Abstract
The attitude of many students all over the world is shaped by the experience of learning impractical algorithms without any relevance for their actual or future life. Many students only learn algorithms and concepts in order to pass examinations and forget them afterwards. The inclusion of mathematical modelling in schools is one current innovative approach, which has the potential to offer students insight into the usefulness of mathematics in their life. In this chapter, the development of the current discussion on teaching and learning mathematical modelling is described by detailing the goals of implementing mathematical modelling in schools and ways of integrating modelling into classrooms. Innovative projects for the integration of modelling into classrooms are described, displaying the innovative power of the teaching and learning of mathematical modelling in school. Based on the results of empirical studies, scaffolding as an approach to support students’ independent modelling processes is discussed in detail distinguishing approaches at a macro- and a micro-level.
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References
Aebli, H. (1983). Zwölf Grundformen des Lehrens. Stuttgart: Klett-Cotta.
Beutel, M., & Krosanke, N. (2012). Rekonstruktion von Handlungsabläufen in komplexen Modellierungsprozessen – Schülerprobleme und Lehrerverhalten, Unpublished master thesis. University of Hamburg, Hamburg.
Blomhøj, M. (2011). Modelling competency: Teaching, learning and assessing competencies – Overview. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 343–349). New York: Springer.
Blomhøj, M., & Højgaard Jensen, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123–139.
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). Wien: Hölder-Pichler-Tempsky.
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). New York: Springer.
Blum, W., & Leiss, D. (2007). How do students and teachers deal with modeling problems? In C. P. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling (ICTMA 12): Education, engineering and economics (pp. 222–231). Chichester: Horwood.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects – State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22, 37–68.
Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (Eds.). (2007). Modeling and applications in mathematics education. The 14th ICMI study. New York: Springer.
Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM – The International Journal on Mathematics Education, 38(2), 86–95.
Borromeo Ferri, R. (2011). Wege zur Innenwelt des mathematischen Modellierens. Wiesbaden: Vieweg-Teubner.
Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1(1/2), 3–8.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Riedel.
Galbraith, P., Stillman, G., Brown, J., & Edwards, I. (2007). Facilitating middle secondary modeling competencies. In C. P. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 130–141). Chichester: Horwood.
García, F. J., Maaß, K., & Wake, G. (2010). Theory meets practice: Working pragmatically within different cultures and traditions. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies. ICTMA 13 (pp. 445–457). New York: Springer.
García, F. J., & Ruiz-Higueras, L. (2011). Modifying teachers’ practices: The case of a European training course on modelling and applications. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. ICTMA14 (pp. 569–578). Cham, Switzerland: Springer.
Grünewald, S. (2013). The development of modelling competencies by year 9 students: Effects of a modelling project. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to teaching and research practices (pp. 185–194). Cham, Switzerland: Springer.
Haines, C. R., Crouch, R. M., & Davis, J. (2000). Understanding students’ modelling skills. In J. F. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and mathematics education: ICTMA9 applications in science and technology (pp. 366–381). Chichester: Horwood.
Hammond, J., & Gibbons, P. (2005). Putting scaffolding to work: The contribution of scaffolding in articulating ESL education. Prospect, 20(1), 6–30.
Hattie, J. (2009). Visible learning. A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
Houston, K., & Neill, N. (2003). Investigating students’ modelling skills. In Q. Ye, W. Blum, S. K. Houston, & Q. Jiang (Eds.), Mathematical modelling in education and culture: ICTMA 10 (pp. 54–66). Chichester: Horwood.
Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.
Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education – Examples and experiences. Journal für Mathematik-Didaktik, 31(1), 51–76.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modeling in mathematics education. ZDM – The International Journal on Mathematics Education, 38(3), 302–310.
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 teaching and research practices (pp. 277–293). Cham, Switzerland: Springer.
Kaiser, G., Blum, W., Borromeo Ferri, R., & Stillman, G. (Eds.). (2011). Trends in teaching and learning of mathematical modelling. Cham, Switzerland: Springer.
Kaiser, G., Bracke, M., Göttlich, S., & Kaland, C. (2013). Realistic complex modelling problems in mathematics education. In R. Strässer & A. Damlamian (Eds.), Educational interfaces between mathematics and industry (ICMI-ICIAM-Study) (pp. 299–307). New York: Springer.
Kaiser-Messmer, G. (1986). Anwendungen im Mathematikunterricht. Vol. 1: Theoretische Konzeptionen. Vol. 2: Empirische Untersuchungen. Bad Salzdetfurth: Franzbecker.
Leiß, D. (2007). Hilf mir es selbst zu tun. Hildesheim: Franzbecker.
Lesh, R., & Doerr, H. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah: Lawrence Erlbaum Associates.
Link, F. (2011). Problemlöseprozesse selbstständigkeitsorientiert begleiten: Kontexte und Bedeutungen strategischer Lehrerinterventionen in der Sekundarstufe I. Hildesheim: Franzbecker.
Maaß, K. (2005). Modellieren im Mathematikunterricht der Sekundarstufe I. Journal für Mathematik-Didaktik, 26(2), 114–142.
Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(2), 113–142.
Maaß, K., & Gurlitt, J. (2011). LEMA – Professional development of teachers in relation to mathematical modelling. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling. ICTMA14 (pp. 629–639). Cham, Switzerland: Springer.
Matos, J., & Carreira, S. (1997). The quest for meaning in students’ mathematical modelling. In K. Houston, W. Blum, I. Huntley, & N. Neill (Eds.), Teaching and learning mathematical modelling (ICTMA 7) (pp. 63–75). Chichester: Horwood Publishing.
Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill: Chestnut Hill TIMSS & PIRLS International Study Center, Boston College.
OECD. (2010). PISA 2009 results: What students know and can do – Student performance in reading, mathematics and science (Vol. 1). Paris: OECD.
Pollak, H. O. (1968). On some of the problems of teaching applications of mathematics. Educational Studies in Mathematics, 1(1/2), 24–30.
Schukajlow, S., & Krug, A. (2013). Considering multiple solutions for modelling problems – Design and first results from the MultiMa-project. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to teaching and research practices. Cham, Switzerland: Springer.
Schukajlow, S., Krämer, J., Blum, W., Besser, M., Brode, R., Leiß, D., et al. (2010). Lösungsplan in Schülerhand: zusätzliche Hürde oder Schlüssel zum Erfolg? In Beiträge zum Mathematikunterricht 2010 (pp. 771–774). Münster: WTM.
Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2012). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79(2), 215–237.
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. ICTMA14 (pp. 165–180). Cham, Switzerland: Springer.
Stillman, G., Galbraith, P., Brown, J., & Edwards, I. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Vol. 2, pp. 688–697). Adelaide: MERGA.
Stillman, G., Brown, J., & Galbraith, P. (2010). Identifying challenges within transition phases of mathematical modeling activities at year 9. In R. Lesh, P. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modelling students’ mathematical modeling competencies ICTMA13 (pp. 385–398). New York: Springer.
Stillman, G., Kaiser, G., Blum, W., & Brown, J. (Eds.). (2013). Teaching mathematical modelling: Connecting to teaching and research practices. Cham, Switzerland: Springer.
Van de Pol, J., Volman, M., & Beishuizen, J. (2010). Scaffolding in teacher-student interaction: A decade of research. Educational Psychology Review, 22, 271–293.
Vorhölter, K. (2009). Sinn im Mathematikunterricht. Opladen: Budrich.
Zech, F. (1998). Grundkurs Mathematikdidaktik. Weinheim: Beltz Verlag.
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). Cham, Switzerland: Springer.
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Vorhölter, K., Kaiser, G., Borromeo Ferri, R. (2014). Modelling in Mathematics Classroom Instruction: An Innovative Approach for Transforming Mathematics Education. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_3
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