Research Article
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The Potential of Dynamic Geometry Software in Bridging the Link Between Experimental Verification and Formal Proof

Year 2016, Volume: 7 Issue: 1, 24 - 34, 05.04.2016
https://doi.org/10.16949/turcomat.65927

Abstract

The national secondary school mathematics curriculum of Turkey, promulgated in 2013, encourages teachers to integrate dynamic geometry software into their classroom practices. One of the reasons for this request is that this kind of software offer teachers the opportunity to design learning environments in which students can experience the processes that constitutes mathematical exploration and proof. However, in order to exploit the possible advantages of integrating such software, teachers need the necessary technical knowledge about the software to be used and concrete examples of how it can be utilized as well. This study aims to contribute to the latter need by analyzing the solution steps of an open-ended geometry problem and exemplifying the role of the software in the solution process.

References

  • Bruckheimer, M., & Arcavi, A. (2001). A Herrick among mathematicians or dynamic geometry as an aid to proof. International Journal of Computers for Mathematical Learning, 6(1), 113-126.
  • Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339-352.
  • Cuoco, A. A., & Goldenberg, E. P. (1997). Dynamic geometry as a bridge from Euclidean geometry to analysis. In J. King & D. Schattschneider (Eds.) Geometry turned on: Dynamic software in learning, teaching and research (pp. 33-46). MAA NOTES
  • Furinghetti, F., & Paola, D. (2003). To produce conjectures and to prove them within a dynamic geometry environment: A case study. International Group for the Psychology of Mathematics Education, 2, 397-404.
  • Guven, B. (2008). Using dynamic geometry software to gain insight into a proof. International Journal of Computers for Mathematical Learning, 13(3), 251-262.
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational studies in mathematics, 44(1-2), 5-23.
  • Hoyles, C. & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.) Perspectives on the Teaching of Geometry for the 21st Century (pp.121-128). London, Springer.
  • Jones, K. (2000). Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational studies in mathematics, 44(1), 55-85.
  • Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutierrez & P. Boero (Eds.) Handbook of Research on the Psychology of Mathematics Education (pp. 173-204). Rotterdam: Sense Publishers
  • MEB (2013). Ortaöğretim Matematik Dersi Öğretim Programı. Ankara
  • Mogetta, C., Olivero, F., & Jones, K. (1999). Providing the motivation to prove in a dynamic geometry environment. Proceedings of the British society for research into learning mathematics, 19(2), 91-96.
  • Polya, G. (1957). How to solve it: A new aspect of mathematical thought (2nd ed.). Princeton, NJ: Princeton University Press
  • Straesser, R. (2002). Cabri-Geometre: Does dynamic geometry software (DGS) change geometry and its teaching and learning?. International Journal of Computers for Mathematical Learning, 6(3), 319-333.

Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli

Year 2016, Volume: 7 Issue: 1, 24 - 34, 05.04.2016
https://doi.org/10.16949/turcomat.65927

Abstract

Ülkemizde 2013 yılında yayımlanan Ortaöğretim Matematik Dersi Öğretim Programı öğretmenlerden, öğretim sürecine dinamik geometri programlarını dâhil etmesini istemektedir. Bu isteğin gerekçelerinden biri, bu yazılımların öğrencilere matematiksel araştırma sürecinde gerçekleşen eylemleri deneyimleme fırsatı sunmasıdır. Bu beklentinin gerçekleşmesi için öğretmenlerin yazılımlara ilişkin teknik bilgiye sahip olmalarının yanı sıra, yazılımların bu amaç doğrultusunda nasıl işe koşulabileceğini gösteren somut örneklere ihtiyaçları bulunmaktadır. Bu gerekçeden hareketle bu çalışmada, yazar tarafından ortaya koyulmuş araştırma türünden bir geometri probleminin, GeoGebra içerisinde gerçekleştirilmiş çözümü aşamalar halinde sunulmuştur.

References

  • Bruckheimer, M., & Arcavi, A. (2001). A Herrick among mathematicians or dynamic geometry as an aid to proof. International Journal of Computers for Mathematical Learning, 6(1), 113-126.
  • Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. International Journal of Science and Mathematics Education, 2(3), 339-352.
  • Cuoco, A. A., & Goldenberg, E. P. (1997). Dynamic geometry as a bridge from Euclidean geometry to analysis. In J. King & D. Schattschneider (Eds.) Geometry turned on: Dynamic software in learning, teaching and research (pp. 33-46). MAA NOTES
  • Furinghetti, F., & Paola, D. (2003). To produce conjectures and to prove them within a dynamic geometry environment: A case study. International Group for the Psychology of Mathematics Education, 2, 397-404.
  • Guven, B. (2008). Using dynamic geometry software to gain insight into a proof. International Journal of Computers for Mathematical Learning, 13(3), 251-262.
  • Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational studies in mathematics, 44(1-2), 5-23.
  • Hoyles, C. & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.) Perspectives on the Teaching of Geometry for the 21st Century (pp.121-128). London, Springer.
  • Jones, K. (2000). Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational studies in mathematics, 44(1), 55-85.
  • Mariotti, M. A. (2006). Proof and proving in mathematics education. In A. Gutierrez & P. Boero (Eds.) Handbook of Research on the Psychology of Mathematics Education (pp. 173-204). Rotterdam: Sense Publishers
  • MEB (2013). Ortaöğretim Matematik Dersi Öğretim Programı. Ankara
  • Mogetta, C., Olivero, F., & Jones, K. (1999). Providing the motivation to prove in a dynamic geometry environment. Proceedings of the British society for research into learning mathematics, 19(2), 91-96.
  • Polya, G. (1957). How to solve it: A new aspect of mathematical thought (2nd ed.). Princeton, NJ: Princeton University Press
  • Straesser, R. (2002). Cabri-Geometre: Does dynamic geometry software (DGS) change geometry and its teaching and learning?. International Journal of Computers for Mathematical Learning, 6(3), 319-333.
There are 13 citations in total.

Details

Primary Language Turkish
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Erdem Çekmez

Publication Date April 5, 2016
Published in Issue Year 2016 Volume: 7 Issue: 1

Cite

APA Çekmez, E. (2016). Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(1), 24-34. https://doi.org/10.16949/turcomat.65927
AMA Çekmez E. Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli. Turkish Journal of Computer and Mathematics Education (TURCOMAT). April 2016;7(1):24-34. doi:10.16949/turcomat.65927
Chicago Çekmez, Erdem. “Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 7, no. 1 (April 2016): 24-34. https://doi.org/10.16949/turcomat.65927.
EndNote Çekmez E (April 1, 2016) Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 7 1 24–34.
IEEE E. Çekmez, “Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli”, Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 7, no. 1, pp. 24–34, 2016, doi: 10.16949/turcomat.65927.
ISNAD Çekmez, Erdem. “Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli”. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 7/1 (April 2016), 24-34. https://doi.org/10.16949/turcomat.65927.
JAMA Çekmez E. Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2016;7:24–34.
MLA Çekmez, Erdem. “Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli”. Turkish Journal of Computer and Mathematics Education (TURCOMAT), vol. 7, no. 1, 2016, pp. 24-34, doi:10.16949/turcomat.65927.
Vancouver Çekmez E. Deneysel Doğrulamadan Formel İspata Uzanan Süreçte Dinamik Geometri Yazılımlarının Potansiyeli. Turkish Journal of Computer and Mathematics Education (TURCOMAT). 2016;7(1):24-3.