From Congruent Angles to Congruent Trıangles: The Role of Dragging, Grid and Angle Tools of A Dynamic Geometry System

Tunç Aryüce; Melih Turgut

From Congruent Angles to Congruent Trıangles: The Role of Dragging, Grid and Angle Tools of A Dynamic Geometry System

Year 2018, Volume: 5 Issue: 1, 46 - 57, 01.05.2018

Abstract

This study aims to establish a conceptual relationship between the angles of two parallel lines intersected by a transversal and the congruent triangles formed through the points on the parallel lines and the transversal. At this point, the study considers semiotic potential of dragging, grid and angle tools of a dynamic geometry system. The study was designed according to qualitative paradigm, and the collected data was analyzed through the techniques used in the same perspective. Within the scope of the study, an instructional task was designed by employing the tools used in a dynamic geometry system and its functions. This task was expected to enable the participants to make a successful conceptual bridging by using their already existing background knowledge. In addition, two sessions of 25-minute clinical interviews were conducted with two students – one from 7th and one from 8th grade – who were selected according to the principles of purposeful sampling method. The findings obtained from qualitative data analysis show that the designed task can be used as a tool for students to figure out conceptual relationships between congruent angles and congruent triangles. The results clearly revealed that the students went through different cognitive processes while using the dragging tool. Generally speaking, the findings are consistent with the findings of similar studies in the literature, and some suggestions were proposed under the light of these findings

Keywords

Congruent Angles, Congruent Triangles, Dynamic Geometry System, Semiotic Potential

References

Baccaglini-Frank, A., and Mariotti, M. A. (2010). Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), 225–253. https://doi.org/10.1007/s10758-010- 9169-3
Bartolini Bussi, M. G., and Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of International Research in Mathematics Education (2., pp. 746–783). Mahwah, NJ: Erlbaum.
Baykul, Y. (2014). Ortaokulda Matematik Öğretimi (5-8. Sınıflar) (2nd ed.). Ankara: Pegem Akademi.
Drijvers, P. (2003). Learning algebra in a computer algebra environment. Design research on the understanding of the concept of parameter. Utrecht: CD-Béta Press.
Freudenthal, H. (1983). Didactic phenomenology of mathematical structures. Dordrecht: Reidel Publishing Company.
Leung, A. (2008). Dragging in a dynamic geometry environment through the lens of variation. International Journal of Computers for Mathematical Learning, 13(2), 135–157. https://doi.org/10.1007/s10758-008-9130-x
Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. https://doi.org/10.1007/s11858-011-0329-2
Leung, A., Baccaglini-Frank, A., and Mariotti, M. A. (2013). Discernment of invariants in dynamic geometry environments. Educational Studies in Mathematics, 84(3), 439–460.
Lopez-Real, F., and Leung, A. (2006). Dragging as a conceptual tool in dynamic geometry environments. International Journal of Mathematical Education in Science and Technology, 37(6), 665–679. https://doi.org/10.1080/00207390600712539
Maher, C. A., and Sigley, R. (2014). Task-Based Interviews in Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 579–582). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_147
Mariotti, M. A. (2013). Introducing students to geometric theorems : how the teacher can exploit the semiotic potential of a DGS. ZDM Mathematics Education, 45(3), 441–452. https://doi.org/10.1007/s11858-013-0495-5
Mariotti, M. A. (2014). Transforming images in a DGS: The semiotic potential of the dragging tool for introducing the notion of conditional statement. In S. Rezat, M. Hattermann, & A. Peter-Koop (Eds.), Transformation - A Fundamental Idea of Mathematics Education (pp. 155–172). New York: Springer. https://doi.org/10.1007/978-1-4614-3489-4_8
MEB. (2013). Ortaokul Matematik Dersi Öğretim Programı [Mathematics Curricula for 5., 6., 7. and 8 Grades]. Ankara: Talim Terbiye Kurulu Başkanlığı.
Narlı, S. (2016). İlişkilendirme Becerisi ve Muhtevası. In E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Eds.), Matematik Eğitiminde Teoriler (pp. 231–244). Ankara: Pegem Akademi.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.
Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.
Van de Walle, J. A., Karp, K. S., and Bay-Williams, J. M. (2010). Elementary and Middle School Mathematics: Teaching Developmentally (3rd ed.). NY, US: Pearson Education, Inc.
Yılmaz, S., ve Nasibov, F. H. (2012). 7. Sınıf öğrencilerinin aynı düzlemdeki üç doğrunun oluşturduğu açılar ile ilgili hata ve kavram yanılgısı türleri. X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi. Niğde Üniversitesi, Niğde, Türkiye. Retrieved from http://kongre.nigde.edu.tr/xufbmek/dosyalar/tam_metin/pdf/2300- 29_05_2012-00_11_52.pdf