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Van Hiele Düzey Numaralandırmaları ve Düzey İsimlendirmelerine Eleştirel Bir Bakış

Year 2022, Volume: 23 Issue: Özel Sayı, 287 - 329, 26.03.2022

Abstract

Yaygın olarak kullanılan ve geometri eğitimini yönlendiren van Hiele teorisini, 1957 yılında Dina van Hiele ve Pierre van Hiele çifti ortaya koymuştur. Van Hiele çiftine göre geometrik düşünme düzeyleri hiyerarşik ve sıralı olan beş düzeyden oluşmaktadır. Alanyazında mevcut olan çalışmalar incelendiğinde, bu düzeyler için farklı numaralandırma ve isimlendirmelerin kullanıldığı görülmektedir. Bu araştırmada, Türkçe ve İngilizce alanyazında yer alan çalışmalarda kullanılan van Hiele düzey numaralandırmalarını ve düzeylere verilen isimlendirmelerdeki benzerlik ve farklılıkların ortaya çıkarılması amaçlanmıştır. Bu kapsamda Türkçe (80) ve İngilizce (46) alanyazında toplam 126 çalışma belirlenmiştir. Araştırmada elde edilen veriler sonucunda Türkçe çalışmaların büyük bir kısmının 1-5; İngilizce çalışmaların ise 0-4 şeklinde numaralandırıldığı tespit edilmiştir. Aynı zamanda düzeylere verilen isimlerde de çok fazla farklılık görülmüştür. En sık kullanılan düzey adlarının; Türkçe isimlendirmelerde sırasıyla “Görsel Dönem”, “Analiz”, “Yaşantıya Bağlı Çıkarım”, “Çıkarım” ve “En İleri Dönem” iken; İngilizce isimlendirmelerde “Visualization”, “Analysis”, “Informal Deduction”, “Deduction” ve 5. Düzey için “Rigor” şeklinde olduğu görülmektedir. Bu araştırmanın, van Hiele geometrik düşünme düzeylerine verilecek Türkçe isimlendirmeler için bir standart oluşturulması yolunda önemli katkılar sağlayacağı düşünülmektedir.

References

  • Alex, J. K. & Mammen, K. J. (2016). Lessons learnt from employing van Hiele theory based instruction in senior secondary school geometry classrooms. EURASIA Journal of Mathematics, Science and Technology Education, 12(8), 2223-2236. https://doi.org/10.12973/eurasia.2016.1228a
  • Altun, M. (2015). Eğitim fakülteleri ve sınıf öğretmenleri için matematik öğretimi (19. Baskı) [Teaching mathematics for education faculties and classroom teachers (19th ed)]. Bursa: Alfa Aktüel.
  • Baah-Duodu, S., Osei-Buabeng, V., Cornelius, E. F., Hegan, J. E., & Nabie, M. J. (2020). Review of literature on teaching and learning geometry and measurement: a case of ghanaian standards based mathematics curriculum. International Journal of Advances in Scientific Research and Engineering (IJASRE), 6(3), 103-123. https://doi.org/10.31695/IJASRE.2020.33766
  • Baki, A. (2019). Matematiği öğretme bilgisi (2. Baskı) [Knowledge of teaching mathematics (2nd ed)]. Ankara: Pegem Publications.
  • Bashiru, A., & Nyarko, J. (2019). Van hiele geometric thinking levels of junior high school students of atebubu municipality in Ghana. African Journal of Educational Studies in Mathematics and Sciences, 15(1), 39-50. https://dx.doi.org/10.4314/ajesms.v15i1.4
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Charlotte, NC: Information Age.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi [Teaching mathematics in secondary school]. Ankara: Pegem Publications.
  • Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 31-48. https://doi.org/10.5951/jresematheduc.17.1.0031
  • Cathcart, G. W., Pothier, Y. M., & Vance, J. H. (2000). Learning Mathematics in Elementary and Middle Schools (3nd ed). Scarborough, ON: Prentice Hall Allyn and Bacon.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (p. 420–464). Macmillan Publishing Co, Inc.
  • Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children's concepts of shape. Journal for Research in Mathematics Education, 30(2), 192-212.
  • Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Learning and teaching geometry, K-12, 1-16.
  • Curcio, F. R. (1986). Structure and insight: A theory of mathematics education (L, P) by Pierre M. van Hiele.
  • Çepni, S. (2018). Araştırma ve proje çalışmalarına giriş (8. Baskı) [Introduction to research and project studies (8th ed)]. Trabzon: Celepler Publications.
  • Çoruk, F., Büyük- Güler, S., ve Kayalı, Y. (2016). Çeviride kültürel aktarım sorunu: karamazov kardeşler örneği [Cultural transmıssıon problems ın translatıon: the case of the brothers karamazov]. Uluslararası Sosyal Araştırmalar Dergisi [Journal of International Social Research], 9(42).
  • Duatepe- Paksu, A. (2016). Van Hiele geometrik düşünme düzeyleri [Van Hiele geometric thinking levels]. In Bingölbali, E., Özarslan, S., & Zembat İ. Ö. (Ed.), Matematik eğitiminde teoriler [Theories in mathematics education] (p. 266-275). Ankara: Pegem Academy.
  • Fuys, D. (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447-462. https://doi.org/10.1177/0013124585017004008
  • Fuys, D., Geddes, D., & Tischler (1988). The van Hiele model of thinking in geometry among adolescents [monograph number 3]. Journal for Research in Mathematics Education. Reston, VA: NCTM. https://doi.org/10.2307/749957
  • Gray, E. (1999). Spatial strategies and visualization. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME Conference (s.235-242). Haifa, Israel: Israel Institute of Technology.
  • Guillen, G. (1996). Identification of Van Hiele levels of reasoning in three-dimensional geometry. In O. Puig & L. Gutierrez, (Eds.), Proceedings of 20th PME International Conference (s.43-50). Valencia, Spain: University of Valencia.
  • Gutierrez, A. (1992). Exploring the links between Van Hiele levels and 3-dimensional geometry. Structural Topology 18, 31-48. http://hdl.handle.net/2099/1073
  • Hoffer, A. (1981). Geometry is more than proff. Mathematics Teacher, 74(1), 11-18. https://doi.org/10.5951/MT.74.1.0011
  • Lawrie, C., Pegg, J., & Gutierrez, A. (2000). Coding the nature of thinking displayed in responses on nets of solids. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME Conference (s.215-222). Hiroshima, Japan: Hiroshima University.
  • Lawrie, C., Pegg, J., & Gutierrez, A. (2002). Unpacking students meaning of cross-sections: A frame for curriculum development. In Cockburn, A. D., Nardi, E. (Edt.) Proceedings of the 26th PME Conference.
  • Mason, M. (2009). The van Hiele levels of geometric understanding. Colección Digital Eudoxus, 1(2).
  • Mayberry, J. (1983). The Van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for Research in Mathematics Education, 14(1), 58- 69. https://doi.org/10.5951/jresematheduc.14.1.0058
  • Owens, K. (1999). The role of visualization in young students’ learning. In O. Zaslavsky (Eds.), Proceedings of the 23rd PME Conference (s.220-234). Haifa, Israel: Israel Institute of Technology.
  • Olivero, F. (2002). The proving process with in a dynamic geometry environment. (Unpublished doctoral dissertation). Bristol, UK: University of Bristol, Graduate School of Education. https://telearn.archives-ouvertes.fr/hal-00190412
  • Pegg, J. (1992). Students’ understanding of geometry: theoretical perspectives. In: Southwell, B., Perry, B. and Owens, K. (eds), Space: The First And Final Frontier, Proceedings Of The 15th Conference Of The Mathematics Education Research Group Of Australasia. Sydney: MERGA.
  • Saads, S., & Davis, G. (1997). Spatial abilities, van Hiele levels and language use in three dimensional geometry. In Erkki Pehkonen (Edt.), Proceedings of the 21th PME Conference (s.104-111). Lahti, Finland: University of Helsinki. http://www.leeds.ac.uk/educol/documents/000000143.htm
  • Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 309-321. https://doi.org/10.5951/jresematheduc.20.3.0309
  • Teppo, A. (1991). Van Hiele levels of geometric thought revisited. The Mathematics Teacher, 84(3), 210-221. https://doi.org/10.5951/MT.84.3.0210
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. Final report of the cognitive development and achievement in secondary school geometry project, University of Chicago, Department of Education.
  • Van Hiele, P. M. (1959). The child’s thought and geometry. English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele, 243-252. http://geometryandmeasurement.pbworks.com/f/VanHiele.pdf
  • Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 310-316. https://doi.org/10.5951/TCM.5.6.0310
  • Van de Walle, J.A. (2004). Elemantary and middle school mathematics (Fifth Edition). Virginia Common Wealth University.
  • Vojkuvkova, I. (2012). The van Hiele model of geometric thinking. WDS’12 Proceedings of Contributed Papers, 1, 72-75. https://www.mff.cuni.cz/veda/konference/wds/proc/pdf12/WDS12_112_m8_Vojkuvkova.pdf

A Critical Overview of Van Hiele Level Numberings and Level Nomenclatures

Year 2022, Volume: 23 Issue: Özel Sayı, 287 - 329, 26.03.2022

Abstract

The widely used van Hiele theory, which guides geometry education, was introduced by Dina van Hiele and Pierre van Hiele in 1957. According to the Van Hiele couple, geometric thinking levels consist of five levels that are hierarchical and sequential. When the studies available in the literature are examined, it is seen that different numbering and naming are used for these levels. In this study, it was aimed to reveal the similarities and differences in the van Hiele level numbering and the naming given to the levels used in the studies in Turkish and English literature. In this context, 126 studies were identified in Turkish (80) and English (46) literature. As a result of the research data, most of the Turkish studies are 1-5; It was determined that English studies are numbered 0-4. There was also a lot of difference in the names given to the levels. The most preferred level names in Turkish for the 5th level are "Görsel Dönem", "Analiz", "Yaşantıya Bağlı Çıkarım", "Çıkarım" and "En İleri Dönem", on the other hand, it is seen that the names in English are "Visualization", "Analysis", "Informal Deduction", "Deduction" and "Rigor". It is thought that this research will make a significant contribution to the creation of a standard for the Turkish nomenclature to be given to van Hiele's geometric thinking levels.

References

  • Alex, J. K. & Mammen, K. J. (2016). Lessons learnt from employing van Hiele theory based instruction in senior secondary school geometry classrooms. EURASIA Journal of Mathematics, Science and Technology Education, 12(8), 2223-2236. https://doi.org/10.12973/eurasia.2016.1228a
  • Altun, M. (2015). Eğitim fakülteleri ve sınıf öğretmenleri için matematik öğretimi (19. Baskı) [Teaching mathematics for education faculties and classroom teachers (19th ed)]. Bursa: Alfa Aktüel.
  • Baah-Duodu, S., Osei-Buabeng, V., Cornelius, E. F., Hegan, J. E., & Nabie, M. J. (2020). Review of literature on teaching and learning geometry and measurement: a case of ghanaian standards based mathematics curriculum. International Journal of Advances in Scientific Research and Engineering (IJASRE), 6(3), 103-123. https://doi.org/10.31695/IJASRE.2020.33766
  • Baki, A. (2019). Matematiği öğretme bilgisi (2. Baskı) [Knowledge of teaching mathematics (2nd ed)]. Ankara: Pegem Publications.
  • Bashiru, A., & Nyarko, J. (2019). Van hiele geometric thinking levels of junior high school students of atebubu municipality in Ghana. African Journal of Educational Studies in Mathematics and Sciences, 15(1), 39-50. https://dx.doi.org/10.4314/ajesms.v15i1.4
  • Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). Charlotte, NC: Information Age.
  • Baykul, Y. (2014). Ortaokulda matematik öğretimi [Teaching mathematics in secondary school]. Ankara: Pegem Publications.
  • Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 31-48. https://doi.org/10.5951/jresematheduc.17.1.0031
  • Cathcart, G. W., Pothier, Y. M., & Vance, J. H. (2000). Learning Mathematics in Elementary and Middle Schools (3nd ed). Scarborough, ON: Prentice Hall Allyn and Bacon.
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (p. 420–464). Macmillan Publishing Co, Inc.
  • Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children's concepts of shape. Journal for Research in Mathematics Education, 30(2), 192-212.
  • Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Learning and teaching geometry, K-12, 1-16.
  • Curcio, F. R. (1986). Structure and insight: A theory of mathematics education (L, P) by Pierre M. van Hiele.
  • Çepni, S. (2018). Araştırma ve proje çalışmalarına giriş (8. Baskı) [Introduction to research and project studies (8th ed)]. Trabzon: Celepler Publications.
  • Çoruk, F., Büyük- Güler, S., ve Kayalı, Y. (2016). Çeviride kültürel aktarım sorunu: karamazov kardeşler örneği [Cultural transmıssıon problems ın translatıon: the case of the brothers karamazov]. Uluslararası Sosyal Araştırmalar Dergisi [Journal of International Social Research], 9(42).
  • Duatepe- Paksu, A. (2016). Van Hiele geometrik düşünme düzeyleri [Van Hiele geometric thinking levels]. In Bingölbali, E., Özarslan, S., & Zembat İ. Ö. (Ed.), Matematik eğitiminde teoriler [Theories in mathematics education] (p. 266-275). Ankara: Pegem Academy.
  • Fuys, D. (1985). Van Hiele levels of thinking in geometry. Education and Urban Society, 17(4), 447-462. https://doi.org/10.1177/0013124585017004008
  • Fuys, D., Geddes, D., & Tischler (1988). The van Hiele model of thinking in geometry among adolescents [monograph number 3]. Journal for Research in Mathematics Education. Reston, VA: NCTM. https://doi.org/10.2307/749957
  • Gray, E. (1999). Spatial strategies and visualization. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME Conference (s.235-242). Haifa, Israel: Israel Institute of Technology.
  • Guillen, G. (1996). Identification of Van Hiele levels of reasoning in three-dimensional geometry. In O. Puig & L. Gutierrez, (Eds.), Proceedings of 20th PME International Conference (s.43-50). Valencia, Spain: University of Valencia.
  • Gutierrez, A. (1992). Exploring the links between Van Hiele levels and 3-dimensional geometry. Structural Topology 18, 31-48. http://hdl.handle.net/2099/1073
  • Hoffer, A. (1981). Geometry is more than proff. Mathematics Teacher, 74(1), 11-18. https://doi.org/10.5951/MT.74.1.0011
  • Lawrie, C., Pegg, J., & Gutierrez, A. (2000). Coding the nature of thinking displayed in responses on nets of solids. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th PME Conference (s.215-222). Hiroshima, Japan: Hiroshima University.
  • Lawrie, C., Pegg, J., & Gutierrez, A. (2002). Unpacking students meaning of cross-sections: A frame for curriculum development. In Cockburn, A. D., Nardi, E. (Edt.) Proceedings of the 26th PME Conference.
  • Mason, M. (2009). The van Hiele levels of geometric understanding. Colección Digital Eudoxus, 1(2).
  • Mayberry, J. (1983). The Van Hiele levels of geometric thought in undergraduate preservice teachers. Journal for Research in Mathematics Education, 14(1), 58- 69. https://doi.org/10.5951/jresematheduc.14.1.0058
  • Owens, K. (1999). The role of visualization in young students’ learning. In O. Zaslavsky (Eds.), Proceedings of the 23rd PME Conference (s.220-234). Haifa, Israel: Israel Institute of Technology.
  • Olivero, F. (2002). The proving process with in a dynamic geometry environment. (Unpublished doctoral dissertation). Bristol, UK: University of Bristol, Graduate School of Education. https://telearn.archives-ouvertes.fr/hal-00190412
  • Pegg, J. (1992). Students’ understanding of geometry: theoretical perspectives. In: Southwell, B., Perry, B. and Owens, K. (eds), Space: The First And Final Frontier, Proceedings Of The 15th Conference Of The Mathematics Education Research Group Of Australasia. Sydney: MERGA.
  • Saads, S., & Davis, G. (1997). Spatial abilities, van Hiele levels and language use in three dimensional geometry. In Erkki Pehkonen (Edt.), Proceedings of the 21th PME Conference (s.104-111). Lahti, Finland: University of Helsinki. http://www.leeds.ac.uk/educol/documents/000000143.htm
  • Senk, S. L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 309-321. https://doi.org/10.5951/jresematheduc.20.3.0309
  • Teppo, A. (1991). Van Hiele levels of geometric thought revisited. The Mathematics Teacher, 84(3), 210-221. https://doi.org/10.5951/MT.84.3.0210
  • Usiskin, Z. (1982). Van Hiele levels and achievement in secondary school geometry. Final report of the cognitive development and achievement in secondary school geometry project, University of Chicago, Department of Education.
  • Van Hiele, P. M. (1959). The child’s thought and geometry. English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele, 243-252. http://geometryandmeasurement.pbworks.com/f/VanHiele.pdf
  • Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 310-316. https://doi.org/10.5951/TCM.5.6.0310
  • Van de Walle, J.A. (2004). Elemantary and middle school mathematics (Fifth Edition). Virginia Common Wealth University.
  • Vojkuvkova, I. (2012). The van Hiele model of geometric thinking. WDS’12 Proceedings of Contributed Papers, 1, 72-75. https://www.mff.cuni.cz/veda/konference/wds/proc/pdf12/WDS12_112_m8_Vojkuvkova.pdf
There are 37 citations in total.

Details

Primary Language Turkish
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Gül Kaleli Yılmaz 0000-0002-8567-3639

Hülya Sert Çelik 0000-0002-5021-7449

Publication Date March 26, 2022
Published in Issue Year 2022 Volume: 23 Issue: Özel Sayı

Cite

APA Kaleli Yılmaz, G., & Sert Çelik, H. (2022). Van Hiele Düzey Numaralandırmaları ve Düzey İsimlendirmelerine Eleştirel Bir Bakış. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 23(Özel Sayı), 287-329. https://doi.org/10.29299/kefad.908248

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