Research in Mathematical Education (한국수학교육학회지시리즈D:수학교육연구)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

Prospective Teachers' Competency in Teaching how to Compare Geometric Figures: The Concept of Congruent Triangles as an Example

  • Leung, K.C. Issic (Department of Mathematics and Information Technology, Hong Kong Institute of Education) ;
  • Ding, Lin (Department of Mathematics and Information Technology, Hong Kong Institute of Education) ;
  • Leung, Allen Yuk Lun (Department of Education Study, Hong Kong Baptist University) ;
  • Wong, Ngai Ying (Department of Curriculum and Instruction, Faculty of Education, Chinese University of Hong Kong)
  • Received : 2014.02.11
  • Accepted : 2014.09.25
  • Published : 2014.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (CDC & HKEAA, 2007, page 15). Ironically, student performance during routine assessments on geometric reasoning, such as proving geometric propositions and justifying geometric properties, is far below teacher expectations. One might argue that this is caused by teachers' lack of relevant subject content knowledge. However, recent research findings have revealed that teachers' knowledge of teaching (e.g., Ball et al., 2009) and their deductive reasoning skills also play a crucial role in student learning. Prior to a comprehensive investigation on teacher competency, we use a case study to investigate teachers' knowledge competency on how to teach their students to mathematically argue that, for example, two triangles are congruent. Deductive reasoning skill is essential to geometry. The initial findings indicate that both subject and pedagogical content knowledge are essential for effectively teaching this challenging topic. We conclude our study by suggesting a method that teachers can use to further improve their teaching effectiveness.

Keywords

References

  1. Ball, D. (2005). Effects of teachers mathematical knowledge for teaching on student achievement. American Educational Research Journal 42(2), 371-406. https://doi.org/10.3102/00028312042002371
  2. Ball, D. L.; Sleep, L.; Boerst, T. A. & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. Elementary School Journal 109(5), 458-474. https://doi.org/10.1086/596996
  3. Barlow, A. T. & Reddish, J. M. (2006). Mathematical myths: Teacher candidates' beliefs and the implication for teacher educators. Teacher Educator 41(3), 145-157. https://doi.org/10.1080/08878730609555380
  4. Brown, M., Jones, K., & Taylor, R. (2003). Developing geometrical reasoning in the secondary school: Outcomes of trialling teaching activities in classrooms (a report to the QCA). London, U. K.: Qualifications and Curriculum Authority (QCA).
  5. Buchholtz, N.; Leung, F.; Ding, L.; Kaiser, G.; Park, K. & Schwarz, B. (2013). Future mathematics teachers' professional knowledge of elementary mathematics from an advanced standpoint. ZDM, Int. J. Math. Educ. 45(1), 107-120. ME 2013c.00123 https://doi.org/10.1007/s11858-012-0462-6
  6. Curriculum Development Council, Hong Kong & Hong Kong Examinations and Assessment Authority (CDC & HKEAA) (2007). Mathematics education key learning area: mathematics curriculum and assessment guide (Secondary 4-6), Hong Kong: Government Printer. Retrieved from:http://334.edb.hkedcity.net/doc/eng/curriculum/Math%20C&A%20Guide_updated_e.pdf
  7. Dreyfus, T. (1999). Why Johnny can't prove. Educational studies in mathematics 38(1-3), 85-109. ME 2000d.02330 https://doi.org/10.1023/A:1003660018579
  8. Fujita, T., Jones, K., & Yamamoto, S. (2004a). Geometrical intuition and the learning and teaching of geometry. Paper presented at the Topic Group on Research and Development in the Teaching and Learning of Geometry, 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark.
  9. Fujita, T., Jones, K., & Yamamoto, S. (2004b). The role of intuition in geometry education: Learning from the teaching practice in the early 20th Century. Paper presented at the Topic Group on the History of the Teaching and the Learning of Mathematics, 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark.
  10. Hill, H. C.; Ball, D. L. & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. J. Res. Math. Educ. 39(4), 372-400. ME 2009d.00095
  11. Jones, K. (1998). Theoretical frameworks for the learning of geometrical reasoning. In: Proceedings of the British Society for Research into Learning Mathematics, 18(1&2) (pp. 29-34). London, U.K.: British Society for Research into Learning Mathematics. http://eprints.soton.ac.uk/41308/1/Jones_BSRLM_18_1998.pdf
  12. Jones, K. & Bills, C. (1998). Visualisation, imagery and the development of geometrical rasoning. In: Proceedings of the British Society for Research into Learning Mathematics, 18(1&2) (pp. 123-128). Birmingham, U.K.: British Society for Research into Learning Mathematics. http://eprints.soton.ac.uk/41306/1/Jones_Bills_BSRLM_18_1998.pdf
  13. Jones, K. & Mooney, C. (2003). Making space for geometry in primary mathematics. In: I. Thompson (Ed.), Enhancing primary mathematics teaching and learning (pp. 3-15). London, U.K.: Open University Press. ME 2003f.04977
  14. Leung, K. C. I.; Ding, L.; Leung, A. Y. L. & Wong, N. Y. (2014). Prospective Teachers' Competency in Teaching how to Compare Geometric Figures: The Concept of Congruent Triangles as an Example. In: H. J. Hwang, S.-G. Lee, Y. H. Choe, (Eds.), Proceedings of the KSME 2014 Spring Conference on Mathematics Education held at Hankuk Univ. of Foreign Studies, Seoul 130-791, Korea; April 4-5, 2014 (pp. 545-558). Seoul, Korea: Korean Society of Mathematical Education.
  15. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ, USA: Lawrence Erlbaum Associates. ME 1999d.02835
  16. Mayer, R. E. (2003), The promise of multimedia learning: Using the same instructional design methods across different media. Learning and Instruction 13, 125-139. https://doi.org/10.1016/S0959-4752(02)00016-6
  17. Piaget, J. & Inhelder, B (1967). The child's conception of geometry. New York. W.W. Norton & Co.
  18. Potarri, D.; Zachariades, T. & Zaslavaky, O. (2009). Mathematics teachers' reasoning for refuting students' invalid claims. In: Proceedings of CERME (pp. 281-290). Lyon, France:
  19. Seufert, T. (2003). Supporting coherence formation in learning from multiple representations. Learning and Instruction 13(2), 227-237. https://doi.org/10.1016/S0959-4752(02)00022-1
  20. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher 57(1), 1-22.
  21. Tapan, M. S. (2009). Preserivce teachers' use of spatio-visual elements and their level of justification dealing with a geometrical construction problem. US-China Education Review 6(3), 54-60.
  22. Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement to middle grades mathematics. Educ. Stud. Math. 76(2), 141-164. ME 2011b.00269 https://doi.org/10.1007/s10649-010-9269-y
  23. Vermunt, J. D. (2007). The Power of teaching-learning environments to influent student learning. In: Entwistle, N. and Tomlinson, P. (eds.), Student Learning and University Teaching. British Journal of Educational Psychological Society Monograph Series II, Number 4 (pp.73-90). Leicester, UK: British Psychological Society.
  24. Wong. N. Y. & Su, S. D. (1995). Universal education and teacher preparation: The new challenge of mathematics teachers in the changing times. In: G. Bell (Ed.), Review of mathematics education in Asia and the Pacific (pp. 137-142). Lismore, Australia: Southern Cross Mathematical Association. ME 1997b.00803