Decoding, understanding, and evaluating extant mathematical models: what does that take?
DOI:
https://doi.org/10.48489/quadrante.24129Keywords:
modelling competency, authentic models, critical model analysis, didactical consequencesAbstract
The far majority of theoretical and empirical studies in the didactics of mathematical modelling focus on actively putting mathematics to use in dealing with extra-mathematical contexts and situations. However, modelling competency as conceptualised in, e.g., the Danish KOM Project, also involves the ability to analyse and relate to extant mathematical models. This ability has only been sparsely considered in research. The present paper proposes a systematic approach to such investigations. It takes its departure in in-depth accounts and analyses of two extant models, the so-called Reilly model of the attraction of shopping centres, and the well-established Michaelis-Menten model of enzyme kinetics. The paper aims at identifying what it takes to grasp and critically analyse such and other extant models and finishes by outlining didactical consequences for fostering students’ ability to undertaking model analysis, a highly important component of the modelling competency.
References
Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123–139. https://doi.org/10.1093/teamat/22.3.123
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). Cham: Springer. https://doi.org/-10.1007/¬978-3-319-12688-3_9
Jankvist, U., & Niss, M. (2020). Upper secondary school students’ difficulties with mathematical modelling. International Journal of Mathematical Education in Science and Technology, 51(4), 467–496. https://doi.org/10.1080/0020739X.2019.1587530
Kaiser, G., & Brand. S. (2015). Modelling competencies: Past development and future perspectives. In G. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (pp. 129–149). Cham: Springer. https://doi.org/10.1007/978-3-319-18272-8
Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh R., P. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling students' mathematical modeling compe-tencies (pp. 43–59). Boston, MA: Springer. https://doi.org/10.1007/978-1-4419-0561-1_4
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: An ICMI Study (pp. 3–32). New York, N.Y.: Springer. https://doi.org/10.1007/978-0-387-29822-1_1
Niss, M., & Blum, W. (2020). The Learning and Teaching of Mathematical Modelling. Milton Park, UK: Routledge.
Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9-28. https://doi.org/10.1007/s10649-019-09903-9
Niss, M. A., & Jensen, T. H. (2002). Kompetencer og matematiklæring: ideer og inspiration til udvikling af matematikundervisning i Danmark. Copenhagen: Undervisningsministeriets forlag.
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