On the influence of knowledge about the ideal-typical modelling processes on individuals’ modelling routes

Authors

DOI:

https://doi.org/10.48489/quadrante.23719

Keywords:

individual modelling routes, structure of modelling processes, MAI-Tool, knowledge about modelling proccesses

Abstract

Working on mathematical modelling tasks is challenging for students. Several studies have shown that knowledge of mathematical modelling on a meta-level has a positive effect on the modelling process. Nevertheless, students mostly do not knowingly and consciously use solution strategies when working on modelling tasks. Within the framework of our study, we investigated whether and to what extent knowledge about ideal-typical modelling processes has an effect on the structure of the solution processes of individuals. Individuals acquired this knowledge in our study in the form of an instruction that includes information about the modelling process, e.g., the modelling cycle and a solution plan. In this article, the structure of individual modelling routes of students who have received an instruction about modelling processes are compared with those students without such an instruction. The data in the study was collected, presented, and analysed using the Modelling-Activity-Interaction-Tool (MAI-Tool), which is also presented here. The MAI-Tool is a newly developed instrument based on quantitative methods to capture and analyse structures and patterns of modelling processes in more detail than with previously known methods.

References

Ärlebäck, J. B., & Albarracin, L. (2019). An extension of the MAD framework and its possible implication for research. Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht, Netherlands. https://hal.archives-ouvertes.fr/hal-02408679/document

Beckschulte, C. (2019). Mathematisches modellieren mit lösungsplan: Eine empirische untersuchung zur entwicklung von modellierungskompetenzen. Springer. https://doi.org/10.1007/978-3-658-27832-8

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodo-logical), 57(1), 289-300. https://www.jstor.org/stable/i316032

Blum, W. (1996). Anwendungsbezüge im mathematikunterricht – Trends und perspektiven. In G. Kadunz, H. Kautschitsch, G. Ossimitz, & E. Schneider (Eds.), Trends und perspektiven (pp. 15-38). Hölder-Pichler-Tempsky.

Blum, W. (2007). Mathematisches modellieren – zu schwer für schüler und lehrer?. In Beiträge zum mathematikunterricht (pp. 3-12). WTM.

Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education - Intellectual and attitudinal challenges (pp. 73-96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9

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. (2006). “Filling up” – The problem of independence-preserving teacher interventions in lessons with demanding modelling tasks. In M. Bosch (Ed.), CERME-4 – Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1623-1633). Sant Feliu de Guíxols, Spain.

Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM – The International Journal for Mathematics Education, 38(2), 86–95. https://doi.org/10.1007/BF02655883

Borromeo Ferri, R. (2007). Modelling problems from a cognitive perspective. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics. ICTMA12 (pp. 260-270). Horwood Publishing.

Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal für Mathematik-Didaktik, 31(1), 99-118. https://doi.org/10.1007/s13138-010-0009-8

Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen modellierens. Kognitive analysen zu modellierungsprozessen im mathematikunterricht. Vieweg+Teubner.

Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling – in school and teacher education. Springer. https://doi.org/10.1007/978-3-319-68072-9

Brand, S., & Vorhölter, K. (2018). Holistische und atomistische vorgehensweisen zum erwerb von modellierungskompetenzen im mathematikunterricht. In S. Schukajlow & W. Blum (Eds.), Evaluierte lernumgebungen zum modellieren (pp. 119-142). Springer.

Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37-46.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Lawrence Erlbaum Associates.

Döring, N., & Bortz, J. (2016). Forschungsmethoden und evaluation. In den sozial- und humanwissenschaften. Springer. https://doi.org/10.1007/978-3-642-41089-5

Flavell, H. J. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34(10), 906-911.

Fritz, C. O., Morris, P. E., & Richler, J. J. (2012). Effect size estimates: Current use, calculations and interpretation. Journal of Experimental Psychology: General, 141(1), 2-18. https://doi.org/10.1037/a0024338

Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 143-162. https://doi.org/10.1007/BF02655886

Greefrath, G. (2014). Lösungshilfen für modellierungsaufgaben. In I. Bausch, G. Pinkernell, & O. Schmitt (Eds.), Unterrichtsentwicklung und kompetenzentwicklung – Festschrift für regina bruder (pp. 131-140). WTM.

Greefrath, G. (2018). Anwendungen und modellieren im mathematikunterricht. Didaktische perspektiven zum sachrechnen in der sekundarstufe. Springer. https://doi.org/10.1007/978-3-662-57680-9

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). Springer. https://doi.org/10.1007/978-3-658-01580-0_1

Kaiser, G., Blum, W., Borromeo Ferri, R. & Greefrath, G. (2015). Anwendungen und modellieren. In R. Bruder et al. (Eds.), Handbuch der mathematikdidaktik (pp. 357-383). Springer. https://doi.org/10.1007/978-3-642-35119-8_13

Kaiser, G., & Stender, P. (2013). Complex modelling problems in co-operative, self-directed learning environments. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 277–293). Springer. https://doi.org/10.1007/978-94-007-6540-5_23

Kolbe, M., & Boos, M. (2018). Observing group interaction: The benefits of taking group dynamics seriously. In E. Brauner, M. Boos, & M. Kolbe (Eds.), The Cambridge handbook of group interaction analysis (pp. 68–85). Cambridge University Press. https://doi.org/10.1017/9781316286302.005

Leuders, T. (2007). Wenn es mathematikern zu bunt wird: Färbeprobleme. In S. Hußmann & B. Lutz Westphal (Eds.), Kombinatorische optimierung erleben. In schule und unterricht (pp. 131-170). Vieweg.

Maaß, K. (2004). Mathematisches modellieren im unterricht. Ergebnisse einer empirischen studie. Franzbecker.

Matos, J. F., & Carreira, S. (1997). The quest for meaning in students’ mathematical modelling activities. In S. K. Houston, W. Blum, I. Huntley, & N. T. Neill (Eds.), Teaching and learning in mathematical modelling (pp. 63-75). Albion.

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. The 14th ICMI Study (pp. 3-32). Springer.

Pollak, H. (1979). The interaction between mathematics and other school subjects. In UNESCO (Eds.), New trends in mathematics teaching IV (pp. 232-248). UNESCO.

Ruzika, S., & Schneider, L. (2020). Modellierungsprozesse erfassen, darstellen und analysieren. In H-S. Siller, W. Weigel, & J. F. Wörler (Eds.), Beiträge zum mathematikunterricht 2020 (pp. 1201-1204). WTM.

Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. Zentralblatt für Didaktik der Mathematik, 47, 1241-1254. https://doi.org/10.1007/s11858-015-0707-2

Stillman, G. (2004). Strategies employed by upper secondary students for overcoming or exploiting conditions affecting accessibility of applications tasks. Mathematics Education Research Journal, 16(1), 41-71. https://doi.org/10.1007/BF03217390

Stillman, G. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 165-180). Springer. https://doi.org/10.1007/978-94-007-0910-2_18

Stillman, G., & Galbraith, P. (1998). Applying mathematics with real world connections: metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36, 157-189. https://doi.org/10.1023/A:1003246329257

Strauß, A., & Corbin, J. (1996). Grounded theory. Grundlagen qualitativer sozialforschung. Beltz.

Vorhölter, K., & Kaiser, G. (2016). Theoretical and pedagogical considerations in promoting students’ metacognitive modeling competencies. In C. R. Hirsch (Ed.), Mathematical modeling and modeling mathematics (pp. 273-280). National Council of Teachers of Mathematics.

Vorhölter, K., Krüger, A., & Wendt, L. (2019). Metacognition in mathematical modelling – An overview. In S. A. Chamberlin, & B. Sriraman (Eds.), Affect in mathematical modeling (pp. 29-51). Springer. https://doi.org/10.1007/978-3-030-37673-4_27

Zöttl, L., Ufer, S., & Reiss, K. (2011). Assessing modelling competencies using a multidimensional IRT approach. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 427-437). Springer. https://doi.org/10.1007/978-94-007-0910-2_42

Downloads

Published

2021-12-31

How to Cite

Schneider, L., Borromeo Ferri, R., & Ruzika, S. (2021). On the influence of knowledge about the ideal-typical modelling processes on individuals’ modelling routes. Quadrante, 30(2), 220–241. https://doi.org/10.48489/quadrante.23719

Issue

Section

Articles