Advertisement

ZDM

, Volume 38, Issue 2, pp 113–142 | Cite as

What are modelling competencies?

  • Katja Maaß
Analyses

Abstract

Modelling and application are seen as a highly important topic for maths lessons. But so far the concept «modelling competencies» has not been described in a comprehensive manner: The aim of this paper is to supplement former descriptions of modelling competencies based on empirical data. An empirical study was carried out which aimed at showing the effects of the integration of modelling tasks into day-to-day math classes. Central questions of this study were—among others: How far do math lessons with focus on modelling enable students to carry out modelling processes on their own? What are modelling competencies? Within the theoretical approach, definitions of modelling processes as a basis for definitions of modelling competencies and important views of modelling competencies are discussed. Based on this theoretical approach the transfer into practice is described. Finally we will look at the results of the study. An analysis of the students' abilities and their mistakes lead to more insight concerning the concept of modelling competencies.

ZDM-Classification

M10 D40 D30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baumert, J., Lehmann, R., Lehrke, M., Clausen, M., Hosenfeld, I., Neubrand, J., et al. (1998).Testaufgaben Mathematik, TIMSS 7./8. Klasse (Population 2). Retrieved November 15, 2001 from http://www.mpib-berlin.mpg.de/TIMSSII-Germany/Die_Testaufgaben/TIMSSII-Math.pdf.Google Scholar
  2. Baumert, J., Klieme, E., Neubrand, M., Prenzel, M., Schiefele, U., Schneider, W., et al. (2001).Pisa 2000, Basiskompetenzen von Schülerinnen und Schülern im internationalen Vergleich. Opladen: Leske+Budrich.Google Scholar
  3. Blomhoej, M., & Jensen, Tomas (2003). Developing mathematical modelling competence: conceptual clarification and educational planning.Teaching mathematics and its applications, 22(3), 123–139.CrossRefGoogle Scholar
  4. Blum, W. (1985): Anwendungsorientierter Mathematikunterricht in der didaktischen Diskussion.Mathematische Semesterberichte, 32(2), 195–232.Google Scholar
  5. Blum, W. (1996). Anwendungsbezüge im Mathematikunterricht—Trends und Perspektiven.Schriftenreihe Didaktik der Mathematik, 23, 15–38.Google Scholar
  6. Blum, W. et al. (2002). ICMI Study 14: Application and Modelling in Mathematics Education—Discussion Document.Journal für Mathematik-Didaktik, 23(3/4), 262–280.Google Scholar
  7. Blum, W., Kaiser, G., Burges, D., & Green, N. (1994). Entwicklung und Erprobung eines Tests zur “mathematischen Leistungsfähigkeit” deutscher und englischer Lernender in der Sekundarstufe I.Journal für Mathematikdidaktik, 15(1/2), 149–168.Google Scholar
  8. Blum, W., & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfähigkeiten von englischen und deutschen LernendenUnpublished application to Deutsche Forschungsgesellschaft.Google Scholar
  9. Böhm, W. (2000).Wörterbuch der Pädagogik. (15th edition). Stuttgart: Kröner VerlagGoogle Scholar
  10. Boekarts, M. (1999). Self-regulated learning: Where we are today.International Journal of Educational Research, 31, 445–457.CrossRefGoogle Scholar
  11. Busse, A. (2001). Zur Rolle des Sachkontextes bei realitätsbezogenen Mathematikaufgaben.Beiträge zum Mathematikunterricht 2001, 141~144.Google Scholar
  12. Christiansen, I. (2001) The effect of task organisation on classroom modelling activities. In: J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.),Modelling and Mathematics Education, Ictma 9: Applications in Science and Technology (pp. 311–320). Chichester: Horwood Publishing.Google Scholar
  13. Cukrowicz, J., & Zimmermann, B. (Eds.) (2000).MatheNetz 7, Ausgabe N. Braunschweig: Westermann.Google Scholar
  14. Cukrowicz, J., & Zimmermann, B. (Hrsg.) (2000b).MatheNetz 8, Ausgabe N. Braunschweig: Westermann.Google Scholar
  15. De Lange, J. (1989): Trends and Barriers to Applications and Modelling in Mathematics Curricula. In W. Blum, M. Niss, I. Huntley, (Eds.).Modelling, applications and applied problem solving (pp. 196–204). Chichester: Ellis Horwood.Google Scholar
  16. De Lange, J. (1993): Innovation in mathematics education using applications: Progress and Problems. In J. de Lange, I. Huntley, Ch. Keitel, M. Niss (Eds.):Innovation in maths education by modelling and applications (pp. 3–17). Chichester: Ellis Horwood.Google Scholar
  17. Dunne, T. (1998). Mathematical modelling in years 8 to 12 of secondary schooling. In P. Galbraith, W. Blum, G. Booker, & I. Huntley (Eds.),Mathematical Modelling, Teaching an Assessment in a Technology-Rich World (pp. 29–37). Chichester: Horwood Publishing.Google Scholar
  18. Flick, U., von Kardorff, E., & Steinke, I. (2002). Was ist qualitative Forschung? Einleitung und Überblick. In U. Flick, E. von Kardorff, & I. Steinke, (Eds.),Qualitative Forschung, Ein Handbuch (pp. 13–29). Reinbek bei Hamburg: Rowohlt.Google Scholar
  19. Galbraith, P. (1995). Modelling, Teaching, Reflecting—What I have learned. In C. Sloyer, W. Blum & I. Huntley (Eds.),Advances and perspectives in the teaching of mathematical modelling and applications (pp. 21–45). Yorklyn: Water Street Mathematics.Google Scholar
  20. Galbraith, P & Clatworthy, N.J. (1990). Beyond standard models—meeting the challenge of modelling.Educational Studies in Mathematics, 21(2), 137–163.CrossRefGoogle Scholar
  21. Galbraith, P., & Stillman, G. (2001). Assumptions and context: Pursuing their role in modelling activity. In J. Matos, W. Blum, K. Houston, & S. Carreira, (Eds.):Modelling and Mathematics Education, Ictma 9: Applications in Science and Technology (pp. 300–310). Chichester: Horwood Publishing.Google Scholar
  22. Gerhardt, U. (1990). Typenbildung. In: U. Flick, E. von Kardorff, & E. Steinke, (Eds.),Handbuch qualitative Sozial-forschung. Grundlagen, Konzepte, Methoden und Anwendungen, (pp. 435–439). München: Beltz Psychologie Verlags Union.Google Scholar
  23. Haines, C., & Izard, J. (1995). Assessment in context for mathematical modelling. In C. Sloyer, W. Blum, I. Huntley, (Eds.),Advances and perspectives in the teaching of mathematical modelling and applications (p. 131–150). Yorklyn: Waterstreet Mathematics.Google Scholar
  24. Haines, C., Crouch, R., & Davies, J. (2001). Understanding students' modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.),Modelling and Mathematics Education, Ictma 9: Applications in Science and Technology (pp. 366–380). Chichester: Horwood Publishing.Google Scholar
  25. Hasemann, K., & Mansfield, H. (1995). Concept Mapping in research on mathematical knowledge developement: Background, Methods, Findings and conclusionsEducational studies in mathematics, 29, 45–72.CrossRefGoogle Scholar
  26. Henn, H. (1988). messwertanalyse—Eine Anwendungsaufgabe im Mathematikunterricht der Sekundarstufe I.Der mathematische und naturwissenschaftliche Unterricht, 41(3), 143–150.Google Scholar
  27. Herget, W., Jahnke, T., Kroll, W. (2001).Produktive Aufgaben für den Mathematikunterricht in der Sekundarstufe I. Berlin: Cornelson.Google Scholar
  28. Hodgson, T. (1997). On the use of open-ended, real-world problems. In: K. Houston, W. Blum, I. Huntley, N.T. Neill, (Eds.),Teaching and learning mathematical modelling. (pp. 211–218). Chichester: Albion publishing limited).Google Scholar
  29. Jäger, R. (2001).Von der Beobachtung zur Notengebung—Ein Lehrbuch. Landau: Verlag Empirische Pädagogik.Google Scholar
  30. Jank, W., Meyer, H. (1994).Didaktische Modelle. Frankfurt am Main: Cornelson Scriptor.Google Scholar
  31. Ikeda, T. (1997). A case study of instruction and assessment in mathematical modelling—‘the delivering problem’. In K. Houston, W. Blum, I. Huntley, N.T. Neill (Eds.),Teaching and learning mathematical modelling (pp. 51–61). Chichester: Albion publishing limited.Google Scholar
  32. Ikeda, T., & Stephens, M. (1998). The influence of problem format on students' approaches to mathematical modelling. In P. Galbraith, W. Blum, G. Booker, I. Huntley, (Eds.).Mathematical Modelling, Teaching and Assessment in a Technology-Rich World (pp. 223–232). Chichester: Horwood Publishing.Google Scholar
  33. Kaiser-Meßmer, G. (1986).Anwendungen im Mathematik-unterricht, 2 Vol. Bad Salzdetfurth: Franzbecker.Google Scholar
  34. Kelle, U. & Kluge, S. (1999). Vom Einzelfall zum Typus. Opladen: Leske und Budrich.Google Scholar
  35. Klaoudatos, N., Papastravridis, S. (2001). Context orientated teaching. In J.F. Matos, W. Blum, K. Houston, S.P. Carreira, (Eds.),Modelling and Mathematics Education, Ictma 9: Applications in Science and Technology (pp. 327–334). Chichester: Horwood Publishing.Google Scholar
  36. Kromrey, H. (1998).Empirische Sozialforschung. Opladen: Leske und Budrich.Google Scholar
  37. Kultusministerkonferenz (2003).Bildungsstandards im Fach Mathematik für den mittleren Bildungsabschnitt. Retrieved January 20, 2004, fromhttp://www.kmk.org/schul/Bildungsstandards/ Mathematik MSA BS 04-12-2003.pdf Google Scholar
  38. Lamon, S.J. (1997). Mathematical modelling and the way the mind works. In K. Houston, W. Blum, I. Huntley, N.T. Neill (Eds.).Teaching and learning mathematical modelling (pp. 23–37). Chichester: Albion publishing limited, West Sussex.Google Scholar
  39. Maaß, K. (2004).Mathematisches Modellieren im Unterricht—Ergebnisse einer empirischen Studie. Hildesheim, Berlin: Verlag Franzbecker.Google Scholar
  40. Maaß, K. (2005): Modellieren im Mathematikunterricht der Sekundarstufe I.Journal für Mathematikdidaktik, 26 (2), 114–142.Google Scholar
  41. Maaß, K. (2005): Stau—eine Aufgabe für alle Jahrgänge!.Praxis der Mathematik, 47 (3), 8–13.Google Scholar
  42. Matos, J.F. (1998): Mathematics Learning and Modelling: Theory and Practice. In P. Galbraith, W. Blum, G. Booker & I. Huntley, (Eds.):Mathematical Modelling, Teaching and Assessment in a Technology-Rich World (pp. 21–27). Chichester: Horwood Publishing.Google Scholar
  43. Maier, H., Beck, C. (2001). Interpretative mathematik-didaktische Forschung.Journal für Mathematikdidaktik, 22(1), 29–50.Google Scholar
  44. Money, R., Stephens, M. (1993). Linking applications, modelling and assessment. In J. de Lange, I. Huntley, Ch. Keitel, M. Niss, (Eds.),Innovation in maths education by modelling and applications (pp. 323–336). Chichester: Ellis Horwood.Google Scholar
  45. Niss, M. (2004). Mathematical competencies and the learning of mathematics: The danish KOM project. In A. Gagtsis & A. Papastavridis (eds):3rd Mediterranean Conference on mathematical education, 3~5 January 2003, Athens, Greece. (pp. 115–124). Athens: The Hellenic mathematical society, 2003.Google Scholar
  46. Profke, Lothar (2000). Modellbildung für alle Schüler. In Hischer, Horst (Ed.),Modellbildung, Computer und Mathematikunterricht (pp. 24–38), Hildesheim: Franzbecker.Google Scholar
  47. Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition and sense-making in Mathematics. In D. Grouws (Eds.),Handbook for Research on mathematics teaching and learning (pp. 334~370). New York.Google Scholar
  48. Sjuts, J. (2003). Metakognition per didaktischsozialem Vertrag.Journal für Mathematikdidatik, 24(1), 18–40.Google Scholar
  49. Tanner, H., Jones, S. (1995). Developing Metacognitive Skills in mathematical modelling—a socio-contructivist interpretation. In C. Sloyer, W. Blum, I. Huntley, (Eds.).Advances and perspectives in the teaching of mathematical modelling and applications (pp. 61–70). Yorklyn: Water Street Mathematics.Google Scholar
  50. Treilibs, V. (1979): Formulation processes in mathematical modelling.—Thesis submitted to the University of Nottingham for the degree of Master of Philosophy.Google Scholar

Copyright information

© ZDM 2006

Authors and Affiliations

  • Katja Maaß
    • 1
  1. 1.University of EducationFreiburgGermany

Personalised recommendations