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Six Principles to Assess Modelling Abilities of Students Working in Groups

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Mathematical Modelling and Applications

Abstract

This chapter sets out how the six instructional design principles for model-eliciting activities (MEAs) can be reworded and may serve as principles for assessing modelling abilities of students working in groups. The chapter explores some modelling assessment ideas and explains how the six principles form a framework for a holistic evaluation of group modelling. A design research study investigated the modelling competencies of grade 7 students working in a group. The assessment unit was that of the group as a whole and not of individual students. It was found that the six principles reworded as an assessment framework enabled the authors to evaluate significant aspects of model-eliciting activities such as model construction, reality integration, quality of documentation, self-evaluation, development of prototypes for thinking and generalisation.

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References

  • Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Dissertation Utrecht University, CD-β Press, Center for Science and Mathematics Education, Utrecht.

    Google Scholar 

  • Biccard, P. (2010). The development of mathematical modelling competencies of grade seven learners. Unpublished Masters Dissertation, University of Stellenbosch, Stellenbosch.

    Google Scholar 

  • Biggs, J. (1996). Enhancing teaching through constructive alignment. Higher Education, 32(3), 347–364.

    Article  Google Scholar 

  • Blomhøj, M., & Jensen, T. H. (2007). What’s all the fuss about competencies? In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 45–57). New York: Springer.

    Chapter  Google Scholar 

  • Chan, C. M. E., Ng, K. E. D., Widjaja, W., & Seto, C. (2012). Assessment of primary 5 students’ mathematical modelling competencies. Journal of Science and Mathematics Education in Southeast Asia, 35(2), 146–178.

    Google Scholar 

  • Clatworthy, N. J. (1989). Assessment at the upper secondary level. In W. Blum, J. S. Berry, R. Biehler, I. D. Huntley, G. Kaiser-Messmer, & L. Profke (Eds.), Applications and modelling in learning and teaching mathematics (pp. 60–65). Chichester: Ellis Horwood.

    Google Scholar 

  • Cohen, S. A. (1987). Instructional alignment: Searching for a magic bullet. Educational Researcher, 16(8), 16–20.

    Article  Google Scholar 

  • Derry, S. J., DuRussel, L. A., & O’Donnell, A. M. (1998). Individual and distributed cognitions in interdisciplinary teamwork: A developing case study and emerging theory. Educational Psychology Review, 10(1), 25–56.

    Article  Google Scholar 

  • English, L. D. (2007). Interdisciplinary modelling in the primary mathematics curriculum. In J. Watson & K. Beswick (Eds.), Proceedings of MERGA30 (Vol. 1, pp. 275–284). Adelaide: MERGA.

    Google Scholar 

  • English, L. D., & Fox, J. L. (2005). Seventh-graders’ mathematical modeling on completion of a three-year program. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Proceedings of MERGA28 (Vol. 1, pp. 321–328). Adelaide: MERGA.

    Google Scholar 

  • Frejd, P. (2013). Modes of modelling assessment—A literature review. Educational Studies in Mathematics, 84, 413–438. doi:10.1007/s10649-013-9491-5.

    Article  Google Scholar 

  • Gijbels, D., Dochy, F., Van den Bossche, P., & Segers, M. (2005). Effects of problem-based learning: A meta-analysis from the angle of assessment. Review of Educational Research, 75(1), 27–61.

    Article  Google Scholar 

  • Iversen, S. M., & Larson, C. (2006). Simple thinking using complex math vs. complex thinking using simple math – A study using model eliciting activities to compare students’ abilities in standardized tests to their modelling abilities. ZDM Mathematics Education, 38(3), 281–292.

    Article  Google Scholar 

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

    Chapter  Google Scholar 

  • Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering and economics (pp. 110–119). Chichester: Horwood.

    Google Scholar 

  • Lesh, R., & Doerr, H. M. (2003). Foundations of a 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). Mahwah: Erlbaum.

    Google Scholar 

  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research in design in mathematics and science education (pp. 591–645). Mahwah: Erlbaum.

    Google Scholar 

  • Lesh, R., Middleton, J. A., Caylor, E., & Gupta, S. (2008). A science need: Designing tasks to engage students in modeling complex data. Educational Studies in Mathematics, 68, 113–130.

    Article  Google Scholar 

  • Lingefjard, T., & Holmquist, M. (2005). To assess students’ attitudes, skills and competencies in mathematical modeling. Teaching Mathematics and its Applications, 24(2), 123–133.

    Article  Google Scholar 

  • Niss, M. (1992). Applications and modeling in school mathematics-directions for future development. In I. Wirszup & R. Streit (Eds.), Developments in school mathematics education around the world (Vol. 3, pp. 346–361). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction to modelling and applications in mathematics education. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: 14th ICMI study (pp. 3–32). New York: Springer.

    Chapter  Google Scholar 

  • Yildirim, T. P., Shuman, L., & Besterfield-Sacre, M. (2010). Model-eliciting activities: Assessing engineering student problem solving and skill integration processes. International Journal of Engineering Education, 26(4), 831–845.

    Google Scholar 

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Acknowledgements

The financial assistance of the National Research Foundation (NRF) towards the research is hereby acknowledged. Opinions expressed and conclusions arrived at are those of the authors and should not be attributed to the NRF.

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Authors and Affiliations

  1. Department of Curriculum and Instructional Studies, University of South Africa, Pretoria, South Africa

    Piera Biccard

  2. Research Unit for Mathematics Education of the University of Stellenbosch, Department of Curriculum Studies, Stellenbosch University, Stellenbosch, Matieland, 7602, South Africa

    Dirk Wessels

Authors
  1. Piera Biccard
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  2. Dirk Wessels
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Corresponding author

Correspondence to Piera Biccard .

Editor information

Editors and Affiliations

  1. Australian Catholic University, Ballarat, Victoria, Australia

    Gloria Ann Stillman

  2. University of Kassel, Kassel, Germany

    Werner Blum

  3. University of Hamburg, Hamburg, Germany

    Gabriele Kaiser

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Biccard, P., Wessels, D. (2017). Six Principles to Assess Modelling Abilities of Students Working in Groups. In: Stillman, G., Blum, W., Kaiser, G. (eds) Mathematical Modelling and Applications. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-62968-1_49

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  • DOI: https://doi.org/10.1007/978-3-319-62968-1_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62967-4

  • Online ISBN: 978-3-319-62968-1

  • eBook Packages: EducationEducation (R0)

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