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LEARNING TO UNDERSTAND INCLUSION RELATIONS OF QUADRILATERALS

Year 2017, Volume: 6 , 9 - 13, 04.08.2017

Abstract

Learning to identify geometric shapes and
understand inclusive properties among these shapes is prerequisite for learning
more complex concepts such as spatial reasoning or deductive thinking. Despite
the importance of understanding geometric shapes and inclusion relations among
these shapes, it has evidenced that pre-service teachers’ subject knowledge of
geometry is amongst their weakest knowledge of mathematics.This study aimed to
investigate pre-service mathematics teachers’ (PSMT), who are going to teach
middle grade mathematics (grade 5-8), understanding of inclusion relationships
of quadrilaterals. A designed questionnaire was administered to 52 PSMTs at the
beginning of the semester and again by the end of the semester. The findings of
this study demonstrated that the majority of the PSMTs struggled with
identifying quadrilaterals and especially inclusion relations of quadrilaterals
primarily. The majority of them held static view of quadrilaterals which
inhibited their understanding of inclusion relations of quadrilaterals.
However, the number of the PSMTs who understood hierarchical relationship
between quadrilaterals increased through the end of the semester.

References

  • Archavsky, N., & Goldenberg, P. (2005). Perceptions of a quadrilateral in a dynamic environment. In D. Carraher, & R. Nemirovsky (Eds.), Medium and meaning: video papers in mathematics education research, Journal of Research in Mathematics Education Monograph XIII[CD-ROM]. Reston, VA: National Council of Teachers of Mathematics 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. 420–464). New York, NY: MacMillan. De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11–18. 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 (pp. 129-136). Prague: PME. Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1, 2), 3–20. Glaser, B. G., & Strauss, A. L. (1967). Discovery of grounded theory. MillValley, CA: Sociology Press. Hershkowitz, R. (1989). Visualization in geometry: Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61–76. Jones, K. (2000). Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1/2), 55-85 Kaur, H. (2015). Two aspects of young children’s thinking about different types of dynamic triangles: prototypicality and inclusion. ZDM Mathematics Education, 47, 407-420. Patton, M. Q. (1990).Qualitative evaluation and research methods (2nd ed.). Newbury Park, CA: Sage Publications, Inc. Walcott, C., Mohr, D., & Kastberg, S. E. (2009). Making sense of shape: An analysis of children’s written responses. The Journal of Mathematical Behavior, 28, 30-40. Zilkova, K. (2015). Misconceptions in pre-service primary education teachers about quadrilaterals. Journal of Education, Psychology and Social Sciences, 3(1), 30-37.
Year 2017, Volume: 6 , 9 - 13, 04.08.2017

Abstract

References

  • Archavsky, N., & Goldenberg, P. (2005). Perceptions of a quadrilateral in a dynamic environment. In D. Carraher, & R. Nemirovsky (Eds.), Medium and meaning: video papers in mathematics education research, Journal of Research in Mathematics Education Monograph XIII[CD-ROM]. Reston, VA: National Council of Teachers of Mathematics 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. 420–464). New York, NY: MacMillan. De Villiers, M. (1994). The role and function of a hierarchical classification of quadrilaterals. For the Learning of Mathematics, 14(1), 11–18. 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 (pp. 129-136). Prague: PME. Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1, 2), 3–20. Glaser, B. G., & Strauss, A. L. (1967). Discovery of grounded theory. MillValley, CA: Sociology Press. Hershkowitz, R. (1989). Visualization in geometry: Two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61–76. Jones, K. (2000). Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1/2), 55-85 Kaur, H. (2015). Two aspects of young children’s thinking about different types of dynamic triangles: prototypicality and inclusion. ZDM Mathematics Education, 47, 407-420. Patton, M. Q. (1990).Qualitative evaluation and research methods (2nd ed.). Newbury Park, CA: Sage Publications, Inc. Walcott, C., Mohr, D., & Kastberg, S. E. (2009). Making sense of shape: An analysis of children’s written responses. The Journal of Mathematical Behavior, 28, 30-40. Zilkova, K. (2015). Misconceptions in pre-service primary education teachers about quadrilaterals. Journal of Education, Psychology and Social Sciences, 3(1), 30-37.
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Details

Journal Section Articles
Authors

Zulfiye Zeybek This is me

Publication Date August 4, 2017
Published in Issue Year 2017 Volume: 6

Cite

APA Zeybek, Z. (2017). LEARNING TO UNDERSTAND INCLUSION RELATIONS OF QUADRILATERALS. The Eurasia Proceedings of Educational and Social Sciences, 6, 9-13.