Matematik Öğretmenliği Lisans Öğrencilerinin Geometrik Alışkanlıklarının İncelenmesi: Trigonometri Örneği

Abstract

Bu çalışmanın temel amacı lise matematik öğretmenliği lisans öğrencilerinin birim çember ve trigonometrik oranlar konularında kullandıkları geometrik alışkanlıkları incelemektir. Bu çalışmanın teorik altyapısını “Zihnin Geometrik Alışkanlıkları” çerçevesi oluşturmaktadır. Durum çalışması ile desenlenen bu çalışmanın katılımcı grubu, lise matematik öğretmenliği lisans programında birinci sınıfta öğrenim gören on iki tane öğrenciden oluşmaktadır. Çalışmanın veri grubu, öğrencilere yazılı olarak verilen ve çözmeleri istenen birim çember ve trigonometrik oranlar kavramlarına dair sorulardan oluşmaktadır. Çalışmanın verileri benimsenen çerçeve ışığında betimsel analiz yöntemi ile analiz edilmiştir. Elde edilen bulgular sonucunda, öğrencilerin trigonometri konusunda en sık kullandıkları geometrik alışkanlıkların ilişki kurarak muhakeme etme ve değişmeyenlerin incelenmesi; en az kullandıkları geometrik alışkanlığın ise keşfetme ve yansıtma dengesi kurma olduğu ortaya çıkmıştır. Çalışmanın bulguları öğrencilerin neredeyse tamamının geometrik alışkanlıkları kullanma konusunda yeterli düzeyde olmadıklarını göstermiştir.

Keywords

• Birim çember
• trigonometri
• trigonometrik oranlar
• zihnin geometrik alışkanlıkları

Investigation of Geometric Habits of Undergraduate Students in Secondary Mathematics Education: Trigonometry Example

Abstract

The main purpose of this study is to examine undergraduate students’, who were enrolled in secondary mathematics education, geometric habits of mind related to the concepts of unit circle and trigonometric ratios. The framework of "Geometric Habits of the Mind" was identified as the theoretical background of the study. This study was designed considering a case study method and the participants were twelve first grade students. The data group of the study consists of questions on the concepts of unit circle and trigonometric ratios and the students were required to answer the question on the paper. The data were analyzed with the descriptive analysis method in the light of the adopted framework. As a result of the findings, the students most frequently used reasoning with relationships and investigating invariants and the least used balancing exploration with reflection. The findings of the study showed that almost all of the students were not at a sufficient level in using geometric habits.

Keywords

• Unit circle
• trigonometry
• trigonometric ratios
• geometric habits of mind

References

1. Brown, S. A. (2005). The trigonometric connection: Students’ understanding of sine and cosine. (Dissertation). Illinois State University. Illinois.
2. Bülbül, B. Ö. (2016). Matematik öğretmeni adaylarının geometrik düşünme alışkanlıklarını geliştirmeye yönelik tasarlanan öğrenme ortamının değerlendirilmesi. (Yayımlanmamış doktora tezi). Karadeniz Teknik Üniversitesi Eğitim Bilimleri Enstitüsü. Trabzon.
3. Bülbül, B. Ö., & Güven, B. (2020). Öğretmen adaylarının geometrik düşünme alışkanlıklarının değişimi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 48, 431-453. Doi:10.9779/pauefd.513220
4. Costa, A. L., & Kallick, B. (2000). Discovering ang exploring habits of mind. Alexandria, Virginia: Association for Supervision & Curriculum Development.
5. Creswell J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches. (4. baskı). Los Angeles, CA: Sage Publications.
6. Cuoco, A. (2008). Mathematical habits of mind: An organizing principle for curriculum design. A Project Next Session on Helping Students Develop Mathematical Habits on Mind, Joint Mathematics Meetings. San Diego January. The United States of America. http://www2.edc.org/CME /showcase.html.
7. Cuoco, A., Goldenberg, E. P., & Mark, J. (1996). Habits of minds: An organizing principle for mathematics curricula. Journal of Mathematical Behavior, 15, 375-402.
8. Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103(9), 682-688.

9. Dikovic, L. (2009). Applications GeoGebra into teaching some topics of mathematics at the college level. Computer Science and Information Systems, 6(2), 191-203.
10. Driscoll, M., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking. A guide for teachers, grades 5-10. Portsmouth: Heinemann.
11. Driscoll, M. J., DiMatteo, R. W., Nikula, J., Egan, M., Mark, J., & Kelemanik, G. (2008). The fostering geometric thinking toolkit: A guide for staff development. Portsmouth, NH: Heinemann.
12. Eraslan-Yalçın, E., & Özgeldi, M. (2019). 1924-2018 ortaokul matematik öğretim programlarının geometrik düşünme alışkanlıkları bakımından incelenmesi. Mersin Üniversitesi Eğitim Fakültesi Dergisi, 15(1), 131-146. DOI: 10.17860/mersinefd.479753
13. Erşen, Z. B., Ezentaş, R., & Altun, M. (2018). Evaluation of the teaching environment for improve the geometric habits of mind of tenth grade students. European Journal of Education Studies, 4(6), 47-65. doi: 10.5281/zenodo.1239849
14. Fi, C. (2003). Preservice secondary school mathematics teachers’ knowledge of trigonometry: Subject matter content knowledge, pedagogical content knowledge and envisioned pedagogy. (Dissertation). University of Iowa. Iowa City.
15. Goldenberg, E. P. (1996). “Habits of Mind” as an organizer for the curriculum. Journal of Education, 178(1), 13-34.
16. Goldenberg, E. P., Shteingold, N., & Feurzeig, N. (2003). Mathematical habits of mind for young children. In F. K. Lester & R. I. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten-Grade 6 (pp. 15-29). Reston, VA: National Council of Teachers of Mathematics.
17. Gürbüz, M. Ç., Ağsu, M., & Güler, H. K. (2018). Investigating geometric habits of mind by using paper folding. Acta Didactica Napocensia, 11(3-4), 157-174, DOI:10.24193/adn.11.3-4.12.
18. Harel, G., & Sowder, L. (2005). Advanced mathematical-thinking at any age: Its nature and its development. Mathematical Thinking & Learning, 7(1), 27–50.
19. Hartatiana, H., Darhim, D., & Nurlaelah, E. (2018). Improving junior high school students’ spatial reasoning ability through model eliciting activities with Cabri 3D. International Education Studies, 11(1), 148-154.
20. Kendal, M, & Stacey, K. (1998). Teaching trigonometry. Aust Math Teach, 54(1), 34–39.
21. Koç, Y., & Bozkurt, A. (2012). Investigating prospective mathematics teachers’ knowledge of volume of cylinders. Energy Education Science and Technology Part B: Social and Educational Studies [Special Issue I], 4, 148-153.
22. Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In Proceedings of the Fifh Congress of the European Society for Research in Mathematics Education (pp. 2330-2339). Larnaca, Cyprus.
23. Levasseur, K., & Cuoco, A. (2009). Mathematical habits of mind. National Council of Teachers of Mathematics.
24. Lin, H. C. K., Chen, M. C., & Chang, C. K. (2015). Assessing the effectiveness of learning solid geometry by using an augmented reality-assisted learning system. Interactive Learning Environments, 23(6), 1-12. Doi: 10.1080/10494820.2013.817435
25. Lim, K. H., & Selden, A. (2009). Mathematical habits of mind. In S. L. Swars, D. W. Stinson & S. Lemons-Smith (Eds.), Proceedings of the 31st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Atlanta, GA: Georgia State University.
26. Mark, J., Cuoco, A., Goldenberg, E. P., & Sword, (2009). Developing mathematical habits of mind in the middle grades. http://www2.edc.org/cme/hom/hom-middle-grades.pdf
27. Matsuura, R., Sword, S., Piecham, M. B., Stevens, G., & Cuoco, A. (2013). Mathematical habits of mind for teaching: Using language in algebra classrooms. The Mathematics Enthusiast, 10(3), 735-776.
28. Moore, K. C. (2013). Making sense by measuring arcs: A teaching experiment in angle measure. Educational Studies in Mathematics, 83(2), 225–245.
29. Moore, K. C. (2014). Quantitative reasoning and the sine function: The case of Zac. Journal for Research in Mathematics Education, 45(1), 102–138.
30. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston (VA): NCTM.
31. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston (VA): NCTM.
32. Özen, D. (2015). Ortaokul matematik öğretmenlerinin geometrik düşünmelerinin geliştirilmesi: Bir ders imecesi. (Yayımlanmamış doktora tezi). Anadolu Üniversitesi Eğitim Bilimleri Enstitüsü. Eskişehir.
33. Rolle, Y. A. (2008). Habits of practice: A qualitative case study of a middle-school mathematics teacher. (Unpublished doctoral dissertation). The Faculty of the Graduate Collage, University of Nebraska. Lincoln, Nebraska, USA
34. Seago, N. M., Jacobs, J. K., Heck, D. J., Nelson, C. L., & Malzahn, K. A. (2014). Impacting teachers’ understanding of geometric similarity: Results from field testing of the learning and teaching geometry Professional development materials. Professional Development in Education, 40(4), 627-653.
35. Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojana & A. Sepulveda (Eds.), Annual Meeting of the International Group for the Psychology of Mathematics Education. Proceedings, 1, 45–64. Morelia: PME.
36. Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10(4–6), 415–432.
37. Tolga, A., & Cantürk-Günhan, B. (2019). Ortaokul matematik öğretmenlerinin zihnin geometrik alışkanlıklarının belirlenmesi. Batı Anadolu Eğitim Bilimleri Dergisi, 10(1), 37-56.
38. Tomaschko, M., & Hohenwarter, M. (2019). Augmented reality in mathematics education: The case of GeoGebra AR. In Theodosia Prodromou (Ed.), Augmented Reality İn Educational Settings (pp. 325-346). The Netherlands: Brill Sense. doi: 10.1163/978900 4408845_014
39. Uygan, C. (2016). Ortaokul öğrencilerinin zihnin geometrik alışkanlıklarının kazanımına yönelik dinamik geometri yazılımındaki öğrenme süreçleri. (Yayımlanmamış doktora tezi). Anadolu Üniversitesi Eğitim Bilimleri Enstitüsü. Eskişehir.
40. Weber, K. (2005). Students’ understanding of trigonometric functions. Mathematics Education Research, 17(3), 91–112.
41. Weber, K., Knott, L., & Evitts, T. (2008). Teaching trigonometric functions: Lessons learned from research. Mathematics Teacher, 102(2), 144–150.
42. Wiles, P. S. (2013). Folding corners of the habits of mind. Mathematics Teaching in the Middle School, 19(4), 208-213.
43. Yavuzsoy-Köse N., & Tanışlı, D. (2014). Primary school teacher candidates’ geometric habits of mind. Educational Sciences: Theory & Practice, 14(3), 1220-1229. http://dx.doi.org/1229.10. 12738/estp.2014.3.1864
44. Yıldız, N. (2018). Ortaokul sınıflarında geometrik düşünmenin geliştirilmesine yönelik bir mesleki gelişim modelinin öğrencilerin Van Hiele geometrik düşünme düzeylerine etkisi. (Yayımlanmamış doktora tezi). Gaziantep Üniversitesi Eğitim Bilimleri Enstitüsü. Gaziantep.
45. Yigit, M. (2014a). Learning of trigonometry: An examination of pre-service secondary mathematics teachers’ trigonometric ratios schema. (Dissertation). Purdue University. West Lafayette.
46. Yigit, M. (2014b). Pre-service secondary mathematics teachers’ conceptions on angles. The Math Enthusiast, 11(3), 707–736.
47. Yiğit-Koyunkaya, M. (2016). Mathematics education graduate students’ understanding of trigonometric ratios. International Journal of Mathematical Education in Science and Technology, 47(7), 1028-1047. DOI: 10.1080/0020739X.2016.1155774
48. Yin, R. (2018). Case study research: Design and methods. (6th edition). London: Sage.