Preservice Middle School Mathematics Teachers’ Understanding of Triangle Inequality through Collective Argumentation
Abstract
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
References
- 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.