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Articles

The challenge of multiple perspectives: multiple solution tasks for students incorporating diverse tools and representation systems

Pages 493-512 | Received 21 Apr 2013, Accepted 12 Nov 2013, Published online: 09 Jun 2014

References

  • Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198.
  • Ainsworth, S. (2008). The educational value of multiple-representations when learning complex scientific concepts. In J. K. Gilbert et al. (Eds.), Visualization: Theory and practice in science education (pp. 191–208). Dordrecht: Springer.
  • Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31, 235–268.
  • Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education. London: Routledge.
  • Crawford, K. (1996). Vygotskian approaches in human development in the information era. Educational Studies in Mathematics, 31, 43–62.
  • Dabbagh, N. (2005). Pedagogical models for e-learning: A theory-based design framework. International Journal of Technology in Teaching and Learning, 1, 25–44.
  • Duffy, T. M., & Cunningham, D. J. (1996). Constructivism: Implications for the design and delivery of instruction. In D. H. Jonassen (Ed.), Handbook of educational communications and technology (pp. 170–198). New York, NY: Simon & Schuster Macmillan.
  • Hakkarainen, P., Saarelainen, T., & Ruokamo, H. (2007). Towards meaningful learning through digital video supported, case based teaching. Australasian Journal of Educational Technology, 23, 87–109.
  • Hart, K.-M. (1981). Measurement. In K. Harrt (Ed.), Children’s understanding of mathematics: 11–16 (pp. 9–22). London: John Murray.
  • Hiebert, J. (1981). Units of measure: Results and implications from National Assessment. Arithmetic Teacher, 28(6), 38–43.
  • Hughes, E. R., & Rogers, J. (1979). The concept of area. In E. R. Hughes (Ed.), Conceptual powers of children: An approach through mathematics and science (pp. 78–135). Schools Council Research Studies. London: Macmillan Education.
  • Johnson, H. C. (1986). Area is a measure. International Journal of Mathematics Education, Science and Technology, 17, 419–424.
  • Jonassen, D. H., Carr, C., & Yueh, H.-P. (1998). Computers as mindtools for engaging learners in critical thinking. Tech Trends, 43(2), 24–32.
  • Kamii, C., & Kysh, J. (2006). The difficulty of ‘length x width’: Is a square the unit of measurement? The Journal of Mathematical Behavior, 25, 105–115.
  • Kordaki, M. (2003). The effect of tools of a computer microworld on students’ strategies regarding the concept of conservation of area. Educational Studies in Mathematics, 52, 177–209.
  • Kordaki, M. (2005, June). The role of multiple representation systems in the enhancement of the learner model. Paper presented at the 3rd International Conference on Multimedia and ICT in Education. Badajoz, Spain.
  • Kordaki, M., & Balomenou, A. (2006). Challenging students to view the concept of area in triangles in a broader context: Exploiting the tools of Cabri II. Ιnternational Jοurnal of Computers for Mathematical Learning, 11, 99–35.
  • Kordaki, M., & Potari, D. (1998). A learning environment for the conservation of area and its measurement: A computer microworld. Computers & Education, 31, 405–422.
  • Kordaki, M., & Potari, D. (2002). The effect of tools of area measurement on students’ strategies: The case of a computer microworld. Ιnternational Jοurnal of Computers for Mathematical Learning, 7, 65–100.
  • Leikin, R., & Lev, M. (2007, July). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. Paper presented at the 33rd Conference of the International Group for the Psychology of Mathematics Education, Seoul, Korea.
  • Leikin, R., Levav-Waynberg, A., Gurevich, I., & Mednikov, L. (2006). Implementation of multiple solution connecting tasks: Do students’ attitudes support teachers’ reluctance? Focus on Learning Problems in Mathematics, 28, 1–22.
  • Levav-Waynberg, A., & Leikin, R. (2012a). The role of multiple solution tasks in developing knowledge and creativity in geometry. The Journal of Mathematical Behavior, 31, 73–90.
  • Levav-Waynberg, A., & Leikin, R. (2012b). Using multiple solution tasks for the evaluation of students’ problem-solving performance in geometry. Canadian Journal of Science, Mathematics and Technology Education, 12, 311–333.
  • Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Lawrence Erlbaum Associates.
  • National Council of Teachers of Mathematics. (2008). Principles and standards for school mathematics. Reston, VA: Author.
  • Piaget, J., Inhelder, B., & Sheminska, A. (1981). The child’s conception of geometry. New York, NY: Norton & Company.
  • Rider, R. (2007). Shifting from traditional to non traditional teaching practices using multiple representations. Mathematics Teacher, 100, 494–500.
  • Schukajlow, S., & Krug, A. (2013, February 6–10). Uncertainty orientation, preference for multiple solutions and modeling. Paper presented at CERME 8, Manavgat Side, Turkey. Retrieved from http://cerme8.metu.edu.tr/wgpapers/WG8/WG8_Schukajlow.pdf
  • Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2012). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79, 215–237.
  • Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287–301.
  • Smith III, J. P., van den Heuvel-Panhuizen, M., & Teppo, A. R. (2011). Learning, teaching, and using measurement: Introduction to the issue. ZDM Mathematics Education, 43, 617–620.
  • Tsamir, P., Tirosh, D., Tabach, M., & Levenson, E. (2010). Multiple solution methods and multiple outcomes – Is it a task for kindergarten children? Educational Studies in Mathematics, 73, 217–231.
  • White, T., & Pea, R. (2011). Distributed by design: On the promises and pitfalls of collaborative learning with multiple representations. The Journal of the Learning Sciences, 20, 489–547.
  • Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. Journal of Mathematical Behavior, 25, 224–239.

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