Abstract
After a short description of the development of the current discussion on teaching and learning mathematical modelling special modelling activities are described. These so-called modelling weeks or days deal with complex modelling problems, which are focusing on students in an autonomous learning environment. Evaluation results of these modelling activities are presented pointing out, that most of the participating students from upper secondary level appraised these positively. Finally scaffolding as an approach to support students’ independent modelling processes is discussed and first results of an empirical study on interventions in modelling activities with complex modelling problems are presented.
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References
Aebli, H. (1983). Zwölf Grundformen des Lehrens. Stuttgart: Klett-Cotta.
Beutel, M., & Krosanke, N. (2012). Rekonstruktion von Handlungsabläufen in komplexen Modellierungsprozessen – Schülerprobleme und Lehrerverhalten. Unpublished master thesis, University of Hamburg, Hamburg.
Blomhøj, M. (2011). Modelling competency: Teaching, learning and assessing competencies – Overview. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 343–349). New York: Springer.
Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123–139.
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). New York: Springer.
Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (Eds.). (2007). Modeling and applications in mathematics education. The 14th ICMI study. New York: Springer.
Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen Modellierens. Wiesbaden: Vieweg-Teubner.
Busse, A., & Borromeo Ferri, R. (2003). Methodological reflections on a three-step-design combining observation, stimulated recall and interview. Zentralblatt für Didaktik der Mathematik, 35(6), 257–264.
Hammond, J., & Gibbons, P. (2005). Putting scaffolding to work: The contribution of scaffolding in articulating ESL education. Prospect, 20(1), 6–30.
Hattie, J. (2009). Visible learning. A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.
Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education – Examples and experiences. Journal für Mathematik-Didaktik, 31(1), 51–76.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM – The International Journal on Mathematics Education, 38(3), 302–310.
Kaiser, G., Blum, W., Borromeo Ferri, R., & Stillman, G. (Eds.). (2011). Trends in teaching and learning of mathematical modelling. ICTMA 14. Dordrecht: Springer.
Kaiser, G., Bracke, M., Göttlich, S., & Kaland, C. (2013). Realistic complex modelling problems in mathematics education. In R. Strässer & A. Damlamian (Eds.), Educational interfaces between mathematics and industry (20th ICMI study). New York: Springer.
Leiß, D. (2007). Hilf mir es selbst zu tun. Hildesheim: Franzbecker.
Link, F. (2011). Problemlöseprozesse selbständigkeitsorientiert begleiten: Kontexte und Bedeutungen strategischer Lehrerinterventionen in der Sekundarstufe I. Wiesbaden: Vieweg + Teubner/Springer.
Maaß, K. (2005). Modellieren im Mathematikunterricht der Sekundarstufe I. Journal für Mathematik-Didaktik, 26(2), 114–142.
Niss, M. (1992). Applications and modelling in school mathematics – Directions for future development. Roskilde: IMFUFA Roskilde Universitetscenter.
Polya, G. (1945). How to solve it. Princeton: Princeton University Press.
Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. ICTMA14 (pp. 165–180). Dordrecht: Springer.
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Vol. 2, pp. 688–697). Adelaide: MERGA.
Strauss, A., & Corbin, J. (1990). Basics of qualitative research. Thousand Oaks: Sage.
Van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher-student interaction: A decade of research. Educational Psychology Review, 22, 271–293.
Zech, F. (1998). Grundkurs Mathematikdidaktik. Weinheim: Beltz Verlag.
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Kaiser, G., Stender, P. (2013). Complex Modelling Problems in Co-operative, Self-Directed Learning Environments. In: Stillman, G., Kaiser, G., Blum, W., Brown, J. (eds) Teaching Mathematical Modelling: Connecting to Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6540-5_23
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