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Complex Modelling Problems in Co-operative, Self-Directed Learning Environments

  • Gabriele KaiserEmail author
  • Peter Stender
Chapter
Part of the International Perspectives on the Teaching and Learning of Mathematical Modelling book series (IPTL)

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.

Keywords

Mathematics Education Modelling Activity Future Teacher Novice Teacher Modelling Competency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Aebli, H. (1983). Zwölf Grundformen des Lehrens. Stuttgart: Klett-Cotta.Google Scholar
  2. Beutel, M., & Krosanke, N. (2012). Rekonstruktion von Handlungsabläufen in komplexen Modellierungsprozessen – Schülerprobleme und Lehrerverhalten. Unpublished master thesis, University of Hamburg, Hamburg.Google Scholar
  3. 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.CrossRefGoogle Scholar
  4. Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123–139.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. 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.Google Scholar
  7. Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen Modellierens. Wiesbaden: Vieweg-Teubner.CrossRefGoogle Scholar
  8. 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.CrossRefGoogle Scholar
  9. Hammond, J., & Gibbons, P. (2005). Putting scaffolding to work: The contribution of scaffolding in articulating ESL education. Prospect, 20(1), 6–30.Google Scholar
  10. Hattie, J. (2009). Visible learning. A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.Google Scholar
  11. 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.Google Scholar
  12. Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education – Examples and experiences. Journal für Mathematik-Didaktik, 31(1), 51–76.CrossRefGoogle Scholar
  13. 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.CrossRefGoogle Scholar
  14. Kaiser, G., Blum, W., Borromeo Ferri, R., & Stillman, G. (Eds.). (2011). Trends in teaching and learning of mathematical modelling. ICTMA 14. Dordrecht: Springer.Google Scholar
  15. 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.Google Scholar
  16. Leiß, D. (2007). Hilf mir es selbst zu tun. Hildesheim: Franzbecker.Google Scholar
  17. Link, F. (2011). Problemlöseprozesse selbständigkeitsorientiert begleiten: Kontexte und Bedeutungen strategischer Lehrerinterventionen in der Sekundarstufe I. Wiesbaden: Vieweg + Teubner/Springer.CrossRefGoogle Scholar
  18. Maaß, K. (2005). Modellieren im Mathematikunterricht der Sekundarstufe I. Journal für Mathematik-Didaktik, 26(2), 114–142.Google Scholar
  19. Niss, M. (1992). Applications and modelling in school mathematics – Directions for future development. Roskilde: IMFUFA Roskilde Universitetscenter.Google Scholar
  20. Polya, G. (1945). How to solve it. Princeton: Princeton University Press.Google Scholar
  21. 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.CrossRefGoogle Scholar
  22. 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.Google Scholar
  23. Strauss, A., & Corbin, J. (1990). Basics of qualitative research. Thousand Oaks: Sage.Google Scholar
  24. Van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher-student interaction: A decade of research. Educational Psychology Review, 22, 271–293.CrossRefGoogle Scholar
  25. Zech, F. (1998). Grundkurs Mathematikdidaktik. Weinheim: Beltz Verlag.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of HamburgHamburgGermany
  2. 2.Faculty of Education, Psychology, Human MovementUniversity of HamburgHamburgGermany

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