Describing Pre-Service Teachers’ Reasoning within Drawing Geometrical Shapes in Logo

Abstract

In this study, it was aimed to determine the mistakes and possible misconceptions of pre-service mathematics teachers made about the Logo-based tasks involving the concepts of angle and rotation when they drawing some geometrical shapes using Logo commands. For this purpose, 37 pre-service mathematics teachers (37) participated in a “Computer based Mathematics Teaching Lesson” lasting 10 hours, in which they could learn and interact with Logo programming language. Then, a five performance tasks about the concept of angle and rotation were utilized to gather required data. The data of the study were obtained from qualitative data collection methods through document analysis and clinical interview. As a result of this study, most of the made mistakes in pen-paper environment were because of geometrical features rather than Logo commands. These are focused on three aspects: rotation of angle, angle-edge relationship and missing/incorrect command. The ability to draw geometrical shapes using Logo primitives is limited for some participants but acceptable for others. It was recommended that teaching Logo should be applied with a constructive approach that gives limited feedback when certain geometrical concepts are being learned.

Keywords

• Pre-service teacher,programming language,Logo,angle and rotation concept

Logo Programlama Sürecinde Öğretmen Adaylarının Yaptıkları Hatalar Üzerine Bir Nitel Çalışma

Öz

Bu çalışmada, ilköğretim matematik öğretmeni adaylarının bilgisayar destekli matematik öğretimi (BDMÖ) dersi kapsamında temel Logo komutlarını kullanarak geometrik şekilleri çizerken açı ve dönme kavramlarını içeren problemlere yönelik yaptıkları hataları ve olası kavram yanılgılarını tespit etmeyi amaçlanmıştır. Bu amaçla, 2016-2017 eğitim-öğretim yılı güz döneminde 37 ilköğretim matematik öğretmeni adayına 10 saatlik Logo programlama dili eğitimi verilmiştir. Daha sonra adaylardan Logo komutlarını kullanarak açı ve dönme kavramıyla ilgili performans gösterebilecekleri 8 sorudan oluşan açık uçlu bir sınav yapılmıştır. Bu çalışmada 8 soru içinden seçilen 5 soru üzerinde durulmaktadır. Çalışmanın verileri, nitel veri toplama yöntemlerinden doküman analizi ve klinik mülakat ile elde edilmiştir. Elde edilen bulgular neticesinde, öğretmen adayları kâğıt-kalem ortamında problemleri çözerken Logo programlama komutlarından daha çok dönme açısı ve geometrik şekillerin özellikleriyle ilgili hatalar yaptıkları tespit edilmiştir. Bu hatalar şu üç noktada yoğunlaşmaktadır: Dönme açısı, açı-kenar bağıntısı ve eksik kodlama. Logo ’da performans gösterebilecekleri problemleri çözerken bazı öğretmen adaylarının programlama becerilerinin sınırlı; diğerlerinin kabul edilebilir seviyede olduğu belirlenmiştir. Araştırma sonucunda elde edilen bulgular dâhilinde Logo programlama dili belirli geometrik kavramların öğrenilmesinde kullanılırken sınırlı geri bildirim veren yapılandırmacı yaklaşımla ile hayata geçirilmelidir.

Anahtar Kelimeler

• Öğretmen adayı,programlama dili,Logo,açı ve dönme kavramı

Kaynakça

1. Appalanayudu, S., & Ismail, Z. (2005). Students’ Problem Solving Processes in LOGO Programming Environment Pengaturcaran LOGO. Reform, Revolution and Paradigm Shifts in Mathematics Education. Johor Bahru, Malaysia.
2. Baki, A. (2002). Öğrenen ve Öğretenler için Bilgisayar Destekli Matematik. İstanbul: Ceren Yayınları.
3. Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Ankara: Harf Eğitim Yayıncılık.
4. Barry-Joyce, M. (2001). The effects of a Logo environment on the metacognitive functioning of Irish students. Ph.D. thesis, University of Hull.
5. Biber, Ç, Tuna, A., & Korkmaz, S. (2013). The mistakes and the misconceptions of the eighth grade students on the subject of angles. European Journal of Science and Mathematics Education, 1(2), 50–59.
6. Clement, J. (2000). Analysis of clinical interview: Foundations and model viability. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 547-589). London: Lawrence Erlbaum Associates Publishers.
7. Clements, D. H., & Meredith, J. S. (1992). Research on Logo: Effects and efficacy. National Science Foundation.
8. Clements, D. H. & Sarama, J. (1997). Research on Logo: A decade of progress. Computers in the Schools, 14(1/2), pp. 9-46.

9. Clements, D. H. & Burns, B. A.(2000). Students’ development of strategies for turn and angle measure. Educational Studies in Mathematics, 41:31–45.
10. Creswell, J. W. (2009). Research Design: Qualitative, quantitative and mixed methods approaches (3rd eds.). Thousand Oaks, CA: Sage.
11. Cope, P., Smith, H. & Simmons, M. (1992). Misconceptions Concerning Rotation and Angle in Logo. Journal for Computer Assisted Learning, 8, pp. 16-24.
12. Çepni, S. (2012). Araştırma ve Proje Çalışmalarına Giriş. Geliştirilmiş 6. Baskı. s 76. Ankara. Ekiz, D. (2003). Eğitimde araştırma yöntem ve metotlarına giriş: nitel, nicel ve eleştirel kuram metodolojileri. Ankara: Anı Yayıncılık.
13. Ersoy, A.& Yalçınoğlu, P.(2012). Nitel araştırmaya giriş. Ankara: Anı Yayıncılık.
14. Goos, M. (2010). Using technology to support effective mathematics teaching and learning: What counts? Make it count: What research tells us about effective teaching and learning of mathematics (pp. 21-26). Camberwell: ACER.
15. Henderson, D.W & Taimina D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history. 3rd ed. New York (NY): Prentice Hall.
16. Higgins, S. (2003). Does ICT improve learning and teaching in schools?, Nottingham: British Educational Research Association.
17. Higgins, S., Z. Xiao, & M. Katsipataki. (2012). The Impact of Digital Technology on Learning: A Summary for the Education Endowment Foundation (Full Report).
18. Karakırık, E. (2016). LogoTürk Kaplumbağa Matematiği. Doğan, M ve Karakırık, E. (Ed.). Matematik Eğitiminde Teknoloji Kullanımı (2.Baskı) (s.47-77). Ankara. Nobel-Atlas Yayıncılık.
19. Karakırık, E., & Durmuş, S. (2005). A New Graphical Logo Design Called LogoTurk. Eurasia Journal of Mathematics, Science and Technology Education,1(1), 61-75.
20. Keiser, J,M. (2014). Struggles with developing the concept of angle: comparing sixth-grade students’ discourse to the history of the angle concept. Mathematical Thinking and Learning, 6, 285–306.
21. Khasawneh, A. A. (2009). Assessing Logo programming among Jordanian seventh grade students through turtle geometry. International journal of Mathematical Education in Science and Technology, 40(5), 619-639.
22. Kokol-Voljc, V. (2007). Use of mathematical software in pre-service teacher training: The case of DGS. Proceedings of The British Society For research into Learning Mathematics, 27(3), 126-131.
23. Lin, C-Y. (2008). Pre-service teachers’ beliefs about using technology in the mathematics classroom. The Journal of Computers in Mathematics and Science Teaching, 27(3), pp. 341 360. Littlefield, J., Delclos, V. R., Bransford, J. D., Clayton, K. N., & Franks, J. J. (1989). Some prerequisites for teaching thinking: Methodological issues in the study of LOGO programming. Cognition and Instruction, 6(4), 331-366.
24. Liu, L., & Cummings, R. (1997). Logo and Geometric Thinking. Computers in the Schools.14 (1-2), 95-110.
25. McMillan, J. H., & Schumacher, S. (2010). Research in Education: Evidence-Based Inquiry. (7th ed.). Boston, MA: Pearson.
26. Milli Eğitim Bakanlığı [MEB]. (2017). Ortaokul matematik dersi 1-8. sınıflar öğretim programı. Ankara: MEB Talim Terbiye Başkanlığı Yayınları.
27. Mitchelmore, M.C. & White, P. (1998). Development of angle concepts: A framework for research. Mathematics Education Research Journal, 10(3), 4–27.
28. National Council of the Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
29. Oldknow, A., Taylor, R., & Tetlow, L.(2010). Teaching Mathematics Using ICT (3rd.ed), New York: Continuum International Publishing Group.
30. Palmer, D. H. (1998). Measuring contextual error in the diagnosis of alternative conceptions in science. Issues in Educational Research, 8(1), 65-76.
31. Papert, S. (1993). Mindstorms: children, computers, and powerful ideas. 2nd ed. New York; London: Harvester Wheatsheaf.
32. Simmons, M., & Cope, P. (1997). Working with a round turtle: the development of angle/rotation concepts under restricted feedback conditions. Computers and Education, 28 (1), p. 23-33.
33. Sinclair, N., & Jackiw, N. (2005). Understanding and projecting ICT trends in mathematics education. In S. Johnston-Wilder & D. Pimm (Eds.), Teaching secondary mathematics with ICT (pp. 235–251). Maidenhead, UK: Open University Press.
34. So H.-J., & Kim, B. (2009). Learning about problem based learning: Student teachers integrating technology, pedagogy and content knowledge. Australasian Journal of Educational Technology. 25(1), 101-116.
35. Sulaiman, N.A.J. (2011). Exploring Kuwaiti mathematics: student-teachers' beliefs toward using Logo and mathematics education. PhD, Nottingham Trent University.
36. Stevens, T., To, Y., Harris, G., & Dwyer, J. (2008).The LOGO project: designing an effective continuing education program for teachers. The Journal of Computers in Mathematics and Science Teaching, 27(2), pp. 195-219.
37. Yelland, N. (1995). Mindstorms or storm in a teacup? A review of research with LOGO. International Journal of Mathematical Education for Science and Technology, 26, 853–869.
38. Yıldırım, A., ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. (6. baskı) Ankara: Seçkin Yayıncılık.
39. Wilson, M., & Cooney, T. (2002). Mathematics teacher change and development. The role of beliefs. In G. C. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127-147). Dordrecht: Kluwer Academic Publishers.
40. Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage.