Research Article
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Investigating Pre-service Teachers’ Ability to Recognize and Classify Geometric Concepts Hierarchically

Year 2019, Volume: 10 Issue: 3, 680 - 710, 13.12.2019

Zülfiye Zeybek Şimşek

https://doi.org/10.16949/turkbilmat.491564

Abstract

Geometry is not only an
essential tool to develop students’ spatial thinking, but it is also a content
strand that provides opportunities for them to develop ability to question,
analytic thinking and reasoning skills. The current educational reforms
emphasize that students should gain the ability to recognize geometric shapes
and solids as well as to classify them hierarchically from early grade levels.
In this study, the ability of pre-service mathematics teachers to recognize and
classify geometric concepts (quadrilaterals and geometric solids) was
investigated. For this purpose, a geometry questionnaire consisting of 10
open-ended questions was developed by the researcher based on an extent review
of the existing literature. As a result of the preliminary examination of the
pre-service teachers’ responses to the questionnaire items, individual
interviews were conducted with five pre-service teachers, who were thought to
have different levels of thinking. The findings of the study showed that the
vast majority of the pre-service teachers did not fully comprehend the
hierarchical classification between quadrilaterals. In addition, this study
demonstrated that pre-service teachers generally used prototype judgments to
identify geometric solids and select examples and non-examples of geometric
solids. Another finding of this study was that the pre-service teachers
identified incorrect hierarchical classification between geometric solids. The
findings of the study is discussed under the light of other studies in the
literature and the recommendations of educational reforms.

Keywords

quadrilaterals Hierarchical classifications geometry geometric solids

References

  • Altneave, F. (1957). Transfer of experience with a class schema to identification of patterns and shapes. Journal of Experimental Psychology, 54, 81–88.
  • 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.
  • Bingolbali, E., & Monaghan, J. (2008). Concept image revisited. Educational Studies in Mathematics, 68(1), 19-35.
  • Bozkurt, A., & Koç, Y. (2012). İlköğretim matematik öğretmenliği birinci sınıf öğrencilerinin prizma kavramına dair bilgilerinin incelenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 12(4), 2941-2952.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2010). Bilimsel araştırma yöntemleri. Ankara: Pegem Yayıncılık.
  • Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), Research companion to principles and standards for school mathematics (pp. 15–78). Reston, VA: National Council of Teachers of Mathematics.
  • De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14, 11-18.
  • Erez, M. M., & Yerushalmy, M. (2006). ‘‘If you can turn a rectangle into a square, you can turn a square into a rectangle ...’’ young students experience. International Journal of Computers for Mathematical Learning, 11, 271–299.
  • Ergin, A. S., & Türnüklü, E. (2015). Ortaokul öğrencilerinin cisim imgelerinin incelenmesi: Geometrik ve uzamsal düşünme ile ilişkiler. Eğitim ve Öğretim Araştırmaları Dergisi, 4(2), 188-199.
  • Fischbein, E. (1993). The theory of figural concept. Educational Studies in Mathematics, 24(2), 139-162.
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31, 60–72.
  • Fujita, T., & Jones, K. (2006). Primary trainee teachers’ understanding of basic geometrical figures in Scotland. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education (Vol.3, pp. 129–136). Prague: PME.
  • Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Toward a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
  • Gökbulut, Y. (2010). Sınıf öğretmeni adaylarının geometrik cisimler konusundaki pedagojik alan bilgileri (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Gökbulut, Y., & Ubuz, B. (2013). Prospective primary teachers’ knowledge on prism: Generating definitions and examples. Elementary Education Online, 12(2), 401-412.
  • Gökkurt, B. (2014). Ortaokul matematik öğretmenlerinin geometrik cisimler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi (Yayınlanmamış doktora tezi). Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Gökkurt, B., Şahin, Ö. Başıbüyük, K., Erdem, E., & Soylu, Y (2014, Mayıs). Öğretmen adaylarının koni kavramına ilişkin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi. 13. Matematik Sempozyumu’nda sunulan bildiri, Karabük Üniversitesi, Karabük.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Öğretmen adaylarının geometrik cisimler konusuna ilişkin öğrenci hatalarına yönelik pedagojik alan bilgileri. İlköğretim Online, 14(1), 55-71.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
  • Hershkowitz, R. (1989). Visualization in geometry – two sides of the coin. Focus Learn Probl Math, 11(1), 61–76.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher, & J. Kilpatric (Eds.), Mathematics and cognition (pp. 70–95). Cambridge: Cambridge University Press.
  • Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.
  • Işıkksal-Bostan, M., & Yemen-Karpuzcu, S. (2017). The role of definitions on classification of solids including (non)prototype examples: The case of cylinder and prism. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (Vol.5, pp. 3320-3327), Dublin: CERME.
  • Koç, Y., & Bozkurt, A. (2011). Evaluating pre-service mathematics teachers’ comprehension level of geometric concepts. In B. Ubuz, (Ed.), The Proceedings of the 35th Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 335). Ankara, Turkey: PME.
  • Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study in children’s reasoning about space and geometry. In R. Lehrer, & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 351–367). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lowrie, T., & Clements, M. A. (2001). Visual and nonvisual processes in grade 6 students’ mathematical problem solving. Journal of Research in Childhood Education, 16, 77–93.
  • Markman, E. M., & Wachtel, G. F. (1988). Children's use of mutual exclusivity to constrain the meaning of words. Cognitive Psychology, 20(2), 121-157.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB Yayınları.
  • Monaghan, F. (2000). What difference does it make? Children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2),179-196.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics [NCTM]. (2007). Curriculum focal points for prekindergarten through grade 8 mathematics. Retrieved May 24, 2017 from www.nctm.org/standards/focalpoints
  • Okazaki, M. (1995). A study on growth of mathematical understanding based on the equilibration theory –an analysis of interviews on understanding “inclusion relations between geometrical figures. Research in Mathematics Education, 1, 45–54.
  • Okazaki, M., & Fujita, T. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In H. Woo, K. Park, & D. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol.4, pp. 41–48). Seoul: PME.
  • Posner, M. I., & Keele, S. W. (1968). On the genesis of abstract ideas. Journal of Experimental Psychology, 77, 353–363.
  • Post, T. R., Harel, G., Behr, M. J., & Lesh, R. (1991). Intermediate teachers’ knowledge of rational number concepts. In E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 194–217). Albany: State University of New York Press.
  • Presmeg, N. C. (2001). Visualization and affect in nonroutine problem solving. Mathematical Thinking and Learning, 3(4), 289–313.
  • Reed, S. K. (1972). Pattern recognition and categorization. Cognitive Psychology, 3, 382–407.
  • Rosch, E. (1973). Natural categories. Cognitive Psychology, 4, 328–350.
  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • 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.
  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69, 81–95.
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM, 47(3), 497–509.
  • Türnüklü, E. (2014). Construction of inclusion relations of quadrilaterals: Analysis of pre-service elementary mathematics teachers’ lesson plans. Education and Science, 39(173), 198–208.
  • 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.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Education, Inc.
  • Van Dormolen, J., & Zaslavsky, O. (2003). The many facets of a definition: The case of periodicity. Journal of Mathematical Behavior, 22(1), 91–106.
  • Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14, 293–305. Vinner, S. (2011). The role of examples in the learning of mathematics and in everyday thought processes. ZDM, 43(2), 247–256.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356–366.
  • Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the Fourth International Conference for the Psychology of Mathematics Education (Vol.1, pp. 177–184). Berkeley: University of California, Lawrence Hall of Science.
  • Walcott, C., Mohr, D., & Katsberg, S. E. (2009). Making sense of shape: An analysis of children’s written responses. The Journal of Mathematical Behavior, 28, 30-40.
  • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Erlbaum.
  • Wheatley, G. H. (1997). Reasoning with images in mathematical activity. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 281–298). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Wilson, P. S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics, 12, 31–47.
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayınevi.
  • Zaslavsky, O., & Peled, I. (1996). Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation. Journal for Research in Mathematics Education, 27(1), 67–78.
  • Zeybek, Z. (2018). Understanding inclusion relations between quadrilaterals. International Journal of Research in Education and Science (IJRES), 4(2), 595-612.
  • Zilkova, K. (2015). Misconceptions in pre-service primary education teachers about quadrilaterals. Journal of Education, Psychology and Social Sciences, 3(1), 30–37.

İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi

Year 2019, Volume: 10 Issue: 3, 680 - 710, 13.12.2019

Zülfiye Zeybek Şimşek

https://doi.org/10.16949/turkbilmat.491564

Abstract

Geometri öğrenciler için
sadece uzamsal düşünme yeteneklerini geliştirici bir araç değil, aynı zamanda
onların sorgulama, muhakeme ve ispat yeteneklerini geliştirmek için önemli
fırsatlar sunan bir öğrenme alanıdır. Güncel eğitim reformları,  öğrencilerin geometrik şekil ve cisimleri
tanıma ve özelliklerinin farkında olma becerilerinin yanı sıra, geometrik
şekilleri ve cisimleri ilişkilendirme becerilerini de erken sınıf
seviyelerinden itibaren kazanması gerektiğine vurgu yaparlar. Bu çalışmada, matematik
öğretmeni adaylarının geometrik kavramları (dörtgenler ve geometrik
cisimler)  tanıma ve bu kavramlar
arasında ilişkilendirme yapabilme düzeyleri incelenmiştir. Bu amaç çerçevesinde
araştırmacı tarafından geniş bir literatür taraması sonucunda geliştirilen 10
açık-uçlu sorudan oluşan bir geometri testi kullanılmıştır. Öğretmen
adaylarının teste verdikleri cevapların ön incelemesi sonucunda farklı düşünme
seviyelerine sahip olduğu düşünülen beş öğretmen adayı ile bireysel görüşmeler
yapılmıştır. Çalışmanın bulguları öğretmen adaylarının büyük çoğunluğunun
dörtgenlerin arasındaki hiyerarşik sınıflandırmayı tam olarak
algılayamadıklarını gösterir niteliktedir. Ayrıca bu çalışma, öğretmen
adaylarının geometrik cisimleri tanıma ve örnekler seçmede genel olarak
prototip yargıyı kullandıklarını ve prototip olmayan örnekleri seçmediklerini
kanıtlar niteliktedir.   Öğretmen
adayları geometrik cisimler arasında yanlış ilişkilendirmeler kurmaları da bu
çalışmanın bir diğer bulgusunu oluşturmaktadır. Çalışmanın bulguları
literatürde yer alan diğer çalmamalar ve eğitim reformları önerileri ışığında
tartışılmıştır.

Keywords

Dörtgenler geometri geometrik cisimler

References

  • Altneave, F. (1957). Transfer of experience with a class schema to identification of patterns and shapes. Journal of Experimental Psychology, 54, 81–88.
  • 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.
  • Bingolbali, E., & Monaghan, J. (2008). Concept image revisited. Educational Studies in Mathematics, 68(1), 19-35.
  • Bozkurt, A., & Koç, Y. (2012). İlköğretim matematik öğretmenliği birinci sınıf öğrencilerinin prizma kavramına dair bilgilerinin incelenmesi. Kuram ve Uygulamada Eğitim Bilimleri, 12(4), 2941-2952.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2010). Bilimsel araştırma yöntemleri. Ankara: Pegem Yayıncılık.
  • Clements, D. H. (2003). Teaching and learning geometry. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), Research companion to principles and standards for school mathematics (pp. 15–78). Reston, VA: National Council of Teachers of Mathematics.
  • De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14, 11-18.
  • Erez, M. M., & Yerushalmy, M. (2006). ‘‘If you can turn a rectangle into a square, you can turn a square into a rectangle ...’’ young students experience. International Journal of Computers for Mathematical Learning, 11, 271–299.
  • Ergin, A. S., & Türnüklü, E. (2015). Ortaokul öğrencilerinin cisim imgelerinin incelenmesi: Geometrik ve uzamsal düşünme ile ilişkiler. Eğitim ve Öğretim Araştırmaları Dergisi, 4(2), 188-199.
  • Fischbein, E. (1993). The theory of figural concept. Educational Studies in Mathematics, 24(2), 139-162.
  • Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31, 60–72.
  • Fujita, T., & Jones, K. (2006). Primary trainee teachers’ understanding of basic geometrical figures in Scotland. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education (Vol.3, pp. 129–136). Prague: PME.
  • Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Toward a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
  • Gökbulut, Y. (2010). Sınıf öğretmeni adaylarının geometrik cisimler konusundaki pedagojik alan bilgileri (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
  • Gökbulut, Y., & Ubuz, B. (2013). Prospective primary teachers’ knowledge on prism: Generating definitions and examples. Elementary Education Online, 12(2), 401-412.
  • Gökkurt, B. (2014). Ortaokul matematik öğretmenlerinin geometrik cisimler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi (Yayınlanmamış doktora tezi). Atatürk Üniversitesi, Eğitim Bilimleri Enstitüsü, Erzurum.
  • Gökkurt, B., Şahin, Ö. Başıbüyük, K., Erdem, E., & Soylu, Y (2014, Mayıs). Öğretmen adaylarının koni kavramına ilişkin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi. 13. Matematik Sempozyumu’nda sunulan bildiri, Karabük Üniversitesi, Karabük.
  • Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Öğretmen adaylarının geometrik cisimler konusuna ilişkin öğrenci hatalarına yönelik pedagojik alan bilgileri. İlköğretim Online, 14(1), 55-71.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
  • Hershkowitz, R. (1989). Visualization in geometry – two sides of the coin. Focus Learn Probl Math, 11(1), 61–76.
  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher, & J. Kilpatric (Eds.), Mathematics and cognition (pp. 70–95). Cambridge: Cambridge University Press.
  • Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371-406.
  • Işıkksal-Bostan, M., & Yemen-Karpuzcu, S. (2017). The role of definitions on classification of solids including (non)prototype examples: The case of cylinder and prism. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (Vol.5, pp. 3320-3327), Dublin: CERME.
  • Koç, Y., & Bozkurt, A. (2011). Evaluating pre-service mathematics teachers’ comprehension level of geometric concepts. In B. Ubuz, (Ed.), The Proceedings of the 35th Annual Meeting of the International Group for the Psychology of Mathematics Education (Vol.2, pp. 335). Ankara, Turkey: PME.
  • Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study in children’s reasoning about space and geometry. In R. Lehrer, & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 351–367). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Lowrie, T., & Clements, M. A. (2001). Visual and nonvisual processes in grade 6 students’ mathematical problem solving. Journal of Research in Childhood Education, 16, 77–93.
  • Markman, E. M., & Wachtel, G. F. (1988). Children's use of mutual exclusivity to constrain the meaning of words. Cognitive Psychology, 20(2), 121-157.
  • Milli Eğitim Bakanlığı [MEB]. (2018). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: MEB Yayınları.
  • Monaghan, F. (2000). What difference does it make? Children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2),179-196.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • National Council of Teachers of Mathematics [NCTM]. (2007). Curriculum focal points for prekindergarten through grade 8 mathematics. Retrieved May 24, 2017 from www.nctm.org/standards/focalpoints
  • Okazaki, M. (1995). A study on growth of mathematical understanding based on the equilibration theory –an analysis of interviews on understanding “inclusion relations between geometrical figures. Research in Mathematics Education, 1, 45–54.
  • Okazaki, M., & Fujita, T. (2007). Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In H. Woo, K. Park, & D. Seo (Eds.), Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol.4, pp. 41–48). Seoul: PME.
  • Posner, M. I., & Keele, S. W. (1968). On the genesis of abstract ideas. Journal of Experimental Psychology, 77, 353–363.
  • Post, T. R., Harel, G., Behr, M. J., & Lesh, R. (1991). Intermediate teachers’ knowledge of rational number concepts. In E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 194–217). Albany: State University of New York Press.
  • Presmeg, N. C. (2001). Visualization and affect in nonroutine problem solving. Mathematical Thinking and Learning, 3(4), 289–313.
  • Reed, S. K. (1972). Pattern recognition and categorization. Cognitive Psychology, 3, 382–407.
  • Rosch, E. (1973). Natural categories. Cognitive Psychology, 4, 328–350.
  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • 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.
  • Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69, 81–95.
  • Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: Triangles, circles, and cylinders. ZDM, 47(3), 497–509.
  • Türnüklü, E. (2014). Construction of inclusion relations of quadrilaterals: Analysis of pre-service elementary mathematics teachers’ lesson plans. Education and Science, 39(173), 198–208.
  • 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.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Education, Inc.
  • Van Dormolen, J., & Zaslavsky, O. (2003). The many facets of a definition: The case of periodicity. Journal of Mathematical Behavior, 22(1), 91–106.
  • Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14, 293–305. Vinner, S. (2011). The role of examples in the learning of mathematics and in everyday thought processes. ZDM, 43(2), 247–256.
  • Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356–366.
  • Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Ed.), Proceedings of the Fourth International Conference for the Psychology of Mathematics Education (Vol.1, pp. 177–184). Berkeley: University of California, Lawrence Hall of Science.
  • Walcott, C., Mohr, D., & Katsberg, S. E. (2009). Making sense of shape: An analysis of children’s written responses. The Journal of Mathematical Behavior, 28, 30-40.
  • Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah, NJ: Erlbaum.
  • Wheatley, G. H. (1997). Reasoning with images in mathematical activity. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 281–298). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Wilson, P. S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics, 12, 31–47.
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayınevi.
  • Zaslavsky, O., & Peled, I. (1996). Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation. Journal for Research in Mathematics Education, 27(1), 67–78.
  • Zeybek, Z. (2018). Understanding inclusion relations between quadrilaterals. International Journal of Research in Education and Science (IJRES), 4(2), 595-612.
  • Zilkova, K. (2015). Misconceptions in pre-service primary education teachers about quadrilaterals. Journal of Education, Psychology and Social Sciences, 3(1), 30–37.
There are 57 citations in total.

Details

Primary Language Turkish
Journal Section Research Articles
Authors

Zülfiye Zeybek Şimşek

Publication Date December 13, 2019
Published in Issue Year 2019 Volume: 10 Issue: 3

Cite

APA Zeybek Şimşek, Z. (2019). İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(3), 680-710. https://doi.org/10.16949/turkbilmat.491564
AMA Zeybek Şimşek Z. İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). December 2019;10(3):680-710. doi:10.16949/turkbilmat.491564
Chicago Zeybek Şimşek, Zülfiye. “İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler Ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10, no. 3 (December 2019): 680-710. https://doi.org/10.16949/turkbilmat.491564.
EndNote Zeybek Şimşek Z (December 1, 2019) İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10 3 680–710.
IEEE Z. Zeybek Şimşek, “İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 10, no. 3, pp. 680–710, 2019, doi: 10.16949/turkbilmat.491564.
ISNAD Zeybek Şimşek, Zülfiye. “İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler Ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10/3 (December 2019), 680-710. https://doi.org/10.16949/turkbilmat.491564.
JAMA Zeybek Şimşek Z. İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019;10:680–710.
MLA Zeybek Şimşek, Zülfiye. “İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler Ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 10, no. 3, 2019, pp. 680-1, doi:10.16949/turkbilmat.491564.
Vancouver Zeybek Şimşek Z. İlköğretim Matematik Öğretmeni Adaylarının Dörtgenler ve Geometrik Cisimleri Hiyerarşik Sınıflandırma Düzeylerinin İncelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2019;10(3):680-71.