ZDM

, Volume 43, Issue 3, pp 441–450 | Cite as

A story-based dynamic geometry approach to improve attitudes toward geometry and geometric proof

Original Article

Abstract

This work is a part of a larger study, which presents geometry through a daily life story using dynamic geometry software. It aimed in particular to enable students to feel the importance of geometry in daily life, to share in the process of formulating geometric statements and conjectures, to experience the geometric proof more than validating the correctness of geometric statements and to start with a real-life situation and go through seven steps to geometric proof. The content of the suggested approach was organized so that every activity was a prerequisite for entering the next one, either in the structure of geometric concepts or in the geometric story context. Some indications will be presented according to three Likert-type questionnaires, which were prepared by the researcher with the purpose of assessing students’ attitudes toward geometry and geometric proof, using computers in mathematics learning and the suggested approach. The analysis of single responses to questionnaire items showed significant changes in students’ beliefs about geometry, importance and functions of geometric proof and toward using the suggested approach.

Keywords

Attitudes toward geometry and geometry proof Real-life geometry Dynamic geometry software Contextual learning 

References

  1. Aarnes, J., & knudtzon, S. (2003). Conjecture and discovery in geometry a dialogue between exploring with dynamic geometric software and mathematical reasoning. Matematiska och Systemtekniska Institutionen. http://vxu.se/msi/picme10/f5aj.pdf. Accessed 15 Feb 2009.
  2. Almeida, D. (2000). A survey of mathematics undergraduates’ interaction with proof some implications for mathematics education. International Journal of Mathematical Education in Science and Technology, 31(6), 869–890.CrossRefGoogle Scholar
  3. Almeqdadi, F. (2000). The effect of using the geometer’s sketchpad (GSP) on Jordanian students’ understanding of geometrical concepts. In Proceeding of the international conference on technology in mathematics education, Beirut, Lebanon, pp. 163–169.Google Scholar
  4. Bjuland, R. (2004). Student teachers’ reflections on their learning process through collaborative problem solving in geometry. Educational Studies in Mathematics, 55, 199–225.CrossRefGoogle Scholar
  5. Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24, 359–387.CrossRefGoogle Scholar
  6. Christou, C. (2005). Problem solving and problem posing in a dynamic geometry environment. The Montana Mathematics Enthusiast, 2(2), 125–143. ISSN 1551-3440. http://www.math.umt.edu/tmme/vol2no2/TMMEv2n2a5.pdf. Accessed 25 Jan 2010.
  7. De Villiers, M. (2003). Rethinking proof with geometer’s sketchpad. Emeryville, CA: Key Curriculum Press.Google Scholar
  8. De Villiers, M. (2006). Rethinking proof with the geometer’s sketchpad. Emeryville, CA: Key Curriculum Press.Google Scholar
  9. Di Martino, P., & Zan, R. (2003). What does ‘positive’ attitude really mean? In N. Pateman, B. Dougherty, & J. Zillix (Eds.), Proceedings of the 2003 joint meeting of PME and PME-NA (Vol. 4, pp. 451–458).Google Scholar
  10. Duatepe-Paksu, A., & Ubuz, B. (2009). Effects of drama-based geometry instruction on student achievement, attitudes, and thinking levels. The Journal of Educational Research, 102, 272–286.CrossRefGoogle Scholar
  11. Fan, L., Quek, K. S., Zhu, Y., Yeo, S. M., Lionel, P., & Lee, P. Y. (2005). Assessing Singapore students’ attitudes toward mathematics and mathematics learning: Findings from a survey of lower secondary students. In East Asia regional conference on mathematics education, Shanghai, pp. 5–12.Google Scholar
  12. Furinghetti, F., & Paola, D. (2008). To produce conjectures and to prove them within a dynamic geometry environment: A case study. In International group psychology of mathematics education. http://www.lettredelapreuve.it/PME/PME27/RR_furinghetti.pdf. Accessed 18 Feb 2009.
  13. Gfeller, M., & Niss, M. (2005). An investigation of tenth grade students’ views of the purposes of geometric proof. In The annual meeting of the American Educational Research Association, Montreal, QC.Google Scholar
  14. Goldin, G., Rösken, B., & Törner, G. (2009). Beliefsno longer a hidden variable in mathematical teaching and learning processes. Library of Congress.Google Scholar
  15. Gómez-Chacón, I., & Haines, C. (2008). Students’ attitudes to mathematics and technology. Comparative study between the United Kingdom and Spain. In ICME-11, 11th international congress on mathematical education.Google Scholar
  16. Habre, S. (2009). Geometric conjectures in a dynamic geometry software environment. Mathematics and Computer Education, 43(2), 151.Google Scholar
  17. Hanna, G. (1993). Proof and application. Educational Studies in Mathematics, 24(4), 421.CrossRefGoogle Scholar
  18. Hay, K., & Barab, S. (2009). Constructivism in practice: A comparison and contrast of apprenticeship and constructionist learning environments. Journal of the Learning Sciences, 10(3), 281–322.CrossRefGoogle Scholar
  19. Herrmann, N. (2005). Mathematik ist überall. Oldenburg: Aufl. München.Google Scholar
  20. Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389–399.CrossRefGoogle Scholar
  21. Jiang, Z. (2002). Developing pre-service teachers’ mathematical reasoning and proof abilities in the geometer’s sketchpad environment. In Annual meeting of the North American chapter of the international group for the psychology of mathematics education, pp. 717–729.Google Scholar
  22. Jones, K. (2001). Learning geometrical concepts using dynamic geometry software. In K. Irwin (Ed.), Mathematics education research: A catalyst for change. University of Auckland, Auckland, New Zealand. pp. 50–58. http://eprints.soton.ac.uk/41222/01/Jones_learning_geometry_using_DGS_2000.pdf. Accessed 10 Feb 2009.
  23. Kanuka, H., & Anderson, T. (1999). Using constructivism in technology mediated learning: Constructing order out of the chaos in the literature. Radical Pedagogy (2). http://radicalpedagogy.icaap.org/content/vol1.1999/issue2/02kanuka1_2.html. Accessed 18 Feb 2008.
  24. Kemeny, V. (2006). Mathematics learning: Geometry. http://www.education.com/reference/article/mathematics-learning-geometry. Accessed 18 May 2009.
  25. Kortenkamp, U. (1999). Foundations of dynamic geometry. PhD thesis, Swiss Federal Institute of Technology Zurich.Google Scholar
  26. Mogari, D. (1999). Attitude and achievement in Euclidean geometry. In Proceedings of the international conference on mathematics education into the 21st century, Cairo.Google Scholar
  27. NCTM. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.Google Scholar
  28. NCTM (2009). Guiding principles for mathematics curriculum and assessment. http://www.nctm.org/standards/content.aspx?id=23273. Accessed May 2010.
  29. Nordström, K. (2003). Swedish university entrants’ experiences about and attitudes towards proofs and proving. A paper presented at the CERME 3, Italy.Google Scholar
  30. Noss, R. (1988). The computer as a cultural influence in mathematical learning. Educational Studies in Mathematics, 19(2), 251–268.CrossRefGoogle Scholar
  31. Phonguttha, R., Tayraukham, S., & Nuangchalerm, P. (2009). Comparisons of mathematics achievement, attitude towards mathematics and analytical thinking between using the geometer’s sketchpad program as media and conventional learning activities. Australian Journal of Basic and Applied Sciences, 3(3), 3036–3039.Google Scholar
  32. Pickens, J. (2005). Attitudes and perceptions. In N. Borkowski (Ed.), Organizational behavior (pp. 43–76). Sudbury, MA: Jones and Bartlett Publishers.Google Scholar
  33. Pierce, P., & Stacey, K. (2006). Enhancing the image of mathematics by association with simple pleasures from real world contexts. Zentralblatt für Didaktik der Mathematik, 38(3), 214–225.CrossRefGoogle Scholar
  34. Refaat, E. (2001). Effects of module-based instruction on developing mathematical proof skills and geometry achievement of preparatory school students Open image in new window Open image in new window Faculty of Education, Library of Suez Canal University, Egypt.Google Scholar
  35. Senk, L. (1989). Van Hiele levels and achievement in writing geometry proofs. Journal for Research in Mathematics Education, 20(3), 309–321.CrossRefGoogle Scholar
  36. Stillman, G. (2006). The role of challenge in engaging lower secondary students in investigating real world tasks. In E. Barbeau & P. Taylor (Eds.), Proceedings of the ICMI study 16: Mathematical challenges, Trondheim, Norway.Google Scholar
  37. Sun, L., & Williams, S. (2003). An instructional design model for constructivist learning. Department of Computer Science, University of Reading, UK. http://www.ais.reading.ac.uk/papers/con50-An%20Intructional%20design.pdf. Accessed 5 May 2009.
  38. Zan, R., & Di Martino, P. (2007). Attitudes towards mathematics: Overcoming positive/negative dichotomy. The Montana Mathematics Enthusiasts Monograph, 3, 157–168.Google Scholar

Copyright information

© FIZ Karlsruhe 2011

Authors and Affiliations

  1. 1.Faculty of EducationSuez Canal UniversityIsmailiaEgypt

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