Geometrik Yapıların İnşasında Pergel ve Çizgecin Kullanımı

Öz

Bu yapıda üç matematik öğretinin pergel ve çizgeçmenin geometrik yapıları süreçleri incelenmektedir. Öğretmenlerin geometri yapı yapımı ve ilgili dersleri video kamera ile kaydedilmiş ve derslerdeki öğretmen-öğrenci-araç üçlüsü arasındaki etkileşim incelenmiştir. Ders Kitaplığı içeren öğretmenlerle görüşmeler yapıldı. Çalışmada üç matematik öğretmeninin pergel ve çizgeci geometrik yapılar yapı mühendisliği. Araştırma pergel ve çizgeçle geometrik yapıların inşasına ezbere bir anlayışla öğretmen yönergelerini takip etme çalıştıkları gözlenmiştir. Öğretmenler pergel ve çizgeç kalmak geometrik yapı oluşturmanın olumlu tarafları ve dersler hale hale getirmek ve ezberden uzaklaştırmak. Geometrik yapıların pergel ve çizgeçle senkron imalatı öğretmen merkezli değil, öğrenci merkezli bir anlayışla gerçekleştirilmesi önerilmektedir.

Anahtar Kelimeler

• geometrik yapı inşa etme, pergel ve çizgeç, geometri öğretimi

The Use of a Compass and Straightedge to Construct Geometric Structures

Abstract

This study investigated three mathematics teachers’ construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results

Keywords

• constructing geometric structure,compass and straightedge,teaching geometry.

Kaynakça

1. Axler, S. ve Ribet, K.A. (2005). Straightedge and compass. In J. Stillwell (Ed.), The Four Pillars of Geometry (pp. 1–19). New York: Springer.
2. Baragar, A. (2002). Constructions using a compass and twice-notched straightedge. Mathematical Association of America, 109(2), 151-164.
3. Boulton-Lewis, G. M. (1998). Children’s strategy use and interpretations of mathematical representations. Journal of Mathematical Behavior, 17(2), 219–237.
4. Cherowitzo, B. (2006). “Geometric Constructions.” [Online] Retrieved on 18-August-2008., at URL http://www-math.cudenver.edu/~wcherowi/courses/m3210/lecchap5.pdf.
5. Clement, D. H, & McMillen, S. (1996). Rethinking concrete materials, Teaching Children Mathematics, 8, 340-343.
6. Cohen, L., Manion, L., Morrison, K. (2002). Research methods in education, London: Routledge.
7. Gilbert, R. & Bush, W. (1988). Familiarity, availability, and use of manipulative devices in mathematics at the primary level. School Science and Mathematics. 88(6), 459-469.
8. Goodman-Strauss, C. (2001). Compass and straightedge in the poincaré disk, The American Mathematical Monthly. 108(1), 38-49.

9. Hartshorne, R. (2000). Geometry: Euclid and beyond. USA: Springer
10. Hawkins, V. (2007). The Effects of Math Manipulative on Student Achievement in Mathematics. YayInlanmamIH doktora tezi, Capella University, USA.
11. Hiebert, J., & Carpenter, T .P. (1992). Learning and teaching with understanding. In D.A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 65-97). New York: Macmillan.
12. Hiebert, J. & Wearne, D. (1992). Links between teaching and learning place value with understanding in first grade, Journal for Research in Mathematics Education, 23, 98–122.
13. Hoffer, A. (1981). Geometry more than proof. Mathematics Teacher, 74(1), 11-18.
14. Kober, N. (1991). What we know about mathematics teaching and learning. Washington, D.C.: Council for Educational Development and Research, Department of Education. (ERIC Document Reproduction Service No. ED 343 793).
15. Lawson M. J. & Chinnappa, M. (2000). Knowledge connectedness in geometry problem solving. Journal for Research in Mathematics Education, 31(1), 26-43.
16. Milli E itim BakanlI I ([MEB], 2005). lkö retim matematik dersi 1-5. sInIflar ö retim programI, Ankara: MEB.
17. Milli E itim BakanlI I ([MEB], 2007). lkö retim matematik dersi 6–8. sInIflar ö retim programI, Ankara: MEB.
18. Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulative to teach mathematics, Educational Studies in Mathematics, 47, 175–197.
19. Napitupulu, B. (2001). An Exploration of Students’ Understanding and Van Hiele Levels of Thinking on Geometric Constructions, YayInlanmamIH yüksek lisans tezi, Simon Fraser University, Indonesia.
20. Olkun, S., Toluk, Z. (2004). Teacher questioning with an appropriate manipulative may make a big difference, IUMPST: The Journal, 2, 1-11.
21. Patton, M. Q. (1987). How to use qualitative methods in evaluation, California: Sage Publications.
22. Schorr, R. Y., Firestone, W. & Monfils, L. (2001). “An analysis of the teaching practices of a group of the fourth grade teachers.” Paper presented at the annual meeting of the North american chapter of the IGPME, USA.
23. Smart, J. R. (1998). Modern geometries ( 5thEdition), Pacific Grove, CA: Brooks/Cole Publishing.
24. Son, J. (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 30th Conference of the International Group for the Psychology of Mathematics Education, (Vol. 5, pp. 145-152). Prague: PME.
25. Sowell, E.J. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20(5), 498–505.
26. Spear-Swerling, L.(2006). “The use of manipulatives in mathematics instruction.” [Online] Retrieved on 21-June-2006, at URL: www.ldonline.org.
27. Stein, M. S. & Bovalino, J. W. (2001). Manipulatives: One piece of the puzzle. Mathematics Teaching in the Middle School. 6(6), 356-359.
28. Thompson, P.W. (1992). Notation, conventions, and constraints: Contributions to effective uses of concrete materials in elementary mathematics. Journal for Research in Mathematics Education. 23(2), 123-147.
29. Tooke, D., Hyatt, B., Leigh, M., Snyder, B. & Borda, T. (1992). Why aren’t manipulatives used in every middle school mathematics classroom? Middle School Journal, 24(2), 61-62.
30. YIldIrIm, A. ve 2imHek, H. (2006). Sosyal bilimlerde nitel ara t rma yöntemleri, Ankara: Seçkin YayIncIlIk.
31. Yin, R. (1994). Case study research: Design and methods. USA: Sage.