Ortaokul Matematik Öğretmen Adaylarının Üçgen Eşitsizliğini Toplu Argümantasyonla Kavrayışları

Bu çalışmanın amacı, ortaokul matematik öğretmen adaylarının üçgen eşitsizliğiyle ilgili düşünce ve öğrenmelerini toplu argümantasyon yoluyla nasıl geliştirdiklerini incelemektir. Veri toplama süreci toplu sınıf tartışmaları, akran grubu tartışmaları ve yazılı belgeler üzerine kurulmuştur. Tartışma süreci Toulmin'in argümantasyon modeli kullanılarak analiz edilmiştir. Katılımcılar kolektif tartışma süreci boyunca, üçgen eşitsizliği konusundaki geometrik fikirlerini öne sürerek ve bunları sorgulayarak gerekli bilgi ve kavrayışa ulaşmışlar ve nihayetinde bu kavram hakkındaki bilgilerini ve kavrayışlarını geliştirmişlerdir. Katılımcıların, ügen eşitsizliği konusundaki bilgi ve kavrayışlarını, matematiksel fikirlerini argümantasyon yoluyla yeniden değerlendirerek geliştirdikleri görülmüştür.

Anahtar Kelimeler:

Argümantasyon, ortaokul matematik öğretmen adayı, sosyal öğrenme ortamı, üçgen Eşitsizliği.

Preservice Middle School Mathematics Teachers’ Understanding of Triangle Inequality through Collective Argumentation

The purpose of the present study was to examine how preservice middle school mathematics teachers develop the understanding and reasoning of triangle inequality through collective argumentation. Data collection process was based on whole class and peer group discussions and written documents. The data including the transcriptions of the discussion processes with the written documents were analyzed by using Toulmin’s model of argumentation. Through this collective argumentation process, they attained the knowledge and understanding of triangle inequality by suggesting and challenging their geometrical ideas about the concept and they developed and constructed their knowledge and understanding of this concept. It was found that the participants improved their knowledge and understanding of triangle inequality by argumentation through criticizing their mathematical ideas.

Keywords:

Argumentation, preservice middle school mathematics teachers, social learning,

PDF

___

Abi-El-Mona, I. & Abd-El-Khalick, F. (2011). Perceptions of the nature and goodness of argument among college students, science teachers and scientists. International Journal of Science Education, 33(4), 573-605.
Andrews, P. (1997). A hungarian perspective on mathematics education. Mathematics Teaching, 161, 14-17.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. rouws(Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: Macmillan.
Cobb, P., Gravemeijer, K., Yackel, E., McClain, K., & Whitenack, J. (1997). Mathematizing and symbolizing: The emergence of chains of signification in one first-grade classroom. In D. Kirshner & J. A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 151–233). Mahwah, NJ: Erlbaum.
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks, CA: SAGE Publications.
Creswell, J. W. (2012). Educational research: planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Thousand Oaks, CA: SAGE Publications. Duschl, R. & Osborne, J. (2002). Supporting argumentation discourse in science education. Studies in Science Education, 38, 39-72.
Flores, H. (2007). Esquemas de argumentación en profesores de matemáticas del bachillerato. Educación Matemática, 19, 63-98.
Forman E. A., Larreamendy-Joerns J., Stein M. K., & Brown C. A. (1998). You’re going to want to find out which and prove it. Collective argumentation in a mathematics classroom. Learning and Instruction, 8(6), 527–548.
Gall, M. D., Gall, J. P., & Borg, W. R. (2007). Educational research: An introduction. Boston: Pearson Education. Hadas, N., Hershkowitz, R., & Shwarz, B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44, 127-150
Halat, E., (2007). Reform-based curriculum & acquisition of the levels. Eurasia Journal of Mathematics, Science and Technology Education, 3(1), 41-49.
Hershkowitz, R., &Vinner, S. (1984). “Children’s concepts in elementary geometry: A reflection of teachers’ concepts?” Southwell, B., Eyland, R., Cooper, M., Conroy, J & Collis, K. (Eds). Proceedings of the Eighth International Conference for the Psychology of Mathematics Education (p. 63-69). Darlinghurst, Austrailia: Mathematical Association of New South Wales.
Jim´enez-Aleixandre, M. P., Bugallo, A., & Duschl, R. A. (2000). Doing the lesson or doing the science: Argument in high school genetics. Science Education, 84(6), 757-792.
Jonassen, D., & Kim, B. (2010). Arguing to learn and learning to argue: Design justifications and guidelines. Educational Technology Research and Development, 58, 439-457.
Krummheuer, G. (1995). The ethnography of argumentation. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 229-269). Hillsdale, NJ: Lawrence Erlbaum Associates.
Lambert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27, 29-63.
Merriam, S.B. (2009). Qualitative Research: A Guide to Design and Implementation. San Francisco: Jossey-Bass.
Muijs, D. & Reynolds, D. (2002). Teachers’ beliefs and behaviors: What really matters? Journal of Classroom Interaction, 37, 3-15.
Olkun, S. & Toluk, Z. (2004). Teacher questioning with an appropriate manipulative may make a big difference. IUMPST: The Journal, 2, 1-11.
Osborne, J., Erduran, S., & Simon, S. (2004). Enhancing the quality of argumentation in school science. Journal of Research in Science Teaching, 41(10), 994-1020. Owen, J. E. (1995). Cooperative learning in secondary schools. London: Routledge.
Toulmin, S. E. (1969). The uses of argument. Cambridge: Cambridge University Press.
Van Zoest, L.R. & Enyart, A. (1998). Discourse of course: encouraging genuine mathematical conversations. Mathematics Teaching in the Middle School, 4(3), 150-157.
Zembaul-Saul, C. (2005, April). “Pre-service teachers’ understanding of teaching elementary school science argument.” Paper presented at the Annual Meeting of the National Association for Research in Science Teaching, Dallas.