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Triangle Concept from the Perspective of Blind Students

Year 2016, Volume: 17 Issue: 2, 275 - 295, 01.05.2016

Abstract

In this study, blind students’ concept images and concept definitions regarding the triangle were investigated. For this purpose, 6 open-ended questions were asked to five blind students. The participants were asked to use the magnetic materials for constructing the triangle and one interview question was presented through a raised-line material. In this qualitative research, data obtained from the interviews, observation notes, the pictures of raised-line materials and geometric figures with magnetic materials constructed by participants, were analyzed through the grounded theory techniques and the constant comparative analysis method. As a result, blind students mostly used the concept images and rarely used incomplete concept definition. Besides, participants had difficulties regarding the triangle such as position and the angles of the triangle, naming, classification. Lastly, the relation between the concept image and the concept definition cells, which the participants utilized for the triangle was emerged in two ways namely heuristic and formal-heuristic

References

  • Clements, D. H., Sarama, J. H., & Battista, M. (1998). Development of concepts of geometric figures in especially designed logo computer environment. Focus on Learning Problems in Mathematics, 20(2-3), 47-64.
  • Delice, A., & Sevimli, E. (2011). İntegral kavramının öğretiminde konu sıralamasının kavram imgeleri bağlamında incelenmesi; Belirli ve belirsiz integraller. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(2), 51-62.
  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2),139-162.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70-95). Cambridge: CUP.
  • Kaplan, A., & Hızarcı, S. (2005). Matematik öğretmen adaylarının üçgen kavramı ile ilgili bilgi düzeyleri. Kazım Karabekir Eğitim Fakültesi Dergisi, 11, 472-478.
  • Kennedy, J. M. (1993). Drawing and the blind. New Haven, CT: Yale Press.
  • Klingenberg, O. G. (2007). Geometry: Educational implications for children with visual impairment. Philosophy of Mathematics Education (Special Issue on Social Justice http://people.exeter.ac.uk/PErnest/pome20/index.htm. 20, 1-15. Retrieved April 10, 2013, from
  • Kohonová, I. (2007, 22-26 February). Comparison of observation of new space and its objects by sighted and non-sighted pupils. In D. Pitta-Pantazi and G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME 5), (pp. 982-991). Larnaca, Cyprus.
  • Landau B., Gleitman, H., & Spelke, E. (1981, September). Spatial knowledge and geometric representation in a child blind from birth. Science, New Series, 213(4513), 1275-1278.
  • Landau,B., Spelke, E., & Gleitman, H. (1984). Spatial knowledge in a young blind child. Cognition, 16(3), 225–260.
  • Leff, L. S.(2009). Baron’s E-Z geometry (Fourth edition). New York: Barron’s Educational Series, Inc.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage.
  • Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı. (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara: M.E.B. 10 Nisan 2014 tarihinde http://ttkb.meb. gov.tr/program2.aspx?islem=2&kno=215 adresinden alınmıştır.
  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  • Öksüz, C. (2010). Seventh grade gifted students’ misconceptions on “point, line and plane” concepts. Elementary Education Online, 9(2), 508–525.
  • Shaughnessy, J. M., & Burger, W. F. (1985). Spadework prior to deduction in geometry. Mathematics Teacher, 78(6), 419-428.
  • Tall, D. O. (1988). Concept image and concept definition. In J. de Lange and M. Doorman (Eds.), Senior secondary mathematics education (pp. 37- 41). OW & OC Utrecht. http://www.davidtall.com/. Accessed 16 November 2012.
  • Tall, D. O. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 495-511). New York, NY: Macmillan Publishing Company.
  • Tall, D. O. (2005, 5-7 July). A theory of mathematical growth through embodiment, symbolism and proof. Paper presented at International Colloquium on Mathematical Learning from Early Childhood to Adulthood, Centre de Recherche sur l’Enseignement des Mathématiques, Nivelles, Belgium. Retrieved March 6, 2011, from http://www.warwick.acuk/staff/David.Tall/pdfs/ dot2005e-crem-child- adult.pdf.
  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics with special reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
  • Tanton, J. S. (2005). Encyclopedia of mathematics. New York: Facts On File.
  • Türnüklü, E., Alaylı, F. G., & Akkaş, E. N. (2013). İlköğretim matematik öğretmen adaylarının dörtgenlere ilişkin algıları ve imgelerinin incelenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1213-1232.
  • Vighi, P. (2003, 28 February-3 March). The triangle as a mathematical object. European Research in Mathematics Education III Congress Proceedings, Bellaria, Italy, 1- 10.
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. O. Tall (Ed.), Advanced Mathematical thinking (pp. 65-81). Kluwer, the Netherlands: Dordrecht.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concepts of functions. Journal for Research in Mathematics Education, 20(4), 356-366.
  • Yeşil-Dağlı, Ü., & Halat, E. (2016). Young children’s conceptual understanding of triangle. Eurasia Journal of Mathematics, Science & Technology Education, 12(2), 189-202.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri (6. baskı) Ankara: Seçkin Yayıncılık.

Total Görme Engelli Öğrencilerin Perspektifinden Üçgen Kavramı

Year 2016, Volume: 17 Issue: 2, 275 - 295, 01.05.2016

Abstract

Bu araştırmada total görme engelli öğrencilerin üçgen kavramına ilişkin kavram imajları ve kavram tanımları araştırılmıştır. Bu amaçla total görme engelli 5 öğrenciye görüşmelerde 6 açık uçlu soru yöneltilmiştir. Katılımcılardan üçgen oluşturmaları için mıknatıslı materyalleri kullanmaları istenmiştir ve ayrıca bir soru kabartılmış çizimler aracılığıyla sunulmuştur. Nitel bir doğaya sahip olan bu araştırmada; görüşmeler, gözlem notları, kabartılmış çizimler ve öğrencilerin mıknatıslı materyallerle oluşturduğu geometrik şekillerin resimleri aracılığıyla elde edilen veriler gömülü teorinin teknikleri ve sürekli karşılaştırmalı analiz yöntemiyle analiz edilmiştir. Araştırmanın sonucunda, katılımcıların çoğunlukla kavram imajlarını kullandıkları ve üçgen tanımlarını eksik kullandıkları gözlemlenmiştir. Ayrıca katılımcılar üçgen kavramı ile ilgili konum, isimlendirme ve sınıflandırma gibi bazı zorluklarla da karşılaşmışlardır. Son olarak üçgen kavramı için katılımcıların sahip oldukları kavram tanımı-kavram imajı hücreleri arasındaki ilişkilerin; sezgisel ve formal-sezgisel olmak üzere iki şekilde ortaya çıktığı tespit edilmiştir.

References

  • Clements, D. H., Sarama, J. H., & Battista, M. (1998). Development of concepts of geometric figures in especially designed logo computer environment. Focus on Learning Problems in Mathematics, 20(2-3), 47-64.
  • Delice, A., & Sevimli, E. (2011). İntegral kavramının öğretiminde konu sıralamasının kavram imgeleri bağlamında incelenmesi; Belirli ve belirsiz integraller. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30(2), 51-62.
  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2),139-162.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition (pp. 70-95). Cambridge: CUP.
  • Kaplan, A., & Hızarcı, S. (2005). Matematik öğretmen adaylarının üçgen kavramı ile ilgili bilgi düzeyleri. Kazım Karabekir Eğitim Fakültesi Dergisi, 11, 472-478.
  • Kennedy, J. M. (1993). Drawing and the blind. New Haven, CT: Yale Press.
  • Klingenberg, O. G. (2007). Geometry: Educational implications for children with visual impairment. Philosophy of Mathematics Education (Special Issue on Social Justice http://people.exeter.ac.uk/PErnest/pome20/index.htm. 20, 1-15. Retrieved April 10, 2013, from
  • Kohonová, I. (2007, 22-26 February). Comparison of observation of new space and its objects by sighted and non-sighted pupils. In D. Pitta-Pantazi and G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME 5), (pp. 982-991). Larnaca, Cyprus.
  • Landau B., Gleitman, H., & Spelke, E. (1981, September). Spatial knowledge and geometric representation in a child blind from birth. Science, New Series, 213(4513), 1275-1278.
  • Landau,B., Spelke, E., & Gleitman, H. (1984). Spatial knowledge in a young blind child. Cognition, 16(3), 225–260.
  • Leff, L. S.(2009). Baron’s E-Z geometry (Fourth edition). New York: Barron’s Educational Series, Inc.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage.
  • Milli Eğitim Bakanlığı, Talim ve Terbiye Kurulu Başkanlığı. (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara: M.E.B. 10 Nisan 2014 tarihinde http://ttkb.meb. gov.tr/program2.aspx?islem=2&kno=215 adresinden alınmıştır.
  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
  • Öksüz, C. (2010). Seventh grade gifted students’ misconceptions on “point, line and plane” concepts. Elementary Education Online, 9(2), 508–525.
  • Shaughnessy, J. M., & Burger, W. F. (1985). Spadework prior to deduction in geometry. Mathematics Teacher, 78(6), 419-428.
  • Tall, D. O. (1988). Concept image and concept definition. In J. de Lange and M. Doorman (Eds.), Senior secondary mathematics education (pp. 37- 41). OW & OC Utrecht. http://www.davidtall.com/. Accessed 16 November 2012.
  • Tall, D. O. (1992). The transition to advanced mathematical thinking: Functions, limits, infinity and proof. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 495-511). New York, NY: Macmillan Publishing Company.
  • Tall, D. O. (2005, 5-7 July). A theory of mathematical growth through embodiment, symbolism and proof. Paper presented at International Colloquium on Mathematical Learning from Early Childhood to Adulthood, Centre de Recherche sur l’Enseignement des Mathématiques, Nivelles, Belgium. Retrieved March 6, 2011, from http://www.warwick.acuk/staff/David.Tall/pdfs/ dot2005e-crem-child- adult.pdf.
  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics with special reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
  • Tanton, J. S. (2005). Encyclopedia of mathematics. New York: Facts On File.
  • Türnüklü, E., Alaylı, F. G., & Akkaş, E. N. (2013). İlköğretim matematik öğretmen adaylarının dörtgenlere ilişkin algıları ve imgelerinin incelenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1213-1232.
  • Vighi, P. (2003, 28 February-3 March). The triangle as a mathematical object. European Research in Mathematics Education III Congress Proceedings, Bellaria, Italy, 1- 10.
  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. O. Tall (Ed.), Advanced Mathematical thinking (pp. 65-81). Kluwer, the Netherlands: Dordrecht.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concepts of functions. Journal for Research in Mathematics Education, 20(4), 356-366.
  • Yeşil-Dağlı, Ü., & Halat, E. (2016). Young children’s conceptual understanding of triangle. Eurasia Journal of Mathematics, Science & Technology Education, 12(2), 189-202.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri (6. baskı) Ankara: Seçkin Yayıncılık.
There are 27 citations in total.

Details

Primary Language Turkish
Journal Section Research Article
Authors

Tuğba Horzum This is me

Publication Date May 1, 2016
Published in Issue Year 2016 Volume: 17 Issue: 2

Cite

APA Horzum, T. (2016). Total Görme Engelli Öğrencilerin Perspektifinden Üçgen Kavramı. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 17(2), 275-295.

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