Some Obstacles on the Way of Constructing Triangular Inequality

Bu çalışma, öğrencilerin üçgen eşitsizliğini keşfetmeleri için oluşturulan etkinlikleri değerlendirmek için yapılmıştır. Geliştirilen bu etkinlikler üzerinde öğrenciler çalışırken ortaya çıkan davranışlar makalede rapor edilmiştir. Araştırma, katılımcı gözlem, kanıtlayıcı sorular ve bazı çalışma yapraklarının kullanıldığı nitel bir çalışmadır. Araştırmanın katılımcıları, bir ilköğretim okulunda öğrenim gören 8. sınıf öğrencileridir. Bu araştırmada elde edilen verilere göre, üçgenleri kavrama ile ilgili bazı öğrenci davranışlarının üçgen eşitsizliğini oluşturmada sorunlara yol açtığı görülmüştür. Makalede bu davranışlar açıklanmış ve öğretimsel açıdan bazı önerilere yer verilmiştir.

Üçgen Eşitsizliğini Oluşturmada Karşılaşılan Bazı Engeller

This study was conducted to evaluate the activities designed to enable pupils to discover triangular inequality. The article reports the behaviors occurred while the pupils were doing these activities. It was a qualitative study utilizing participant observation, probe type questions, and worksheets. The participants were 8th grade pupils in a primary school. According to the data obtained in this research, some behaviors related to pupils’ conceptions of triangle, caused problems on the way of constructing triangular inequality. These behaviors are explained and some implications for teaching are discussed in the paper.

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Clements, D.H., Swaminathan, S., Hannibal, M.A., & Sarama, J. (1999). Young children’s conceptions of shape. Journal for Research in Mathematics Education, 30(2), 192-212.
Fox, R. (2001). Constructivism Examined. Oxford Review of Education, 27 (1), 23-35.
Gray, E., Pinto, M., Pitta, D., & Tall, D. (1999). Knowledge Construction and Diverging Thinking in Elementary & Advance Mathematics. Educational Studies in Mathematics 38, 11-133.
Gray, E., Pitta, D., & Tall, D. (2000). Objects, Actions and Images: A Perspective on Early Number Development. Journal of Mathematical Behavior, 18 (4), 1– 13. Retrieved on 12-11-2004, at URL: http://www.warwick.ac.uk/staff/David.Tall/pdfs/dot2000b-graypitta-jmb.pdf.
Hannibal, M. A. (1999) Young children’s developing understanding of geometric shapes. Teaching Children Mathematics, 5(6), 353-360.
Hejny, M. (2003). Understanding and Structure. Proceedings of CERME III, Bellaria, Italy. Retrieved on 06, 10, 2004, at URL: http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG3/TG3Hejny cerme3.pdf.
Marchini, C., & Rinaldi, M.G. (2005). Geometrical pre-conceptions of 8 years old pupils. In European Research in Mathematics Education IV Congress proceedings, Spain, 17-21 February, 748-755.
Oberdorf, C. D., & Taylor-Cox, J. (1999). Shape up. Teaching Children Mathematics, 5(6), 340-345.
Orton, A., & Frobisher, L. (1996). Insights into Teaching Mathematics, London: Cassell.
Singer, M. (2001). Thinking structures involved in mathematics learning. In European research in Mathematics Education II Congress proceedings, Charles University Faculty of Education, 24-27 February, 92-100.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity, Educational Studies in Mathematics, 12(2), 151-169.
Turnuklu, E. B., & Yesildere, S. (2005). 14 years old pupils’ thought processes: a case study of constructing the triangular inequality, in: European Research in Mathematics Education IV Congress proceedings, Spain, 17-21 February, 374-382.
Van der Sandt, S. (2001). A case study of four grade 7 geometry classes, in: Psychology of Mathematics Education Congress proceedings, Netherlands, 343-351.
Vighi, P. (2003) The triangle as a mathematical object, In: European Research in Mathematics Education III Congress proceedings, Bellaria, Italy, 28 February-3 March, 1-10.