PROSPECTIVE MIDDLE SCHOOL MATHEMATICS TEACHERS’ USE OF PARAMETERS IN EXPLAINING GEOMETRIC TRANSFORMATIONS
Abstract
National and international curriculum documents give emphasize on
geometric transformations. In particular, parameters of geometric
transformations play crucial role in defining geometric transformations. Thus, it
needs to be explored to what extent prospective teachers use parameters in explaining
geometric transformations. In this study, qualitative case study methodology
was used and participants were sixteen prospective middle school mathematics
teachers enrolled in a teacher education program in Turkey. To reveal
prospective teachers’ use of parameters in explaining geometric
transformations, a transformation geometry activity was designed and
implemented. During the implementation of activity, classroom observations were
carried out. The classroom observations focused on participants’ small group
discussions and whole class discussions surrounding geometric transformation
concepts. Moreover, implementation of the activity was audio-taped and
video-taped. Participants’ use of parameters was revealed by using written
materials and participants’ explanations during the whole class discussions. The
findings showed none of the pairs provided totally correct explanations for
geometric transformations. They had partial understanding about the parameters
of rotation. Even worse, one of the pairs held incorrect ideas about
identification of the angle of rotation.
Keywords
Parameters of geometric transformations prospective teachers reflection line angle of rotation center of rotation
References
- Battista, M. T. (2001). Shape makers: A computer environment that engenders students’ construction of geometric ideas and reasoning. Computers in Schools, 17, 105-120.
- Clements, D. H., & Battista, M. T. (1992). Geometry and spatial understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-465). New York: McMillan Publishing Company.
- Edwards, L. D. (1997). Exploring the territory before proof: Students’ generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2, 187-215.
- Farmer, D. W. (1996). Groups and symmetry: A guide to discovering mathematics. Providence: American Mathematical Society.
- Harper, S. (2003). Enhancing elementary pre-service teachers’ knowledge of geometric transformations through the use of dynamic geometry computer software. In C. Crawford, N. Davis, J. Price, R. Weber, & D. Willis (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference (pp. 2909-2916). Chesapeake, VA: Association for the Advancement of Computing in Education.
- Hegarty, M., & Waller, D. (2005). Individual differences in spatial abilities. In P. Shah & A. Miyake (Eds.), The Cambridge handbook of visuospatial thinking (pp. 121–169). New York: Cambridge University Press.
- Hollebrands, K. F. (2004). High school students’ intuitive understandings of geometric transformations. Mathematics Teacher, 97, 207-214.
- Leong Y. H., & Lim-Teo S. K. (2003). Effects of Geometer’s Sketchpad on spatial ability and achievement in transformation geometry among secondary two students in Singapore. The Mathematics Educator, 7(1), 32-48.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
- Portnoy, N., Grundmeier, T. A., & Graham, J. G. (2006). Students’ understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs. Journal of Mathematical Behavior, 25, 196-207.
- Ramful, A., Ho, S. Y., & Lowrie, T. (2015). Visual and analytical strategies in spatial visualization: Perspectives from bilateral symmetry and reflection. Mathematics Education Research Journal, 27, 443-470.
- Thaqi, X., Gimenez, J., & Rosich, N. (2011). Geometrical transformation as viewed by prospective teachers. In Pytlak, M., Rowland, T., & Swoboda, E. (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 578-587). Univerity of Rszeszów, Poland.
- Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2016). Elementary and middle school mathematics: Teaching developmentally (9th ed.). New York, NY: Pearson Education.
- Yanık, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78(2), 231-260.
- Yanık, H. B. (2014). Middle-school students’ concept images of geometric translations. The Journal of Mathematical Behavior, 36(1), 33-50.
PROSPECTIVE MIDDLE SCHOOL MATHEMATICS TEACHERS’ USE OF PARAMETERS IN EXPLAINING GEOMETRIC TRANSFORMATIONS
Abstract
National and international curriculum documents give emphasis to geometric transformations. In particular, parameters of geometric transformations play crucial role in defining geometric transformations. Thus, it needs to be explored to what extent prospective teachers use parameters in explaining geometric transformations. In this study, qualitative case study methodology was used and participants were sixteen prospective middle school mathematics teachers enrolled in a teacher education program in Turkey. To reveal prospective teachers’, use of parameters in explaining geometric transformations, a transformation geometry activity was designed and implemented. During the implementation of the activity, classroom observations were carried out. The classroom observations focused on participants’ small group discussions and whole class discussions regarding geometric transformation concepts. Moreover, implementation of the activity was audio-taped and video-taped. Participants’ use of parameters was revealed by using written materials and participants’ explanations during the whole class
discussions. The findings showed that none of the pairs provided totally correct explanations for geometric transformations. They had partial understanding about the parameters of rotation. Moreover, one of the pairs held incorrect ideas about identification of the angle of rotation.
Keywords
Parameters of geometric transformations prospective teachers reflection line angle of rotation center of rotation
References
- Battista, M. T. (2001). Shape makers: A computer environment that engenders students’ construction of geometric ideas and reasoning. Computers in Schools, 17, 105-120.
- Clements, D. H., & Battista, M. T. (1992). Geometry and spatial understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-465). New York: McMillan Publishing Company.
- Edwards, L. D. (1997). Exploring the territory before proof: Students’ generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2, 187-215.
- Farmer, D. W. (1996). Groups and symmetry: A guide to discovering mathematics. Providence: American Mathematical Society.
- Harper, S. (2003). Enhancing elementary pre-service teachers’ knowledge of geometric transformations through the use of dynamic geometry computer software. In C. Crawford, N. Davis, J. Price, R. Weber, & D. Willis (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference (pp. 2909-2916). Chesapeake, VA: Association for the Advancement of Computing in Education.
- Hegarty, M., & Waller, D. (2005). Individual differences in spatial abilities. In P. Shah & A. Miyake (Eds.), The Cambridge handbook of visuospatial thinking (pp. 121–169). New York: Cambridge University Press.
- Hollebrands, K. F. (2004). High school students’ intuitive understandings of geometric transformations. Mathematics Teacher, 97, 207-214.
- Leong Y. H., & Lim-Teo S. K. (2003). Effects of Geometer’s Sketchpad on spatial ability and achievement in transformation geometry among secondary two students in Singapore. The Mathematics Educator, 7(1), 32-48.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
- Portnoy, N., Grundmeier, T. A., & Graham, J. G. (2006). Students’ understanding of mathematical objects in the context of transformational geometry: Implications for constructing and understanding proofs. Journal of Mathematical Behavior, 25, 196-207.
- Ramful, A., Ho, S. Y., & Lowrie, T. (2015). Visual and analytical strategies in spatial visualization: Perspectives from bilateral symmetry and reflection. Mathematics Education Research Journal, 27, 443-470.
- Thaqi, X., Gimenez, J., & Rosich, N. (2011). Geometrical transformation as viewed by prospective teachers. In Pytlak, M., Rowland, T., & Swoboda, E. (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 578-587). Univerity of Rszeszów, Poland.
- Van de Walle, J. A., Karp, K. S., & Williams, J. M. B. (2016). Elementary and middle school mathematics: Teaching developmentally (9th ed.). New York, NY: Pearson Education.
- Yanık, H. B. (2011). Prospective middle school mathematics teachers’ preconceptions of geometric translations. Educational Studies in Mathematics, 78(2), 231-260.
- Yanık, H. B. (2014). Middle-school students’ concept images of geometric translations. The Journal of Mathematical Behavior, 36(1), 33-50.
Details
| Primary Language | English |
|---|---|
| Subjects | Studies on Education |
| Journal Section | Online First |
| Authors | |
| Publication Date | June 30, 2019 |
| Submission Date | January 30, 2019 |
| Published in Issue | Year 2019Volume: 4 Issue: 1 |
Dear Colleagues,
We are very pleased to announce that the latest issue of IHEAD (Vol. 9- Iss. 1) has been released. We kindly want to express our speacial thanks to the editorial board members, reviewers, and authors for their invaluable contribution to this issue. Also, we are delighted to announce that the next issue (Vol. 9- Iss. 2) of the IHEAD will be available online in December, 2024. As of January, 2024, IHEAD has been accepting submissions in English along with Turkish. Handling your papers within the scope education for the next issue will be a great pleasure for us. Many thanks in advance for your contributions.
Editorial Board
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