Research in Mathematical Education (한국수학교육학회지시리즈D:수학교육연구)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지

The Role of "Personal Knowledge" in Solid Geometry among Primary School Mathematics Teachers

  • Patkin, Dorit (Mathematical Education, lecturer at the Kibbutzim College of Education)
  • Received : 2010.07.14
  • Accepted : 2010.09.24
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.

Keywords

References

  1. Allen, R. M. & Casbergue, R. M. (1997). Evolution of Novice through Expert Teachers' Recall: Implications for Effective on Practice. Teaching and Teacher Education 7(13), 741-755. ERIC EJ556269
  2. Ben-Chaim, D.; Lappan, G. & Houang, R. T. (1989). Adolescents' ability to communicate spatial information: Analyzing and effecting students' performance. Educ. Stud. Math. 20(2), 121-146. ERIC EJ395739 ME 1990e.02958 https://doi.org/10.1007/BF00579459
  3. Calderhead, J. (). Reflective Teaching and Teacher Education. Teaching and Teacher Education 5(1),43-51. ERIC EJ395970 https://doi.org/10.1016/0742-051X(89)90018-8
  4. Caplan, P.; Crawford, M.; Hyde, J. & Richardson, J. T. (1997). Gender Differences in Human Cognition. New York: Oxford University Press. ERIC ED437187
  5. Clandinin, D. J. (1987). Personal Practical Knowledge: A Study of Teacher's Classroom Image, Calgary. University of Calgary. Curriculum Inquiry 15(4), 361-85 ERIC EJ327899
  6. Clandinin, D. J. & Connelly, F. M. (1996). Teachers' Professional Knowledge landscapes: Teachers stories- stories of teachers- school stories- stories of schools. Educational Researcher 19(2), 2-11. ERIC EJ 525455
  7. Colom, R.; Contreras, M. J.; Botella, J. & Santacreu, J. (2002). Vehicles of spatial ability. Personality and Individual Differences 32(5), 903-912. https://doi.org/10.1016/S0191-8869(01)00095-2
  8. Connelly, F. M. & Clandinin, D. J. (1991). Teachers as Curriculum Planners Narratives of Experience. New York, Teachers College Press. ERIC ED295928
  9. Connelly, F. M. & Diens, B. (1982). The teacher's role in curriculum studies. In: K. A. Leithwood (Ed.), Studies in Curriculum Decision-Making (pp. 183-198). Toronto, Canada: Ontario Inst. for Studies in Education.
  10. Creswell, J. W. (1998). Qualitative inquiry and Research design; choosing among five traditions. Thousands Oaks, CA: Sage Publication Ltd. ERIC ED500417
  11. Creswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed methods approaches. Thousand Oaks, CA: Sage Publication Ltd.
  12. Elbaz, F. L. (1983). Teacher Thinking: A Study of Practical Knowledge. London, Croom-Helm. ERIC ED224797
  13. Fuys, D. & Tischler, R. (1988). The Van-Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education Monograph Number 3. ERIC ED294770
  14. Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York: Basic Books.
  15. Gorn, L. (1977). 'Expert judgment as evaluation data'. In: Levy, A. (Ed.), Handbook of Curriculum Evaluation, UNESCO.
  16. Gutierrez, A.; Jaime, A. & Fortuny, J. (1991). An alternative paradigm to evaluate the acquisition of the van Hiele levels. J. Res. Math. Educ. 22(3), 237-251. ERIC EJ429213 ME 1992a.00854 https://doi.org/10.2307/749076
  17. Halat, E. & Sahin, O. (2008). Van-Hiele Levels of Pre- and In-Service Turkish Elementary School Teachers and Gender Related Difference in Geometry. The Mathematics Educator 11(112), 143-158.
  18. Halpern, F. D. (2005). Sex, Brains & Hands - Gender Differences in Cognitive Abilities. Skeptic 2(3),96-103.
  19. Kinach, B. M. (1998). Developing prospective teachers' pedagogical content knowledge in the secondary mathematics methods course. Paper presented at the Annual Meeting of the American Educational Research Association (AERA), San Diego, April 13-17, 1998.
  20. Knight, K. C. (2006). An investigation into the change in the Van-Hiele level of understanding geometry of pre-service elementary and secondary mathematics teachers. Unpublished masters' thesis, University of Maine, France.
  21. Linn, M. C. & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development 56(6), 1479-1498. ERIC E1328551 ME 1987d.12085 https://doi.org/10.2307/1130467
  22. Louden, W. (1992). 'Understanding Reflection through Collaboratory Research'. In: Hargreaves, A. & Fullen, M. G. (Eds.), Understanding Teacher Development, N. Y. Teacher College Press, Columbia University (pp. 178-215).
  23. Mason, M. M. (1997). The Van-Hiele model of geometric understanding and mathematically talented students. Journal for the Education of the Gifted 21(1), 39-53. ERIC EJ556932 ME 1998f.03913
  24. National Council of Teachers of Mathematics (NCTM) (1989). Curriculum and Evaluation Standards for School Mathematics. National Council of Teachers of Mathematics Reston, VA. (pp.48-50). ERIC ED304336 ME 1996f.03595
  25. National Council of Teachers of Mathematics (NCTM) (1992). Curriculum and Evaluation Standards for School Mathematics' Geometry in the Middle Grades, Addenda Series Grades 5- 8, (pp. 4-7). Reston, VA: National Council of Teachers of Mathematics.
  26. National Council of Teachers of Mathematics (NCTM) (1991). Professional Standards for Teaching Mathematics. National Council of Teachers of Mathematics, Reston, VA. ERIC ED344779 ME 1991e.00332
  27. National Council of Teachers of Mathematics (NCTM.) (2000): Principles and standards for school mathematics. Reston, VA: NCTM. ME 1999f.03937 for discussion draft (1998)
  28. Ross, D. D.; Bondy, E. & Kyle, D. W. (1993). Reflective Teachingfor Student Empowerment. N. Y. McMillan Publishing Co.
  29. Schön, D. A (1983). The Reflective Practitioner: How Professionals Think in Action. New York, Basic Books.
  30. Schön, D. A (1987). Educating the Reflective Practitioner. San Francisco, Joss-Bass Publishers.
  31. Shulman, L. S. (1987). Knowledge and Teaching: Foundation of the New Reform. Harvard Educational Review 57(1), 1-22. ERIC EJ351846
  32. Sorby, S. A; Wysocki, A. F. & Baartmans, B. G. (2002). Introduction to 3D Spatial Visualization. New York: Cengage Learning
  33. Van-Hiele, P. M. (1999). Developing Geometric Thinking through Activities That Begin With Play. Teaching Children Mathematics. 5(6), 310-318. ERIC EJ580493 ME 2000b.01169
  34. Zeichner, K. M. (1994). Research in teacher thinking and different views of reflective practice in teaching and teacher education. In: J. Carlgren, G. Handal & S. Vaage (Eds.), Teachers' mind and actions: Research on teachers' thinking and practice (pp. 9-27). London: The Falmer Press.
  35. Zeichner, K. M. & Liston, D. P. (1996). Reflective Teaching an Introduction. Lawrence Erlbaum Associates Publishers, N. J.