksel düşünmenin aşamalarındaki yaşantılarından yansımalar, Eğitim ve Bilim, 35, 17-31.
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843- 908). North Carolina: Information Age Publishing.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: MacMillan.
  • Driscoll, M. (2007). Fostering geometric thinking: A guide for teachers grades 5-10. New Hampshire: Heinemann.
  • Güven, B. (2008). Using dynamic geometry software to gain insight into a proof, International Journal of Computers for Mathematical Learning, 13, 251-262.
  • Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. CBMS Issues in Mathematics Education, 7, 234-283.
  • Healy, L., & Hoyles, C. (1999). Visual and symbolic reasoning in mathematics: Making connections with computers. Mathematical Thinking and Learning, 1, 59-84.
  • Heinze, A., Cheng, Y. H., Ufer, S., Lin, F. L., & Reiss, K. (2008). Strategies to foster students’ competencies in constructing multi-steps geometric proofs: Teaching experiments in Taiwan and Germany. ZDM Mathematics Education, 40, 443-453.
  • Hershkowitz, R., Dreyfus, T., Ben-Zvi, D., Friedlander, A., Hadas, N., Resnick, T., et al. (2002). Mathematics curriculum development for computerized environments: A designer-research-teacher-learner activity. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (pp. 657-694). New Jersey: Erlbaum.
  • Jones, K. (2000). Proving a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44, 55-85.
  • Jones, K. (2002). Issues in the teaching and learning geometry. In L. Haggarty (Ed.) Aspects of Teaching Secondary Mathematics: Perspectives on Practice (pp.121-139). London: Routledge Falmer.
  • July, R. A. (2001). Thinking in three dimensions: exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad. Yayınlanmamış doktora tezi, Florida International University, ABD.
  • Leong, Y. H. (2002). Effects of Geometers’ Sketchpad on spatial ability and achievement in transformation geometry among secondary 2 students in Singapore. Yayınlanmamış yüksek lisans tezi, Nanyang Technological University, Singapur.
  • Liu, L., & Cummings, R., A (2001). Learning model that stimulates geometric thinking through use of PCLogo and Geometers’ Sketchpad, Computers in the Schools, 17, 85- 104.
  • Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, 87-125.
  • Milli Eğitim Bakanlığı (MEB). (2010). Ortaöğretim geometri dersi 9.-10. sınıflar öğretim programı. Ankara: Komisyon.
  • Milli Eğitim Bakanlığı Eğitimi Araştırma ve Geliştirme Dairesi Başkanlığı. ÖBBS 2009 Raporu. http://earged.meb.gov.tr/arasayfa.php?g=81 adresinden alınmıştır.
  • Miller, M. D., Linn, R. L., & Gronlund, N. E. (2009). Measurement and assessment in teaching. New Jersey: Pearson.
  • Mullis, I.V.S., Martin, M.O., & Foy, P. (with Olson, J.F., Preuschoff, C., Erberber, E., Arora, A., Galia, J.), (2008). TIMSS 2007 International mathematics report. Massachusetts: TIMSS & PIRLS International Study Center.
  • Olkun, S., & Altun, A. (2003). İlköğretim öğrencilerinin bilgisayar deneyimleri ile uzamsal düşünme ve geometri başarıları arasındaki ilişki, The Turkish Online Journal of Educational Technology, 2, 86-91.
  • PISA 2009 Results: What students know and can co – Student performance in reading, mathematics and science (Volume I). http://dx.doi.org/10.1787/9789264091450-en adresinden alınmıştır.
  • Reiss, K., Klieme, E., & Heinze, A. (2001). Prerequisites for the understanding of proofs in the geometry classroom. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (pp. 97 - 104). Utrecht University: PME.
  • Scher, D. (2005). Square or not? Assessing constructions in an interactive geometry software environment. In W. J. Masalaski & P. C. Elliott (Eds.), Technology supported mathematics learning environments (pp. 113-124). Virginia: NCTM.
  • Senemoğlu, N. (2009). Gelişim, öğrenme ve öğretim: Kuramdan uygulamaya. Ankara: Pegem Akademi.
  • Stylianides, G. J. (2008). An analytical framework of reasoning and proving, For the Learning of Mathematics, 28, 9-16.
  • Ubuz, B., Üstün, I., & Erbaş, A. K. (2009). Effect of dynamic geometry environment on immediate and retention level achievements of seventh grade students, Eurasian Journal of Educational Research, 35, 147-164.
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry (Cognitive Development and Achievement in Secondary School Geometry Project). University of Chicago, ABD.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20, 356-366.
There are 28 citations in total.

Details

Primary Language Turkish
Journal Section Makaleler
Authors

Hülya Kılıç This is me

Publication Date June 1, 2013
Submission Date January 2, 2015
Published in Issue Year 2013 Volume: 7 Issue: 1

Cite

APA Kılıç, H. (2013). Lise Öğrencilerinin Geometrik Düşünme, Problem Çözme ve İspat Becerileri. Necatibey Eğitim Fakültesi Elektronik Fen Ve Matematik Eğitimi Dergisi, 7(1), 222-241. https://doi.org/10.12973/nefmed160