Research Article
Year 2019,
, 467 - 496, 23.01.2020
Abstract
Supporting Institution
TÜBİTAK/University of Massachusetts Dartmouth
References
- Bulf, C. (2010). The effects of the concept of symmetry on learning geometry at French secondary school. Proceedings of CERME, Volume 6 (pp. 726–735). Caspi, S., & Sfard, A. (2012). Spontaneous meta-arithmetic as a first step toward school algebra. International Journal of Educational Research, 51–52, 45–65. Clements, D. H., Battista, M. T., Sarama, J., and Swaminathan, S. (1997). Development of students’ spatial thinking in a unit on geometric motions and area. Elementary School Journal, 98(2), 171–186. Confrey, J. (1981). Using the clinical interview to explore student's mathematical understandings. The annual meeting of the American Educational Research Association kongresinde sunulmuş bildiri, Los Angeles. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage. DeJarnette, A. F., Gonzalez, G., Deal, J. T., & Rosado Lausell, S. (2016). Students’ conceptions of reflective symmetry: Opportunities for making connections with perpendicular bisector. Journal of Mathematical Behavior, 43, 35–52. Edwards, L. D. (2003). The nature of mathematics as viewed from cognitive science. Paper presented at the Third Conference of European Research in Mathematics Education, Bellaria, Italy. Emre-Akdoğan, E., Güçler, B., & Argün, Z. (2018). The development of two high school students’ discourses on geometric translation in relation to the teacher’s discourse in the classroom. Eurasia Journal of Mathematics, Science and Technology Education, 14(5), 1605-1619. Flanagan, K. A. (2001). High school students’ understandings of geometric transformations in the context of a technological environment. Doktora Tezi, The Pennsilvanya State University, Pennsilvanya. Güçler, B. (2016). Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning. Educational Studies in Mathematics, 91(3), 375-393. Güçler, B. (2016). Matematiksel Bilişe İletişimsel Yaklaşım. Editör: E. Bingölbali, S. Arslan ve İ. Ö. Zembat, Matematik Eğitiminde Teoriler (ss. 629-641). Ankara: Pegem. Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82(3), 439-453. Hacısalihoğlu-Karadeniz, M., Baran, T., Bozkuş, F. & Gündüz, N. (2015). İlköğretim matematik öğretmeni adaylarının yansıma simetrisi ile ilgili yaşadıkları zorluklar. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 6(1), 117-138. Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22, 55–72. Hollebrands, K. F. (2004). High school students’ intuitive understandings of geometric transformations. Mathematics Teacher, 97(3), 207–214. Hoyles, C., & Healy, L. (1997). Unfolding meanings for reflective symmetry. International Journal of Computer for Mathematical Learning, 2(1), 27-59. Jones, K. (2000). Critical issues in the design of the geometry curriculum. B. Barton (Ed), Readings in Mathematics Education. Auckland, New Zealand. Knuchel, C. (2004). Teaching symmetry in the elementary curriculum. The Montana Mathematics Enthusiast, 1(1), 3-8. Küchemann D. (1981). Reflection and rotation. In Hart K (Ed.) Children’s understanding of mathematics (pp. 137-157). London: John Murray. Lavie, I., Steiner, A., & Sfard, A. (2019). Routines we live by: From ritual to exploration. Educational Studies in Mathematics, 101(2), 153-176. Leikin, R., Berman, A., & Zaslavsky, O. (2000). Applications of symmetry to problem solving. International Journal of Mathematical Education in Science and Technology, 31(6), 799-809. Mhlolo, M. K., & Schäfer, M. (2014). Potential Gaps during the Transition from the Embodied through Symbolic to Formal Worlds of Reflective Symmetry. African Journal of Research in Mathematics, Science and Technology Education, 18 (2), 125-138. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: A sourcebook of new methods (2nd ed.). Thousand Oaks, CA: Sage. Milli Eğitim Bakanlığı (MEB). (2010). Talim ve Terbiye Kurulu Başkanlığı, Ortaöğretim geometri dersi (9-10.sınıflar) öğretim programı. Ankara: MEB. Milli Eğitim Bakanlığı (MEB). (2013). Talim ve Terbiye Kurulu Başkanlığı, Ortaöğretim matematik dersi (9.-12.sınıflar) öğretim programı. Ankara: MEB. Miyakawa, T. (2004). Reflective symmetry in constructions and proving. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th annual meeting ofthe international group for the psychology of mathematics education (Vol. 3) (pp. 337–344). National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA. Panaoura, A., Elia, I., Stamboulides, N., & Spyrou, P. (2009). Students' structure for the understanding of the axis of symmetry in mathematics. Acta Didactica Universitatis Comenianae Mathematics, 9, 41-62. Patton, M.Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage. Portnoy, N., Grundmeimer, T. A., & Graham, K. J. (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. Sfard, A. (2001). There is more to discourse than meets the ears: looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3) 13-57. Sfard, A. (2008). Thinking as Communicating: human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University. Sfard, A. (2012). Introduction: Developing mathematical discourse–Some insights from communicational research. International Journal of Educational Research, 51–52, 1–9. Son, J.-W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 11(1), 31–46. Son, J.-W. (2006). Investigating preservice teachers’ understanding and strategies on a student’s errors of reflective symmetry. In J. Novotná, H. Moraová,M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 5) (pp.145–152). Tatar, E., Akkaya, A. and Kağizmanli, T. B. (2014). Using dynamic software in mathematics: the case of reflection symmetry. International Journal of Mathematical Education in Science and Technology, 45 (7), 980-995. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University. Yanik, H. B. (2006). Prospective elementary teachers’ growth in knowledge and understanding of rigid geometric transformations. Doktora Tezi, Arizona State University, Arizona. Yin, R. K. (1994). Case study research: Designs and methods. Newbury Park, CA: Sage. Xistouri, X. (2007). Students' ability in solving line symmetry tasks. Paper presented at the meeting of Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, Department of Education, University of Cyprus, Cyprus. Xistouri, Χ., & Pitta-Pantazi, D. (2006). Spatial rotation and perspective taking abilities in relation to performance in reflective symmetry tasks. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 5, (pp. 425-432). Prague: PME.
Lise Öğrencilerinin Yansıma Dönüşümü Hakkındaki Matematiksel Söylemlerinin Öğretim Bağlamında Gelişimi
Abstract
Bu araştırmanın amacı, lise öğrencilerinin yansıma dönüşümü ile ilgili matematiksel söylemlerinin gelişimini ve söylem gelişiminin öğretimle olan ilişkisini ortaya koymaktır. Durum çalışması desenine sahip olan araştırmanın katılımcıları iki 10. sınıf öğrencisi ve bir öğretmendir. Araştırmanın verileri, öğretmen ve öğrencilerle yapılan görev temelli görüşmeler ve sınıf gözlemleri aracılığıyla sekiz haftada toplanmıştır. Verilerin analizi ise matematiksel bilişe iletişimsel yaklaşım teorisine göre yapılmıştır. Matematiksel bilişe iletişimsel yaklaşım teorisi bize öğretim ve öğrenme ile ilgili önemli perspektifler sunmuştur. Öğrencilerin yansıma dönüşümündeki söylemlerinin gelişiminin sınıfta öğretmenin kullandığı söylem ile karşılaştırmalı analizleri sonucunda, öğretmenin kullandığı söylemin, öğrencilerin söylemlerinin gelişimsel seviyesinin üstünde olduğu tespit edilmiştir. Ayrıca öğretmen ve öğrencilerin söylemleri arasında farklılıkların olduğu gözlemlenmiştir. Öğretmenin söylemlerinin açık ve anlaşılır olması durumunda öğrencilerin öğretmen söylemini kendilerine adapte edebildikleri, fakat öğretmenin söyleminde belli ögelerin üstünün örtük kaldığı durumlarda öğrencilerin söylemlerini öğretmenin söylemine adapte etmekte zorluk yaşadıkları ortaya çıkarılmıştır. Sınıf içerisindeki matematiksel iletişimi geliştirmek ve öğrencilerin söylemsel gelişimlerini desteklemek için öğretmenlerin, öğrencilerin söylemlerinin gelişimsel süreçlerinin farkında olması ve söylemlerini daha açık ve net bir hâle getirmeleri gerekmektedir.
References
- Bulf, C. (2010). The effects of the concept of symmetry on learning geometry at French secondary school. Proceedings of CERME, Volume 6 (pp. 726–735). Caspi, S., & Sfard, A. (2012). Spontaneous meta-arithmetic as a first step toward school algebra. International Journal of Educational Research, 51–52, 45–65. Clements, D. H., Battista, M. T., Sarama, J., and Swaminathan, S. (1997). Development of students’ spatial thinking in a unit on geometric motions and area. Elementary School Journal, 98(2), 171–186. Confrey, J. (1981). Using the clinical interview to explore student's mathematical understandings. The annual meeting of the American Educational Research Association kongresinde sunulmuş bildiri, Los Angeles. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage. DeJarnette, A. F., Gonzalez, G., Deal, J. T., & Rosado Lausell, S. (2016). Students’ conceptions of reflective symmetry: Opportunities for making connections with perpendicular bisector. Journal of Mathematical Behavior, 43, 35–52. Edwards, L. D. (2003). The nature of mathematics as viewed from cognitive science. Paper presented at the Third Conference of European Research in Mathematics Education, Bellaria, Italy. Emre-Akdoğan, E., Güçler, B., & Argün, Z. (2018). The development of two high school students’ discourses on geometric translation in relation to the teacher’s discourse in the classroom. Eurasia Journal of Mathematics, Science and Technology Education, 14(5), 1605-1619. Flanagan, K. A. (2001). High school students’ understandings of geometric transformations in the context of a technological environment. Doktora Tezi, The Pennsilvanya State University, Pennsilvanya. Güçler, B. (2016). Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning. Educational Studies in Mathematics, 91(3), 375-393. Güçler, B. (2016). Matematiksel Bilişe İletişimsel Yaklaşım. Editör: E. Bingölbali, S. Arslan ve İ. Ö. Zembat, Matematik Eğitiminde Teoriler (ss. 629-641). Ankara: Pegem. Güçler, B. (2013). Examining the discourse on the limit concept in a beginning-level calculus classroom. Educational Studies in Mathematics, 82(3), 439-453. Hacısalihoğlu-Karadeniz, M., Baran, T., Bozkuş, F. & Gündüz, N. (2015). İlköğretim matematik öğretmeni adaylarının yansıma simetrisi ile ilgili yaşadıkları zorluklar. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 6(1), 117-138. Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. Journal of Mathematical Behavior, 22, 55–72. Hollebrands, K. F. (2004). High school students’ intuitive understandings of geometric transformations. Mathematics Teacher, 97(3), 207–214. Hoyles, C., & Healy, L. (1997). Unfolding meanings for reflective symmetry. International Journal of Computer for Mathematical Learning, 2(1), 27-59. Jones, K. (2000). Critical issues in the design of the geometry curriculum. B. Barton (Ed), Readings in Mathematics Education. Auckland, New Zealand. Knuchel, C. (2004). Teaching symmetry in the elementary curriculum. The Montana Mathematics Enthusiast, 1(1), 3-8. Küchemann D. (1981). Reflection and rotation. In Hart K (Ed.) Children’s understanding of mathematics (pp. 137-157). London: John Murray. Lavie, I., Steiner, A., & Sfard, A. (2019). Routines we live by: From ritual to exploration. Educational Studies in Mathematics, 101(2), 153-176. Leikin, R., Berman, A., & Zaslavsky, O. (2000). Applications of symmetry to problem solving. International Journal of Mathematical Education in Science and Technology, 31(6), 799-809. Mhlolo, M. K., & Schäfer, M. (2014). Potential Gaps during the Transition from the Embodied through Symbolic to Formal Worlds of Reflective Symmetry. African Journal of Research in Mathematics, Science and Technology Education, 18 (2), 125-138. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: A sourcebook of new methods (2nd ed.). Thousand Oaks, CA: Sage. Milli Eğitim Bakanlığı (MEB). (2010). Talim ve Terbiye Kurulu Başkanlığı, Ortaöğretim geometri dersi (9-10.sınıflar) öğretim programı. Ankara: MEB. Milli Eğitim Bakanlığı (MEB). (2013). Talim ve Terbiye Kurulu Başkanlığı, Ortaöğretim matematik dersi (9.-12.sınıflar) öğretim programı. Ankara: MEB. Miyakawa, T. (2004). Reflective symmetry in constructions and proving. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th annual meeting ofthe international group for the psychology of mathematics education (Vol. 3) (pp. 337–344). National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA. Panaoura, A., Elia, I., Stamboulides, N., & Spyrou, P. (2009). Students' structure for the understanding of the axis of symmetry in mathematics. Acta Didactica Universitatis Comenianae Mathematics, 9, 41-62. Patton, M.Q. (2002). Qualitative research and evaluation methods. Thousand Oaks, CA: Sage. Portnoy, N., Grundmeimer, T. A., & Graham, K. J. (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. Sfard, A. (2001). There is more to discourse than meets the ears: looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1-3) 13-57. Sfard, A. (2008). Thinking as Communicating: human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University. Sfard, A. (2012). Introduction: Developing mathematical discourse–Some insights from communicational research. International Journal of Educational Research, 51–52, 1–9. Son, J.-W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 11(1), 31–46. Son, J.-W. (2006). Investigating preservice teachers’ understanding and strategies on a student’s errors of reflective symmetry. In J. Novotná, H. Moraová,M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 5) (pp.145–152). Tatar, E., Akkaya, A. and Kağizmanli, T. B. (2014). Using dynamic software in mathematics: the case of reflection symmetry. International Journal of Mathematical Education in Science and Technology, 45 (7), 980-995. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University. Yanik, H. B. (2006). Prospective elementary teachers’ growth in knowledge and understanding of rigid geometric transformations. Doktora Tezi, Arizona State University, Arizona. Yin, R. K. (1994). Case study research: Designs and methods. Newbury Park, CA: Sage. Xistouri, X. (2007). Students' ability in solving line symmetry tasks. Paper presented at the meeting of Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, Department of Education, University of Cyprus, Cyprus. Xistouri, Χ., & Pitta-Pantazi, D. (2006). Spatial rotation and perspective taking abilities in relation to performance in reflective symmetry tasks. In J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.), Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 5, (pp. 425-432). Prague: PME.
There are 1 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | January 23, 2020 |
| Submission Date | January 8, 2019 |
| Published in Issue | Year 2019 |
