Matematik Öğretmeni Adaylarının Geometrik Şekillerin Elemanları ile İlgili Konu Alan Bilgilerinin Geometer’s Sketchpad Yardımıyla Geliştirilmesi

Abstract

Çalışmanın amacı ortaokul matematik öğretmeni adaylarının (OMÖA) geometrik şekillerin elemanlarıyla ilgili alan bilgilerinin dinamik geometri ortamında nasıl geliştirdiklerini incelemektir. Bu amaç doğrultusunda tasarlanan çalışmada nitel araştırma desenlerinden durum çalışması kullanılmıştır.  Araştırma sürecine ilköğretim matematik öğretmenliği lisans programına kayıtlı 23 kişi katılmıştır. Araştırmanın verilerini toplu sınıf tartışmalarının video kayıtları, Geometer’s Sketchpad programıyla yaptıkları etkinliklerin bilgisayar ortamındaki kayıtları ve doldurdukları etkinlik kâğıtları oluşturmaktadır. Veri analiz kısmında Smart’ın (1998) geometrik şekillerin inşa edilmesi adımları, çalışmanın kategorileri olarak kullanılmıştır. Araştırma bulguları, OMÖA’nın bu elemanlarla ilgili alan bilgilerini ve öğrenmelerini teknoloji yardımıyla daha kolay ve etkili bir şekilde analiz ederek ve anlayarak geliştirebildikleri görülmüştür. Ayrıca bu elemanların önemine ve rollerine odaklanılarak OMÖA’nın anlamalarının sağlandığı tespit edilmiştir.

Keywords

• Temel Eleman,Yardımcı Eleman,Matematik Öğretmen Adayı,Geometrik Şekiller,Geometer’s Sketchpad

Development of Preservice Middle School Mathematics Teachers’ Subject Matter Knowledge about Elements of Geometric Shapes

Abstract

The aim of the study is to examine how preservice middle school mathematics teachers (PMSMT) developed their subject matter knowledge about elements of geometric shapes in the dynamic geometry environment. In the study designed for this purpose, case study was used from qualitative research designs. 23 students enrolled in the undergraduate program of elementary mathematics education participated in the research process. The data of the research were composed of video recordings of collective class discussions, computer-generated records of the activities performed by Geometer's Sketchpad program and activity papers that they fill out. In the data analysis section, Smart’s (1998) steps of constructing geometric shapes were used as categories of study. The research findings showed that the PMSMT could develop and understand the field knowledge and learnings of these members more easily and effectively with the help of technology. It has also been determined that the PMSMT have provided meaning by focusing on the importance and roles of these elements.  

Keywords

• Main Element,Auxiliary Element,Geometrical Figures,Preservice Mathematics Teacher,Geometers’ Sketchpad

References

1. Akyuz, D. (2014). Mathematical practices in a technological setting: A design research experiment for teaching circle properties. International Journal of Science and Mathematics Education, DOI 10.1007/s10763-014-9588-z.
2. Alatorre, S., & Saiz, M. (2009). Teachers and triangles. Proceedings of Congress of Educational Research in Mathematics Education. 28 January- 1 February, Lyon; France.
3. Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation. Michigan State University, East Lansing, MI.
4. Ball, D. L., Hill, H.H., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14-46.
5. Bryan, L. A. (2003). Nestedness of beliefs: Examining a prospective elementary teacher's belief system about science teaching and learning. Journal of Research in Science Teaching, 40(9), 33.
6. Chan, Y. C. (2006). Dynamic Geometry Software Environment for Conjecturing and Proving Geometry Statements. Research Studies in Education: the 9th Postgraduate Research Conference. The University of Hong Kong; China.
7. Chapman, O. (2007). Facilitating preservice teachers' development of mathematics knowledge for teaching arithmetic operations. Journal of Mathematics Teacher Education, 10(4), 341-349.
8. Cherowitzo, B. (2006). Geometric constructions. [Online] Retrieved on 18-August-2012., at URL http://wwwmath.cudenver.edu/~wcherowi/courses/m3210/lecchap5.pdf.

9. Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Problem solving and problem posing in a dynamic geometry environments. International Journal of Science and Mathematics Education, 2, 339-352.
10. Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children’s concepts of shape. Journal for Research in Mathematics Education, 30, 192–212.
11. Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: SAGE Publications.
12. Creswell, J. W. (2012). Educational research: planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Thousand Oaks, CA: SAGE Publications.
13. De Villiers, M. D. (2003). Rethinking Proof: with the Geometer’s Sketchpad. Key Curriculum Press.
14. Dye, B. (2001). The impact of dynamic geometry software on learning. Teaching Mathematics and Its Application, 20(4).
15. Forsythe, S. (2007). Learning geometry through dynamic geometry. Mathematics Teaching, 202, 31-35.
16. Gall, M. D., Gall, J. P., & Borg, W. R. (2007) Educational research: An introduction. Boston: Pearson Education.
17. Godwin, S., & Sutherland, R. (2004). Whole class technology for learning mathematics: the case of functions and graphs. Education, Communication and Information Journal (ECi) 4, 131-152.
18. Goldenberg, E. P. & Cuoco, A. A., (1998). What is dynamic geometry? In R. Lehrer and D. Chazan (Eds.). Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 351-368). Lawrence Erlbaum, Mahwah: USA.
19. Gutierrez, A. & Jaime, A. (1999). Pre-service primary teachers’ understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher of Education, 2(3), 253-275.
20. Han, H. (2007). Middle school students’ quadrilateral learning: a comparison study. Unpublished doctoral dissertation. University of Minnesota, Minnessota, USA.
21. Healy, L., & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-256.
22. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 534-549.
23. Hill, H. C. & Ball, D. L. (2004). Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351.
24. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 372-400.
25. Hill, C. H., Rowan, B., & Ball, D. L. (2005). Effects of teacher’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.
26. Hill, J. R., & Hannafin, M. J. (2001). Teaching and learning in digital environments: the resurgence of resource –based learning. Educational Technology Research Development, 49(3), 37-52.
27. Hoyles, C., & Healy, L. (1999). Liking informal argumentation with formal proof through computer-integrated teaching experiments, In o. Zaslavsky (Ed.), Proceedings of the 23rd Conference of the International Group for the Pschology of Mathematics Education (pp. 105-112). Haifa, Israel.
28. Jackiw, N., (2001). The Geometer’s Sketchpad (Version 4.0) [Computer software]. Emeryville, CA: Key Curriculum Press.
29. Jones, K. (2000). Teacher knowledge and professional development in geometry. Proceedings of the British Society for Research into Learning Mathematics, 20(3), 109-114.
30. Kellogg, M. S. (2010). Preservice elementary teachers’ pedagogical content knowledge related to area and perimeter: A teacher development experiment investigating anchored instruction with web-based microworlds. Unpublished doctoral dissertation. University of South Florida, Florida.
31. Khoh, L. S. (1997). Compass constructions: A vehicle for promoting relational understanding and higher order thinking skills. The Mathematics Educator, 2(2), 138-147.
32. Kuzle, A. (2013). Constructions with various tools in two geometry didactics courses in the United States and Germany. B. Ubuz, (ed.), Proceedings of the eighth congress of the European Society of Research in Mathematics Education (pp. 6-10), Antalya.
33. Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283-317.
34. Leung, A., & Lee, A. M. S. (2013). Students’ geometrical perception on a task-based dynamic geometry platform. Educational Studies in Mathematics, 82(3), 361-377.
35. Leung, A., & Lopez-Real, F. (2002). Theorem justification and acquisition in dynamic geometry: Acase of proofby contradiction. International Journal of Computers for Mathematical Learning, 7(2), 145-165.
36. Liang, H. N., & Sedig, K. (2010). Can interactive visualization tools engage and support pre-university students in exploring non-trivial mathemaical concepts? Compters & Education, 54(4), 972-991.
37. Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal of Research in Mathematics Education, 30(5), 520-540.
38. Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in dynamic computer environment. Educational Studies in Mathematics, 44(1/2), 87-125.
39. Merriam, S. B. (2009). Qualitative research: A guide to design and implemantation (2nd ed.). San Francisco, CA: Jossey-Bass.
40. Mariotti, M. A. (2002). Influences of technologies advances in students’ math learning. In L. D. English (ed.) Handbook of International Research in Mathematics Education, pp. 695-723. Lawrence Erlbaum Associates publishers, Mahwah, New Jersey.
41. Napitupulu, B. (2001). An exploration of students’ understanding and van hiele levels of thinking on geometric constructions. Unpublished master’s thesis, Simon Fraser University, Indonesia.
42. NCTM. (1991). Professional standards for teaching mathematics. Reston, VA: Author.
43. NCTM. (2000). Principles and Standards for School Mathematics. Reston, VA:Author.
44. Smart, J. R. (1998). Modern geometries (5th Edition). Pacific Grove, CA: Brooks/Cole Publishing.
45. Straesser, R. (2002). Cabri-geometre: Does dynamic geometry software (DGS) change geometry and its teaching and learning? International Journal of Computers for Mathematical Learning, 6(3), 319-333.
46. Tsamir, P., Tirosh, D., & Levenson, E. (2008). Intuitive nonexamples: The case of triangles. Educational Studies in Mathematics, 69(2), 81-95.
47. Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2014). Early years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDM- Mathematics Education, DOI 10.1007/s11858-014-0641-8.
48. Turner, C. S. V., Wood, J. L., Montoya, Y. J., Essien-Wood, I. R., Neal, R., Escontrias, G., & Coe, A. (2012). Advancing the next generation of higher education scholars: An examination of one doctoral classroom. International Journal of Teaching and Learning in Higher Education, 24(1), 103-112.
49. Uygun, T. (2016). Preservice middle school mathematics teachers’ understanding of altitudes of triangles. Uluslararası Çağdaş Eğitim Araştırmaları Kongresi, 29 Eylül- 2 Ekim, Muğla, Türkiye.Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayınclık.
50. Uygun, T., & Akyüz, D. (2017). Preservice middle school mathematics teachers’ conception of auxiliary elements of triangles. International Conference on Education in Mathematics, Science and Technology, 18-21 Mayıs 2017, Kuşadası, Türkiye.
51. Ward, R. A. (2004). An investigation of K-8 preservice teachers’ concept images and definitions of polygons. Issues in Teacher Education, 13(2)39-56.
52. Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Thousands Oaks, CA:Sage.