Abstract
This study aims at supporting learners’ competency of mathematical modelling in ordinary mathematics lessons by using increasing learning aids in a self-regulated learning environment. The study intends to evaluate the feasibility of the approach by carrying out a case study. Thirty seventh-graders were video- and audio-recorded while working on complex modelling problems supported by increasing learning aids and a diagram of the modelling cycle enhanced to indicate potential areas of difficulty or blockages to progress as a metacognitive aid. First results point out that the usage of increasing learning aids for solving mathematical modelling problems supports modelling activities. In this chapter, an overview on the modelling tasks is presented, with one task presented in detail. General results and results for one specific group will be reported.
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References
Aebli, H. (1985). Zwölf Grundformen des Lehrens. Stuttgart: Klett-Cotta.
Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.
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 (pp. 73–96). Cham: Springer.
Collins, A., Brown, J. S., & Newman, S. E. (1989). Cognitive apprenticeship: Teaching the craft of reading, writing and mathematics. In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 453–494). Hillsdale: Erlbaum.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM–Mathematics Education, 38(3), 302–310.
Kaiser, G., & Stender, P. (2013). Complex modelling problems in co-operative, self-directed learning environments. In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 277–293). Dordrecht: Springer.
Kaiser, G., Blum, W., Borromeo Ferri, R., & Stillman, G. (2011). Trends in teaching and learning of mathematical modelling—Preface. In Trends in teaching and learning of mathematical modelling (pp. 1–5). Dordrecht: Springer.
Kaiser, G., Bracke, M., Göttlich, S., & Kaland, C. (2013). Authentic complex modelling problems in mathematics education. In A. Damlamian, J. F. Rodrigues, & R. Sträßer (Eds.), Educational interfaces between mathematics and industry (pp. 287–297). Cham: Springer.
Kaiser, G., Blum, W., Borromeo Ferri, R., & Greefrath, G. (2015). Anwendungen und Modellieren. In R. Bruder, L. Hefendehl-Hebeker, B. Schmidt-Thieme, & H.-G. Weigand (Eds.), Handbuch der Mathematikdidaktik (pp. 357–381). Berlin: Springer.
Kuckartz, U. (2014). Qualitative text analysis: A guide to methods, practice and using software. London: Sage.
Leisen, J. (Ed.). (1999). Methodenhandbuch deutschsprachiger Fachunterricht. Bonn: DFU.
Maaß, K. (2006). What are modelling competencies? ZDM–Mathematics Education, 38(2), 113–142.
Schmidt-Weigand, F., Hänze, M., & Wodzinski, R. (2012). How can self-regulated problem solving be implemented in the school curriculum? Results from a research project on incremental worked examples. In M. Edwards & S. O. Adams (Eds.), Learning strategies, expectations and challenges (pp. 45–69). Hauppauge: Nova.
Van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher-student interaction: A decade of research. Education Psychology Review, 22, 271–293.
Weinert, F. E. (1996). Lerntheorien und Instruktionsmodelle. In F. E. Weinert (Ed.), Psychologie des Lernens und der Instruktion. Enzyklopädie der Psychologie (Vol. DI2, pp. 1–48). Göttingen: Hofgrefe.
Wodzinski, R., Hänze, M., & Stäudel, L. (2006). Lernen von Physik und Chemie durch Aufgaben mit gestuften Hilfen. In A. Pitton (Ed.), Lehren und Lernen mit Neuen Medien. Gesellschaft für Didaktik der Chemie und Physik. Jahrestagung der GDCP in Paderborn 2005 (pp. 251–253). Münster: Lit-Verlag.
Zech, F. (2002). Grundkurs Mathematikdidaktik, Theoretische und praktische Anleitungen für das Lehren und Lernen von Mathematik. Weinheim: Belz.
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Alfke, D.S. (2017). Mathematical Modelling with Increasing Learning Aids: A Video Study. 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_2
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DOI: https://doi.org/10.1007/978-3-319-62968-1_2
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