Abstract
We urge the reader to solve these problems before reading the paper. Then we suggest that the reader asks himself whether there is a different route or a different analysis of the given situation that leads to a different solution to any of the problems.
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References
Blum, M., & Leiβ, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modeling (ICTMA 12): Education, engineering and economics (pp. 222–231). Chichester: Horwood Publishing.
Blum, V., & Niss, M. (1991). Applied mathematical problem solving, modeling, applications, and links to other subjects – State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37–68.
Elia, I., Van den Heuvel-Panhuizen, M., & Kolovou A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM Mathematics Education, 41, 605–618.
Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht, The Netherlands: Kluwer.
Fennema, E., & Romberg, T. A. (Eds.). (1999). Classrooms that promote mathematical understanding. Mahwah, NJ: Erlbaum.
House, P. A., & Coxford, A.F. (1995). Connecting mathematics across the curriculum: 1995 Yearbook. Reston, VA: NCTM.
Kwon, O. N., Park, J. S., & Park, J. H. (2006). Cultivating divergent thinking in mathematics through an open-ended approach. Asia Pacific Education Review, 7, 51–61.
Leikin, R. (2003). Problem-solving preferences of mathematics teachers: Focusing on symmetry. Journal of Mathematics Teacher Education, 6, 297–329.
Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In D. Pitta-Pantazi & G. Philippo (Eds.), Proceeding of The Fifth Conference of the European Society for Research in Mathematics Education – CERME-5 (pp. 2330–2339) (CD-ROM and On-line). Retrieved June 2, 2016, from http://ermeweb.free.fr/Cerme5.pdf
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–145). Rotterdam, The Netherlands: Sense Publishers.
Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: A model and modeling perspective on teaching, learning, and problem solving in mathematics education. Mahwah, NJ: Lawrence Erlbaum.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Mahwah, NJ: Lawrence Erlbaum.
Liljedahl, P., & Sriraman, B. (2006). Musings on mathematical creativity. For the Learning of Mathematics, 26, 20–23.
Lo, M. L., & Marton, F. (2012). Toward a science of the art of teaching: Using variation theory as a guiding principle of pedagogical design. International Journal for Lesson and Learning Studies, 1(1), 7–22.
Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Erlbaum.
Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. The Journal of the Learning Science, 15, 193–220.
Maaβ, K. (2006). What are modelling competencies? ZDM Mathematics Education, 38, 113–142.
National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
Peled, I., & Balacheff, N. (2011). Beyond realistic considerations: Modeling conceptions and controls in task examples with simple word problems. ZDM Mathematics Education, 43, 307–315.
Peled, I., & Bassan-Cincenatus, R. (2005). Degrees of freedom in modeling: Taking certainty out of proportion. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th International Conference for the Psychology of Mathematics Education, 4, 57–64.
Polya, G. (1981). Mathematical discovery: On understanding, learning and teaching problem solving. New York, NY: Wiley.
Ryve, A., Nilsson, P., & Mason, J. (2012). Establishing mathematics for teaching within classroom interactions in teacher education. Educational Studies in Mathematics, 81, 1–14.
Schoenfeld, A. H. (1994). What do we know about mathematics curricula? Journal of Mathematical Behaviour, 13, 55–80.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM Mathematics Education, 3, 75–80.
Star, J. R., & Newton, k. J. (2009). The nature and development of experts’ strategy flexibility for solving equations. ZDM Mathematics Education, 41, 557–567.
Stigler J. W., & Hiebert J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York, NY: The Free Press.
Torbeyns, J. De Smedt, B. Ghesquiere, P., & Verschaffel, L. (2009). Jump or compensate? Strategy flexibility in the number domain up to 100. ZDM Mathematics Education, 41, 581–590.
Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8, 91–111.
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Peled, I., Leikin, R. (2017). Using Variation of Multiplicity in Highlighting Critical Aspects of Multiple Solution Tasks and Modeling Tasks. In: Huang, R., Li, Y. (eds) Teaching and Learning Mathematics through Variation. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-782-5_19
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DOI: https://doi.org/10.1007/978-94-6300-782-5_19
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