Overcoming the Obstacle of Poor Knowledge in Proving Geometry Tasks
Keywords:
Computer-aided observation, Dynamic geometry, OK Geometry, Proof
Abstract
Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves several processes, the most salient being visual observation and deductive argumentation. These two processes are interwoven, but often poor observation hinders deductive argumentation. In the present article, we consider the possibility of overcoming the obstacle of a student’s poor observation by making use of computer-aided observation with appropriate software. We present the results of two small-scale research projects, both of which indicate that students are able to work out considerably more deductions if computer-aided observation is used. Not all students use computer-aided observation effectively in proving tasks: some find an exhaustive computer-provided list of properties confusing and are not able to choose the properties that are relevant to the task.
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References
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Pedemonte, B. (2007). How can the relationship between argumentation and proof be analyzed? Educational Studies in Mathematics, 66, 23–41.
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Fujita, T., Jones, K., & Kunimune, S. (2010). Students’ geometrical constructions and proving activities: a case of cognitive unity? In M. F. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th
Annual Conference of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 9–16). Belo Horizonte, Brazil.
Furinghetti, F., & Morselli, F. (2011). Beliefs and beyond: hows and whys in the teaching of proof. Zentralblatt für Didaktik der Mathematik, 43, 587–599.
Hadas, N., Hershkowitz, R., & Schwarz, 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.
Hanna, G., & Sidoli, N. (2007). Visualization and proof: a brief survey of philosophical perspectives, Zentralblatt für Didaktik der Mathematik, 39, 73–78.
Hanna, G. (2000). Proof, Explanation and Exploration: an Overview. Educational Studies in Mathematics, 44, 5–23.
Hemmi, K. (2010). Three styles characterising mathematicians’ pedagogical perspectives on proof. Educational Studies in Mathematics, 75, 271–291.
Herbst, P. G. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49, 283–312.
Jahnke, H. N. (2007). Proofs and Hypotheses. Zentralblatt für Didaktik der Mathematik, 39(1-2), 79–86.
Kahney, H. (1993). Problem Solving: Current Issues. Buckingham: Open University Press.
Knuth, E. J. (2002). Teachers’ Conceptions of Proof in the Context of Secondary School Mathematics. Journal of Mathematics Teacher Education, 5, 61–88.
Lingefjärd, T. (2011). Rebirth of Euclidean geometry? In L. Bu & R. Schoen (Eds.), Model-Centered Learning: Pathways to Mathematical Understanding Using GeoGebra (pp. 205–215). Rotterdam: Sense Publishers.
Mariotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44, 25–53.
Nunokawa, K. (2010). Proof, mathematical problem-solving, and explanation in mathematics teaching. In G. Hanna (Ed.), Explanation and proof in mathematics. Philosophical and educational perspectives (pp. 223–236). Berlin: Springer.
Orton, A., & Frobisher, L. J. (1996). Insights into Teaching Mathematics. London: Cassel.
Pedemonte, B. (2007). How can the relationship between argumentation and proof be analyzed? Educational Studies in Mathematics, 66, 23–41.
Raman, M. (2003). Key ideas: what are they and how can they help us understand how people view proof? Educational Studies in Mathematics, 52, 319–325.
Schoenfeld, A. H. (1985). Mathematical Problem Solving. San Diego: Academic Press.
Stylianides, A., & Stylianides, G. J. (2009). Proof Constructions and Evaluations. Educational Studies in Mathematics, 72(2), 237–253.
Published
2013-12-31
How to Cite
Magajna, Z. (2013). Overcoming the Obstacle of Poor Knowledge in Proving Geometry Tasks. Center for Educational Policy Studies Journal, 3(4), 99-116. https://doi.org/10.26529/cepsj.225
Section
FOCUS
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