Abstract
Geometric shapes are one of the primary subjects in mathematics education during early childhood Even before entering formal schooling children will have some basic information about geometric shapes through their everyday experiences Some of this early information about geometric shapes might be erroneous which might negatively impact children’s further understanding of geometric shapes For that reason exploring how children recognize and classify geometric shapes and the criteria they use for classification is critical in determining the content of early mathematics education Van Hiele’s theory about the development of geometrical thinking is regarded as one of the basis theories concerning children’s classification of geometric shapes However recently there seems to be some arguments put forward claiming that van Hiele’s theory is insufficient in explaining development of geometric thinking in early childhood Thus this study was conducted to determine 3 to 6 year old preschoolers’ and primary 1st grade and 4th grade students’ recognition levels of geometric shapes and the criteria they use to distinguish one group of shape from the other To this end individual interviews were conducted with 150 children Four classification tasks triangle rectangle square and circle were used in this study as data collection tool The data collection tool used in this study was developed by the researchers based on the previous studies Each classification task consisted of classifying 12 shapes which were outlined on an A4 size paper Results of the study revealed that while young children were successful in recognizing typical examples of the geometric shapes they were not successful enough in recognizing the atypical examples such as shapes with different size orientation aspect ratio skewness It was also determined that younger children were paying attention mostly to visual attributes of the shapes in the process of classification In contrast older children were found to pay attention both to visual and property attributes or only to property attributes Thus results of the present study hand support to recent criticism of van Hiele’s theory Key Words: Early childhood mathematics geometry classification of geometric shapes
References
- Aktas, Y. (2002). Okul öncesi dönemde matematik [mathematics education in preschool]. Adana: Nobel Tıp Kitapevi.
- Altun, M. (1997). Eğitim fakülteleri ve sınıf öğretmenleri icin matematik öğretimi [Mathematics education for school of education and elementary teachers]. Bursa: Erkam Matbaacılık.
- Aktas Arnas, Y. & Aslan, D. (2004). '3-6 yas grubu cocuklarda geometrik düsüncenin gelisimi' [the development of geometrical thinking in 3 to 6 years old children group]. Paper presented at the meeting of the 1stInternational Pre-School Education Conference, İstanbul, Turkey.
- Bennie, K. (1998). 'An analysis of the geometric understanding of grade 9 pupils using Fuys Et al’s Interpretation of the van Hiele model'. Available at http://academic.sun.ac.za/mathed/MALATI/Files/Geo981.pdf (accessed 29 November 2004).
- Burger, W.F. & Shaughnessy J.M. (1986). 'Characterizing the van Hiele levels of development in geometry'. Journal for Research in Mathematics Education, 17(1), 31-48.
- Calıkoglu Bali, G. & Boz, M. (2004). Cocuklarda Geometrik Algılama [Children’s Geometric Perception]. In G.Haktanır & T.Güler (Eds.), OMEP World Council and Conference.
- Clements, D. H., & Battista, M.T. (1992). 'Geometry and spatial reasoning', in D.A.
- İstanbul:Ya-Pa Yayıncılık. Grouws (Ed.), Handbook of research on mathematics teaching and learning, pp.420-464. New York: Macmillan.
- Clements, D. H. (1999). 'Geometric and spatial thinking in young children', in J. V Copley (Ed.), Mathematics in the early years, pp. 66-79. Reston, VA: National Council of Teachers of Mathematics.
- 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, 192-212.
- Copeland, R.W. (1974). How children learn mathematics: teaching implications of Piaget's rese. New York: Macmillan.
- Calıkoğlu Bali, G. & Boz, M. (2003). 'Cocuklarda geometrik algılama' [Children’s geometric perception], in G.Haktanır & T.Güler (Eds.), OMEP World Council and Conference, vol.3, pp.393-410. İstanbul: Ya-Pa Yayıncılık.
- De Villers M. (1996). 'Some developments in geometry education'. Available at http://www.didactique.imag.fr/preuve/Resumes/deVilliers/deVilliers98/deVilliers9 8.html (accessed 29 November 2004).
- Dodwell, P.C. (1963). 'Children understanding of spatial concepts: Piaget’s theory'. Canadian Journal of Psychology, 17(1), 141-143.
- Hannibal, M.A.Z. (1999). 'Young children’s developing understanding of geometric shapes'. Teaching Children Mathematics, 5 (6), 353-358.
- Hannibal, M.A.Z. & Clements D.H. (2000). 'Young children’s understanding of basic geometric shapes'. National Science Foundation, Grant Number: ESI-8954644.
- Jami, A. & Gutierrez, A. (1994). 'A model of test design to assess the van Hiele levels' Proceedings of the 18PME conference. 3:41-48. Lisboa. th
- Kellough, R.D., Carin, A.A., Seefeldt, C., Barbour, N. & Souviney, R.J. (1996). Integrating mathematics and science for kindergarten and primary children. Columbus Ohio: Merrill Publishing Company.
- Piaget, J., & Inhelder, B. (1967). The child's conception of space. New York: W. W. Norton
- Satlow, E. & Newcombe, N. (1998). When is a triangle not triangle? Young children's
- developing concepts of geometric shapes. Cognitive Development, 13, 547 - 559
- Schultz, K., Colarusso, R. & Strawderman, V. (1989). Mathematics for every young
- child New York: Merrill.
- van Hiele, P. M. (1986). Structure and insight: a theory of mathematics education. Orlando: Academic Press.
- van Hiele, P.M. (1999). 'Developing geometric thinking through activities that begin with play'. Teaching Children Mathematics, 5(6): 310-316. Appendix 1- Triangle- classification task TD1 T1 T2 TD2 TD3 T3 TD4 TD5 T4 T5 T6
Abstract
Geometrik şekiller erken çocukluk döneminde matematik eğitiminin temel konularından
biridir. Çocuklar günlük yaşamlarındaki deneyimler aracılığıyla, formal eğitime
başlamadan önce de geometrik şekillerle ilgili bir takım informal bilgilere sahip
olabilmektedirler. Bu dönemde edinilen bilgilerin bir kısmı yanlış olabilmekte ve bu
yanlış bilgiler çocukların ileriki geometri eğitimlerini olumsuz yönde
etkileyebilmektedir. Bu nedenle de, çocukların geometrik şekilleri ne kadar tanıyıp
sınıflandırabildiklerinin ve sınıflandırmada kullandıkları kriterlerin neler olduğunun
incelenmesi, okul öncesi dönemde verilecek matematik eğitimin içeriğinin belirlenmesi
açısından son derece önemlidir. Geometrik düşüncenin gelişimi ile ilgili olan Van Hiele
teorisi, çocukların geometrik şekilleri sınıflandırması ile ilgili temel teorilerden biri
olarak kabul edilmektedir. Öte yandan, van Hiele teorisinin erken çocukluk döneminde
geometrik düşüncenin gelişimini açıklamada yetersiz kaldığına son dönemlerde bir
takım iddialar bulunmaktadır. Bu nedenle, bu araştırma okul öncesi dönem 3- 6 yaş
çocuklarının ve ilköğretim 1. ve 4.sınıf öğrencilerinin geometrik şekilleri tanıması ve
şekilleri bir birinden ayırt ederken kullandıkları kriterleri belirlemek amacıyla
gerçekleştirilmiştir. Bu amaçla 150 çocukla bireysel görüşmeler gerçekleştirilmiştir.
Veri toplama aracı olarak dört tane sınıflama testi kullanılmıştır (üçgen, dikdörtgen,
kare ve daire sınıflama testi). Veri toplama aracı, önceki araştırmalar temel alınarak
araştırmacılar tarafından geliştirilmiştir. Her bir sınıflama testi, A4 kâğıdı üzerine
yerleştirilmiş 12 tane şekilden meydana gelmektedir. Araştırmanın sonuçları, küçük
çocukların geometrik şekillerin tipik örneklerini tanımada başarılıyken, tipik olmayan
örneklerini (örneğin, farklı boyut, konum ve basıklıktaki şekiller) tanımada yeterince
başarılı olmadıklarını ortaya koymaktadır. Aynı zamanda, küçük çocukların sınıflama
işlemi sırasında çoğunlukla şekillerin görsel özelliklerine dikkat ettikleri belirlenmiştir.
Bunun aksine, daha büyük yaştaki çocukların ya hem görsel hem de niteliksel
özelliklere ya da sadece niteliksel özelliklere dikkat ettikleri saptanmıştır. Böylece, bu
araştırmanın sonuçları van Hiele teorisine yönelik son dönemdeki iddiaları
desteklemektedir.
References
- Aktas, Y. (2002). Okul öncesi dönemde matematik [mathematics education in preschool]. Adana: Nobel Tıp Kitapevi.
- Altun, M. (1997). Eğitim fakülteleri ve sınıf öğretmenleri icin matematik öğretimi [Mathematics education for school of education and elementary teachers]. Bursa: Erkam Matbaacılık.
- Aktas Arnas, Y. & Aslan, D. (2004). '3-6 yas grubu cocuklarda geometrik düsüncenin gelisimi' [the development of geometrical thinking in 3 to 6 years old children group]. Paper presented at the meeting of the 1stInternational Pre-School Education Conference, İstanbul, Turkey.
- Bennie, K. (1998). 'An analysis of the geometric understanding of grade 9 pupils using Fuys Et al’s Interpretation of the van Hiele model'. Available at http://academic.sun.ac.za/mathed/MALATI/Files/Geo981.pdf (accessed 29 November 2004).
- Burger, W.F. & Shaughnessy J.M. (1986). 'Characterizing the van Hiele levels of development in geometry'. Journal for Research in Mathematics Education, 17(1), 31-48.
- Calıkoglu Bali, G. & Boz, M. (2004). Cocuklarda Geometrik Algılama [Children’s Geometric Perception]. In G.Haktanır & T.Güler (Eds.), OMEP World Council and Conference.
- Clements, D. H., & Battista, M.T. (1992). 'Geometry and spatial reasoning', in D.A.
- İstanbul:Ya-Pa Yayıncılık. Grouws (Ed.), Handbook of research on mathematics teaching and learning, pp.420-464. New York: Macmillan.
- Clements, D. H. (1999). 'Geometric and spatial thinking in young children', in J. V Copley (Ed.), Mathematics in the early years, pp. 66-79. Reston, VA: National Council of Teachers of Mathematics.
- 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, 192-212.
- Copeland, R.W. (1974). How children learn mathematics: teaching implications of Piaget's rese. New York: Macmillan.
- Calıkoğlu Bali, G. & Boz, M. (2003). 'Cocuklarda geometrik algılama' [Children’s geometric perception], in G.Haktanır & T.Güler (Eds.), OMEP World Council and Conference, vol.3, pp.393-410. İstanbul: Ya-Pa Yayıncılık.
- De Villers M. (1996). 'Some developments in geometry education'. Available at http://www.didactique.imag.fr/preuve/Resumes/deVilliers/deVilliers98/deVilliers9 8.html (accessed 29 November 2004).
- Dodwell, P.C. (1963). 'Children understanding of spatial concepts: Piaget’s theory'. Canadian Journal of Psychology, 17(1), 141-143.
- Hannibal, M.A.Z. (1999). 'Young children’s developing understanding of geometric shapes'. Teaching Children Mathematics, 5 (6), 353-358.
- Hannibal, M.A.Z. & Clements D.H. (2000). 'Young children’s understanding of basic geometric shapes'. National Science Foundation, Grant Number: ESI-8954644.
- Jami, A. & Gutierrez, A. (1994). 'A model of test design to assess the van Hiele levels' Proceedings of the 18PME conference. 3:41-48. Lisboa. th
- Kellough, R.D., Carin, A.A., Seefeldt, C., Barbour, N. & Souviney, R.J. (1996). Integrating mathematics and science for kindergarten and primary children. Columbus Ohio: Merrill Publishing Company.
- Piaget, J., & Inhelder, B. (1967). The child's conception of space. New York: W. W. Norton
- Satlow, E. & Newcombe, N. (1998). When is a triangle not triangle? Young children's
- developing concepts of geometric shapes. Cognitive Development, 13, 547 - 559
- Schultz, K., Colarusso, R. & Strawderman, V. (1989). Mathematics for every young
- child New York: Merrill.
- van Hiele, P. M. (1986). Structure and insight: a theory of mathematics education. Orlando: Academic Press.
- van Hiele, P.M. (1999). 'Developing geometric thinking through activities that begin with play'. Teaching Children Mathematics, 5(6): 310-316. Appendix 1- Triangle- classification task TD1 T1 T2 TD2 TD3 T3 TD4 TD5 T4 T5 T6
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | March 1, 2010 |
| Submission Date | December 29, 2013 |
| Published in Issue | Year 2010 Volume: 19 Issue: 1 |