Skip to main content
SpringerLink
Log in
Book cover

Trends in Teaching and Learning of Mathematical Modelling pp 427–437Cite as

Assessing Modelling Competencies Using a Multidimensional IRT Approach

  • Conference paper
  • First Online:

Abstract

We assessed students’ modelling competency using a test consisting of different classes of items. Within the first class there are items which cover the whole modelling process, whereas items of the second class focus only on certain parts of this process. To cope with the requirements of the two different classes of items we used a multidimensional Rasch model including subdimensions. In this chapter we describe the structure of the test instrument and compare the subdimensional scaling of the test results with a unidimensional one. The analyses show the superiority of the subdimensional scaling.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    According to Rost (2004, S. 381) the reliability is estimated as follows: \( rel\text{=}\frac{{\hat{\sigma}}_{\theta}^{2}}{\nu ar\hat{\theta}} \), with \( {\hat{\sigma}}_{\theta}^{2} \) as variance of the latent distribution and \( \nu ar\hat{\theta} \) as variance of the estimated person parameters.

References

  • Blum, W. (1996). Anwendungsbezüge im Mathematikunterricht: Trends und Perspektiven. In G. Kadunz, H. Kautschitsch, G. Ossimitz & E. Schneider (Eds.), Trends und Perspektiven: Beiträge zum 7. Internationalen Symposium zur Didaktik der Mathe-matik (pp. 15–38). Wien: Hölder-Pichler-Tempsky.

    Google Scholar 

  • Blum, W. (2002). ICMI Study 14: Application and modelling in mathematics education - discussion document. Journal für Mathematikdidaktik, 23(3/4), 262–280.

    Google Scholar 

  • Blum, W., & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfähigkeiten von englischen und deutschen Lernenden (unpublished document). Cited according to K. Maaß (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(2), 113–142.

    Google Scholar 

  • Blum, W., & Leiss, D. (2006). Investigating quality mathematics teaching: The DISUM project. In: C. Bergsten, & B. Grevsholm, (Eds). Developing and researching quality in mathematics teaching and learning. Proceeding of MADIF-5. SMDF, Linköping 2007, 3–16.

    Google Scholar 

  • Brandt, S. (2008). Estimation of a Rasch model including subdimensions. In M. von Davier & D. Hastedt (Eds.), Issues and methodologies in large-scale assessments, issues and methodologies in large-scale assessments (pp. 53–71). Hamburg: IEA-ETS Research Institute.

    Google Scholar 

  • Bühner, M. (2006). Einführung in die Test- und Fragebogenkonstruktion (2nd ed.). München: Pearson Studium.

    Google Scholar 

  • Haines, C. R., & Crouch, R. M. (2001). Recognising constructs within mathematical modelling. Teaching Mathematics and Its Applications, 20(3), 129–138.

    Article  Google Scholar 

  • Izard, J. (2007). Assessing progress in mathematical modelling. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 158–167). Chichester: Horwood.

    Google Scholar 

  • Jensen, T. H. (2007). Assessing mathematical modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 141–148). Chichester: Horwood.

    Google Scholar 

  • Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(2), 113–142.

    Article  Google Scholar 

  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press.

    Google Scholar 

  • Reiss, K., Pekrun, R., Kuntze, S., Lindmeier, A., Nett, U., & Zöttl, L. (2007). KOMMA: Ein Projekt zur Entwicklung und Evaluation einer computergestützten Lernumgebung. GDM-Mitteilungen, 83, 16–17.

    Google Scholar 

  • Rost, J. (2004). Lehrbuch Testtheorie – Testkonstruktion (2nd ed.). Bern: Huber.

    Google Scholar 

  • Treilibs, V., Burkhardt, H., & Low, B. (1980). Formulation processes in mathematical modelling. Nottingham: Shell Centre for Mathematical Education.

    Google Scholar 

  • Wright, B., & Linacre, M. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions Contents, 8(3), 370. Retrieved Feb. 11 2009, from http://www.rasch.org/rmt/rmt83b.htm.

  • Wu, M., Adams, R., & Wilson, M. (1997). ConQuest: Generalised item response modelling software, Draft Release 2. Australian Council for Educational Research, Camberwell.

    Google Scholar 

  • Zöttl, L., Ufer, S., & Reiss, K. (2010). Modelling with heuristic worked-out examples in the KOMMA project. Journal für Mathematikdidaktik, 31(1), 143–165.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ludwig-Maximilian Universität, Theresienstr. 39, D-80333, Munich, Germany

    Luzia Zöttl, Stefan Ufer & Kristina Reiss

Authors
  1. Luzia Zöttl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Ufer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kristina Reiss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Luzia Zöttl .

Editor information

Editors and Affiliations

  1. FB Erziehungswissenschaft, Inst. Didaktik der Mathematik, Universität Hamburg, Von Melle Park 8, Hamburg, 20146, Germany

    Gabriele Kaiser

  2. Abt. Mathematik/Informatik, Universität Kassel, Kassel, 34109, Germany

    Werner Blum

  3. University of Hamburg, Germany, Doscherstrasse 1, Hamburg, 22083, Germany

    Rita Borromeo Ferri

  4. University of Melbourne, Australia, 23 Grampian Street, Victoria, 3072, Australia

    Gloria Stillman

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this paper

Cite this paper

Zöttl, L., Ufer, S., Reiss, K. (2011). Assessing Modelling Competencies Using a Multidimensional IRT Approach. In: Kaiser, G., Blum, W., Borromeo Ferri, R., Stillman, G. (eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_42

Download citation

Publish with us

Policies and ethics

Search

Navigation