Abstract
Providing a method for problem solving can support students working on modelling tasks. A few candidate methods are presented here. In a qualitative study, one of these problem solving methods was introduced to students in grades 4 and 6 (Germany), to be used in their work on modelling tasks. The students were observed as they worked and were subsequently interviewed. The results reveal differences between grades, and widely varying problem solving processes. The differences in written final solutions are considerably less pronounced.
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Notes
- 1.
The DISUM Project (Didactical intervention modes for mathematics teaching oriented towards self-regulation and directed by tasks) led by W. Blum, R. Messner and R. Pekrun.
- 2.
KOMMA (KOMpendium MAthematik) is a project aiming at the implementation and evaluation of a learning environment for mathematical modelling.
References
Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.
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.
Böhm, U. (2010). “Aller Anfang ist schwer, Modellieren lernen umso mehr!?”– Erste Schritte auf dem Weg zur langfristigen Förderung von Modellierungskompetenzen im Mathematikunterricht. In R. Bruder & A. Eichler (Eds.), Materialien für einen realitätsbezogenen Mathematikunterricht Band 15 (pp. 1–14). Hildesheim: Franzbecker.
Borromeo Ferri, R. (2007). Personal experiences and extra-mathematical knowledge as an influence factor on modelling routes of students. Proceedings of the fifth congress of the European society for research in mathematics education (pp. 2080–2089), Larnaca.
Förderer, M. (2013). Modellieren mit Hilfe eines Lösungsplans – Analyse der Bearbeitung einer Fermi-Aufgabe in der 4. Klasse. Unpublished master’s thesis, University of Münster.
Franke, M., & Ruwisch, S. (2010). Didaktik Sachrechnens in der Grundschule. Heidelberg: Spektrum Akademischer Verlag.
Garofalo, J., & Lester, F. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176.
Greefrath, G., & Leuders, T. (2013). Verbrauch im Haushalt – Schätzen und Überschlagen. In S. Prediger, B. Barzel, S. Hussmann, & T. Leuders (Eds.), mathewerkstatt (pp. 5–22). Berlin: Cornelsen.
Greefrath, G., Kaiser, G., Blum, W., & Borromeo Ferri, R. (2013). Mathematisches Modellieren – Eine Einführung in theoretische und didaktische Hintergründe. In R. Borromeo Ferri, G. Greefrath, & G. Kaiser (Eds.), Mathematisches Modellieren für Schule und Hochschule. Theoretische und didaktische Hintergründe (pp. 11–37). Wiesbaden: Springer Spektrum.
Hilmer, A. (2012). Modellieren mithilfe eines Lösungsplans – Analyse der Bearbeitung eines Fermiproblems in der 6. Klasse. Unpublished master’s thesis, University of Münster.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302–310.
Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92(1), 109–129.
Maaß, K. (2004). Mathematisches Modellieren im Unterricht. Ergebnisse einer empirischen Studie. Hildesheim: Franzbecker.
Maaß, K. (2006). What are modelling competencies? ZDM, 38(2), 113–142.
Meyer, M., & Voigt, J. (2010). Rationale Modellierungsprozesse. In B. Brandt, M. Fetzer, & M. Schütte (Eds.), Auf den Spuren Interpretativer Unterrichtsforschung in der Mathematikdidaktik (pp. 117–148). Münster: Waxmann.
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 3–32). New York: Springer.
Ortlieb, C. P. (2004). Mathematische Modelle und Naturerkenntnis. Mathematica Didactica, 27(1), 23–40.
Polya, G. (1973). How to solve it. A new aspect of mathematical method. Princeton: Princeton University Press.
Reiss, K., & Renkl, A. (2002). Learning to prove: The idea of heuristic examples. Zentralblatt für Didaktik der Mathematik, 34(1), 29–35.
Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando: Academic.
Schukajlow, S., Krämer, J., Blum, W., Besser, M., Brode, R., Leiss, D., & Messner, R. (2010). Lösungsplan in Schülerhand: zusätzliche Hürde oder Schlüssel zum Erfolg? Beiträge zum Mathematikunterricht, Bd. 2, 771–774.
Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park: Sage.
Zech, F. (1998). Grundkurs Mathematikdidaktik. Weinheim und Basel: Beltz.
Zöttl, L., Ufer, S., & Reiss, K. (2010). Modelling with heuristic worked examples in the KOMMA learning environment. Journal für Mathematik-Didaktik, 31(1), 143–165.
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Greefrath, G. (2015). Problem Solving Methods for Mathematical Modelling. In: Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_13
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