Uzamsal Görselleştirme Problemleri Çözme Etkinliklerinin Öğretmen Adaylarının Zihinsel Döndürme Problemleri Çözmelerine Nasıl Yardımcı Olduğu Üzerine Bir Durum Çalışması

Abstract

Bu çalışmanın amacı uzamsal görselleştirme problemleri çözme etkinliklerinin öğretmen adaylarının zihinsel döndürme problemleri çözmelerine nasıl yardımcı olduğunu araştırmaktır. Bu amaçla bir durum çalışması yapılmıştır ve çalışmada incelenen durum Ankara’da bir devlet üniversitesinde eğitim gören matematik öğretmen adaylarıdır. Veri toplama araçları olarak Uzamsal Yetenek Testi (SAT) ve görev temelli görüşmeler kullanılmıştır. Çalışmanın bulguları göstermiştir ki katılımcılar zihinsel döndürme problemleri çözerken farklı yollar kullanmışlardır; verilen şekli zihinde döndürme veya verilen şeklin parçalarının konumlarını veya desenlerini karşılaştırma. Buna ek olarak, uzamsal görselleştirme problemleri çözmek katılımcıların çözüm yollarını keşfetmelerini, değiştirmelerini veya pratik yapmalarını sağlayarak zihinsel döndürme problemlerini doğru ve pratik bir biçimde çözerken karşılaştıkları zorlukları aşmalarına yardımcı olmuştur.

Keywords

• Uzamsal yetenek, uzamsal görselleştirme, zihinsel döndürme problemleri, matematik öğretmen adayları, görev temelli görüşmeler

A Case Study on the Ways How Engagement with Spatial Visualization Problem Solving Activities Helps Pre-Service Mathematics Teachers in Solving Mental Rotation Problems

Abstract

The purpose of the present study is to investigate in what ways engagement with spatial visualization problem solving activities helps pre-service mathematics teachers in solving mental rotation problems. To achieve this purpose, a case study is conducted and the case of the study is the group of five pre-service mathematics teachers studying in a public university in Ankara. Spatial Ability Test (SAT) and task-based interviews are used as data collecting instruments. The results of the study show that participants use different ways in solving mental rotation problems; mentally rotating the figure or comparing the relative positions or patterns of the parts of the given figure. Additionally, solving spatial problems help participants in exploring, practicing or shifting their ways of solving problems to cope with the difficulties in solving spatial visualization problems requiring mental rotation accurately and practically.

Keywords

• Spatial ability,spatial visualization,mental rotation problems,pre-service mathematics teachers,task-based interviews

References

1. Baron, J. (1978). Intelligence and general strategies. In G. Underwood (Ed.), Strategies in information pro- cessing, pp. 403-450). London: Academic Press.
2. Battista, M. T., Wheatley, G. H., & Talsma, G. (1989). Spatial Visualization, Formal Reasoning, and Geometric Problem-Solving Strategies of Pre-service Elementary Teachers, Focus on Learning Problems in Mathematics, 11(4), 17-30.
3. Bennie, K., & Smit, S. (1999). “Spatial Sense”: Translating Curriculum Innovation in to Classroom Practice, Proceedings of the Fifth Annual Congress of the Association for Mathematics Education of South Africa: 1, 22-29. Port Elizabeth: Port Elizabeth Technikon.
4. Burin, D. I., Delgado, A. R. & Prieto, G. (2000) Solution strategies and gender differences in spatial visualization tasks. Psicológica, 21, 275-286.
5. Çakmak, S., Işıksal, M., Koç, Y. (2013). Investigating Effect of Origami-Based Instruction on Elementary Students’ Spatial Skills and Perceptions. Journal of Educational Researc, Sep 2013.
6. Delialioğlu, Ö. (1996). Contribution of students’ logical thinking ability, mathematical skills and spatial ability on achievement in secondary school physics, Unpublished Master Thesis, Middle East Technical University, Ankara, Turkey.
7. Ekstrom, R. B., et al. (1976). Kit of Factor-Referenced Cognitive Tests. ETS, Princeton, NJ. Ekstrom, R. B.,French, J. W., & Harman, H. H. (1979). Cognitive factors: Their identification and replication. Multivariate Behavioral Research Monographs, 79(2).
8. Glück, J., & Fitting, S., (2003). Spatial Strategy Selection: Interesting Incremental Information. International Journal of Testing, 3(3), 293-308.

9. Güven, B.,& Kosa, T. (2008). The Effect of Dynamic Geometry Software on Student Mathematics Teachers’ Spatial Visualization Skills. The Turkish Online Journal of Educational Technology, Vol 7(4),100-107.
10. Hershkowitz, R. (1989). Visualization in Geometry- Two Sides of the Coin, Focus on Learning Problems in Mathematics, 11(1), 61-76.
11. Hershkowitz, R., Parzysz, B., & Dormolen J. V. (1996). Space and Shape, International Handbook of Mathematics Education, 161-204.
12. Hsi, S., Linn, M.C. & Bell, J.E. (1997). The Role of Spatial Reasoning in Engineering and the Design of Spatial Instruction. Journal of EngineeringEducation, 151-158.
13. Hodgson, T. (1996). Students’ Ability to Visualize Set Expressions: An Initial Investigation. Educational Studies in Mathematics, 30, 159- 178.
14. Kayhan, E. B. (2005). Investigation of high school students’ spatial ability. Unpublished master’s thesis, Middle East Technical University, Ankara, Turkey.
15. Kolb, B., & Whishaw, I. Q. (1981). Neonatal frontal lesions in the rat: Sparing of learned but not species-typical behavior in the presence of reduced brain weight and cortical thickness. Journal of Comparative and Physiological Psychology, 95(6), 863-879.
16. Kyllonen, P. C.; Lohman, D. F. & Woltz, D. J. (1984). Componential modeling of alternative strategies for perfoming spatial tasks. Journal of Educational Psychology, 76 , 1325- 1345.
17. McGee, M.G. (1979) Human Spatial Abilities: Psychometric Studies and Environmental, Genetic, Hormonal, and Neurological Influences. Psychological Bulletin, 86(5), 889-918.
18. Milli Eğitim Bakanlığı, (2005). Talim Terbiye Kurulu Başkanşığı, İlköğretim Matematik Dersi Öğretim Programı ve Kılavuzu 6-8. Sınıflar. Milli Eğitim Basımevi-Ankara.
19. Milli Eğitim Bakanlığı, (2006). Talim Terbiye Kurulu Başkanşığı, İlköğretim Matematik Dersi Öğretim Programı ve Kılavuzu 6-8. Sınıflar. Milli Eğitim Basımevi-Ankara.
20. Milli Eğitim Bakanlığı, (2009). Talim Terbiye Kurulu Başkanşığı, Ortaöğretim Geometri Dersi Öğretim Programı ve Kılavuzu 9-10. Sınıflar. Milli Eğitim Basımevi-Ankara.
21. Milli Eğitim Bakanlığı, (2010). Talim Terbiye Kurulu Başkanşığı, Ortaöğretim Geometri Dersi Öğretim Programı ve Kılavuzu 11. Sınıflar. Milli Eğitim Basımevi-Ankara.
22. Milli Eğitim Bakanlığı, (2011). Talim Terbiye Kurulu Başkanşığı, Ortaöğretim Geometri Dersi Öğretim Programı ve Kılavuzu 12. Sınıflar. Milli Eğitim Basımevi-Ankara.
23. National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: The Council.
24. National Council of Teachers of Mathematics (2001). Navigating through Geometry in Grades 9-12. Reston Va.:20191-9988.
25. National Council of Teachers of Mathematics (2003). Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: The Council.
26. Olkun, S. (2003) Making Connections: Improving Spatial Abilities with Engineering Drawing Activities, International Journal of MathematicsTeaching and Learning, (Apr,17). [Online]: http://www.ex.ac.uk/cimt/ijmtl /ijabout.htm.
27. Osberg, K. M. (1997). Spatial Cognition in the Virtual Environment, Technical R-97-18. Seattle: HIT Lab.
28. Owens, K. D., & Clements, M.A. (1998). Representations in Spatial Problem Solving in the Classroom, Journal of Mathematical Behavior, 17 (2), 197-218.
29. Pallascio, R., Allaire, R., & Mongeau, P. (1993). The Development of Spatial Competencies through Alternating Analytic and Synthetic Activities, For the Learning of Mathematics, 13(3), 175-190.
30. Presmeg, N. (1997). Research on Visualization in Learning and Teaching Mathematics.
31. Sorby, S.A. (1999) Computer aided design instruction. 1999 ASEE Annual Conference Proceedings Session 1438. [Online] In M. Alias, T. R. Black, & D. E.Gray, (2002). Attitudes Towards Sketching and Drawing and the Relationship with Spatial Visualization Ability in Engineering Students, International Education Journal, 3(3), 1-12.
32. Schultz, K. (1991) The contribution of solution strategy to spatial performance. Canadian Journal of Psychology/Revue canadienne de psychologie, Vol 45(4), Dec 1991, 474-491.
33. Smith, G.G., Gerretson, H., Olkun ,S., Yuan., Y., Dogbey, J., & Erdem, A. (2009). Stills, not full motion, for interactive spatial training: American, Turkish and Taiwanese female pre- service teachers learn spatial visualization. Computers& Education, Vol 52(1), Jan 2009, 201-209.
34. Sorby, S. A. (1999). Developing 3-D Spatial Visualization Skills, Engineering Design Graphics Journal,63(2), 21-32.
35. Tartre, L. A. (1990). Spatial Orientation Skill and Mathematical Problem Solving, Journal for Research in Mathematics Education,21(3), 216- 229.
36. Toptaş, V., Çelik, S., & Karaca, E. T. (2012). Improving 8th Grades Spatial Thinking Abilities Through a 3D Modeling Program. The Turkish Online Journal of Educational Technology – April 2012, volume 11(2), 128-134.
37. Turğut, M. & Yılmaz, S. (2012). Relationships Among Preservice Primary Mathematics Teachers’ Gender, Academic Success and spatial ability. International Journal of Instruction, July 2012,Vol.5(2), 5-20
38. Usiskin Z. (1987) Resolving the Continuing Dilemmas in School Geometry. In R. Hershkowitz, Visualization in Geometry: Two Sides of the Coin, Focus in Learning Problems in Mathematics, 11(1), 61- 76.
39. Yin, R. K. (1994). Case Study Research; Design and Methods, Sage Publications, California, 1994.
40. Yıldırım, A.& Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin.