Abstrakt
Studie se zabývá vztahem mezi stylem myšlení žáků a procesem modelování. Zúčastnilo se jí 35 žáků osmého ročníku. V první fázi žáci řešili úlohy a na základě jejich řešení byli klasifikovány do jednoho ze tří stylů myšlení: vizuálního, analytického a integrativního. V ohnisku našeho zájmu byl vizuální a analytický styl. Vybrali jsme pět žáků z každé skupiny (N = 10), kterým byly zadány tři úlohy vyžadující modelování. Výsledky naznačují rozdíly v modelování mezi oběma skupinami. Hlavní rozdíly se projevily ve zjednodušení, matematizaci a tvorbě matematického modelu. Kromě toho žáci z analytické skupiny přeskočili ve všech úlohách fázi reálného modelu, zatímco žáci z vizuální skupiny reálný model v každé úloze vytvořili.
Reference
Ben-Chaim, D., Keret, Y., & Ilany, S.-B. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education (Pre- and in-service mathematics teachers of elementary and middle school classes). Sense Publisher.
Blum, W., & Borromeo Ferri, R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Application, 1(1), 45–58.
Blum, W., & Leiß, D. (2005). “Filling Up” – the problem of independence-preserving teacher interventions in lessons with demanding modeling tasks. In M. Bosch (Ed.), Proceedings of the fourth congress of the European Society for Research in Mathematics Education (CERME 4) (pp. 1623–1633). Sant Feliu de Guíxols, Spain, Fundemi IQS Universitat Ramon Llull.
Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modeling process. ZDM, 38(2), 86–95. https://doi.org/10.1007/bf02655883
Borromeo Ferri, R. (2007). Modeling problems from a cognitive perspective. In C. P. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA12): Education, engineering and economics (pp. 260–270). Horwood Publishing Limited.
Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal fur Mathematik-Didaktik, 31(1), 99–118. https://doi.org/10.1007/s13138-010-0009-8
Borromeo Ferri, R. (2015). Mathematical thinking styles in school and across cultures. In S. Cho (Eds.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 153–173). Springer. https://doi.org/10.1007/978-3-319-17187-6 9
Borromeo Ferri, R., & Kaiser, G. (2003). First results of a study of different mathematical thinking styles of schoolchildren. In L. Burton (Ed.), Which way in social justice in mathematics education? (pp. 209–239). Greenwood.
Burton, L. (2001). Research mathematicians as learners – and what mathematics education can learn from them. British Educational Research Journal, 27(5), 589–599. https://doi.org/10.1080/01411920120095762
Campbell, K. J., Collis, K.F., & Watson, J. M. (1995). Visual processing during mathematical problem solving. Educational Studies in Mathematics, 28(2), 177–194. https://doi.org/10.1007/BF01295792
Cakan, M. (2000). Interaction between cognitive styles and assessment approaches. In LSU Historical dissertations and theses. https://digitalcommons.lsu.edu/gradschool disstheses/7145
Dwyer, F. M., & Moore, D. M. (1994). Effect of colour coding and test type (visual/verbal) on students identified as possessing different field dependence levels. British Journal of Educational Technology, 25(3), 217–219.
English, L.D., & Fox, J. L. (2005). Seventh-graders’ mathematical modeling on completion of a three-year program. In P. Clarkson et al. (Eds.), Building connections: Theory, research and practice (Vol. 1, pp. 321–328). Deakin University Press.
English, L.D., & Watters, J. J. (2005). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(3), 58–79. https://doi.org/10.1007/BF03217401
Huang, C.-H. (2013). Engineering students’ visual thinking of the concept of definite integral. Global Journal of Engineering Education, 15(2), 111–117.
Glaser, B.G., & Strauss, A.L. (1967). Discovery of grounded theory: Strategies for qualitative research. Aldine Publishing Company.
Kaiser, G. (2007). Mathematical modeling at schools how to promote modeling competencies. In C.P. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA12): Education, engineering and economics (pp. 110–119). Horwood Publishing Limited.
Kaiser, G., & Stender, P. (2013). Complex modeling problems in co-operative, self-directed learning environments. In G.A. Stillman, G. Kaiser, W. Blum, & J.P. Brown (Eds.), Teaching mathematical modeling: Connecting to research and practice (pp. 277–294). Springer. https://doi.org/10.1007/978-94-007-6540-5 23
Kaput, J. J., & Blanton, M. (2001). Algebrafying the elementary mathematics experience: Part 1: Transforming task structures. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th International Commission on Mathematics Instruction Study Conference (pp. 344–351). University of Melbourne, Melbourne, Australia.
Lean, G., & Clements, M.A. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12(3), 267–299. https://doi.org/10.1007/BF00311060
Lesh, R., & Doerr, H. M. (2003). Foundations of models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H.M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3–33). Erlbaum.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh, & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Lawrence Erlbaum.
Lesh, R., & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2–3), 109–129. https://doi.org/10.1080/10986065.2003.9679996
Lowrie, T., & Clements, M.A. (2001). Visual and nonvisual processes in grade 6 students’ mathematical problem solving. Journal of Research in Childhood Education, 16(1), 77–93. https://doi.org/10.1080/02568540109594976
Lowrie, T., & Kay, R. (2001). Relationship between visual and nonvisual solution methods and difficulty in elementary mathematics. The Journal of Educational Research, 94(4), 248–255. https://doi.org/10.1080/00220670109598758
Maaß, K. (2006). What are modeling competencies? ZDM, 38(2), 113–142. https://doi.org/10.1007/BF02655885 Monga, A. B., & John, D.R. (2007). Cultural differences in brand extension evaluation: the influence of analytic versus holistic thinking. Journal of Consumer Research, 33(4), 529–536. https://doi.org/10.1086/510227
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modeling and applications in mathematics education (pp. 3–32). Springer.
Organization for Economic Cooperation and Development (OECD). (2004). Learning for tomorrow’s world: First results from PISA 2003. OECD.
Presmeg, N. C. (1986). Visualization in high school mathematics. For the Learning of Mathematics, 6(3), 42–46.
Shahbari, J.A., & Daher, W. (2016). Mathematical models’ features: Technology and non-technology. European Journal of Science and Mathematics Education, 4(4), 523–533.
Shahbari, J.A., & Peled, I. (2017). Modeling in primary schools: Constructing a conceptual system and making sense of fractions. International Journal of Science and Mathematics Education, 15(2), 371–391. https://doi.org/10.1007/s10763-015-9702-x
Shahbari, J.A., & Tabach, M. (2016). Different generality levels in the product of a modeling activity. In C. Csikos, A. Rausch, & J. Szitanyi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 179–186). PME.
Shahbari, J. A., & Tabach, M. (2018). Developing prospective mathematics teachers’ knowledge of the modeling approach. Scientia in educatione, 9(2), 46–158. https://doi.org/10.14712/18047106.1183
Shahbari, J.A., & Tabach, M. (2019). Adopting the modeling cycle for representing prospective and practicing teachers’ interpretations of students’ modeling activities. In G. Stillman, & J. Brown (Eds.), Lines of inquiry in mathematical modeling research in education (pp. 179–196). ICME-13 Monographs, Springer. https://doi.org/10.1007/978-3-030-14931-4 10
Sternberg, R. J. (1997). Thinking styles. Cambridge University Press.
Sternberg, R. J., & Zhang, L.–F. (2005). Styles of thinking as a basis of differentiated instruction. Theory into Practice, 44(3), 245–253. https://doi.org/10.1207/s15430421tip4403 9
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modeling in the secondary school. In J. Watson, & K. Beswick (Eds.), Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) (Vol. 2, pp. 688–697). MERGA.