Mathematical modelling competence: selected current research developments

Referencias

Arzarello, F., Ferrara, F., & Robutti, O. (2012). Mathematical modelling with technology: The role of dynamic representations. Teaching Mathematics and Its Applications, 31(1), 20–30. Barquero, B., Carreira, S., & Kaiser, G. (2017). Introduction to the papers of TWG06 ‘Application and modelling’. In T. Dooley, & G. Gueudet (Eds.), Proceedings of CERME10 (pp. 877–883), Dublin, Ireland: ERME. Baumert J., & Kunter M. (2013) The COACTIV Model of teachers’ professional competence. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 25–48). Boston, MA: Springer. Beckschulte, C. (2019). Mathematisches Modellieren mit Lösungsplan. Eine empirische Untersuchung zur Entwicklung der Modellierungskompetenzen. Wiesbaden, Germany: Springer Spektrum. Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift Für Psychologie, 223(1), 3–13. Blomhøj, M., & Jensen, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123–139. Blum, W. (1985). Anwendungsorientierter Mathematikunterricht in der didaktischen Diskussion. Mathematische Semesterberichte 32(2), 195–232. Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example sugarloaf and the DISUM project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12). Education, engineering and economics (pp. 222–231). Chichester, England: Horwood. Borromeo Ferri, R., & Blum, W. (2009). Mathematical modelling in teacher education. Experiences from a modelling seminar. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 2046–2055). Lyon, France: ERME. Brand, S. (2014). Erwerb von Modellierungskompetenzen. Empirischer Vergleich eines holistischen und eines atomistischen Ansatzes zur Förderung von Modellierungskompetenzen. Wiesbaden, Germany: Springer Spektrum. Brown, J. (2015). Visualisation tactics for solving real world tasks. In G.A. Stillman, W. Blum & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 431–442). Cham, Switzerland: Springer. Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41(2), 143–163. Geiger, V., & Frejd, P. (2015). A reflection on mathematical modelling and applications as a field of research: Theoretical orientation and diversity. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice (pp. 161–171). Cham, Switzerland: Springer. Geiger, V., Galbraith, P., Renshaw, P., & Goos, M. (2003). Technology enriched classrooms: some implications for teaching applications and modelling. In Q.-X. Ye, W. Blum, K. Houston & Q.-Y. Jiang (Eds.), Mathematical modelling in education and culture, ICTMA 10 (pp. 126–140). Chichester, England: Horwood. Greefrath G., & Vorhölter K. (2016). Teaching and learning mathematical modelling. Approaches and developments from German speaking countries. Cham, Switzerland: Springer. Greefrath, G. (2011). Using technologies: New possibilities of teaching and learning modelling. Overview. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling, ICTMA 14 (pp. 301–304). Dordrecht, the Netherlands: Springer. Greefrath, G., & Siller, H.-S. (2017). Modelling and simulation with the help of digital tools. In G. Stillman, W. Blum W, & G. Kaiser (Eds.), Mathematical modelling and applications (pp. 529–539). Cham, Switzerland: Springer. Greefrath, G., Hertleif, C., & Siller, H.-S. (2018). Mathematical modelling with digital tools. A quantitative study on mathematizing with dynamic geometry software. ZDM Mathematics Education, 50(1), 233–244. 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 (pp. 11–37). Wiesbaden, Germany: Springer. Grigutsch, S., Raatz, U. & Törner, G. (1998). Einstellungen gegenüber Mathematik bei Mathematiklehrern. Journal für Mathematik-Didaktik, 19(98), 3–45. Haines, C., Crouch, R., & Davies, J (2001). Understanding students’ modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and mathematics Education, ICTMA 9: Applications in science and technology (pp. 366–380). Chichester, England: Horwood. Hankeln, C. (2018). Mathematisches Modellieren mit dynamischer Geometrie-Software. Ergebnisse einer Interventionsstudie. Wiesbaden, Germany: Springer Spektrum. Hankeln, C., Adamek, C., & Greefrath G. (2019). Assessing sub-competencies of mathematical modelling. Development of a new test instrument. In G. A. Stillman, & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 143–160). Cham, Switzerland: Springer. Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 110–119). Chichester, England: Horwood. Klock, H., & Wess, R. (2018). Lehrerkompetenzen zum mathematischen Modellieren - Test zur Erfassung von Aspekten professioneller Kompetenz zum Lehren mathematischen Modellierens. WWU-Publikationsserver MIAMI. Klock, H, Wess, R, Greefrath, G, & Siller, H.-S. (2019). Aspekte professioneller Kompetenz zum Lehren mathematischen Modellierens bei (angehenden) Lehrkräften - Erfassung und Evaluation. In T. Leuders, E. Christophel, M. Hemmer, F. Korneck, & P. Labudde (Eds.), Fachdidaktische Forschungen zur Lehrerbildung (pp. 135–146). Münster, Germany: Waxmann. KMK (2012). Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife. Köln, Germany: Wolters Kluwer. Kreckler, J. (2017). Implementing modelling into the classroom: Results of an empirical research study. In G. A. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 277–287). Cham, Switzerland: Springer. Maass, K. (2004). Mathematisches Modellieren im Unterricht. Ergebnisse einer empirischen Studie. Franzbecker, Germany: Hildesheim. Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15. Rellensmann, J., Schukajlow, S., & Leopold, C. (2017). Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students’ mathematical modelling performance. Educational Studies in Mathematics, 95(1), 53–78. Savelsbergh, E. R., Drijvers, P. H. M., van de Giessen, C., Heck, A., Hooyman, K., et al. (2008). Modelleren en computer-modellen in de b-vakken: advies op verzoek van de gezamenlijke b-vernieuwingscommissies. Utrecht, the Netherlands: Freudenthal Instituut voor Didactiek van Wiskunde en Natuurwetenschappen. Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89(3), 393–417. Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. ZDM Mathematics Education, 47(7), 1241–1254. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. Staub, F. C., & Stern, E. (2002). The nature of teachers’ pedagogical content beliefs matters for students’ achievement gains. Journal of Educational Psychology, 94(2), 344–355. Stillman, G. (2019). State of the art on modelling in mathematics education. Lines of Inquiry. In G. A. Stillman & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 1–19). Cham, Switzerland: Springer. Wess, R., & Greefrath, G. (2020). Lehr-Lern-Prozesse zum mathematischen Modellieren im Lehr-Labor MiRA+ initiieren und erforschen. Mathematica Didactica, 43. 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). Dordrecht, the Netherlands: Springer.