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Prospective Mathematics Teachers’ Processes for Solving Optimization Problems Using Cabri 3D

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Abstract

In this study, based on task-based interviews, prospective mathematics teachers were asked, using Cabri 3D, to find the minimal distance from one point to another on a cube and on rectangular prisms and then the epistemic modes used as they solved these optimization problems were analyzed. The results indicate that these prospective teachers had difficulty reasoning about the location of the optimal points. They made sense of the optimal distances and produced conjectures after dragging objects and making measurements. As they became more comfortable comparing and contrasting the lengths of different paths, they became more purposeful in using the tools in Cabri 3D (e.g. the Length tool) to identify optimal distances. Once the participants had represented the problem situation in two dimensions, they used Cabri 3D sparingly and produced a generalized conjecture.

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References

  • Accascina, G., & Rogora, E. (2006). Using Cabri 3D diagrams for teaching geometry. International Journal for Technology in Mathematics Education, 13(1), 11–22.

    Google Scholar 

  • Assude, T. (2007). Teachers’ practices and degree of ICT integration. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of CERME V (pp. 1339–1348). Larnaca, Cyprus: European Society for Research in Mathematics Education.

    Google Scholar 

  • Baccaglini-Frank, A., & Mariotti, M. (2010). Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), 225–253.

    Article  Google Scholar 

  • Bainville, E. & Laborde, J.-M. (2004). Cabri 3D (version 2.0). Grenoble, France: Cabrilog. (http://www.cabri.com)

    Google Scholar 

  • Barrera-Mora, F., & Reyes-Rodríguez, A. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments. The Mathematics Enthusiast, 10(1–2), 109–136.

    Google Scholar 

  • Bernard, H., & Ryan, R. (2010). Analyzing qualitative data: Systematic approaches. Thousand Oaks, CA: Sage Publications.

    Google Scholar 

  • Blake, R. (1985). The spider and the fly: A geometric encounter in three dimensions. The Mathematics Teacher, 78(2), 98–104.

    Google Scholar 

  • Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Mathematics Enthusiast, 2(2), 125–143.

    Google Scholar 

  • Cuoco, A., & Goldenberg, P. (1997). Dynamic geometry as a bridge from Euclidian geometry to analysis. In J. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching and research (pp. 33–44). Washington, DC: The Mathematical Association of America.

    Google Scholar 

  • Dick, T., & Hollebrands, K. (2011). Focus in high school mathematics: Technology to support reasoning and sense making. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Erez, M., & Yerushalmy, M. (2006). “if you can turn a rectangle into a square, you can turn a square into a rectangle …”: Young students experience the dragging tool. International Journal of Computers for Mathematical Learning, 11(3), 271–299.

    Article  Google Scholar 

  • Fahlgren, M., & Brunström, M. (2014). A model for task design with focus on exploration, explanation, and generalization in a dynamic geometry environment. Technology, Knowledge and Learning, 19(3), 287–315.

    Article  Google Scholar 

  • Furinghetti, F., Morselli, F., & Paola, D. (2005). Interaction of modalities in Cabri: A case study. In H. Chick & J. Vincent (Eds.), Proceedings of the 29th conference of the International Group for the Psychology of mathematics education (Vol. 3, pp. 9–16). Melbourne: PME.

    Google Scholar 

  • Guven, B. (2008). Using dynamic geometry software to convey real-world situations into the classroom: The experience of student mathematics teachers with a minimum network problem. Teaching Mathematics and its Applications, 27(1), 24–37.

    Article  Google Scholar 

  • Hollebrands, K. (2007). The role of a dynamic software program for geometry in the strategies high school mathematics students employ. Journal for Research in Mathematics Education, 38(2), 164–192.

    Google Scholar 

  • Hollebrands, K., Laborde, C., & Sträβer, R. (2008). Technology and the learning of geometry at the secondary level. In K. Heid & G. Blume (Eds.), Research on technology and the teaching and learning of mathematics: Research syntheses (Vol. 1, pp. 155–206). Charlotte: Information Age Publishing.

    Google Scholar 

  • Jiang, Z., & McClintock, E. (1997). Using the Geometer’s Sketchpad with preservice teachers. In J. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching and research (pp. 129–136). Washington, DC: The Mathematical Association of America.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Laborde, C. (2008). Experiencing the multiple dimensions of mathematics with dynamic 3D geometry environments: Illustration with Cabri 3D. The Electronic Journal of Mathematics and Technology, 2(1), 1–10.

    Google Scholar 

  • Laborde, C., Kynigos, C., Hollebrands, K., & Sträβer, R. (2006). Teaching and learning geometry with technology. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 275–304). Rotterdam: Sense Publications.

    Google Scholar 

  • Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM: The International Journal on Mathematics Education, 43(3), 325–336.

    Article  Google Scholar 

  • Leung, A. (2017). Exploring techno-pedagogic task design in the mathematics classroom. In A. Leung & A. Baccaglini-Frank (Eds.), Digital technologies in designing mathematics education tasks: Potential and pitfalls (pp. 3–16). Cham: Springer.

    Chapter  Google Scholar 

  • Leung, A., & Or, A. (2009). Cognitive apprehension in Cabri 3D environment. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 417). Thessaloniki: PME.

    Google Scholar 

  • Mamolo, A., Ruttenberg-Rozen, R., & Whiteley, W. (2015). Developing a network of and for geometric reasoning. ZDM: The International Journal on Mathematics Education, 47(3), 483–496.

    Article  Google Scholar 

  • Merriam, S. (2009). 3rd edn. In Qualitative research: A guide to design and implementation. San Francisco: Jossey-Bass.

    Google Scholar 

  • Morrow, J. (1997). Dynamic visualization from middle school through college. In J. King & D. Schattschneider (Eds.), Geometry turned on! Dynamic software in learning, teaching and research (pp. 47–54). Washington, DC: The Mathematical Association of America.

    Google Scholar 

  • NCTM. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • NCTM. (2009). Focus in high school mathematics: Reasoning and sense making. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • NCTM. (2014). Principles to actions: Ensuring mathematical success for all students. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Pratt, D., & Ainley, J. (1997). The construction of meanings for geometric construction: Two contrasting cases. International Journal of Computers for Mathematical Learning, 1(3), 293–322.

    Article  Google Scholar 

  • Santos-Trigo, M., & Reyes-Rodriguez, A. (2011). Teachers’ use of computational tools to construct and explore dynamic mathematical models. International Journal of Mathematical Education in Science and Technology, 42(3), 313–336.

    Article  Google Scholar 

  • Scher, D. (2005). Square or not? Assessing constructions in an interactive geometry software environment. In W. Masalski & P. Elliott (Eds.), Technology-supported mathematics learning environments (pp. 113–136). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.

    Article  Google Scholar 

  • Widder, M., & Gorsky, P. (2013). How students use a software application for visualizing 3D geometric objects to solve problems. Journal of Computers in Mathematics and Science Teaching, 32(1), 89–120.

    Google Scholar 

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Authors and Affiliations

  1. North Carolina State University, Raleigh, NC, USA

    Karen Hollebrands

  2. Recep Tayyip Erdogan University, Rize, Turkey

    Samet Okumus

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  1. Karen Hollebrands
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  2. Samet Okumus
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Correspondence to Samet Okumus.

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Hollebrands, K., Okumus, S. Prospective Mathematics Teachers’ Processes for Solving Optimization Problems Using Cabri 3D. Digit Exp Math Educ 3, 206–232 (2017). https://doi.org/10.1007/s40751-017-0033-0

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  • DOI: https://doi.org/10.1007/s40751-017-0033-0

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