• Ilhan Koyuncu
  • Didem AkyuzEmail author
  • Erdinc Cakiroglu


This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies developed by 2 prospective teachers. The results revealed that although the participants mostly used algebraic solutions in the PPB environment, they preferred geometric solutions in the GGB environment even though algebraic solutions were still possible (the software did not preclude them). Furthermore, different proofing strategies were developed in each environment. This suggests that changing the environment may prompt students to seek for additional solutions, which, in turn, results in a deeper understanding of the problem. As such, using both environments simultaneously in solving the same problems appears to bring about important benefits.

Key words

dynamic geometry software GeoGebra mathematical problem solving 


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  1. Blum, W. & Niss, M. (1991). Applied mathematical problem solving, modeling, applications, and links to the other subjects—State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37–68.CrossRefGoogle Scholar
  2. Booker, G. & Bond, D. (2008). Problem-solving in mathematics. Greenwood, Western Australia: R.I.C. Publications.Google Scholar
  3. Borwein, J. M. & Bailey, D. H. (2003). Mathematics by experiment: Plausible reasoning in the 21st century. Natick, MA: AK Peters.Google Scholar
  4. Cai, J. & Hwang, S. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21(4), 401–421.CrossRefGoogle Scholar
  5. Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments. 28th Conference of the International Group for the Psychology of Mathematics Education, Norway.Google Scholar
  6. Coşkun, Ş. (2011). A multiple case study investigating the effects of technology on students‘visual and nonvisual thinking preferences: comparing paper-pencil and dynamic software based strategies of algebra word problems. Unpublished doctoral dissertation, University of Central Florida, Florida, USAGoogle Scholar
  7. Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches. Thousand Oaks, CA: Sage.Google Scholar
  8. Cuban, L., Kirkpatrick, H. & Peck, C. (2001). High access and low use of technologies in high school classrooms: Explaining an apparent paradox. American Educational Research Journal, 38(4), 813–834.CrossRefGoogle Scholar
  9. Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 37–52). Dordrecht: Kluwer.Google Scholar
  10. Gal, H. & Linchevski, L. (2010). To see or not to see: Analyzing difficulties in geometry from the perspective of visual perception. Educational Studies in Mathematics, 74(2), 163–183.CrossRefGoogle Scholar
  11. Ginsburg, H. P. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4–11.Google Scholar
  12. Gomes, A. S., & Vergnaud, G. (2010). On the learning of geometric concepts using dynamic geometry software. RENOTE, 2(1)Google Scholar
  13. Hohenwarter, M., & Fuchs, K. (2004). Combination of dynamic geometry, algebra and calculus in the software system GeoGebra. Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching Conference, Pecs, HungaryGoogle Scholar
  14. Iranzo-Domenech, N. (2009). Influence of dynamic geometry software on plane geometry problem solving strategies. Unpublished doctoral dissertation, Universitat Autonoma de Barcelona, SpainGoogle Scholar
  15. Koehler, M. J. & Mishra, P. (2005). What happens when teachers design educational technology? The development of technological pedagogical content knowledge. Journal of Educational Computing Research, 32(2), 131–152.CrossRefGoogle Scholar
  16. Kokol-Voljc, V. (2007). Use of mathematical software in pre-service teacher training: The case of GeoGebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 55–60.Google Scholar
  17. Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: The University of Chicago Press. Eds.: J. Kilpatrick & I. Wirszup.Google Scholar
  18. Laborde, C. (2002). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.CrossRefGoogle Scholar
  19. Lee, H. & Hollebrands, K. (2008). Preparing to teach mathematics with technology: An integrated approach to developing technological pedagogical content knowledge. Contemporary Issues in Technology and Teacher Education, 8(4), 326–341.Google Scholar
  20. Mariotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44(1–2), 25–53.CrossRefGoogle Scholar
  21. Meydiyev, R. (2009). Exploring students’ learning experiences when using a dynamic geometry software tool in a geometry class at a secondary class in Azerbaijan. Unpublished master’s thesis, Universiteit van Amsterdam, The NetherlandsGoogle Scholar
  22. Ministry of National Education [MoNE] (2009). İlköğretim Matematik Dersi 6–8. Sınıflar Öğretim Programı. Ankara, Turkey: Talim ve Terbiye KuruluGoogle Scholar
  23. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  24. Preiner, J. (2008). Introducing dynamic mathematics software to mathematics teachers: The case of GeoGebra. Unpublished doctoral dissertation, University of Salzburg, Salzburg, AustriaGoogle Scholar
  25. Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6, 42–46.Google Scholar
  26. Yerushalmy, M. (2006). Slower algebra students meet faster tools: Solving algebra word problems with graphing software. Journal for Research in Mathematics Education, 37(5), 356–387.Google Scholar
  27. Zbiek, R. M. (2003). Using technology to foster mathematical meaning through problem solving. In H. L. Schoen & R. I. Charles (Eds.), Teaching mathematics through problem solving (pp. 93–104). Reston: The National Council of Teachers of Mathematics, Inc.Google Scholar
  28. Zbiek, R. M., Heid, M. K., Blume, G. W. & Dick, T. P. (2007). Research on technology in mathematics education. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169–1207). Charlotte, NC: Information Age Publishing.Google Scholar

Copyright information

© National Science Council, Taiwan 2014

Authors and Affiliations

  1. 1.Middle East Technical UniversityAnkaraTurkey

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