Abstract
In this chapter, we present an observation study which investigated the solution processes of two groups of students. While solving the task, the students’ key activity was the analysis of a mathematical model given in the form of a simulation. The study focused on difficulties in the modelling process, especially on the intensity of difficulties which were identified by video recording and time taken. The aim of this study was to identify the most persistent difficulties in the solution process. For that purpose, a method consisting of a time-based measurement will be presented. A coding scheme for identifying difficulties in the modelling process based on previous studies was created and used for the evaluation of the solution processes. Measuring the time, the students spent overcoming their difficulties allowed us to make a statement about the intensities of these difficulties.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222–231). Chichester: Horwood.
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM Mathematics Education, 38(2), 143–162.
Galbraith, G., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modelling competencies. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 130–140). Chichester: Horwood.
Kauertz, A., & Siller, H.-S. (2016). MoSAiK – Modulare Schulpraxiseinbindung als Ausgangspunkt zur individuellen Kompetenzentwicklung [Modular integration of school practice as a starting point for individual competence development]. Project of the University of Koblenz-Landau in the framework of “Qualitätsoffensive Lehrerbildung”.http://mosaik.uni-koblenz-landau.de
Maaß, K. (2004). Mathematisches Modellieren im Unterricht. Ergebnisse einer empirischen Studie [Mathematical model building in the mathematics classroom. Results of an empirical study]. Hildesheim: Franzbecker.
McCown, F. (2017). Schelling’s model of segregation [Simulation]. Searcy, AR: Computer Science Department, Harding University. http://nifty.stanford.edu/2014/mccown-schelling-model-segregation/. Accessed 13 July 2017.
Niss, M., & Højgaard, T. (2011). Competencies and mathematical learning. Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Roskilde: Roskilde University.
Schaap, S., Vos, P., & Goedhart, M. (2011). Students overcoming blockages while building a mathematical model: Exploring a framework. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 137–146). Dordrecht: Springer.
Schelling, T. (1971). Dynamic models of segregation. Journal of Mathematical Sociology, 1, 143–186.
Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modelling activities at year 9. In R. Lesh, P. Galbraith, C. Haines, & A. Hurford (Eds.), Modelling students’ mathematical modelling competencies (pp. 385–398). New York: Springer.
Stillman, G., Brown, J., & Galbraith, P. (2013). Challenges in modelling challenges: Intents and purposes. In G. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 217–228). Dordrecht: Springer.
Tropper, N., Leiss, D., & Hänze, M. (2015). Teachers’ temporary support and worked-out examples as elements of scaffolding in mathematical modeling. ZDM Mathematics Education, 47(7), 1225–1240.
Acknowledgments
We thank the German Ministry for Education and Research for funding the project MoSAiK (Kauertz and Siller 2016) – support code 01JA1605 – in the framework of “Qualitätsoffensive Lehrerbildung”.
A special thanks to Pauline Vos for supporting us and discussing the idea of the “Segregation Tasks”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Klock, H., Siller, HS. (2020). A Time-Based Measurement of the Intensity of Difficulties in the Modelling Process. In: Stillman, G.A., Kaiser, G., Lampen, C.E. (eds) Mathematical Modelling Education and Sense-making. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-37673-4_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-37672-7
Online ISBN: 978-3-030-37673-4
eBook Packages: EducationEducation (R0)