Young Children's Conceptual Understanding of Triangle

Ümmühan Yeşil Dağlı; Erdoğan Halat

doi:10.12973/eurasia.2016.1398a

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Ümmühan Yeşil Dağlı ¹ ^* , Erdoğan Halat ²

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¹ Yildiz Technical University, TURKEY² Afyon Kocatepe University, TURKEY^* Corresponding Author

Abstract

This study explored 5-6 year-old children's conceptual understanding of one geometric shape, the triangle. It focused on whether children could draw a triangle from memory, and identify triangles of different types, sizes, and orientations. The data were collected from 82 children attending state preschool programs through a one-on-one interview, during which children completed five paper-pencil tasks. Findings showed that the majority of the children (93%-96%) successfully identified a prototyped triangle. Approximately half of the children experienced difficulties in identifying triangles of different sizes, types, and orientations. The most difficult area was identifying types of triangles, where an isosceles triangle and a right triangle were presented, followed by identifying triangles in different orientations, specifically flipped and rotated ones. Children appeared to identify and classify the triangle relying on the visual prototype. These findings provide support for the Prototyped Theory, van Hiele theory, and for works by Clement and colleagues.

Keywords

conceptual understanding of triangle
young children
prototype theory
van Hiele

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2016, Volume 12, Issue 2, 189-202

https://doi.org/10.12973/eurasia.2016.1398a

Publication date: 17 Jun 2016

Article Views: 3896

Article Downloads: 3870

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References

Alisinanoğlu, F., & Bay, N. (2007, Eylül). Okul Öncesi Eğitim Programlarının Tarihsel Gelişimi. XVI. Ulusal Eğitim Bilimleri Kongresi. Tokat. Retrieved October 24, 2014 from http://www.pegem.net/akademi/kongrebildiri_detay.aspx?id=5773
Antell, S., & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Development, 54, 695-701.
Bodovski, K., & Farkas, G. (2007). Mathematics growth in early elementary school: The roles of beginning knowledge, student engagement, and instruction. The Elementary School Journal, 108(2), 115-130. http://dx.doi.org/10.1086/525550
Boonen, A. J. H., Kolkman, M. E., & Kroesbergen, E. H. (2011). The relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms. Journal of School Psychology, 49, 281-299. doi:10.1016/j.jsp.2011.03.002
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31-48.
Casey, M. B., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26(3), 269-309. doi:10.1080/07370000802177177
Clements, D. H., &Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-64). New York, NY: 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. (2001). Mathematics in the preschool. Teaching Children Mathematics, 7, 270- 275.
Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements, Sarama, & A. M. Dibiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp.7-72). Mahwah, NJ: Erlbaum.
Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In J. F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461-555). New York: Information Age Publishing.
Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a researchbased preschool mathematics curriculum. American Educational Research Journal, 45, 443-494.
Clements, D. H., & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333(6045), 968-970. doi:10.1126/science.1204537.
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.
Cross, T. C., Woods, T. A., & Schweingruber, H. (Eds.). (2009). Mathematics learning in early childhood: Paths towards excellence and equity. Washington, DC: National Academies Press.
Denton, K., & West, J. (2002). Children’s reading and mathematics achievement in kindergarten and first grade. Washington, DC: National Center for Education Statistics. NCES 2002-125. Retrieved from http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2002125
Duncan, G., Dowsett, C., Claessens, A., Magnuson, K., Huston, A., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. http://dx.doi.org/10.1037/0012-1649.43.6.1428
Finnish National Board of Education (2010). National Core Curriculum for Pre-primary Education. Retrieved from http://www.oph.fi/download/153504_national_core_curriculum_for_preprimary_education_2010.pdf
Gagatsis, A., & Patronis, T. (1990). Using geometrical models in a process of reflective thinking in learning and teaching mathematics. Educational Studies in Mathematics, 21, 29-54.
Gal, H., & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Education Studies in Mathematics, 74, 163–183.
Geist, E. (2009). Children are born mathematicians: Supporting mathematical development, birth to age 8. Upper Saddle River, NJ: Pearson.
Gelişli, Y. & Yazıcı, E. (2012).Türkiye`de Uygulanan Okul Öncesi Eğitim Programlarının Tarihsel Süreç İçerisinde Değerlendirilmesi. Gazi Üniversitesi Endüstriyel Sanatlar Eğitim Fakültesi Dergisi, 29, 85-93. from http://esefdergi.gazi.edu.tr/makaleler/290.pdf
Hachey, A. C. (2013). The early childhood mathematics education revolution. Early Education & Development, 24(4), 419-430. doi: 10.1080/10409289.2013.777286
Halat, E. (2006). Sex-related differences in the acquisition of the van Hiele levels and motivation in learning geometry. Asia Pacific Education Review, 7(2), 173-183.
Halat, E. (2007). Reform-based curriculum & acquisition of the levels. Eurasia Journal of Mathematics, Science and Technology Education, 3(1), 41-49.
Halat, E. (2008). In-service middle and high school mathematics teachers: Geometric reasoning stages and gender. The Mathematics Educator, 18 (1), 8-14.
Hannibal, M. A. Z. (1999). Young children's developing understanding of geometric shapes. Teaching Children Mathematics, 5(6), 353-357.
Hershkowitz, R. (1987). The acquisition of concepts and misconceptions in basic geometry— Or when “a little learning is a dangerous thing.”. In J. D. Novak (Ed.), Proceedings of the second international seminar on Misconceptions and Educational Strategies in Science and Mathematics, vol. 3 (pp. 236–251). Ithaca, NY: Cornell University.
Hershkowitz, R. (1989). Visualization in geometry: Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61-76.
Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850-867. doi:10.1016/j.lindif.2009.07.004
Mason, M. M. (1989, March). Geometric understanding and misconceptions among gifted fourth-eighth graders. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA. ED 310922
National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM) [NAEYC/NCTM]. (2002). Early childhood mathematics: Promoting good beginnings. Washington, DC:
National Association for the Education of Young Children National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards for School Mathematics. Math Standards and Expectations: Geometry Strand. Retrieved from http://www.nctm.org/standards/content.aspx?id=314
National Governors Association Center for Best Practices, Council of Chief State School Officers. Common Core State Standards (Mathematics Content Standards: Geometry). Washington D.C. Copyright Date: 2010. Retrieved from http://www.corestandards.org/Math/Content/K/G/
National Ministry of Education [Milli Egitim Bakanligi; MEB]. (2013).Turkish Preschool Education Program (Okul Öncesi Eğitim Programı). Ankara. Retrieved from http://tegm.meb.gov.tr/dosya/okuloncesi/ooproram.pdf
Oberdorf, C. D., & Taylor-Cox, J. (1999). Shape up! Teaching Children Mathematics, 5, 340-345.
Rosch, E. H. (1973). Natural categories. Cognitive Psychology, 4, 328–350.
Smith, S. S. (2006). Early childhood mathematics (3rd Ed.), Boston, MA: Pearson Education.
Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical abstraction by human infants. Cognition, 36, 97-128.
United Kingdom Department for Education (2013).National curriculum in England Mathematics programmes of study: key stages 1 and 2. Retrieved from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/335 158/PRIMARY_national_curriculum_-_Mathematics_220714.pdf
van Hiele, P. M. (1959/1985). The child’s thought and geometry. In D. Fuys, D. Geddes, & R. Tishchler (Eds.), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243–252). ERIC/SMEAC.
van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. New York: Academic Press.
van Hiele, P. M. (1999). Developing geometrical thinking through activities that begin with play. Teaching Children Mathematics, 6, 310-316.
Walcott, C., Mohrb, D., & Kastberg, S. E. (2009). Making sense of shape: An analysis of children’s written responses. Journal of Mathematical Behavior, 28, 30-40. doi:10.1016/j.jmathb.2009.04.001
Wynn, K. (1992). Evidence against empiricist accounts of origins of numerical knowledge. Mind and Language, 7, 315-332.
Zur, O., & Gelman, R. (2004). Young children can add and subtract by predicting and checking. Early Childhood Quarterly Review, 19, 121-137. doi:10.1016/j.ecresq.2004.01.003

How to cite this article

APA

Dağlı, Ü. Y., & Halat, E. (2016). Young Children's Conceptual Understanding of Triangle. Eurasia Journal of Mathematics, Science and Technology Education, 12(2), 189-202. https://doi.org/10.12973/eurasia.2016.1398a

Vancouver

Dağlı ÜY, Halat E. Young Children's Conceptual Understanding of Triangle. EURASIA J Math Sci Tech Ed. 2016;12(2):189-202. https://doi.org/10.12973/eurasia.2016.1398a

AMA

Dağlı ÜY, Halat E. Young Children's Conceptual Understanding of Triangle. EURASIA J Math Sci Tech Ed. 2016;12(2), 189-202. https://doi.org/10.12973/eurasia.2016.1398a

Chicago

Dağlı, Ümmühan Yeşil, and Erdoğan Halat. "Young Children's Conceptual Understanding of Triangle". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 2 (2016): 189-202. https://doi.org/10.12973/eurasia.2016.1398a

Harvard

Dağlı, Ü. Y., and Halat, E. (2016). Young Children's Conceptual Understanding of Triangle. Eurasia Journal of Mathematics, Science and Technology Education, 12(2), pp. 189-202. https://doi.org/10.12973/eurasia.2016.1398a

MLA

Dağlı, Ümmühan Yeşil et al. "Young Children's Conceptual Understanding of Triangle". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 2, 2016, pp. 189-202. https://doi.org/10.12973/eurasia.2016.1398a